Finite Group Databasebeta

← C109×#16526 #42134520

Subgroups — C109×#16526 #42134520

Order 27904.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C109C211yesmaximal, characteristic, complemented
2C2×#394×C109C211yesmaximal, characteristic, complemented
3C2×#394×C109C211yesmaximal, characteristic, complemented
4C2×#394×C109C211yesmaximal, characteristic, complemented
5C2×#392×C109C211yesmaximal, characteristic
6C2×#390×C109C211yesmaximal, characteristic, complemented
7C109×#1444C211yesmaximal, characteristic, complemented
8C109×#1440C211yesmaximal, characteristic, complemented
9C109×#1439C211yesmaximal, 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
19C22×C4⋊C4×C109C2211yescharacteristic
20C22×C4⋊C4×C109C2211yescharacteristic
21C22×C4⋊C4×C109C2211yescharacteristic
22C22×C4⋊C4×C109C2211yescharacteristic
23C22×C22⋊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#397×C109—24no—
40#394×C109—24no—
41#394×C109—24no—
42#394×C109—24no—
43#392×C109—24no—
44#390×C109—24no—
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
57C25×C109C2311yescharacteristic
58C25×C109C2311yescharacteristic
59C25×C109C2311yescharacteristic
60C22×D4×C109—22no—
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—22no—
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×C109—41no—
78C22×D4×C109—41no—
79C22×D4×C109—41no—
80C22×D4×C109D414yes—
81C23×C4×C109C2311yescharacteristic
82C23×C4×C109C2311yescharacteristic
83C23×C4×C109C2311yescharacteristic
84C23×C4×C109C2311yescharacteristic
85C23×C4×C109C2311yescharacteristic
86C23×C4×C109C2311yescharacteristic
87C23×C4×C109C2311yescharacteristic
88C23×C4×C109C2311yescharacteristic
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91C23×C4×C109C2311yescharacteristic
92C23×C4×C109C2311yescharacteristic
93C2×C4⋊C4×C109—22no—
94C2×C4⋊C4×C109—22no—
95C2×C4⋊C4×C109—22no—
96C2×C4⋊C4×C109—22no—
97C2×C4⋊C4×C109—22no—
98C2×C4⋊C4×C109—22no—
99C2×C4⋊C4×C109—41no—
100C2×C4⋊C4×C109—41no—
101C2×C4⋊C4×C109—41no—
102C2×C4⋊C4×C109—41no—
103C2×C4⋊C4×C109—41no—
104C2×C4⋊C4×C109—41no—
105C2×C22⋊C4×C109—22no—
106C2×C22⋊C4×C109—22no—
107C2×C22⋊C4×C109—22no—
108C2×C22⋊C4×C109—22no—
109C2×C22⋊C4×C109—22no—
110C2×C22⋊C4×C109—22no—
111C2×C22⋊C4×C109—22no—
112C2×C22⋊C4×C109—22no—
113C2×C22⋊C4×C109—22no—
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—41no—
132C2×C22⋊C4×C109—41no—
133C2×C22⋊C4×C109—41no—
134C2×C22⋊C4×C109—41no—
135C2×C22⋊C4×C109—41no—
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×C109D414yescomplemented
150C2×C42×C109—22no—
151C2×C42×C109—41no—
152C2×C42×C109—41no—
153#95×C109—22no—
154#95×C109—22no—
155#95×C109—22no—
156#95×C109—22no—
157#95×C109—22no—
158#95×C109—22no—
159#95×C109—22no—
160#95×C109—41no—
161#95×C109—41no—
162#95×C109—41no—
163#95×C109—41no—
164#95×C109D414yescomplemented
165C24×C109—21no—
166C24×C109—21no—
167C24×C109—21no—
168C24×C109—21no—
169C24×C109—21no—
170C24×C109—21no—
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×C109C2×D412yes—
208C24×C109C2×D412yes—
209C24×C109C2×D412yes—
210C24×C109C2411yescharacteristic
211C2×D4×C109—28no—
212C2×D4×C109—44no—
213C2×D4×C109—44no—
214C2×D4×C109—44no—
215C2×D4×C109—44no—
216C2×D4×C109—44no—
217C2×D4×C109—44no—
218C2×D4×C109—44no—
219C2×D4×C109—44no—
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—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—21no—
