Finite Group Databasebeta

← C109×#14363 #42132357

Subgroups — C109×#14363 #42132357

Order 27904.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C109C211yesmaximal, characteristic
2C2×#390×C109C211yesmaximal, characteristic, complemented
3C2×#386×C109C211yesmaximal, characteristic, complemented
4C2×#386×C109C211yesmaximal, characteristic, complemented
5C2×#381×C109C211yesmaximal, characteristic, complemented
6C109×#1441C211yesmaximal, characteristic, complemented
7C109×#1440C211yesmaximal, characteristic, complemented
8C109×#1439C211yesmaximal, characteristic, complemented
9C109×#1438C211yesmaximal, characteristic, complemented
10C109×#1438C211yesmaximal, characteristic, complemented
11C109×#1438C211yesmaximal, characteristic, complemented
12C109×#1437C211yesmaximal, characteristic, complemented
13C109×#1436C211yesmaximal, characteristic, complemented
14C109×C22⋊#95C211yesmaximal, characteristic, complemented
15C109×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C24×C4×C109C2211yescharacteristic
20C24×C4×C109C2211yescharacteristic
21C2×#121×C109—24no—
22C2×#121×C109—24no—
23C2×#121×C109C418yescomplemented
24C22×C4⋊C4×C109C2211yescharacteristic
25C22×C4⋊C4×C109C2211yescharacteristic
26C22×C22⋊C4×C109C2211yescharacteristic
27C22×C22⋊C4×C109C2211yescharacteristic
28C22×C22⋊C4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2211yescharacteristic
30C22×C22⋊C4×C109C2211yescharacteristic
31C22×C22⋊C4×C109C2211yescharacteristic
32C22×C22⋊C4×C109C2211yescharacteristic
33C22×C22⋊C4×C109C2211yescharacteristic
34C22×C22⋊C4×C109C2211yescharacteristic
35C22×C22⋊C4×C109C2211yescharacteristic
36C22×C22⋊C4×C109C2211yescharacteristic
37C22×C22⋊C4×C109C2211yescharacteristic
38C22×C22⋊C4×C109C2211yescharacteristic
39C22×C42×C109C2211yescharacteristic
40#390×C109—24no—
41#386×C109—24no—
42#386×C109—24no—
43#381×C109—24no—
44C2×#95×C109C2211yescharacteristic
45C2×#95×C109C2211yescharacteristic
46C2×#95×C109C2211yescharacteristic
47C2×#95×C109C2211yescharacteristic
48C2×#95×C109C2211yescharacteristic
49C2×#95×C109C2211yescharacteristic
50C2×#95×C109C2211yescharacteristic
51C2×#95×C109C2211yescharacteristic
52C2×#95×C109C2211yescharacteristic
53C2×#95×C109C2211yescharacteristic
54C2×#95×C109C2211yescharacteristic
55C2×#95×C109C2211yescharacteristic
56C2×#95×C109C2211yescharacteristic
57C2×#95×C109C2211yescharacteristic
58C25×C109C2311yescharacteristic
59C25×C109C2311yescharacteristic
60C25×C109C2311yescharacteristic
61C22×D4×C109—22no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—41no—
68C22×D4×C109—41no—
69C22×D4×C109—41no—
70C22×D4×C109—41no—
71C22×D4×C109—41no—
72C22×D4×C109—41no—
73C22×D4×C109—41no—
74C22×D4×C109—41no—
75C22×D4×C109—41no—
76C22×D4×C109—41no—
77C22×D4×C109C2×C414yes—
78C22×D4×C109C2×C414yes—
79C22×D4×C109C2×C414yescomplemented
80C22×D4×C109D414yes—
81C22×D4×C109D414yes—
82C23×C4×C109—22no—
83C23×C4×C109—22no—
84C23×C4×C109—22no—
85C23×C4×C109—22no—
86C23×C4×C109—22no—
87C23×C4×C109—22no—
88C23×C4×C109—22no—
89C23×C4×C109—41no—
90C23×C4×C109—41no—
91C23×C4×C109—41no—
92C23×C4×C109—41no—
93C23×C4×C109—41no—
94C23×C4×C109—41no—
