Finite Group Databasebeta

← C109×#15493 #42133487

Subgroups — C109×#15493 #42133487

Order 27904.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C109C211yesmaximal, characteristic, complemented
2C2×#397×C109C211yesmaximal, characteristic, complemented
3C2×#394×C109C211yesmaximal, characteristic, complemented
4C2×#392×C109C211yesmaximal, characteristic
5C2×#390×C109C211yesmaximal, characteristic, complemented
6C2×#386×C109C211yesmaximal, characteristic, complemented
7C2×#386×C109C211yesmaximal, characteristic, complemented
8C2×#380×C109C211yesmaximal, characteristic, complemented
9C109×#1445C211yesmaximal, characteristic, complemented
10C109×#1439C211yesmaximal, characteristic, complemented
11C109×#1439C211yesmaximal, characteristic, complemented
12C109×#1438C211yesmaximal, characteristic, complemented
13C109×#1438C211yesmaximal, characteristic, complemented
14C109×#1437C211yesmaximal, characteristic, complemented
15C109×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C24×C4×C109C2211yescharacteristic
20C22×C4⋊C4×C109C2211yescharacteristic
21C22×C4⋊C4×C109C2211yescharacteristic
22C22×C4⋊C4×C109C2211yescharacteristic
23C22×C4⋊C4×C109C2211yescharacteristic
24C22×C22⋊C4×C109C2211yescharacteristic
25C22×C22⋊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×C42×C109C2211yescharacteristic
39#399×C109—24no—
40#397×C109—24no—
41#394×C109—24no—
42#392×C109—24no—
43#390×C109—24no—
44#386×C109—24no—
45#386×C109—24no—
46#380×C109—24no—
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
58C2×#95×C109C2211yescharacteristic
59C25×C109C2311yescharacteristic
60C25×C109C2311yescharacteristic
61C25×C109C2311yescharacteristic
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—22no—
68C22×D4×C109—22no—
69C22×D4×C109—22no—
70C22×D4×C109—22no—
71C22×D4×C109—22no—
72C22×D4×C109—22no—
73C22×D4×C109—22no—
74C22×D4×C109—41no—
75C22×D4×C109—41no—
76C22×D4×C109—41no—
77C22×D4×C109—41no—
78C22×D4×C109—41no—
79C22×D4×C109—41no—
80C22×D4×C109—41no—
81C22×D4×C109—41no—
82C22×D4×C109D414yes—
83C23×C4×C109—22no—
84C23×C4×C109—22no—
85C23×C4×C109—22no—
86C23×C4×C109—22no—
87C23×C4×C109—22no—
88C23×C4×C109—41no—
89C23×C4×C109—41no—
90C23×C4×C109C2311yescharacteristic
91C23×C4×C109C2311yescharacteristic
92C23×C4×C109C2311yescharacteristic
93C23×C4×C109C2311yescharacteristic
94C23×C4×C109C2311yescharacteristic
95C23×C4×C109C2311yescharacteristic
96C23×C4×C109C2311yescharacteristic
97C23×C4×C109C2311yescharacteristic
98C23×C4×C109C2311yescharacteristic
99C23×C4×C109C2311yescharacteristic
100C23×C4×C109C2311yescharacteristic
101C23×C4×C109C2311yescharacteristic
102C2×C4⋊C4×C109—22no—
103C2×C4⋊C4×C109—22no—
104C2×C4⋊C4×C109—22no—
105C2×C4⋊C4×C109—22no—
106C2×C4⋊C4×C109—22no—
107C2×C4⋊C4×C109—22no—
108C2×C4⋊C4×C109—22no—
109C2×C4⋊C4×C109—41no—
110C2×C4⋊C4×C109—41no—
111C2×C4⋊C4×C109—41no—
112C2×C4⋊C4×C109—41no—
113C2×C4⋊C4×C109D414yescomplemented
114C2×C22⋊C4×C109—22no—
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—22no—
137C2×C22⋊C4×C109—22no—
138C2×C22⋊C4×C109—22no—
139C2×C22⋊C4×C109—22no—
140C2×C22⋊C4×C109—22no—
141C2×C22⋊C4×C109—22no—
142C2×C22⋊C4×C109—22no—
143C2×C22⋊C4×C109—22no—
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×C109—41no—
153C2×C22⋊C4×C109—41no—
154C2×C22⋊C4×C109—41no—
155C2×C22⋊C4×C109—41no—
156C2×C42×C109—22no—
157C2×C42×C109—41no—
158C2×C42×C109—41no—
159#95×C109—22no—
160#95×C109—22no—
161#95×C109—22no—
