Finite Group Databasebeta

← C109×#18708 #42136702

Subgroups — C109×#18708 #42136702

Order 27904.

908 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×#3554C211yesmaximal, characteristic, complemented
2C109×#3251C211yesmaximal, characteristic, complemented
3C109×#3216C211yesmaximal, characteristic, complemented
4C109×#3169C211yesmaximal, characteristic, complemented
5C109×#1649C211yesmaximal, characteristic, complemented
6C109×#1648C211yesmaximal, characteristic, complemented
7C109×#1641C211yesmaximal, characteristic, complemented
8C109×#1640C211yesmaximal, characteristic, complemented
9C109×#1627C211yesmaximal, characteristic, complemented
10C109×#1626C211yesmaximal, characteristic, complemented
11C109×#1621C211yesmaximal, characteristic, complemented
12C109×#1620C211yesmaximal, characteristic, complemented
13C109×#1557C211yesmaximal, characteristic, complemented
14C109×#1494C211yesmaximal, characteristic, complemented
15C109×#1493C211yesmaximal, characteristic, complemented
16#562×C109—22no—
17#559×C109—21no—
18#559×C109C2211yescharacteristic
19#557×C109C2211yescharacteristic
20#554×C109—21no—
21#550×C109C2211yescharacteristic
22D4×Q8×C109C2211yescharacteristic
23#548×C109—21no—
24#547×C109—21no—
25#542×C109—21no—
26#542×C109—21no—
27#540×C109—21no—
28#539×C109—22no—
29#536×C109—21no—
30#533×C109C2211yescharacteristic
31#532×C109C2211yescharacteristic
32#532×C109C2211yescharacteristic
33#529×C109C2211yescharacteristic
34#500×C109C2211yescharacteristic
35#497×C109—21no—
36#493×C109C2211yescharacteristic
37#489×C109—21no—
38#486×C109C2211yescharacteristic
39#486×C109C2211yescharacteristic
40#478×C109—21no—
41#475×C109C2211yescharacteristic
42#474×C109C2211yescharacteristic
43#469×C109—21no—
44#468×C109—21no—
45#466×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×D8×C109—22no—
56#432×C109C2211yescharacteristic
57#423×C109C2211yescharacteristic
58C2×C4×C8×C109C2211yescharacteristic
59#332×C109C2211yescharacteristic
60#332×C109C2211yescharacteristic
61#331×C109C2211yescharacteristic
62#331×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×#41×C109—21no—
73C2×#41×C109—21no—
74C22×Q8×C109—21no—
75C2×Q16×C109—21no—
76C2×Q16×C109—21no—
77C2×SD16×C109—21no—
78C2×SD16×C109—21no—
79C2×SD16×C109—21no—
80C2×D8×C109—22no—
81C2×D8×C109—21no—
82C2×M16×C109—21no—
83C22×C8×C109—21no—
84C4⋊Q8×C109—21no—
85C4⋊Q8×C109—21no—
86C4⋊Q8×C109D411yescharacteristic
87C4⋊Q8×C109D411yescharacteristic
88C4⋊Q8×C109C2311yescharacteristic
89C4⋊Q8×C109C2311yescharacteristic
90#127×C109—21no—
91#127×C109C2311yescharacteristic
92#127×C109C2311yescharacteristic
93#126×C109—22no—
94#126×C109—21no—
95#125×C109—22no—
96#125×C109—21no—
97#125×C109—21no—
98#125×C109D411yescharacteristic
99#124×C109—22no—
100#124×C109—22no—
101#124×C109—21no—
102#124×C109—21no—
103#124×C109—21no—
104#124×C109—21no—
105#124×C109D411yescharacteristic
106#123×C109—22no—
107#123×C109—22no—
108#123×C109—22no—
109#123×C109—22no—
110#123×C109—22no—
111#123×C109—22no—
112#123×C109—21no—
113C22⋊Q8×C109—22no—
114C22⋊Q8×C109—22no—