95C23×C4×C109C2×C414yescomplemented
96C23×C4×C109C2311yescharacteristic
97C23×C4×C109C2311yescharacteristic
98C23×C4×C109C2311yescharacteristic
99C23×C4×C109C2311yescharacteristic
100C23×C4×C109C2311yescharacteristic
101C23×C4×C109C2311yescharacteristic
102C23×C4×C109C2311yescharacteristic
103C23×C4×C109C2311yescharacteristic
104C23×C4×C109C2311yescharacteristic
105C23×C4×C109C2311yescharacteristic
106C23×C4×C109C2311yescharacteristic
107C23×C4×C109C2311yescharacteristic
108#121×C109—232no—
109C2×C4⋊C4×C109—22no—
110C2×C4⋊C4×C109—22no—
111C2×C4⋊C4×C109—22no—
112C2×C4⋊C4×C109—41no—
113C2×C4⋊C4×C109—41no—
114C2×C4⋊C4×C109C2×C414yescomplemented
115C2×C22⋊C4×C109—22no—
116C2×C22⋊C4×C109—22no—
117C2×C22⋊C4×C109—22no—
118C2×C22⋊C4×C109—22no—
119C2×C22⋊C4×C109—22no—
120C2×C22⋊C4×C109—22no—
121C2×C22⋊C4×C109—22no—
122C2×C22⋊C4×C109—22no—
123C2×C22⋊C4×C109—22no—
124C2×C22⋊C4×C109—22no—
125C2×C22⋊C4×C109—22no—
126C2×C22⋊C4×C109—22no—
127C2×C22⋊C4×C109—22no—
128C2×C22⋊C4×C109—22no—
129C2×C22⋊C4×C109—22no—
130C2×C22⋊C4×C109—22no—
131C2×C22⋊C4×C109—22no—
132C2×C22⋊C4×C109—22no—
133C2×C22⋊C4×C109—22no—
134C2×C22⋊C4×C109—22no—
135C2×C22⋊C4×C109—22no—
136C2×C22⋊C4×C109—41no—
137C2×C22⋊C4×C109—41no—
138C2×C22⋊C4×C109—41no—
139C2×C22⋊C4×C109—41no—
140C2×C22⋊C4×C109—41no—
141C2×C22⋊C4×C109—41no—
142C2×C22⋊C4×C109—41no—
143C2×C22⋊C4×C109—41no—
144C2×C22⋊C4×C109—41no—
145C2×C22⋊C4×C109—41no—
146C2×C22⋊C4×C109—41no—
147C2×C22⋊C4×C109—41no—
148C2×C22⋊C4×C109—41no—
149C2×C22⋊C4×C109—41no—
150C2×C22⋊C4×C109—41no—
151C2×C22⋊C4×C109—41no—
152C2×C22⋊C4×C109C2×C414yes—
153C2×C22⋊C4×C109C2×C414yescomplemented
154C2×C42×C109—22no—
155C2×C42×C109—41no—
156C2×C42×C109—41no—
157#95×C109—22no—
158#95×C109—22no—
159#95×C109—22no—
160#95×C109—22no—
161#95×C109—22no—
162#95×C109—22no—
163#95×C109—22no—
164#95×C109—41no—
165#95×C109—41no—
166#95×C109—41no—
167#95×C109—41no—
168#95×C109—41no—
169#95×C109—41no—
170#95×C109D414yescomplemented
171C24×C109—21no—
172C24×C109—21no—
173C24×C109—21no—
174C24×C109—21no—
175C24×C109—21no—
176C24×C109—21no—
177C24×C109—21no—
178C24×C109—21no—
179C24×C109—21no—
180C24×C109—21no—
181C24×C109—21no—
182C24×C109—21no—
183C24×C109—21no—
184C24×C109—21no—
185C24×C109—21no—
186C24×C109—21no—
187C24×C109—21no—
188C24×C109—21no—
189C24×C109—21no—
190C24×C109—21no—
191C24×C109—21no—
192C24×C109—21no—
193C24×C109—21no—
194C24×C109—21no—
195C24×C109—21no—
196C24×C109—21no—
197C24×C109—21no—
198C24×C109—21no—
199C24×C109—21no—
200C24×C109—21no—
201C24×C109—21no—
202C24×C109—21no—
203C24×C109—21no—
204C24×C109—21no—
205C24×C109—21no—
206C24×C109—21no—
207C24×C109—21no—
208C24×C109—21no—
209C24×C109C22×C412yes—
210C24×C109C22×C412yes—
211C24×C109C22×C412yes—
212C24×C109C2×D412yes—
213C24×C109C2×D412yes—
214C24×C109C2×D412yes—
215C24×C109C2×D412yes—
216C24×C109C2411yescharacteristic
217C2×D4×C109—28no—
218C2×D4×C109—28no—
219C2×D4×C109—28no—
220C2×D4×C109—44no—
221C2×D4×C109—44no—
222C2×D4×C109—44no—
223C2×D4×C109—44no—
224C2×D4×C109—44no—
225C2×D4×C109—44no—
226C2×D4×C109—44no—
227C2×D4×C109—44no—
228C2×D4×C109—44no—
229C2×D4×C109—44no—