162#95×C109—22no—
163#95×C109—22no—
164#95×C109—22no—
165#95×C109—22no—
166#95×C109—22no—
167#95×C109—41no—
168#95×C109—41no—
169#95×C109D414yescomplemented
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×C109—21no—
210C24×C109—21no—
211C24×C109C2×D412yes—
212C24×C109C2×D412yes—
213C24×C109#4112yes—
214C24×C109#4112yes—
215C24×C109#4112yes—
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×C109—44no—
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—21no—
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—44no—
312C22×C4×C109—44no—
313C22×C4×C109—44no—
314C22×C4×C109—44no—
315C22×C4×C109—44no—
316C22×C4×C109—44no—
317C22×C4×C109C2×D412yes—
318C22×C4×C109C2×D412yes—
319C22×C4×C109C2×D412yes—
320C22×C4×C109C2×D412yes—
321C22×C4×C109C2×D412yes—
322C22×C4×C109C2×D412yes—
323C22×C4×C109C2×D412yes—
324C22×C4×C109C2×D412yes—
325C22×C4×C109C2×D412yes—
326C22×C4×C109C2×D412yes—
327C22×C4×C109#4112yes—
328C22×C4×C109#4112yes—
329C4⋊C4×C109—44no—
330C4⋊C4×C109—44no—
331C4⋊C4×C109—44no—
332C4⋊C4×C109—44no—
333C22⋊C4×C109—44no—
334C22⋊C4×C109—44no—
335C22⋊C4×C109—44no—
336C22⋊C4×C109—44no—
337C22⋊C4×C109—44no—
338C22⋊C4×C109—44no—
339C22⋊C4×C109—44no—
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—
347C42×C109—44no—
348C23×C109—22no—
349C23×C109—22no—
350C23×C109—22no—
351C23×C109—22no—
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—41no—
381C23×C109—41no—
382C23×C109—41no—
383C23×C109—41no—
384C23×C109—41no—
385C23×C109—41no—
386C23×C109—41no—
387C23×C109—41no—
388C23×C109—41no—
389C23×C109—41no—
390C23×C109—41no—
391C23×C109—41no—
392C23×C109—41no—
393C23×C109—41no—
394C23×C109—41no—
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#12314yes—
453C23×C109C22×D411yescharacteristic
454C23×C109C22×D411yescharacteristic
455C23×C109C22×D411yescharacteristic
456C23×C109C22×D411yescharacteristic
457C23×C109C2×#4111yescharacteristic
458C23×C109C2×#4111yescharacteristic
459C23×C109C2×#4111yescharacteristic
460C23×C109C2×#4111yescharacteristic
461C23×C109C2×#4111yescharacteristic
462C23×C109H(5,𝔽2)11yescharacteristic
463C23×C109H(5,𝔽2)11yescharacteristic
464C23×C109H(5,𝔽2)11yescharacteristic
465C23×C109H(5,𝔽2)11yescharacteristic
466C23×C109H(5,𝔽2)11yescharacteristic
467C23×C1092−1+411yescharacteristic
468D4×C109—416no—
469D4×C109—416no—
470D4×C109—416no—
471C2×C4×C109—22no—
472C2×C4×C109—22no—
473C2×C4×C109—22no—
474C2×C4×C109—22no—
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—416no—
502C2×C4×C109—41no—
503C2×C4×C109—41no—
504C2×C4×C109—41no—
505C2×C4×C109—41no—
506C2×C4×C109—41no—
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#12114yes—
555C2×C4×C109#12714yes—
556C22×C109—24no—
557C22×C109—24no—
558C22×C109—24no—
559C22×C109—42no—
560C22×C109—42no—
561C22×C109—42no—
562C22×C109—42no—
563C22×C109—42no—
564C22×C109—42no—
565C22×C109—42no—
566C22×C109—42no—
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—81no—
586C22×C109—81no—
587C22×C109—81no—
588C22×C109—81no—
589C22×C109—81no—
590C22×C109—81no—
591C22×C109—81no—
592C22×C109—81no—
593C22×C109—81no—
594C22×C109—81no—
595C22×C109—81no—
596C22×C109—81no—
597C22×C109—81no—
598C22×C109—81no—
599C22×C109—81no—
600C22×C109—81no—
601C22×C109C2×#12111yescharacteristic
602C22×C109C2×#12311yescharacteristic
603C22×C109#52511yescharacteristic
604C22×C109#52511yescharacteristic
605C22×C109#52911yescharacteristic
606C22×C109C2×#12711yescharacteristic