115C22⋊Q8×C109—22no—
116C22⋊Q8×C109—22no—
117C22⋊Q8×C109—21no—
118C22⋊Q8×C109—22no—
119C22⋊Q8×C109—21no—
120C22⋊Q8×C109D411yescharacteristic
121C22⋊Q8×C109D411yescharacteristic
122C22⋊Q8×C109D411yescharacteristic
123#121×C109—22no—
124#121×C109—22no—
125#121×C109—22no—
126#121×C109—21no—
127#121×C109—21no—
128#121×C109—21no—
129#121×C109—21no—
130#121×C109D411yescharacteristic
131#121×C109D412yes—
132C4×Q8×C109—21no—
133C4×Q8×C109—21no—
134C4×Q8×C109—21no—
135C4×Q8×C109C2311yescharacteristic
136C4×Q8×C109C2311yescharacteristic
137C4×Q8×C109C2311yescharacteristic
138C4×D4×C109—22no—
139C4×D4×C109—21no—
140C4×D4×C109—21no—
141C4×D4×C109—21no—
142C4×D4×C109—21no—
143C4×D4×C109—21no—
144C4×D4×C109—21no—
145C4×D4×C109—21no—
146C4×D4×C109—21no—
147C4×D4×C109D412yes—
148C4×D4×C109C2311yescharacteristic
149#117×C109—21no—
150#117×C109—21no—
151C2×C4⋊C4×C109—22no—
152C2×C42×C109C2311yescharacteristic
153#107×C109—22no—
154#107×C109—21no—
155#106×C109—21no—
156C4⋊C8×C109—21no—
157C4⋊C8×C109C2311yescharacteristic
158C4⋊C8×C109C2311yescharacteristic
159C4⋊C8×C109C2311yescharacteristic
160C4⋊C8×C109C2311yescharacteristic
161#103×C109—21no—
162#103×C109—21no—
163#103×C109—21no—
164#102×C109—22no—
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—
178#41×C109—81no—
179#41×C109—81no—
180#41×C109—81no—
181#41×C109—81no—
182C2×Q8×C109—22no—
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×Q8×C109C2×D411yescharacteristic
190C2×Q8×C109C2×D411yescharacteristic
191C2×D4×C109—22no—
192C2×D4×C109—22no—
193C2×D4×C109—21no—
194C2×D4×C109—22no—
195C2×D4×C109—21no—
196C2×D4×C109—21no—
197C2×D4×C109—21no—
198C2×D4×C109—21no—
199C2×D4×C109—21no—
200C2×D4×C109—41no—
201C2×D4×C109C2×D411yescharacteristic
202C2×D4×C109C2×D412yes—
203C22×C4×C109—22no—
204C22×C4×C109—22no—
205C22×C4×C109—22no—
206C22×C4×C109—21no—
207C22×C4×C109—22no—
208C22×C4×C109—41no—
209C22×C4×C109C2×D411yescharacteristic
210C22×C4×C109C2×D411yescharacteristic
211C22×C4×C109C2×D411yescharacteristic
212Q16×C109—81no—
213Q16×C109—81no—
214SD16×C109—81no—
215SD16×C109—81no—
216SD16×C109—81no—
217D8×C109—44no—
218D8×C109—81no—
219M16×C109—81no—
220C2×C8×C109—21no—
221C2×C8×C109—21no—
222C2×C8×C109—21no—
223C2×C8×C109—21no—
224C2×C8×C109—21no—
225C2×C8×C109—21no—
226C2×C8×C109—42no—
227C4⋊C4×C109—22no—
228C4⋊C4×C109—22no—
229C4⋊C4×C109—22no—
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×C109—21no—
240C4⋊C4×C109—21no—
241C4⋊C4×C109—21no—
242C4⋊C4×C109—21no—
243C4⋊C4×C109—21no—
244C4⋊C4×C109—21no—
245C4⋊C4×C109C2×D411yescharacteristic
246C4⋊C4×C109C2×D411yescharacteristic
247C4⋊C4×C109C2×D411yescharacteristic
248C4⋊C4×C109C2×D411yescharacteristic
249C4⋊C4×C109C2×D412yes—
250C22⋊C4×C109—22no—
251C22⋊C4×C109—22no—
252C22⋊C4×C109—22no—
253C22⋊C4×C109—22no—
254C22⋊C4×C109—22no—
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—22no—
262C22⋊C4×C109—22no—
263C22⋊C4×C109—21no—
264C22⋊C4×C109—41no—
265C22⋊C4×C109—41no—
266C42×C109—22no—
267C42×C109—21no—
268C42×C109—21no—
269C42×C109—21no—
270C42×C109C2×D411yescharacteristic