230C2×D4×C109—44no—
231C2×D4×C109—44no—
232C2×D4×C109—44no—
233C2×D4×C109—44no—
234C2×D4×C109—44no—
235C2×D4×C109—44no—
236C2×D4×C109—44no—
237C2×D4×C109C22⋊C4116yescomplemented
238C22×C4×C109—21no—
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
245C22×C4×C109—21no—
246C22×C4×C109—28no—
247C22×C4×C109—21no—
248C22×C4×C109—21no—
249C22×C4×C109—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109—21no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—21no—
257C22×C4×C109—21no—
258C22×C4×C109—21no—
259C22×C4×C109—21no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—21no—
263C22×C4×C109—21no—
264C22×C4×C109—21no—
265C22×C4×C109—21no—
266C22×C4×C109—21no—
267C22×C4×C109—21no—
268C22×C4×C109—21no—
269C22×C4×C109—21no—
270C22×C4×C109—21no—
271C22×C4×C109—21no—
272C22×C4×C109—21no—
273C22×C4×C109—21no—
274C22×C4×C109—21no—
275C22×C4×C109—21no—
276C22×C4×C109—21no—
277C22×C4×C109—21no—
278C22×C4×C109—21no—
279C22×C4×C109—21no—
280C22×C4×C109—21no—
281C22×C4×C109—21no—
282C22×C4×C109—21no—
283C22×C4×C109—28no—
284C22×C4×C109—21no—
285C22×C4×C109—21no—
286C22×C4×C109—21no—
287C22×C4×C109—21no—
288C22×C4×C109—21no—
289C22×C4×C109—21no—
290C22×C4×C109—21no—
291C22×C4×C109—21no—
292C22×C4×C109—21no—
293C22×C4×C109—21no—
294C22×C4×C109—21no—
295C22×C4×C109—21no—
296C22×C4×C109—21no—
297C22×C4×C109—21no—
298C22×C4×C109—21no—
299C22×C4×C109—21no—
300C22×C4×C109—21no—
301C22×C4×C109—21no—
302C22×C4×C109—21no—
303C22×C4×C109—21no—
304C22×C4×C109—21no—
305C22×C4×C109—21no—
306C22×C4×C109—21no—
307C22×C4×C109—21no—
308C22×C4×C109—21no—
309C22×C4×C109—21no—
310C22×C4×C109—21no—
311C22×C4×C109—21no—
312C22×C4×C109—44no—
313C22×C4×C109—44no—
314C22×C4×C109—44no—
315C22×C4×C109—44no—
316C22×C4×C109—44no—
317C22×C4×C109—44no—
318C22×C4×C109—44no—
319C22×C4×C109—44no—
320C22×C4×C109—44no—
321C22×C4×C109—44no—
322C22×C4×C109—44no—
323C22×C4×C109—44no—
324C22×C4×C109C22×C412yes—
325C22×C4×C109C22×C412yes—
326C22×C4×C109C22×C412yes—
327C22×C4×C109C22×C412yes—
328C22×C4×C109C2×D412yes—
329C22×C4×C109C2×D412yes—
330C22×C4×C109C2×D412yes—
331C22×C4×C109C2×D412yes—
332C22×C4×C109C2×D412yes—
333C22×C4×C109#4112yes—
334C22×C4×C109#4112yes—
335C22×C4×C109#4112yes—
336C4⋊C4×C109—28no—
337C4⋊C4×C109—44no—
338C22⋊C4×C109—28no—
339C22⋊C4×C109—28no—
340C22⋊C4×C109—44no—
341C22⋊C4×C109—44no—
342C22⋊C4×C109—44no—
343C22⋊C4×C109—44no—
344C22⋊C4×C109—44no—
345C22⋊C4×C109—44no—
346C22⋊C4×C109—44no—
347C22⋊C4×C109—44no—
348C22⋊C4×C109—44no—
349C22⋊C4×C109—44no—
350C22⋊C4×C109—44no—
351C42×C109—44no—
352C23×C109—22no—
353C23×C109—22no—
354C23×C109—22no—
355C23×C109—22no—
356C23×C109—22no—
357C23×C109—22no—
358C23×C109—22no—
359C23×C109—22no—
360C23×C109—22no—
361C23×C109—22no—
362C23×C109—22no—
363C23×C109—22no—
364C23×C109—22no—
365C23×C109—22no—
366C23×C109—22no—
367C23×C109—22no—
368C23×C109—22no—
369C23×C109—22no—
370C23×C109—22no—
371C23×C109—22no—
372C23×C109—22no—
373C23×C109—22no—
374C23×C109—22no—
375C23×C109—22no—
376C23×C109—22no—
377C23×C109—22no—
378C23×C109—22no—
379C23×C109—22no—
380C23×C109—22no—
381C23×C109—22no—
382C23×C109—22no—
383C23×C109—22no—
384C23×C109—22no—