237C22×C4×C109—21no—
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—21no—
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×C109C2×D412yes—
307C22×C4×C109C2×D412yes—
308C22×C4×C109C2×D412yes—
309C22×C4×C109C2×D412yes—
310C22×C4×C109C2×D412yes—
311C22×C4×C109C2×D412yes—
312C22×C4×C109#4112yes—
313C22×C4×C109#4112yes—
314C22×C4×C109#4112yes—
315C22×C4×C109#4112yes—
316C4⋊C4×C109—44no—
317C4⋊C4×C109—44no—
318C4⋊C4×C109—44no—
319C4⋊C4×C109—44no—
320C22⋊C4×C109—44no—
321C22⋊C4×C109—44no—
322C22⋊C4×C109—44no—
323C22⋊C4×C109—44no—
324C22⋊C4×C109—44no—
325C22⋊C4×C109—44no—
326C22⋊C4×C109—44no—
327C22⋊C4×C109—44no—
328C22⋊C4×C109—44no—
329C22⋊C4×C109—44no—
330C22⋊C4×C109—44no—
331C22⋊C4×C109—44no—
332C22⋊C4×C109—44no—
333C22⋊C4×C109—44no—
334C22⋊C4×C109—44no—
335C42×C109—44no—
336C23×C109—22no—
337C23×C109—22no—
338C23×C109—22no—
339C23×C109—22no—
340C23×C109—22no—
341C23×C109—22no—
342C23×C109—22no—
343C23×C109—22no—
344C23×C109—22no—
345C23×C109—22no—
346C23×C109—22no—
347C23×C109—22no—
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—41no—
358C23×C109—41no—
359C23×C109—41no—
360C23×C109—41no—
361C23×C109—41no—
362C23×C109—41no—
363C23×C109—41no—
364C23×C109—41no—
365C23×C109—41no—
366C23×C109—41no—
367C23×C109—41no—
368C23×C109—41no—
369C23×C109—41no—
370C23×C109—41no—
371C23×C109—41no—
372C23×C109—41no—
373C23×C109—41no—
374C23×C109—41no—
375C23×C109—41no—
376C23×C109—41no—
377C23×C109—41no—
378C23×C109—41no—
379C23×C109—41no—
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×C109C22×D411yescharacteristic
442C23×C109C22×D411yescharacteristic
443C23×C109C22×D411yescharacteristic
444C23×C109C2×#4111yescharacteristic
445C23×C109C2×#4111yescharacteristic
446C23×C109C2×#4111yescharacteristic
447C23×C109C2×#4111yescharacteristic
448C23×C109H(5,𝔽2)11yescharacteristic
449C23×C109H(5,𝔽2)11yescharacteristic
450C23×C109H(5,𝔽2)11yescharacteristic
451C23×C109H(5,𝔽2)11yescharacteristic
452C23×C109H(5,𝔽2)11yescharacteristic
453C23×C109H(5,𝔽2)11yescharacteristic
454C23×C109H(5,𝔽2)11yescharacteristic
455C23×C1092−1+411yescharacteristic
456D4×C109—416no—
457D4×C109—416no—
458D4×C109—416no—
459C2×C4×C109—22no—
460C2×C4×C109—22no—
461C2×C4×C109—22no—
462C2×C4×C109—22no—
463C2×C4×C109—22no—
464C2×C4×C109—22no—
465C2×C4×C109—22no—
466C2×C4×C109—22no—
467C2×C4×C109—22no—
468C2×C4×C109—22no—
469C2×C4×C109—22no—
470C2×C4×C109—22no—
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—41no—
487C2×C4×C109—41no—
488C2×C4×C109—41no—
489C2×C4×C109—41no—
490C2×C4×C109—41no—
491C2×C4×C109—41no—
492C2×C4×C109—41no—
493C2×C4×C109—41no—
494C2×C4×C109—41no—
495C2×C4×C109—41no—
496C2×C4×C109—41no—
497C2×C4×C109—41no—
498C2×C4×C109—41no—
499C2×C4×C109—41no—
500C2×C4×C109—41no—
501C2×C4×C109—41no—
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#12314yes—
543C22×C109—42no—
544C22×C109—42no—
545C22×C109—42no—
546C22×C109—42no—
547C22×C109—42no—
548C22×C109—42no—
549C22×C109—42no—
550C22×C109—42no—
551C22×C109—42no—
552C22×C109—42no—
553C22×C109—42no—
554C22×C109—42no—
555C22×C109—42no—
556C22×C109—42no—
557C22×C109—42no—
558C22×C109—42no—
559C22×C109—42no—
560C22×C109—42no—
561C22×C109—42no—
562C22×C109—42no—
563C22×C109—42no—
564C22×C109—81no—
565C22×C109—81no—
566C22×C109—81no—
567C22×C109—81no—
