Finite Group Databasebeta

← C109×#18710 #42136704

Subgroups — C109×#18710 #42136704

Order 27904.

852 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3555C211yesmaximal, characteristic, complemented
2C109×#3251C211yesmaximal, characteristic
3C109×#3216C211yesmaximal, characteristic, complemented
4C109×#3167C211yesmaximal, characteristic, complemented
5C109×#1653C211yesmaximal, characteristic, complemented
6C109×#1652C211yesmaximal, characteristic, complemented
7C109×#1645C211yesmaximal, characteristic, complemented
8C109×#1644C211yesmaximal, characteristic, complemented
9C109×#1628C211yesmaximal, characteristic, complemented
10C109×#1626C211yesmaximal, characteristic, complemented
11C109×#1623C211yesmaximal, characteristic, complemented
12C109×#1622C211yesmaximal, characteristic, complemented
13C109×#1559C211yesmaximal, characteristic, complemented
14C109×#1494C211yesmaximal, characteristic, complemented
15C109×#1493C211yesmaximal, characteristic, complemented
16#563×C109—22no—
17Q82×C109C2211yescharacteristic
18#557×C109—21no—
19#557×C109C2211yescharacteristic
20#556×C109—21no—
21#556×C109—21no—
22#556×C109C2211yescharacteristic
23#554×C109C2211yescharacteristic
24#552×C109—21no—
25#544×C109—21no—
26#542×C109—21no—
27#541×C109—21no—
28#541×C109—21no—
29#541×C109—22no—
30#533×C109C2211yescharacteristic
31#533×C109C2211yescharacteristic
32#532×C109C2211yescharacteristic
33#529×C109C2211yescharacteristic
34#498×C109C2211yescharacteristic
35#497×C109—21no—
36#492×C109C2211yescharacteristic
37#489×C109—21no—
38#487×C109C2211yescharacteristic
39#486×C109C2211yescharacteristic
40#478×C109—21no—
41#475×C109C2211yescharacteristic
42#474×C109C2211yescharacteristic
43#469×C109—21no—
44#468×C109—21no—
45#465×C109—22no—
46#463×C109—21no—
47#462×C109C2211yescharacteristic
48#462×C109C2211yescharacteristic
49#460×C109C2211yescharacteristic
50#460×C109C2211yescharacteristic
51#460×C109C2211yescharacteristic
52#459×C109C2211yescharacteristic
53#452×C109—21no—
54#452×C109—21no—
55C4×SD16×C109—22no—
56#432×C109C2211yescharacteristic
57#423×C109C2211yescharacteristic
58C2×C4×C8×C109C2211yescharacteristic
59#333×C109C2211yescharacteristic
60#333×C109C2211yescharacteristic
61#332×C109C2211yescharacteristic
62#332×C109C2211yescharacteristic
63Q8⋊C8×C109C2211yescharacteristic
64Q8⋊C8×C109C2211yescharacteristic
65Q8⋊C8×C109C2211yescharacteristic
66Q8⋊C8×C109C2211yescharacteristic
67Q8⋊C8×C109C2211yescharacteristic
68Q8⋊C8×C109C2211yescharacteristic
69D4⋊C8×C109C2211yescharacteristic
70D4⋊C8×C109C2211yescharacteristic
71C2×#41×C109—21no—
72C2×Q16×C109—21no—
73C2×Q16×C109—21no—
74C2×SD16×C109—22no—
75C2×SD16×C109—21no—
76C2×SD16×C109—21no—
77C2×SD16×C109—21no—
78C2×D8×C109—21no—
79C2×M16×C109—21no—
80C22×C8×C109—21no—
81C4⋊Q8×C109—22no—
82C4⋊Q8×C109—21no—
83C4⋊Q8×C109—22no—
84C4⋊Q8×C109—21no—
85C4⋊Q8×C109—21no—
86C4⋊Q8×C109D411yescharacteristic
87C4⋊Q8×C109D411yescharacteristic
88C4⋊Q8×C109C2311yescharacteristic
89C4⋊Q8×C109C2311yescharacteristic
90C4⋊Q8×C109C2311yescharacteristic
91#127×C109C2311yescharacteristic
92#126×C109—22no—
93#126×C109—22no—
94#126×C109—22no—
95#126×C109—22no—
96#126×C109—22no—
97#126×C109—22no—
98#126×C109—21no—
99#125×C109—22no—
100#125×C109—22no—
101#125×C109—22no—
102#125×C109—22no—
103#125×C109—21no—
104#125×C109—22no—
