Finite Group Databasebeta

← C109×#18648 #42136642

Subgroups — C109×#18648 #42136642

Order 27904.

934 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3520C211yesmaximal, characteristic
2C109×#3248C211yesmaximal, characteristic, complemented
3C109×#3160C211yesmaximal, characteristic, complemented
4C109×#3110C211yesmaximal, characteristic, complemented
5C109×#1654C211yesmaximal, characteristic, complemented
6C109×#1654C211yesmaximal, characteristic, complemented
7C109×#1652C211yesmaximal, characteristic, complemented
8C109×#1651C211yesmaximal, characteristic, complemented
9C109×#1650C211yesmaximal, characteristic, complemented
10C109×#1649C211yesmaximal, characteristic, complemented
11C109×#1647C211yesmaximal, characteristic, complemented
12C109×#1647C211yesmaximal, characteristic, complemented
13C109×#1552C211yesmaximal, characteristic, complemented
14C109×#1494C211yesmaximal, characteristic, complemented
15C2×D4⋊C8×C109C211yesmaximal, characteristic, complemented
16#556×C109C2211yescharacteristic
17#554×C109—21no—
18#552×C109—21no—
19#551×C109—22no—
20D4×Q8×C109C2211yescharacteristic
21#548×C109—21no—
22#547×C109C2211yescharacteristic
23#547×C109C2211yescharacteristic
24#546×C109—21no—
25#542×C109—21no—
26#539×C109—22no—
27#533×C109C2211yescharacteristic
28#533×C109C2211yescharacteristic
29#529×C109C2211yescharacteristic
30#525×C109—21no—
31C2×C22⋊Q8×C109—21no—
32#520×C109—21no—
33C2×C4×D4×C109C2211yescharacteristic
34#500×C109C2211yescharacteristic, complemented
35#500×C109C2211yescharacteristic, complemented
36#499×C109—22no—
37#498×C109C2211yescharacteristic, complemented
38#498×C109C2211yescharacteristic, complemented
39#484×C109—21no—
40#479×C109—21no—
41#475×C109C2211yescharacteristic, complemented
42#474×C109C2211yescharacteristic
43#474×C109C2211yescharacteristic
44#474×C109C2211yescharacteristic, complemented
45#467×C109—21no—
46#465×C109—21no—
47#464×C109—21no—
48#462×C109C2211yescharacteristic, complemented
49#461×C109C2211yescharacteristic
50#461×C109C2211yescharacteristic
51#461×C109C2211yescharacteristic, complemented
52#450×C109—21no—
53#440×C109—21no—
54#440×C109—21no—
55#432×C109C2211yescharacteristic
56#427×C109—22no—
57C2×C4⋊C8×C109C2211yescharacteristic
58C2×C4×C8×C109C2211yescharacteristic
59#332×C109C2211yescharacteristic, complemented
60#332×C109C2211yescharacteristic, complemented
61#332×C109C2211yescharacteristic, complemented
62#332×C109C2211yescharacteristic, complemented
63Q8⋊C8×C109C2211yescharacteristic, complemented
64Q8⋊C8×C109C2211yescharacteristic, complemented
65D4⋊C8×C109C2211yescharacteristic
66D4⋊C8×C109C2211yescharacteristic
67D4⋊C8×C109C2211yescharacteristic
68D4⋊C8×C109C2211yescharacteristic
69D4⋊C8×C109C2211yescharacteristic, complemented
70D4⋊C8×C109C2211yescharacteristic, complemented
71C2×#41×C109—21no—
72C2×#41×C109—21no—
73C22×Q8×C109—21no—
74C22×D4×C109D411yescharacteristic
75C23×C4×C109—21no—
76C2×Q16×C109—21no—
77C2×SD16×C109—21no—
78C2×SD16×C109—21no—
79C2×SD16×C109—21no—
80C22×C8×C109—21no—
81C22×C8×C109—21no—