385C23×C109—22no—
386C23×C109—22no—
387C23×C109—22no—
388C23×C109—22no—
389C23×C109—22no—
390C23×C109—22no—
391C23×C109—22no—
392C23×C109—22no—
393C23×C109—22no—
394C23×C109—22no—
395C23×C109—41no—
396C23×C109—41no—
397C23×C109—41no—
398C23×C109—41no—
399C23×C109—41no—
400C23×C109—41no—
401C23×C109—41no—
402C23×C109—41no—
403C23×C109—41no—
404C23×C109—41no—
405C23×C109—41no—
406C23×C109—41no—
407C23×C109—41no—
408C23×C109—41no—
409C23×C109—41no—
410C23×C109—41no—
411C23×C109—41no—
412C23×C109—41no—
413C23×C109—41no—
414C23×C109—41no—
415C23×C109—41no—
416C23×C109—41no—
417C23×C109—41no—
418C23×C109—41no—
419C23×C109—41no—
420C23×C109—41no—
421C23×C109—41no—
422C23×C109—41no—
423C23×C109—41no—
424C23×C109—41no—
425C23×C109—41no—
426C23×C109—41no—
427C23×C109—41no—
428C23×C109—41no—
429C23×C109—41no—
430C23×C109—41no—
431C23×C109—41no—
432C23×C109—41no—
433C23×C109—41no—
434C23×C109—41no—
435C23×C109—41no—
436C23×C109—41no—
437C23×C109—41no—
438C23×C109—41no—
439C23×C109—41no—
440C23×C109—41no—
441C23×C109—41no—
442C23×C109—41no—
443C23×C109—41no—
444C23×C109—41no—
445C23×C109—41no—
446C23×C109—41no—
447C23×C109—41no—
448C23×C109—41no—
449C23×C109—41no—
450C23×C109—41no—
451C23×C109—41no—
452C23×C109—41no—
453C23×C109—41no—
454C23×C109—41no—
455C23×C109C2×C22⋊C414yes—
456C23×C109C2×C22⋊C414yes—
457C23×C109C23×C411yescharacteristic
458C23×C109C22×D411yescharacteristic
459C23×C109C22×D411yescharacteristic
460C23×C109C22×D411yescharacteristic
461C23×C109C2×#4111yescharacteristic
462C23×C109C2×#4111yescharacteristic
463C23×C109C2×#4111yescharacteristic
464C23×C109H(5,𝔽2)11yescharacteristic
465C23×C109H(5,𝔽2)11yescharacteristic
466C23×C109H(5,𝔽2)11yescharacteristic
467C23×C109H(5,𝔽2)11yescharacteristic
468C23×C109H(5,𝔽2)11yescharacteristic
469C23×C109H(5,𝔽2)11yescharacteristic
470C23×C109H(5,𝔽2)11yescharacteristic
471C23×C1092−1+411yescharacteristic
472D4×C109—416no—
473D4×C109—416no—
474D4×C109—416no—
475C2×C4×C109—22no—
476C2×C4×C109—22no—
477C2×C4×C109—22no—
478C2×C4×C109—22no—
479C2×C4×C109—22no—
480C2×C4×C109—22no—
481C2×C4×C109—22no—
482C2×C4×C109—22no—
483C2×C4×C109—22no—
484C2×C4×C109—22no—
485C2×C4×C109—22no—
486C2×C4×C109—22no—
487C2×C4×C109—22no—
488C2×C4×C109—22no—
489C2×C4×C109—22no—
490C2×C4×C109—22no—
491C2×C4×C109—22no—
492C2×C4×C109—22no—
493C2×C4×C109—22no—
494C2×C4×C109—22no—
495C2×C4×C109—22no—
496C2×C4×C109—22no—
497C2×C4×C109—22no—
498C2×C4×C109—22no—
499C2×C4×C109—22no—
500C2×C4×C109—22no—
501C2×C4×C109—22no—
502C2×C4×C109—22no—
503C2×C4×C109—22no—
504C2×C4×C109—22no—
505C2×C4×C109—416no—
506C2×C4×C109—416no—
507C2×C4×C109—41no—
508C2×C4×C109—41no—
509C2×C4×C109—41no—
510C2×C4×C109—41no—
511C2×C4×C109—41no—
512C2×C4×C109—41no—
513C2×C4×C109—41no—
514C2×C4×C109—41no—
515C2×C4×C109—41no—
516C2×C4×C109—41no—
517C2×C4×C109—41no—
518C2×C4×C109—41no—
519C2×C4×C109—41no—
520C2×C4×C109—41no—
521C2×C4×C109—41no—
522C2×C4×C109—41no—
523C2×C4×C109—41no—
524C2×C4×C109—41no—
525C2×C4×C109—41no—
526C2×C4×C109—41no—
527C2×C4×C109—41no—
528C2×C4×C109—41no—
529C2×C4×C109—41no—
530C2×C4×C109—41no—
531C2×C4×C109—41no—
532C2×C4×C109—41no—