568C22×C109—81no—
569C22×C109—81no—
570C22×C109—81no—
571C22×C109—81no—
572C22×C109—81no—
573C22×C109—81no—
574C22×C109—81no—
575C22×C109—81no—
576C22×C109—81no—
577C22×C109—81no—
578C22×C109—81no—
579C22×C109—81no—
580C22×C109—81no—
581C22×C109—81no—
582C22×C109—81no—
583C22×C109—81no—
584C22×C109—81no—
585C22×C109—81no—
586C22×C109—81no—
587C22×C109—81no—
588C22×C109C2×#12311yescharacteristic
589C22×C109#53211yescharacteristic
590C22×C109#53211yescharacteristic
591C22×C109#53411yescharacteristic
592C22×C109#53411yescharacteristic
593C22×C109#53411yescharacteristic
594C22×C109#53511yescharacteristic
595C22×C109#53511yescharacteristic
596C22×C109#53711yescharacteristic
597C22×C109#53811yescharacteristic
598C22×C109#53811yescharacteristic
599C22×C109#53811yescharacteristic
600C22×C109#53811yescharacteristic
601C22×C109#53811yescharacteristic
602C22×C109#53811yescharacteristic
603C22×C109#54011yescharacteristic
604C22×C109#54011yescharacteristic
605C22×C109#54211yescharacteristic
606C22×C109#54211yescharacteristic
607C22×C109D4211yescharacteristic
608C22×C109D4211yescharacteristic
609C22×C109D4211yescharacteristic
610C22×C109#54611yescharacteristic
611C22×C109#54611yescharacteristic
612C22×C109#54611yescharacteristic
613C22×C109#54711yescharacteristic
614C22×C109#54711yescharacteristic
615C22×C109#55011yescharacteristic
616C22×C109#55311yescharacteristic
617C22×C109#55511yescharacteristic
618C22×C109#55911yescharacteristic
619C22×C109#56011yescharacteristic
620C22×C109#56011yescharacteristic
621C22×C109#56211yescharacteristic
622C22×C109#56211yescharacteristic
623C4×C109—24no—
624C4×C109—42no—
625C4×C109—42no—
626C4×C109—42no—
627C4×C109—42no—
628C4×C109—42no—
629C4×C109—42no—
630C4×C109—42no—
631C4×C109—81no—
632C4×C109—81no—
633C4×C109—81no—
634C4×C109—81no—
635#16526C10911yesmaximal, characteristic, direct product factor, Sylow
636C2×C109—82no—
637C2×C109—82no—
638C2×C109—82no—
639C2×C109#242211yescharacteristic
640C2×C109#244511yescharacteristic
641C2×C109#255511yescharacteristic
642C2×C109#262211yescharacteristic
643C2×C109#266111yescharacteristic
644C2×C109#266211yescharacteristic
645C2×C109#266811yescharacteristic
646C2×C109#266911yescharacteristic
647C2×C109#267111yescharacteristic
648C2×C109#268211yescharacteristic
649C2×C109#268611yescharacteristic
650C2×C109#271011yescharacteristic
651C2×C109#271411yescharacteristic
652C2×C109#280311yescharacteristic
653C2×C109#282911yescharacteristic
654C2×#397C2×C10911yescharacteristic, complemented
655C2×#394C2×C10911yescharacteristic, complemented
656C2×#394C2×C10911yescharacteristic, complemented
657C2×#394C2×C10911yescharacteristic, complemented
658C2×#392C2×C10911yescharacteristic
659C2×#390C2×C10911yescharacteristic, complemented
660#1444C2×C10911yescharacteristic, complemented
661#1440C2×C10911yescharacteristic, complemented
662#1439C2×C10911yescharacteristic, complemented
663#1439C2×C10911yescharacteristic, complemented
664#1439C2×C10911yescharacteristic, complemented
665#1438C2×C10911yescharacteristic, complemented
666#1438C2×C10911yescharacteristic, complemented
667#1437C2×C10911yescharacteristic, complemented
668#1436C2×C10911yescharacteristic, complemented
669C109#1652611yescharacteristic, direct product factor, Sylow
670C23×D4C22×C10911yescharacteristic