607C22×C109#53411yescharacteristic
608C22×C109#53411yescharacteristic
609C22×C109#53511yescharacteristic
610C22×C109#53711yescharacteristic
611C22×C109#53811yescharacteristic
612C22×C109#53811yescharacteristic
613C22×C109#53911yescharacteristic
614C22×C109#54011yescharacteristic
615C22×C109#54211yescharacteristic
616C22×C109D4211yescharacteristic
617C22×C109D4211yescharacteristic
618C22×C109#54611yescharacteristic
619C22×C109#54611yescharacteristic
620C22×C109#54611yescharacteristic
621C22×C109#54611yescharacteristic
622C22×C109#54611yescharacteristic
623C22×C109#54611yescharacteristic
624C22×C109#54611yescharacteristic
625C22×C109#54711yescharacteristic
626C22×C109#54811yescharacteristic
627C22×C109#54811yescharacteristic
628C22×C109#55011yescharacteristic
629C22×C109#55011yescharacteristic
630C22×C109#55111yescharacteristic
631C22×C109#55111yescharacteristic
632C22×C109#55111yescharacteristic
633C22×C109#55311yescharacteristic
634C22×C109#56011yescharacteristic
635C22×C109#56211yescharacteristic
636C4×C109—24no—
637C4×C109—24no—
638C4×C109—42no—
639C4×C109—42no—
640C4×C109—42no—
641C4×C109—42no—
642C4×C109—42no—
643C4×C109—42no—
644C4×C109—81no—
645C4×C109—81no—
646C4×C109—81no—
647C4×C109—81no—
648#15493C10911yesmaximal, characteristic, direct product factor, Sylow
649C2×C109—44no—
650C2×C109—82no—
651C2×C109—82no—
652C2×C109#241211yescharacteristic
653C2×C109#241811yescharacteristic
654C2×C109#242711yescharacteristic
655C2×C109#244311yescharacteristic
656C2×C109#246711yescharacteristic
657C2×C109#247111yescharacteristic
658C2×C109#253911yescharacteristic
659C2×C109#254011yescharacteristic
660C2×C109#254111yescharacteristic
661C2×C109#266811yescharacteristic
662C2×C109#267111yescharacteristic
663C2×C109#269611yescharacteristic
664C2×C109#270311yescharacteristic
665C2×C109#270511yescharacteristic
666C2×C109#273011yescharacteristic
667C2×#399C2×C10911yescharacteristic, complemented
668C2×#397C2×C10911yescharacteristic, complemented
669C2×#394C2×C10911yescharacteristic, complemented
670C2×#392C2×C10911yescharacteristic
671C2×#390C2×C10911yescharacteristic, complemented
672C2×#386C2×C10911yescharacteristic, complemented
673C2×#386C2×C10911yescharacteristic, complemented
674C2×#380C2×C10911yescharacteristic, complemented
675#1445C2×C10911yescharacteristic, complemented
676#1439C2×C10911yescharacteristic, complemented
677#1439C2×C10911yescharacteristic, complemented
678#1438C2×C10911yescharacteristic, complemented
679#1438C2×C10911yescharacteristic, complemented
680#1437C2×C10911yescharacteristic, complemented
681#1436C2×C10911yescharacteristic, complemented
682C109#1549311yescharacteristic, direct product factor, Sylow
683C23×D4C22×C10911yescharacteristic
684C23×D4C22×C10911yescharacteristic
685C23×D4C22×C10911yescharacteristic
686C24×C4C22×C10911yescharacteristic
687C22×C4⋊C4C22×C10911yescharacteristic
688C22×C4⋊C4C22×C10911yescharacteristic
689C22×C4⋊C4C22×C10911yescharacteristic
690C22×C4⋊C4C22×C10911yescharacteristic
691C22×C22⋊C4C22×C10911yescharacteristic
692C22×C22⋊C4C22×C10911yescharacteristic
693C22×C22⋊C4C22×C10911yescharacteristic
694C22×C22⋊C4C22×C10911yescharacteristic
695C22×C22⋊C4C22×C10911yescharacteristic
696C22×C22⋊C4C22×C10911yescharacteristic
697C22×C22⋊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×C42C22×C10911yescharacteristic
706#399—24no—
707#397—24no—
708#394—24no—
709#392—24no—
710#390—24no—
711#386—24no—