533C2×C4×C109—41no—
534C2×C4×C109—41no—
535C2×C4×C109—41no—
536C2×C4×C109—41no—
537C2×C4×C109—41no—
538C2×C4×C109—41no—
539C2×C4×C109—41no—
540C2×C4×C109—41no—
541C2×C4×C109—41no—
542C2×C4×C109—41no—
543C2×C4×C109—41no—
544C2×C4×C109—41no—
545C2×C4×C109—41no—
546C2×C4×C109—41no—
547C2×C4×C109—41no—
548C2×C4×C109—41no—
549C2×C4×C109—41no—
550C2×C4×C109—41no—
551C2×C4×C109—41no—
552C2×C4×C109—41no—
553C2×C4×C109—41no—
554C2×C4×C109—41no—
555C2×C4×C109—41no—
556C2×C4×C109—41no—
557C2×C4×C109—41no—
558C2×C4×C109—41no—
559C2×C4×C109C2×C22⋊C414yes—
560C2×C4×C109C4×D414yes—
561C22×C109—24no—
562C22×C109—24no—
563C22×C109—24no—
564C22×C109—24no—
565C22×C109—24no—
566C22×C109—24no—
567C22×C109—42no—
568C22×C109—42no—
569C22×C109—42no—
570C22×C109—42no—
571C22×C109—42no—
572C22×C109—42no—
573C22×C109—42no—
574C22×C109—42no—
575C22×C109—42no—
576C22×C109—42no—
577C22×C109—42no—
578C22×C109—42no—
579C22×C109—42no—
580C22×C109—42no—
581C22×C109—42no—
582C22×C109—42no—
583C22×C109—42no—
584C22×C109—42no—
585C22×C109—42no—
586C22×C109—42no—
587C22×C109—42no—
588C22×C109—42no—
589C22×C109—42no—
590C22×C109—42no—
591C22×C109—42no—
592C22×C109—42no—
593C22×C109—42no—
594C22×C109—42no—
595C22×C109—42no—
596C22×C109—42no—
597C22×C109—42no—
598C22×C109—81no—
599C22×C109—81no—
600C22×C109—81no—
601C22×C109—81no—
602C22×C109—81no—
603C22×C109—81no—
604C22×C109—81no—
605C22×C109—81no—
606C22×C109C22×C22⋊C411yescharacteristic
607C22×C109C2×C4×D411yescharacteristic
608C22×C109C4×#4111yescharacteristic
609C22×C109#51811yescharacteristic
610C22×C109#51811yescharacteristic
611C22×C109#51811yescharacteristic
612C22×C109#52011yescharacteristic
613C22×C109#53411yescharacteristic
614C22×C109#53411yescharacteristic
615C22×C109#53411yescharacteristic
616C22×C109#53411yescharacteristic
617C22×C109#53511yescharacteristic
618C22×C109#53711yescharacteristic
619C22×C109#53811yescharacteristic
620C22×C109#53811yescharacteristic
621C22×C109#54011yescharacteristic
622C22×C109#54011yescharacteristic
623C22×C109#54011yescharacteristic
624C22×C109#54211yescharacteristic
625C22×C109D4211yescharacteristic
626C22×C109D4211yescharacteristic
627C22×C109#54611yescharacteristic
628C22×C109#54611yescharacteristic
629C22×C109#54611yescharacteristic
630C22×C109#54611yescharacteristic
631C22×C109#54611yescharacteristic
632C22×C109#54711yescharacteristic
633C22×C109#54711yescharacteristic
634C22×C109#55011yescharacteristic
635C22×C109#55311yescharacteristic
636C22×C109#55511yescharacteristic
637C22×C109#56011yescharacteristic
638C22×C109#56011yescharacteristic
639C22×C109#56211yescharacteristic
640C22×C109#56211yescharacteristic
641C4×C109—24no—
642C4×C109—24no—
643C4×C109—42no—
644C4×C109—42no—
645C4×C109—42no—
646C4×C109—42no—
647C4×C109—42no—
648C4×C109—42no—
649C4×C109—81no—
650C4×C109—81no—
651C4×C109—81no—
652C4×C109—81no—
653#14363C10911yesmaximal, characteristic, direct product factor, Sylow
654C2×C109—44no—
655C2×C109—44no—
656C2×C109—82no—
657C2×C109#230811yescharacteristic
658C2×C109#232411yescharacteristic
659C2×C109#233311yescharacteristic
660C2×C109D4×C22⋊C411yescharacteristic