671C23×D4C22×C10911yescharacteristic
672C23×D4C22×C10911yescharacteristic
673C22×C4⋊C4C22×C10911yescharacteristic
674C22×C4⋊C4C22×C10911yescharacteristic
675C22×C4⋊C4C22×C10911yescharacteristic
676C22×C4⋊C4C22×C10911yescharacteristic
677C22×C22⋊C4C22×C10911yescharacteristic
678C22×C22⋊C4C22×C10911yescharacteristic
679C22×C22⋊C4C22×C10911yescharacteristic
680C22×C22⋊C4C22×C10911yescharacteristic
681C22×C22⋊C4C22×C10911yescharacteristic
682C22×C22⋊C4C22×C10911yescharacteristic
683C22×C22⋊C4C22×C10911yescharacteristic
684C22×C22⋊C4C22×C10911yescharacteristic
685C22×C22⋊C4C22×C10911yescharacteristic
686C22×C22⋊C4C22×C10911yescharacteristic
687C22×C22⋊C4C22×C10911yescharacteristic
688C22×C22⋊C4C22×C10911yescharacteristic
689C22×C22⋊C4C22×C10911yescharacteristic
690C22×C22⋊C4C22×C10911yescharacteristic
691C22×C22⋊C4C22×C10911yescharacteristic
692C22×C42C22×C10911yescharacteristic
693#397—24no—
694#394—24no—
695#394—24no—
696#394—24no—
697#392—24no—
698#390—24no—
699C2×#95C22×C10911yescharacteristic
700C2×#95C22×C10911yescharacteristic
701C2×#95C22×C10911yescharacteristic
702C2×#95C22×C10911yescharacteristic
703C2×#95C22×C10911yescharacteristic
704C2×#95C22×C10911yescharacteristic
705C2×#95C22×C10911yescharacteristic
706C2×#95C22×C10911yescharacteristic
707C2×#95C22×C10911yescharacteristic
708C2×#95C22×C10911yescharacteristic
709C2×#95C22×C10911yescharacteristic
710C2×#95C22×C10911yescharacteristic
711C25C23×C10911yescharacteristic
712C25C23×C10911yescharacteristic
713C25C23×C10911yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4D4×C10914yes—
735C23×C4C23×C10911yescharacteristic
736C23×C4C23×C10911yescharacteristic
737C23×C4C23×C10911yescharacteristic
738C23×C4C23×C10911yescharacteristic
739C23×C4C23×C10911yescharacteristic
740C23×C4C23×C10911yescharacteristic
741C23×C4C23×C10911yescharacteristic
742C23×C4C23×C10911yescharacteristic
743C23×C4C23×C10911yescharacteristic
744C23×C4C23×C10911yescharacteristic
745C23×C4C23×C10911yescharacteristic
746C23×C4C23×C10911yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4D4×C10914yescomplemented
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C10914yescomplemented
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
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—
861C24C2×D4×C10912yes—
862C24C2×D4×C10912yes—
863C24C2×D4×C10912yes—
864C24C24×C10911yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
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—21no—
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×C4C2×D4×C10912yes—
961C22×C4C2×D4×C10912yes—
962C22×C4C2×D4×C10912yes—
963C22×C4C2×D4×C10912yes—
964C22×C4C2×D4×C10912yes—
965C22×C4C2×D4×C10912yes—
966C22×C4#41×C10912yes—
967C22×C4#41×C10912yes—
968C22×C4#41×C10912yes—
969C22×C4#41×C10912yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
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—
1095C23C22×D4×C10911yescharacteristic
1096C23C22×D4×C10911yescharacteristic
1097C23C22×D4×C10911yescharacteristic
1098C23C2×#41×C10911yescharacteristic
1099C23C2×#41×C10911yescharacteristic
1100C23C2×#41×C10911yescharacteristic
1101C23C2×#41×C10911yescharacteristic
1102C23H(5,𝔽2)×C10911yescharacteristic
1103C23H(5,𝔽2)×C10911yescharacteristic
1104C23H(5,𝔽2)×C10911yescharacteristic
1105C23H(5,𝔽2)×C10911yescharacteristic