105#125×C109—21no—
106#125×C109—21no—
107#125×C109—21no—
108#125×C109D411yescharacteristic
109#124×C109—22no—
110#124×C109—21no—
111#124×C109—21no—
112#124×C109D411yescharacteristic
113#123×C109—22no—
114#123×C109—21no—
115C22⋊Q8×C109—22no—
116C22⋊Q8×C109—22no—
117C22⋊Q8×C109—21no—
118C22⋊Q8×C109—21no—
119C22⋊Q8×C109—22no—
120C22⋊Q8×C109—21no—
121C22⋊Q8×C109—21no—
122C22⋊Q8×C109D411yescharacteristic
123C22⋊Q8×C109D411yescharacteristic
124C22⋊Q8×C109D411yescharacteristic
125C22⋊Q8×C109D412yes—
126#121×C109—21no—
127#121×C109—21no—
128#121×C109D411yescharacteristic
129C4×Q8×C109—22no—
130C4×Q8×C109—21no—
131C4×Q8×C109—21no—
132C4×Q8×C109—21no—
133C4×Q8×C109—21no—
134C4×Q8×C109—21no—
135C4×Q8×C109—21no—
136C4×Q8×C109—21no—
137C4×Q8×C109D412yes—
138C4×Q8×C109C2311yescharacteristic
139C4×Q8×C109C2311yescharacteristic
140C4×Q8×C109C2311yescharacteristic
141C4×D4×C109—21no—
142C4×D4×C109—21no—
143C4×D4×C109—21no—
144C4×D4×C109—21no—
145C4×D4×C109C2311yescharacteristic
146#117×C109—22no—
147#117×C109—21no—
148#117×C109—21no—
149#117×C109—21no—
150#117×C109—21no—
151C2×C4⋊C4×C109—21no—
152C2×C42×C109C2311yescharacteristic
153#107×C109—21no—
154#106×C109—22no—
155#106×C109—21no—
156C4⋊C8×C109—21no—
157C4⋊C8×C109C2311yescharacteristic
158C4⋊C8×C109C2311yescharacteristic
159C4⋊C8×C109C2311yescharacteristic
160C4⋊C8×C109C2311yescharacteristic
161#103×C109—22no—
162#103×C109—21no—
163#103×C109—21no—
164#103×C109—21no—
165#102×C109—21no—
166#102×C109—22no—
167#102×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
176#41×C109—81no—
177#41×C109—81no—
178C2×Q8×C109—22no—
179C2×Q8×C109—21no—
180C2×Q8×C109—21no—
181C2×Q8×C109—21no—
182C2×Q8×C109C2×D411yescharacteristic
183C2×Q8×C109C2×D411yescharacteristic
184C2×Q8×C109C2×D411yescharacteristic
185C2×Q8×C109C2×D412yes—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—21no—
189C2×D4×C109—21no—
190C2×D4×C109—41no—
191C2×D4×C109C2×D411yescharacteristic
192C22×C4×C109—22no—
193C22×C4×C109—21no—
194C22×C4×C109—41no—
195C22×C4×C109C2×D411yescharacteristic
196C22×C4×C109C2×D411yescharacteristic
197C22×C4×C109C2×D411yescharacteristic
198Q16×C109—81no—
199Q16×C109—81no—
200SD16×C109—44no—
201SD16×C109—81no—
202SD16×C109—81no—
203SD16×C109—81no—
204D8×C109—81no—
205M16×C109—81no—
206C2×C8×C109—21no—
207C2×C8×C109—21no—
208C2×C8×C109—21no—
209C2×C8×C109—21no—
210C2×C8×C109—21no—
211C2×C8×C109—21no—
212C2×C8×C109—42no—
213C4⋊C4×C109—22no—
214C4⋊C4×C109—22no—
215C4⋊C4×C109—22no—
216C4⋊C4×C109—22no—
217C4⋊C4×C109—22no—
218C4⋊C4×C109—22no—
219C4⋊C4×C109—22no—
220C4⋊C4×C109—22no—
221C4⋊C4×C109—21no—
222C4⋊C4×C109—21no—
223C4⋊C4×C109—21no—
224C4⋊C4×C109—21no—
225C4⋊C4×C109—21no—
226C4⋊C4×C109—21no—
227C4⋊C4×C109—21no—
228C4⋊C4×C109—22no—
229C4⋊C4×C109—21no—
230C4⋊C4×C109—22no—
231C4⋊C4×C109—21no—
232C4⋊C4×C109—21no—
233C4⋊C4×C109—21no—
234C4⋊C4×C109—21no—
235C4⋊C4×C109—21no—
236C4⋊C4×C109—21no—
237C4⋊C4×C109—21no—
238C4⋊C4×C109—21no—
239C4⋊C4×C109C2×D411yescharacteristic
240C4⋊C4×C109C2×D411yescharacteristic
241C4⋊C4×C109C2×D411yescharacteristic
242C4⋊C4×C109C2×D412yes—
243C4⋊C4×C109C2×D411yescharacteristic
244C22⋊C4×C109—22no—
245C22⋊C4×C109—22no—
246C22⋊C4×C109—22no—
247C22⋊C4×C109—21no—
248C22⋊C4×C109—22no—
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—41no—
256C22⋊C4×C109—41no—
257C42×C109—22no—