661C2×C109#233911yescharacteristic
662C2×C109#236311yescharacteristic
663C2×C109#237711yescharacteristic
664C2×C109#267111yescharacteristic
665C2×C109#267311yescharacteristic
666C2×C109#267811yescharacteristic
667C2×C109#268211yescharacteristic
668C2×C109#268611yescharacteristic
669C2×C109#268811yescharacteristic
670C2×C109#269911yescharacteristic
671C2×C109#270111yescharacteristic
672C22×#121C2×C10911yescharacteristic
673C2×#390C2×C10911yescharacteristic, complemented
674C2×#386C2×C10911yescharacteristic, complemented
675C2×#386C2×C10911yescharacteristic, complemented
676C2×#381C2×C10911yescharacteristic, complemented
677#1441C2×C10911yescharacteristic, complemented
678#1440C2×C10911yescharacteristic, complemented
679#1439C2×C10911yescharacteristic, complemented
680#1438C2×C10911yescharacteristic, complemented
681#1438C2×C10911yescharacteristic, complemented
682#1438C2×C10911yescharacteristic, complemented
683#1437C2×C10911yescharacteristic, complemented
684#1436C2×C10911yescharacteristic, complemented
685C22⋊#95C2×C10911yescharacteristic, complemented
686C22⋊#95C2×C10911yescharacteristic, complemented
687C109#1436311yescharacteristic, direct product factor, Sylow
688C23×D4C22×C10911yescharacteristic
689C23×D4C22×C10911yescharacteristic
690C23×D4C22×C10911yescharacteristic
691C24×C4C22×C10911yescharacteristic
692C24×C4C22×C10911yescharacteristic
693C2×#121—24no—
694C2×#121—24no—
695C2×#121C4×C10918yescomplemented
696C22×C4⋊C4C22×C10911yescharacteristic
697C22×C4⋊C4C22×C10911yescharacteristic
698C22×C22⋊C4C22×C10911yescharacteristic
699C22×C22⋊C4C22×C10911yescharacteristic
700C22×C22⋊C4C22×C10911yescharacteristic
701C22×C22⋊C4C22×C10911yescharacteristic
702C22×C22⋊C4C22×C10911yescharacteristic
703C22×C22⋊C4C22×C10911yescharacteristic
704C22×C22⋊C4C22×C10911yescharacteristic
705C22×C22⋊C4C22×C10911yescharacteristic
706C22×C22⋊C4C22×C10911yescharacteristic
707C22×C22⋊C4C22×C10911yescharacteristic
708C22×C22⋊C4C22×C10911yescharacteristic
709C22×C22⋊C4C22×C10911yescharacteristic
710C22×C22⋊C4C22×C10911yescharacteristic
711C22×C42C22×C10911yescharacteristic
712#390—24no—
713#386—24no—
714#386—24no—
715#381—24no—
716C2×#95C22×C10911yescharacteristic
717C2×#95C22×C10911yescharacteristic
718C2×#95C22×C10911yescharacteristic
719C2×#95C22×C10911yescharacteristic
720C2×#95C22×C10911yescharacteristic
721C2×#95C22×C10911yescharacteristic
722C2×#95C22×C10911yescharacteristic
723C2×#95C22×C10911yescharacteristic
724C2×#95C22×C10911yescharacteristic
725C2×#95C22×C10911yescharacteristic
726C2×#95C22×C10911yescharacteristic
727C2×#95C22×C10911yescharacteristic
728C2×#95C22×C10911yescharacteristic
729C2×#95C22×C10911yescharacteristic
730C25C23×C10911yescharacteristic
731C25C23×C10911yescharacteristic
732C25C23×C10911yescharacteristic
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4C2×C4×C10914yes—
750C22×D4C2×C4×C10914yes—
751C22×D4C2×C4×C10914yescomplemented
752C22×D4D4×C10914yes—
753C22×D4D4×C10914yes—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C2×C4×C10914yescomplemented
768C23×C4C23×C10911yescharacteristic
769C23×C4C23×C10911yescharacteristic