82C4⋊Q8×C109—21no—
83C4⋊Q8×C109C2311yescharacteristic
84C4⋊Q8×C109C2311yescharacteristic
85C4⋊Q8×C109C2311yescharacteristic
86C4⋊Q8×C109C2311yescharacteristic
87#126×C109—22no—
88#126×C109—22no—
89#126×C109—21no—
90#125×C109—22no—
91#125×C109—21no—
92#125×C109D412yes—
93#125×C109D411yescharacteristic
94#124×C109—22no—
95#124×C109—21no—
96#124×C109D411yescharacteristic
97#123×C109—22no—
98#123×C109—22no—
99#123×C109—21no—
100#123×C109—22no—
101#123×C109—22no—
102C22⋊Q8×C109—22no—
103C22⋊Q8×C109—22no—
104C22⋊Q8×C109—22no—
105C22⋊Q8×C109—21no—
106C22⋊Q8×C109—21no—
107C22⋊Q8×C109—21no—
108C22⋊Q8×C109—21no—
109C22⋊Q8×C109—21no—
110C22⋊Q8×C109—22no—
111C22⋊Q8×C109—21no—
112C22⋊Q8×C109—21no—
113C22⋊Q8×C109—21no—
114C22⋊Q8×C109D411yescharacteristic
115#121×C109—22no—
116#121×C109—21no—
117#121×C109—21no—
118#121×C109D411yescharacteristic
119#120×C109—22no—
120C4×Q8×C109—21no—
121C4×Q8×C109—21no—
122C4×Q8×C109—21no—
123C4×Q8×C109—21no—
124C4×Q8×C109—21no—
125C4×Q8×C109C2311yescharacteristic
126C4×D4×C109—22no—
127C4×D4×C109—22no—
128C4×D4×C109—22no—
129C4×D4×C109—21no—
130C4×D4×C109—21no—
131C4×D4×C109—21no—
132C4×D4×C109—21no—
133C4×D4×C109D411yescharacteristic
134C4×D4×C109D411yescharacteristic
135C4×D4×C109C2311yescharacteristic
136C4×D4×C109C2311yescharacteristic
137C4×D4×C109C2311yescharacteristic
138#117×C109—22no—
139#117×C109—21no—
140#117×C109—21no—
141#117×C109—21no—
142#117×C109D412yes—
143C2×C4⋊C4×C109—22no—
144C2×C4⋊C4×C109—21no—
145C2×C4⋊C4×C109—21no—
146C2×C4⋊C4×C109D411yescharacteristic
147C2×C22⋊C4×C109—22no—
148C2×C22⋊C4×C109—21no—
149C2×C42×C109C2311yescharacteristic
150#107×C109—22no—
151#107×C109—22no—
152#107×C109—21no—
153#107×C109—21no—
154#107×C109—21no—
155#106×C109—22no—
156#106×C109—22no—
157#106×C109—21no—
158C4⋊C8×C109—21no—
159C4⋊C8×C109C2311yescharacteristic
160C4⋊C8×C109C2311yescharacteristic
161C4⋊C8×C109C2311yescharacteristic
162C4⋊C8×C109C2311yescharacteristic
163#103×C109—21no—
164#103×C109—21no—
165#103×C109—21no—
166#103×C109—21no—
167#103×C109—21no—
168#102×C109—21no—
169#102×C109—21no—
170#102×C109—21no—
171C22⋊C8×C109—21no—
172#97×C109—21no—
173C4×C8×C109—21no—
174C4×C8×C109C2311yescharacteristic
175C4×C8×C109C2311yescharacteristic
176C24×C109—21no—
177#41×C109—42no—
178#41×C109—42no—
179#41×C109—81no—
180#41×C109—81no—
181C2×Q8×C109—22no—
182C2×Q8×C109—21no—
183C2×Q8×C109—21no—
184C2×Q8×C109—21no—
185C2×Q8×C109—21no—
186C2×Q8×C109—81no—
187C2×Q8×C109—81no—
188C2×Q8×C109C2×D411yescharacteristic
189C2×D4×C109—22no—
190C2×D4×C109—22no—
191C2×D4×C109—21no—
192C2×D4×C109—22no—
193C2×D4×C109—21no—
194C2×D4×C109—41no—
195C2×D4×C109C2×D411yescharacteristic
196C2×D4×C109C2×D411yescharacteristic
197C2×D4×C109C2×D411yescharacteristic
198C22×C4×C109—22no—
199C22×C4×C109—22no—
200C22×C4×C109—22no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—21no—
206C22×C4×C109—21no—
207C22×C4×C109—81no—
208C22×C4×C109—81no—
209C22×C4×C109C2×D411yescharacteristic
210C22×C4×C109C2×D411yescharacteristic
211C22×C4×C109C2×D411yescharacteristic
212Q16×C109—81no—
213SD16×C109—42no—