258C42×C109—22no—
259C42×C109—22no—
260C42×C109—22no—
261C42×C109—21no—
262C42×C109—21no—
263C42×C109—21no—
264C42×C109C2×D411yescharacteristic
265C42×C109C2×D411yescharacteristic
266C42×C109C2×D411yescharacteristic
267C42×C109C2411yescharacteristic
268C23×C109—21no—
269C23×C109—41no—
270C23×C109#12011yescharacteristic
271Q8×C109—21no—
272Q8×C109—21no—
273Q8×C109—21no—
274Q8×C109—21no—
275Q8×C109—21no—
276Q8×C109—21no—
277Q8×C109—42no—
278Q8×C109—41no—
279Q8×C109—41no—
280Q8×C109—41no—
281Q8×C109—41no—
282Q8×C109—81no—
283Q8×C109—82no—
284D4×C109—21no—
285D4×C109—21no—
286D4×C109—42no—
287D4×C109—41no—
288D4×C109—41no—
289D4×C109—41no—
290D4×C109—41no—
291D4×C109—81no—
292D4×C109—82no—
293C2×C4×C109—21no—
294C2×C4×C109—21no—
295C2×C4×C109—21no—
296C2×C4×C109—21no—
297C2×C4×C109—21no—
298C2×C4×C109—21no—
299C2×C4×C109—21no—
300C2×C4×C109—22no—
301C2×C4×C109—21no—
302C2×C4×C109—21no—
303C2×C4×C109—21no—
304C2×C4×C109—22no—
305C2×C4×C109—21no—
306C2×C4×C109—41no—
307C2×C4×C109—41no—
308C2×C4×C109—41no—
309C2×C4×C109—41no—
310C2×C4×C109—82no—
311C2×C4×C109—82no—
312C2×C4×C109#12011yescharacteristic
313C2×C4×C109#12011yescharacteristic
314C2×C4×C109#12011yescharacteristic
315C2×C4×C109C22×D411yescharacteristic
316C2×C4×C109C22×D411yescharacteristic
317C2×C4×C109C22×D411yescharacteristic
318C8×C109—22no—
319C8×C109—41no—
320C8×C109—41no—
321C8×C109—41no—
322C8×C109—41no—
323C8×C109—41no—
324C22×C109—21no—
325C22×C109—21no—
326C22×C109—21no—
327C22×C109—41no—
328C22×C109—41no—
329C22×C109—41no—
330C22×C109—81no—
331C22×C109—81no—
332C22×C109—81no—
333C22×C109C2×#12011yescharacteristic
334C4×C109—21no—
335C4×C109—21no—
336C4×C109—21no—
337C4×C109—21no—
338C4×C109—41no—
339C4×C109—41no—
340C4×C109—41no—
341C4×C109—41no—
342C4×C109—42no—
343C4×C109—41no—
344C4×C109—42no—
345C4×C109—41no—
346C4×C109—41no—
347C4×C109—81no—
348C4×C109#57711yescharacteristic
349C4×C109#57711yescharacteristic
350C4×C109#57711yescharacteristic
351C4×C109#57811yescharacteristic
352#18710C10911yesmaximal, characteristic, direct product factor, Sylow
353C2×C109—41no—
354C2×C109—81no—
355C2×C109—161no—
356C2×C109#301011yescharacteristic
357C2×C109#301311yescharacteristic
358C2×C109#301811yescharacteristic
359#3555C2×C10911yescharacteristic, complemented
360#3251C2×C10911yescharacteristic
361#3216C2×C10911yescharacteristic, complemented
362#3167C2×C10911yescharacteristic, complemented
363#1653C2×C10911yescharacteristic, complemented
364#1652C2×C10911yescharacteristic, complemented
365#1645C2×C10911yescharacteristic, complemented
366#1644C2×C10911yescharacteristic, complemented
367#1628C2×C10911yescharacteristic, complemented
368#1626C2×C10911yescharacteristic, complemented
369#1623C2×C10911yescharacteristic, complemented
370#1622C2×C10911yescharacteristic, complemented
371#1559C2×C10911yescharacteristic, complemented
372#1494C2×C10911yescharacteristic, complemented
373#1493C2×C10911yescharacteristic, complemented
374C109#1871011yescharacteristic, direct product factor, Sylow
375#563—22no—
376Q82C22×C10911yescharacteristic
377#557—21no—
378#557C22×C10911yescharacteristic
379#556—21no—
380#556—21no—
381#556C22×C10911yescharacteristic
382#554C22×C10911yescharacteristic
383#552—21no—
384#544—21no—
385#542—21no—
386#541—21no—
387#541—21no—
388#541—22no—