770C23×C4C23×C10911yescharacteristic
771C23×C4C23×C10911yescharacteristic
772C23×C4C23×C10911yescharacteristic
773C23×C4C23×C10911yescharacteristic
774C23×C4C23×C10911yescharacteristic
775C23×C4C23×C10911yescharacteristic
776C23×C4C23×C10911yescharacteristic
777C23×C4C23×C10911yescharacteristic
778C23×C4C23×C10911yescharacteristic
779C23×C4C23×C10911yescharacteristic
780#121—232no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—41no—
785C2×C4⋊C4—41no—
786C2×C4⋊C4C2×C4×C10914yescomplemented
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4C2×C4×C10914yes—
825C2×C22⋊C4C2×C4×C10914yescomplemented
826C2×C42—22no—
827C2×C42—41no—
828C2×C42—41no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95—41no—
840#95—41no—
841#95—41no—
842#95D4×C10914yescomplemented
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24C22×C4×C10912yes—
882C24C22×C4×C10912yes—
883C24C22×C4×C10912yes—
884C24C2×D4×C10912yes—
885C24C2×D4×C10912yes—
886C24C2×D4×C10912yes—
887C24C2×D4×C10912yes—
888C24C24×C10911yescharacteristic
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4C22⋊C4×C109116yescomplemented
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—28no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—28no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4C22×C4×C10912yes—
997C22×C4C22×C4×C10912yes—
998C22×C4C22×C4×C10912yes—
999C22×C4C22×C4×C10912yes—
1000C22×C4C2×D4×C10912yes—
1001C22×C4C2×D4×C10912yes—
1002C22×C4C2×D4×C10912yes—
1003C22×C4C2×D4×C10912yes—
1004C22×C4C2×D4×C10912yes—
1005C22×C4#41×C10912yes—
1006C22×C4#41×C10912yes—
1007C22×C4#41×C10912yes—
1008C4⋊C4—28no—
1009C4⋊C4—44no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C42—44no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23C2×C22⋊C4×C10914yes—
1128C23C2×C22⋊C4×C10914yes—
1129C23C23×C4×C10911yescharacteristic
1130C23C22×D4×C10911yescharacteristic
1131C23C22×D4×C10911yescharacteristic
1132C23C22×D4×C10911yescharacteristic
1133C23C2×#41×C10911yescharacteristic
1134C23C2×#41×C10911yescharacteristic
1135C23C2×#41×C10911yescharacteristic
1136C23H(5,𝔽2)×C10911yescharacteristic
1137C23H(5,𝔽2)×C10911yescharacteristic
1138C23H(5,𝔽2)×C10911yescharacteristic
1139C23H(5,𝔽2)×C10911yescharacteristic
1140C23H(5,𝔽2)×C10911yescharacteristic
1141C23H(5,𝔽2)×C10911yescharacteristic
1142C23H(5,𝔽2)×C10911yescharacteristic
1143C232−1+4×C10911yescharacteristic
1144D4—416no—
1145D4—416no—
1146D4—416no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—416no—
1178C2×C4—416no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4C2×C22⋊C4×C10914yes—
1232C2×C4C4×D4×C10914yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22C22×C22⋊C4×C10911yescharacteristic
1279C22C2×C4×D4×C10911yescharacteristic
1280C22C4×#41×C10911yescharacteristic
1281C22#518×C10911yescharacteristic
1282C22#518×C10911yescharacteristic
1283C22#518×C10911yescharacteristic
1284C22#520×C10911yescharacteristic
1285C22#534×C10911yescharacteristic
1286C22#534×C10911yescharacteristic
1287C22#534×C10911yescharacteristic
1288C22#534×C10911yescharacteristic
1289C22#535×C10911yescharacteristic
1290C22#537×C10911yescharacteristic