214SD16×C109—42no—
215SD16×C109—81no—
216C2×C8×C109—24no—
217C2×C8×C109—21no—
218C2×C8×C109—21no—
219C2×C8×C109—21no—
220C2×C8×C109—21no—
221C2×C8×C109—21no—
222C2×C8×C109—21no—
223C2×C8×C109—81no—
224C4⋊C4×C109—22no—
225C4⋊C4×C109—22no—
226C4⋊C4×C109—22no—
227C4⋊C4×C109—22no—
228C4⋊C4×C109—21no—
229C4⋊C4×C109—22no—
230C4⋊C4×C109—21no—
231C4⋊C4×C109—21no—
232C4⋊C4×C109—21no—
233C4⋊C4×C109—22no—
234C4⋊C4×C109—21no—
235C4⋊C4×C109—21no—
236C4⋊C4×C109—21no—
237C4⋊C4×C109—21no—
238C4⋊C4×C109—21no—
239C4⋊C4×C109—21no—
240C4⋊C4×C109—21no—
241C4⋊C4×C109—41no—
242C4⋊C4×C109—41no—
243C4⋊C4×C109C2×D411yescharacteristic
244C4⋊C4×C109C2×D411yescharacteristic
245C4⋊C4×C109C2×D411yescharacteristic
246C4⋊C4×C109C2×D411yescharacteristic
247C4⋊C4×C109C2×D412yes—
248C4⋊C4×C109C2×D412yes—
249C22⋊C4×C109—22no—
250C22⋊C4×C109—22no—
251C22⋊C4×C109—22no—
252C22⋊C4×C109—22no—
253C22⋊C4×C109—22no—
254C22⋊C4×C109—21no—
255C22⋊C4×C109—22no—
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—41no—
265C42×C109—22no—
266C42×C109—22no—
267C42×C109—21no—
268C42×C109—41no—
269C42×C109C2×D411yescharacteristic
270C42×C109C2×D411yescharacteristic
271C42×C109C2×D411yescharacteristic
272C42×C109C2411yescharacteristic
273C23×C109—21no—
274C23×C109—21no—
275C23×C109—21no—
276C23×C109—42no—
277C23×C109—42no—
278C23×C109—81no—
279C23×C109#12011yescharacteristic
280Q8×C109—21no—
281Q8×C109—21no—
282Q8×C109—41no—
283Q8×C109—41no—
284Q8×C109—41no—
285Q8×C109—41no—
286Q8×C109—41no—
287Q8×C109—41no—
288Q8×C109—41no—
289Q8×C109—41no—
290Q8×C109—82no—
291D4×C109—21no—
292D4×C109—21no—
293D4×C109—21no—
294D4×C109—21no—
295D4×C109—21no—
296D4×C109—42no—
297D4×C109—44no—
298D4×C109—42no—
299D4×C109—82no—
300D4×C109#13512yes—
301C2×C4×C109—22no—
302C2×C4×C109—21no—
303C2×C4×C109—21no—
304C2×C4×C109—21no—
305C2×C4×C109—21no—
306C2×C4×C109—21no—
307C2×C4×C109—22no—
308C2×C4×C109—21no—
309C2×C4×C109—21no—
310C2×C4×C109—22no—
311C2×C4×C109—21no—
312C2×C4×C109—21no—
313C2×C4×C109—44no—
314C2×C4×C109—41no—
315C2×C4×C109—41no—
316C2×C4×C109—41no—
317C2×C4×C109—41no—
318C2×C4×C109—41no—
319C2×C4×C109—41no—
320C2×C4×C109—41no—
321C2×C4×C109—41no—
322C2×C4×C109—81no—
323C2×C4×C109—81no—
324C2×C4×C109—81no—
325C2×C4×C109—82no—
326C2×C4×C109—82no—
327C2×C4×C109#12011yescharacteristic
328C2×C4×C109#12011yescharacteristic
329C2×C4×C109#12011yescharacteristic
330C2×C4×C109C22×D411yescharacteristic
331C2×C4×C109C22×D411yescharacteristic
332C2×C4×C109C22×D411yescharacteristic
333C8×C109—22no—
334C8×C109—22no—
335C8×C109—41no—
336C8×C109—41no—
337C8×C109—41no—
338C8×C109—41no—
339C22×C109—21no—
340C22×C109—21no—
341C22×C109—22no—
342C22×C109—41no—
343C22×C109—41no—
344C22×C109—41no—
345C22×C109—41no—
346C22×C109—41no—
347C22×C109—41no—
348C22×C109—41no—
349C22×C109—41no—
350C22×C109—84no—
351C22×C109#45612yes—
352C22×C109C2×#12011yescharacteristic
353C4×C109—21no—
354C4×C109—21no—
355C4×C109—21no—
356C4×C109—21no—
357C4×C109—41no—
358C4×C109—42no—
359C4×C109—41no—
360C4×C109—41no—
361C4×C109—42no—
362C4×C109—41no—
363C4×C109—41no—
364C4×C109—81no—