1106C23H(5,𝔽2)×C10911yescharacteristic
1107C23H(5,𝔽2)×C10911yescharacteristic
1108C23H(5,𝔽2)×C10911yescharacteristic
1109C232−1+4×C10911yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
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#123×C10914yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#123×C10911yescharacteristic
1243C22#532×C10911yescharacteristic
1244C22#532×C10911yescharacteristic
1245C22#534×C10911yescharacteristic
1246C22#534×C10911yescharacteristic
1247C22#534×C10911yescharacteristic
1248C22#535×C10911yescharacteristic
1249C22#535×C10911yescharacteristic
1250C22#537×C10911yescharacteristic
1251C22#538×C10911yescharacteristic
1252C22#538×C10911yescharacteristic
1253C22#538×C10911yescharacteristic
1254C22#538×C10911yescharacteristic
1255C22#538×C10911yescharacteristic
1256C22#538×C10911yescharacteristic
1257C22#540×C10911yescharacteristic
1258C22#540×C10911yescharacteristic
1259C22#542×C10911yescharacteristic
1260C22#542×C10911yescharacteristic
1261C22D42×C10911yescharacteristic
1262C22D42×C10911yescharacteristic
1263C22D42×C10911yescharacteristic
1264C22#546×C10911yescharacteristic
1265C22#546×C10911yescharacteristic
1266C22#546×C10911yescharacteristic
1267C22#547×C10911yescharacteristic
1268C22#547×C10911yescharacteristic
1269C22#550×C10911yescharacteristic
1270C22#553×C10911yescharacteristic
1271C22#555×C10911yescharacteristic
1272C22#559×C10911yescharacteristic
1273C22#560×C10911yescharacteristic
1274C22#560×C10911yescharacteristic
1275C22#562×C10911yescharacteristic
1276C22#562×C10911yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C109×#242211yescharacteristic
1293C2C109×#244511yescharacteristic
1294C2C109×#255511yescharacteristic
1295C2C109×#262211yescharacteristic
1296C2C109×#266111yescharacteristic
1297C2C109×#266211yescharacteristic
1298C2C109×#266811yescharacteristic
1299C2C109×#266911yescharacteristic
1300C2C109×#267111yescharacteristic
1301C2C109×#268211yescharacteristic
1302C2C109×#268611yescharacteristic
1303C2C109×#271011yescharacteristic
1304C2C109×#271411yescharacteristic
1305C2C109×#280311yescharacteristic
1306C2C109×#282911yescharacteristic
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×#397×C109C2semidirect
2. C2×#394×C109C2semidirect
3. C2×#394×C109C2semidirect
4. C2×#394×C109C2semidirect
6. C2×#390×C109C2semidirect
7. C109×#1444C2semidirect
8. C109×#1440C2semidirect
9. C109×#1439C2semidirect
10. C109×#1439C2semidirect
11. C109×#1439C2semidirect
12. C109×#1438C2semidirect
13. C109×#1438C2semidirect
14. C109×#1437C2semidirect
15. C109×#1436C2semidirect
149. C2×C22⋊C4×C109D4semidirect
164. #95×C109D4semidirect
635. #16526C109direct (N × H)
654. C2×#397C2×C109semidirect
655. C2×#394C2×C109semidirect
656. C2×#394C2×C109semidirect
657. C2×#394C2×C109semidirect
659. C2×#390C2×C109semidirect
660. #1444C2×C109semidirect
661. #1440C2×C109semidirect
662. #1439C2×C109semidirect
663. #1439C2×C109semidirect
664. #1439C2×C109semidirect
665. #1438C2×C109semidirect
666. #1438C2×C109semidirect
667. #1437C2×C109semidirect
668. #1436C2×C109semidirect
669. C109#16526direct (N × H)
803. C2×C22⋊C4D4×C109semidirect
818. #95D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1092
C2×#394×C1092
C2×#392×C1092
C2×#390×C1092
C109×#14442
C109×#14402
C109×#14392
C109×#14382
C109×#14372
C109×#14362
#16526109