1291C22#538×C10911yescharacteristic
1292C22#538×C10911yescharacteristic
1293C22#540×C10911yescharacteristic
1294C22#540×C10911yescharacteristic
1295C22#540×C10911yescharacteristic
1296C22#542×C10911yescharacteristic
1297C22D42×C10911yescharacteristic
1298C22D42×C10911yescharacteristic
1299C22#546×C10911yescharacteristic
1300C22#546×C10911yescharacteristic
1301C22#546×C10911yescharacteristic
1302C22#546×C10911yescharacteristic
1303C22#546×C10911yescharacteristic
1304C22#547×C10911yescharacteristic
1305C22#547×C10911yescharacteristic
1306C22#550×C10911yescharacteristic
1307C22#553×C10911yescharacteristic
1308C22#555×C10911yescharacteristic
1309C22#560×C10911yescharacteristic
1310C22#560×C10911yescharacteristic
1311C22#562×C10911yescharacteristic
1312C22#562×C10911yescharacteristic
1313C4—24no—
1314C4—24no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C2—44no—
1326C2—44no—
1327C2—82no—
1328C2C109×#230811yescharacteristic
1329C2C109×#232411yescharacteristic
1330C2C109×#233311yescharacteristic
1331C2D4×C22⋊C4×C10911yescharacteristic
1332C2C109×#233911yescharacteristic
1333C2C109×#236311yescharacteristic
1334C2C109×#237711yescharacteristic
1335C2C109×#267111yescharacteristic
1336C2C109×#267311yescharacteristic
1337C2C109×#267811yescharacteristic
1338C2C109×#268211yescharacteristic
1339C2C109×#268611yescharacteristic
1340C2C109×#268811yescharacteristic
1341C2C109×#269911yescharacteristic
1342C2C109×#270111yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutatorC23C23×C4×C109
Frattini, cosocleC24C24×C109
prime radicalC22×#121×C109C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#390×C109C2semidirect
3. C2×#386×C109C2semidirect
4. C2×#386×C109C2semidirect
5. C2×#381×C109C2semidirect
6. C109×#1441C2semidirect
7. C109×#1440C2semidirect
8. C109×#1439C2semidirect
9. C109×#1438C2semidirect
10. C109×#1438C2semidirect
11. C109×#1438C2semidirect
12. C109×#1437C2semidirect
13. C109×#1436C2semidirect
14. C109×C22⋊#95C2semidirect
15. C109×C22⋊#95C2semidirect
23. C2×#121×C109C4semidirect
79. C22×D4×C109C2×C4semidirect
95. C23×C4×C109C2×C4semidirect
114. C2×C4⋊C4×C109C2×C4semidirect
153. C2×C22⋊C4×C109C2×C4semidirect
170. #95×C109D4semidirect
237. C2×D4×C109C22⋊C4semidirect
653. #14363C109direct (N × H)
673. C2×#390C2×C109semidirect
674. C2×#386C2×C109semidirect
675. C2×#386C2×C109semidirect
676. C2×#381C2×C109semidirect
677. #1441C2×C109semidirect
678. #1440C2×C109semidirect
679. #1439C2×C109semidirect
680. #1438C2×C109semidirect
681. #1438C2×C109semidirect
682. #1438C2×C109semidirect
683. #1437C2×C109semidirect
684. #1436C2×C109semidirect
685. C22⋊#95C2×C109semidirect
686. C22⋊#95C2×C109semidirect
687. C109#14363direct (N × H)
695. C2×#121C4×C109semidirect
751. C22×D4C2×C4×C109semidirect
767. C23×C4C2×C4×C109semidirect
786. C2×C4⋊C4C2×C4×C109semidirect
825. C2×C22⋊C4C2×C4×C109semidirect
842. #95D4×C109semidirect
909. C2×D4C22⋊C4×C109semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#121×C1092
C2×#390×C1092
C2×#386×C1092
C2×#381×C1092
C109×#14412
C109×#14402
C109×#14392
C109×#14382
C109×#14372
C109×#14362
C109×C22⋊#952
#14363109