365C4×C109—81no—
366C4×C109C2×#13511yescharacteristic
367C4×C109#57511yescharacteristic
368C4×C109#57611yescharacteristic
369C4×C109#57711yescharacteristic
370#18648C10911yesmaximal, characteristic, direct product factor, Sylow
371C2×C109—22no—
372C2×C109—42no—
373C2×C109—81no—
374C2×C109—81no—
375C2×C109#300211yescharacteristic
376C2×C109#301211yescharacteristic
377C2×C109C2×#45611yescharacteristic
378#3520C2×C10911yescharacteristic
379#3248C2×C10911yescharacteristic, complemented
380#3160C2×C10911yescharacteristic, complemented
381#3110C2×C10911yescharacteristic, complemented
382#1654C2×C10911yescharacteristic, complemented
383#1654C2×C10911yescharacteristic, complemented
384#1652C2×C10911yescharacteristic, complemented
385#1651C2×C10911yescharacteristic, complemented
386#1650C2×C10911yescharacteristic, complemented
387#1649C2×C10911yescharacteristic, complemented
388#1647C2×C10911yescharacteristic, complemented
389#1647C2×C10911yescharacteristic, complemented
390#1552C2×C10911yescharacteristic, complemented
391#1494C2×C10911yescharacteristic, complemented
392C2×D4⋊C8C2×C10911yescharacteristic, complemented
393C109#1864811yescharacteristic, direct product factor, Sylow
394#556C22×C10911yescharacteristic
395#554—21no—
396#552—21no—
397#551—22no—
398D4×Q8C22×C10911yescharacteristic
399#548—21no—
400#547C22×C10911yescharacteristic
401#547C22×C10911yescharacteristic
402#546—21no—
403#542—21no—
404#539—22no—
405#533C22×C10911yescharacteristic
406#533C22×C10911yescharacteristic
407#529C22×C10911yescharacteristic
408#525—21no—
409C2×C22⋊Q8—21no—
410#520—21no—
411C2×C4×D4C22×C10911yescharacteristic
412#500C22×C10911yescharacteristic, complemented
413#500C22×C10911yescharacteristic, complemented
414#499—22no—
415#498C22×C10911yescharacteristic, complemented
416#498C22×C10911yescharacteristic, complemented
417#484—21no—
418#479—21no—
419#475C22×C10911yescharacteristic, complemented
420#474C22×C10911yescharacteristic
421#474C22×C10911yescharacteristic
422#474C22×C10911yescharacteristic, complemented
423#467—21no—
424#465—21no—
425#464—21no—
426#462C22×C10911yescharacteristic, complemented
427#461C22×C10911yescharacteristic
428#461C22×C10911yescharacteristic
429#461C22×C10911yescharacteristic, complemented
430#450—21no—
431#440—21no—
432#440—21no—
433#432C22×C10911yescharacteristic
434#427—22no—
435C2×C4⋊C8C22×C10911yescharacteristic
436C2×C4×C8C22×C10911yescharacteristic
437#332C22×C10911yescharacteristic, complemented
438#332C22×C10911yescharacteristic, complemented
439#332C22×C10911yescharacteristic, complemented
440#332C22×C10911yescharacteristic, complemented
441Q8⋊C8C22×C10911yescharacteristic, complemented
442Q8⋊C8C22×C10911yescharacteristic, complemented
443D4⋊C8C22×C10911yescharacteristic
444D4⋊C8C22×C10911yescharacteristic
445D4⋊C8C22×C10911yescharacteristic
446D4⋊C8C22×C10911yescharacteristic
447D4⋊C8C22×C10911yescharacteristic, complemented
448D4⋊C8C22×C10911yescharacteristic, complemented
449C2×#41—21no—
450C2×#41—21no—
451C22×Q8—21no—
452C22×D4D4×C10911yescharacteristic