712#386—24no—
713#380—24no—
714C2×#95C22×C10911yescharacteristic
715C2×#95C22×C10911yescharacteristic
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
726C25C23×C10911yescharacteristic
727C25C23×C10911yescharacteristic
728C25C23×C10911yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
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×D4D4×C10914yes—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4C23×C10911yescharacteristic
758C23×C4C23×C10911yescharacteristic
759C23×C4C23×C10911yescharacteristic
760C23×C4C23×C10911yescharacteristic
761C23×C4C23×C10911yescharacteristic
762C23×C4C23×C10911yescharacteristic
763C23×C4C23×C10911yescharacteristic
764C23×C4C23×C10911yescharacteristic
765C23×C4C23×C10911yescharacteristic
766C23×C4C23×C10911yescharacteristic
767C23×C4C23×C10911yescharacteristic
768C23×C4C23×C10911yescharacteristic
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C4⋊C4—41no—
779C2×C4⋊C4—41no—
780C2×C4⋊C4D4×C10914yescomplemented
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
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—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
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×C42—22no—
824C2×C42—41no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—41no—
835#95—41no—
836#95D4×C10914yescomplemented
837#95D4×C10914yescomplemented
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
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—
878C24C2×D4×C10912yes—
879C24C2×D4×C10912yes—
880C24#41×C10912yes—
881C24#41×C10912yes—
882C24#41×C10912yes—
883C24C24×C10911yescharacteristic
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
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—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—28no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
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—21no—
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—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4C2×D4×C10912yes—
985C22×C4C2×D4×C10912yes—
986C22×C4C2×D4×C10912yes—
987C22×C4C2×D4×C10912yes—
988C22×C4C2×D4×C10912yes—
989C22×C4C2×D4×C10912yes—
990C22×C4C2×D4×C10912yes—
991C22×C4C2×D4×C10912yes—
992C22×C4C2×D4×C10912yes—
993C22×C4C2×D4×C10912yes—
994C22×C4#41×C10912yes—
995C22×C4#41×C10912yes—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C42—44no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
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—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
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#123×C10914yes—
1120C23C22×D4×C10911yescharacteristic
1121C23C22×D4×C10911yescharacteristic
1122C23C22×D4×C10911yescharacteristic
1123C23C22×D4×C10911yescharacteristic
1124C23C2×#41×C10911yescharacteristic
1125C23C2×#41×C10911yescharacteristic
1126C23C2×#41×C10911yescharacteristic
1127C23C2×#41×C10911yescharacteristic
1128C23C2×#41×C10911yescharacteristic
1129C23H(5,𝔽2)×C10911yescharacteristic
1130C23H(5,𝔽2)×C10911yescharacteristic
1131C23H(5,𝔽2)×C10911yescharacteristic
1132C23H(5,𝔽2)×C10911yescharacteristic
1133C23H(5,𝔽2)×C10911yescharacteristic
1134C232−1+4×C10911yescharacteristic
1135D4—416no—
1136D4—416no—
1137D4—416no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
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—416no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