389#533C22×C10911yescharacteristic
390#533C22×C10911yescharacteristic
391#532C22×C10911yescharacteristic
392#529C22×C10911yescharacteristic
393#498C22×C10911yescharacteristic
394#497—21no—
395#492C22×C10911yescharacteristic
396#489—21no—
397#487C22×C10911yescharacteristic
398#486C22×C10911yescharacteristic
399#478—21no—
400#475C22×C10911yescharacteristic
401#474C22×C10911yescharacteristic
402#469—21no—
403#468—21no—
404#465—22no—
405#463—21no—
406#462C22×C10911yescharacteristic
407#462C22×C10911yescharacteristic
408#460C22×C10911yescharacteristic
409#460C22×C10911yescharacteristic
410#460C22×C10911yescharacteristic
411#459C22×C10911yescharacteristic
412#452—21no—
413#452—21no—
414C4×SD16—22no—
415#432C22×C10911yescharacteristic
416#423C22×C10911yescharacteristic
417C2×C4×C8C22×C10911yescharacteristic
418#333C22×C10911yescharacteristic
419#333C22×C10911yescharacteristic
420#332C22×C10911yescharacteristic
421#332C22×C10911yescharacteristic
422Q8⋊C8C22×C10911yescharacteristic
423Q8⋊C8C22×C10911yescharacteristic
424Q8⋊C8C22×C10911yescharacteristic
425Q8⋊C8C22×C10911yescharacteristic
426Q8⋊C8C22×C10911yescharacteristic
427Q8⋊C8C22×C10911yescharacteristic
428D4⋊C8C22×C10911yescharacteristic
429D4⋊C8C22×C10911yescharacteristic
430C2×#41—21no—
431C2×Q16—21no—
432C2×Q16—21no—
433C2×SD16—22no—
434C2×SD16—21no—
435C2×SD16—21no—
436C2×SD16—21no—
437C2×D8—21no—
438C2×M16—21no—
439C22×C8—21no—
440C4⋊Q8—22no—
441C4⋊Q8—21no—
442C4⋊Q8—22no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8D4×C10911yescharacteristic
446C4⋊Q8D4×C10911yescharacteristic
447C4⋊Q8C23×C10911yescharacteristic
448C4⋊Q8C23×C10911yescharacteristic
449C4⋊Q8C23×C10911yescharacteristic
450#127C23×C10911yescharacteristic
451#126—22no—
452#126—22no—
453#126—22no—
454#126—22no—
455#126—22no—
456#126—22no—
457#126—21no—
458#125—22no—
459#125—22no—
460#125—22no—
461#125—22no—
462#125—21no—
463#125—22no—
464#125—21no—
465#125—21no—
466#125—21no—
467#125D4×C10911yescharacteristic
468#124—22no—
469#124—21no—
470#124—21no—
471#124D4×C10911yescharacteristic
472#123—22no—
473#123—21no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8D4×C10911yescharacteristic
482C22⋊Q8D4×C10911yescharacteristic
483C22⋊Q8D4×C10911yescharacteristic
484C22⋊Q8D4×C10912yes—
485#121—21no—
486#121—21no—
487#121D4×C10911yescharacteristic
488C4×Q8—22no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8D4×C10912yes—
497C4×Q8C23×C10911yescharacteristic
498C4×Q8C23×C10911yescharacteristic
499C4×Q8C23×C10911yescharacteristic
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4C23×C10911yescharacteristic
505#117—22no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510C2×C4⋊C4—21no—
511C2×C42C23×C10911yescharacteristic
512#107—21no—
513#106—22no—
514#106—21no—
515C4⋊C8—21no—
516C4⋊C8C23×C10911yescharacteristic
517C4⋊C8C23×C10911yescharacteristic
518C4⋊C8C23×C10911yescharacteristic
519C4⋊C8C23×C10911yescharacteristic
520#103—22no—
521#103—21no—
522#103—21no—
523#103—21no—
524#102—21no—
525#102—22no—
526#102—21no—
527#102—21no—
528#102—21no—
529#102—21no—
530C22⋊C8—21no—
531#97—21no—
532C4×C8—21no—
533C4×C8C23×C10911yescharacteristic
534C4×C8C23×C10911yescharacteristic
535#41—81no—
536#41—81no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×D4×C10911yescharacteristic
542C2×Q8C2×D4×C10911yescharacteristic