453C23×C4—21no—
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C22×C8—21no—
459C22×C8—21no—
460C4⋊Q8—21no—
461C4⋊Q8C23×C10911yescharacteristic
462C4⋊Q8C23×C10911yescharacteristic
463C4⋊Q8C23×C10911yescharacteristic
464C4⋊Q8C23×C10911yescharacteristic
465#126—22no—
466#126—22no—
467#126—21no—
468#125—22no—
469#125—21no—
470#125D4×C10911yescharacteristic
471#125D4×C10912yes—
472#124—22no—
473#124—21no—
474#124D4×C10911yescharacteristic
475#123—22no—
476#123—22no—
477#123—21no—
478#123—22no—
479#123—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8D4×C10911yescharacteristic
493#121—22no—
494#121—21no—
495#121—21no—
496#121D4×C10911yescharacteristic
497#120—22no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8C23×C10911yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4D4×C10911yescharacteristic
512C4×D4D4×C10911yescharacteristic
513C4×D4C23×C10911yescharacteristic
514C4×D4C23×C10911yescharacteristic
515C4×D4C23×C10911yescharacteristic
516#117—22no—
517#117—21no—
518#117—21no—
519#117—21no—
520#117D4×C10912yes—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4D4×C10911yescharacteristic
525C2×C22⋊C4—22no—
526C2×C22⋊C4—21no—
527C2×C42C23×C10911yescharacteristic
528#107—22no—
529#107—22no—
530#107—21no—
531#107—21no—
532#107—21no—
533#106—22no—
534#106—22no—
535#106—21no—
536C4⋊C8—21no—
537C4⋊C8C23×C10911yescharacteristic
538C4⋊C8C23×C10911yescharacteristic
539C4⋊C8C23×C10911yescharacteristic
540C4⋊C8C23×C10911yescharacteristic
541#103—21no—
542#103—21no—
543#103—21no—
544#103—21no—
545#103—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C10911yescharacteristic
553C4×C8C23×C10911yescharacteristic
554C24—21no—
555#41—42no—
556#41—42no—
557#41—81no—
558#41—81no—
559C2×Q8—22no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C10911yescharacteristic
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—41no—
573C2×D4C2×D4×C10911yescharacteristic
574C2×D4C2×D4×C10911yescharacteristic
575C2×D4C2×D4×C10911yescharacteristic
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4C2×D4×C10911yescharacteristic
588C22×C4C2×D4×C10911yescharacteristic
589C22×C4C2×D4×C10911yescharacteristic
590Q16—81no—
591SD16—42no—
592SD16—42no—
593SD16—81no—
594C2×C8—24no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—81no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4C2×D4×C10911yescharacteristic
622C4⋊C4C2×D4×C10911yescharacteristic
623C4⋊C4C2×D4×C10911yescharacteristic
624C4⋊C4C2×D4×C10911yescharacteristic
625C4⋊C4C2×D4×C10912yes—
626C4⋊C4C2×D4×C10912yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—21no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C42—22no—
644C42—22no—
645C42—21no—
646C42—41no—
647C42C2×D4×C10911yescharacteristic
648C42C2×D4×C10911yescharacteristic
649C42C2×D4×C10911yescharacteristic
650C42C24×C10911yescharacteristic
651C23—21no—
652C23—21no—
653C23—21no—
654C23—42no—
655C23—42no—
656C23—81no—
657C23#120×C10911yescharacteristic
658Q8—21no—
659Q8—21no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—41no—
668Q8—82no—
669D4—21no—