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#121×C10914yes—
1222C2×C4#127×C10914yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
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—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22C2×#121×C10911yescharacteristic
1269C22C2×#123×C10911yescharacteristic
1270C22#525×C10911yescharacteristic
1271C22#525×C10911yescharacteristic
1272C22#529×C10911yescharacteristic
1273C22C2×#127×C10911yescharacteristic
1274C22#534×C10911yescharacteristic
1275C22#534×C10911yescharacteristic
1276C22#535×C10911yescharacteristic
1277C22#537×C10911yescharacteristic
1278C22#538×C10911yescharacteristic
1279C22#538×C10911yescharacteristic
1280C22#539×C10911yescharacteristic
1281C22#540×C10911yescharacteristic
1282C22#542×C10911yescharacteristic
1283C22D42×C10911yescharacteristic
1284C22D42×C10911yescharacteristic
1285C22#546×C10911yescharacteristic
1286C22#546×C10911yescharacteristic
1287C22#546×C10911yescharacteristic
1288C22#546×C10911yescharacteristic
1289C22#546×C10911yescharacteristic
1290C22#546×C10911yescharacteristic
1291C22#546×C10911yescharacteristic
1292C22#547×C10911yescharacteristic
1293C22#548×C10911yescharacteristic
1294C22#548×C10911yescharacteristic
1295C22#550×C10911yescharacteristic
1296C22#550×C10911yescharacteristic
1297C22#551×C10911yescharacteristic
1298C22#551×C10911yescharacteristic
1299C22#551×C10911yescharacteristic
1300C22#553×C10911yescharacteristic
1301C22#560×C10911yescharacteristic
1302C22#562×C10911yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2C109×#241211yescharacteristic
1319C2C109×#241811yescharacteristic
1320C2C109×#242711yescharacteristic
1321C2C109×#244311yescharacteristic
1322C2C109×#246711yescharacteristic
1323C2C109×#247111yescharacteristic
1324C2C109×#253911yescharacteristic
1325C2C109×#254011yescharacteristic
1326C2C109×#254111yescharacteristic
1327C2C109×#266811yescharacteristic
1328C2C109×#267111yescharacteristic
1329C2C109×#269611yescharacteristic
1330C2C109×#270311yescharacteristic
1331C2C109×#270511yescharacteristic
1332C2C109×#273011yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC24C24×C109
prime radicalC2×#392×C109C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#399×C109C2semidirect
2. C2×#397×C109C2semidirect
3. C2×#394×C109C2semidirect
5. C2×#390×C109C2semidirect
6. C2×#386×C109C2semidirect
7. C2×#386×C109C2semidirect
8. C2×#380×C109C2semidirect
9. C109×#1445C2semidirect
10. C109×#1439C2semidirect
11. C109×#1439C2semidirect
12. C109×#1438C2semidirect
13. C109×#1438C2semidirect
14. C109×#1437C2semidirect
15. C109×#1436C2semidirect
113. C2×C4⋊C4×C109D4semidirect
169. #95×C109D4semidirect
170. #95×C109D4semidirect
648. #15493C109direct (N × H)
667. C2×#399C2×C109semidirect
668. C2×#397C2×C109semidirect
669. C2×#394C2×C109semidirect
671. C2×#390C2×C109semidirect
672. C2×#386C2×C109semidirect
673. C2×#386C2×C109semidirect
674. C2×#380C2×C109semidirect
675. #1445C2×C109semidirect
676. #1439C2×C109semidirect
677. #1439C2×C109semidirect
678. #1438C2×C109semidirect
679. #1438C2×C109semidirect
680. #1437C2×C109semidirect
681. #1436C2×C109semidirect
682. C109#15493direct (N × H)
780. C2×C4⋊C4D4×C109semidirect
836. #95D4×C109semidirect
837. #95D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1092
C2×#397×C1092
C2×#394×C1092
C2×#392×C1092
C2×#390×C1092
C2×#386×C1092
C2×#380×C1092
C109×#14452
C109×#14392
C109×#14382
C109×#14372
C109×#14362
#15493109