543C2×Q8C2×D4×C10911yescharacteristic
544C2×Q8C2×D4×C10912yes—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—41no—
550C2×D4C2×D4×C10911yescharacteristic
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—41no—
554C22×C4C2×D4×C10911yescharacteristic
555C22×C4C2×D4×C10911yescharacteristic
556C22×C4C2×D4×C10911yescharacteristic
557Q16—81no—
558Q16—81no—
559SD16—44no—
560SD16—81no—
561SD16—81no—
562SD16—81no—
563D8—81no—
564M16—81no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—42no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4C2×D4×C10911yescharacteristic
599C4⋊C4C2×D4×C10911yescharacteristic
600C4⋊C4C2×D4×C10911yescharacteristic
601C4⋊C4C2×D4×C10912yes—
602C4⋊C4C2×D4×C10911yescharacteristic
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—21no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42C2×D4×C10911yescharacteristic
624C42C2×D4×C10911yescharacteristic
625C42C2×D4×C10911yescharacteristic
626C42C24×C10911yescharacteristic
627C23—21no—
628C23—41no—
629C23#120×C10911yescharacteristic
630Q8—21no—
631Q8—21no—
632Q8—21no—
633Q8—21no—
634Q8—21no—
635Q8—21no—
636Q8—42no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—81no—
642Q8—82no—
643D4—21no—
644D4—21no—
645D4—42no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—81no—
651D4—82no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4#120×C10911yescharacteristic
672C2×C4#120×C10911yescharacteristic
673C2×C4#120×C10911yescharacteristic
674C2×C4C22×D4×C10911yescharacteristic
675C2×C4C22×D4×C10911yescharacteristic
676C2×C4C22×D4×C10911yescharacteristic
677C8—22no—
678C8—41no—
679C8—41no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22C2×#120×C10911yescharacteristic
693C4—21no—
694C4—21no—
695C4—21no—
696C4—21no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—41no—
703C4—42no—
704C4—41no—
705C4—41no—
706C4—81no—
707C4#577×C10911yescharacteristic
708C4#577×C10911yescharacteristic
709C4#577×C10911yescharacteristic
710C4#578×C10911yescharacteristic
711C2—41no—
712C2—81no—
713C2—161no—
714C2C109×#301011yescharacteristic
715C2C109×#301311yescharacteristic
716C2C109×#301811yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC42C24×C109
prime radicalC109×#3251C2
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
1. C109×#3555C2semidirect
3. C109×#3216C2semidirect
4. C109×#3167C2semidirect
5. C109×#1653C2semidirect
6. C109×#1652C2semidirect
7. C109×#1645C2semidirect
8. C109×#1644C2semidirect
9. C109×#1628C2semidirect
10. C109×#1626C2semidirect
11. C109×#1623C2semidirect
12. C109×#1622C2semidirect
13. C109×#1559C2semidirect
14. C109×#1494C2semidirect
15. C109×#1493C2semidirect
352. #18710C109direct (N × H)
359. #3555C2×C109semidirect
361. #3216C2×C109semidirect
362. #3167C2×C109semidirect
363. #1653C2×C109semidirect
364. #1652C2×C109semidirect
365. #1645C2×C109semidirect
366. #1644C2×C109semidirect
367. #1628C2×C109semidirect
368. #1626C2×C109semidirect
369. #1623C2×C109semidirect
370. #1622C2×C109semidirect
371. #1559C2×C109semidirect
372. #1494C2×C109semidirect
373. #1493C2×C109semidirect
374. C109#18710direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#35552
C109×#32512
C109×#32162
C109×#31672
C109×#16532
C109×#16522
C109×#16452
C109×#16442
C109×#16282
C109×#16262
C109×#16232
C109×#16222
C109×#15592
C109×#14942
C109×#14932
#18710109