670D4—21no—
671D4—21no—
672D4—21no—
673D4—21no—
674D4—42no—
675D4—44no—
676D4—42no—
677D4—82no—
678D4#135×C10912yes—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—44no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C10911yescharacteristic
706C2×C4#120×C10911yescharacteristic
707C2×C4#120×C10911yescharacteristic
708C2×C4C22×D4×C10911yescharacteristic
709C2×C4C22×D4×C10911yescharacteristic
710C2×C4C22×D4×C10911yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—21no—
718C22—21no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—84no—
729C22#456×C10912yes—
730C22C2×#120×C10911yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—41no—
739C4—42no—
740C4—41no—
741C4—41no—
742C4—81no—
743C4—81no—
744C4C2×#135×C10911yescharacteristic
745C4#575×C10911yescharacteristic
746C4#576×C10911yescharacteristic
747C4#577×C10911yescharacteristic
748C2—22no—
749C2—42no—
750C2—81no—
751C2—81no—
752C2C109×#300211yescharacteristic
753C2C109×#301211yescharacteristic
754C2C2×#456×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC42C24×C109
prime radicalC109×#3520C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#3248C2semidirect
3. C109×#3160C2semidirect
4. C109×#3110C2semidirect
5. C109×#1654C2semidirect
6. C109×#1654C2semidirect
7. C109×#1652C2semidirect
8. C109×#1651C2semidirect
9. C109×#1650C2semidirect
10. C109×#1649C2semidirect
11. C109×#1647C2semidirect
12. C109×#1647C2semidirect
13. C109×#1552C2semidirect
14. C109×#1494C2semidirect
15. C2×D4⋊C8×C109C2semidirect
34. #500×C109C22semidirect
35. #500×C109C22semidirect
37. #498×C109C22semidirect
38. #498×C109C22semidirect
41. #475×C109C22semidirect
44. #474×C109C22semidirect
48. #462×C109C22semidirect
51. #461×C109C22semidirect
59. #332×C109C22semidirect
60. #332×C109C22semidirect
61. #332×C109C22semidirect
62. #332×C109C22semidirect
63. Q8⋊C8×C109C22semidirect
64. Q8⋊C8×C109C22semidirect
69. D4⋊C8×C109C22semidirect
70. D4⋊C8×C109C22semidirect
370. #18648C109direct (N × H)
379. #3248C2×C109semidirect
380. #3160C2×C109semidirect
381. #3110C2×C109semidirect
382. #1654C2×C109semidirect
383. #1654C2×C109semidirect
384. #1652C2×C109semidirect
385. #1651C2×C109semidirect
386. #1650C2×C109semidirect
387. #1649C2×C109semidirect
388. #1647C2×C109semidirect
389. #1647C2×C109semidirect
390. #1552C2×C109semidirect
391. #1494C2×C109semidirect
392. C2×D4⋊C8C2×C109semidirect
393. C109#18648direct (N × H)
412. #500C22×C109semidirect
413. #500C22×C109semidirect
415. #498C22×C109semidirect
416. #498C22×C109semidirect
419. #475C22×C109semidirect
422. #474C22×C109semidirect
426. #462C22×C109semidirect
429. #461C22×C109semidirect
437. #332C22×C109semidirect
438. #332C22×C109semidirect
439. #332C22×C109semidirect
440. #332C22×C109semidirect
441. Q8⋊C8C22×C109semidirect
442. Q8⋊C8C22×C109semidirect
447. D4⋊C8C22×C109semidirect
448. D4⋊C8C22×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35202
C109×#32482
C109×#31602
C109×#31102
C109×#16542
C109×#16522
C109×#16512
C109×#16502
C109×#16492
C109×#16472
C109×#15522
C109×#14942
C2×D4⋊C8×C1092
#18648109