271C42×C109C2×D411yescharacteristic
272C42×C109C2×D411yescharacteristic
273C42×C109C2411yescharacteristic
274C23×C109—21no—
275C23×C109—22no—
276C23×C109—41no—
277C23×C109#12011yescharacteristic
278Q8×C109—21no—
279Q8×C109—21no—
280Q8×C109—21no—
281Q8×C109—21no—
282Q8×C109—21no—
283Q8×C109—21no—
284Q8×C109—41no—
285Q8×C109—41no—
286Q8×C109—41no—
287Q8×C109—41no—
288Q8×C109—81no—
289Q8×C109—82no—
290D4×C109—21no—
291D4×C109—21no—
292D4×C109—42no—
293D4×C109—42no—
294D4×C109—41no—
295D4×C109—41no—
296D4×C109—41no—
297D4×C109—41no—
298D4×C109—41no—
299D4×C109—41no—
300D4×C109—41no—
301D4×C109—41no—
302D4×C109—81no—
303D4×C109—82no—
304D4×C109—82no—
305D4×C109—82no—
306D4×C109—82no—
307C2×C4×C109—21no—
308C2×C4×C109—21no—
309C2×C4×C109—21no—
310C2×C4×C109—21no—
311C2×C4×C109—21no—
312C2×C4×C109—21no—
313C2×C4×C109—21no—
314C2×C4×C109—21no—
315C2×C4×C109—21no—
316C2×C4×C109—22no—
317C2×C4×C109—21no—
318C2×C4×C109—21no—
319C2×C4×C109—41no—
320C2×C4×C109—41no—
321C2×C4×C109—41no—
322C2×C4×C109—41no—
323C2×C4×C109—82no—
324C2×C4×C109—82no—
325C2×C4×C109—82no—
326C2×C4×C109—82no—
327C2×C4×C109—82no—
328C2×C4×C109#12011yescharacteristic
329C2×C4×C109#12011yescharacteristic
330C2×C4×C109#12011yescharacteristic
331C2×C4×C109C22×D411yescharacteristic
332C2×C4×C109C22×D411yescharacteristic
333C2×C4×C109C22×D411yescharacteristic
334C8×C109—22no—
335C8×C109—41no—
336C8×C109—41no—
337C8×C109—41no—
338C8×C109—41no—
339C8×C109—41no—
340C22×C109—21no—
341C22×C109—21no—
342C22×C109—21no—
343C22×C109—41no—
344C22×C109—42no—
345C22×C109—41no—
346C22×C109—42no—
347C22×C109—42no—
348C22×C109—41no—
349C22×C109—81no—
350C22×C109—81no—
351C22×C109—81no—
352C22×C109C2×#12011yescharacteristic
353C4×C109—21no—
354C4×C109—21no—
355C4×C109—21no—
356C4×C109—21no—
357C4×C109—41no—
358C4×C109—41no—
359C4×C109—42no—
360C4×C109—41no—
361C4×C109—41no—
362C4×C109—41no—
363C4×C109—41no—
364C4×C109—41no—
365C4×C109—81no—
366C4×C109#57611yescharacteristic
367C4×C109#57611yescharacteristic
368C4×C109#57711yescharacteristic
369C4×C109#57811yescharacteristic
370#18708C10911yesmaximal, characteristic, direct product factor, Sylow
371C2×C109—41no—
372C2×C109—81no—
373C2×C109—82no—
374C2×C109—161no—
375C2×C109#300811yescharacteristic
376C2×C109#301311yescharacteristic
377C2×C109#301811yescharacteristic
378#3554C2×C10911yescharacteristic, complemented
379#3251C2×C10911yescharacteristic, complemented
380#3216C2×C10911yescharacteristic, complemented
381#3169C2×C10911yescharacteristic, complemented
382#1649C2×C10911yescharacteristic, complemented
383#1648C2×C10911yescharacteristic, complemented
384#1641C2×C10911yescharacteristic, complemented
385#1640C2×C10911yescharacteristic, complemented
386#1627C2×C10911yescharacteristic, complemented
387#1626C2×C10911yescharacteristic, complemented
388#1621C2×C10911yescharacteristic, complemented
389#1620C2×C10911yescharacteristic, complemented
390#1557C2×C10911yescharacteristic, complemented
391#1494C2×C10911yescharacteristic, complemented
392#1493C2×C10911yescharacteristic, complemented
393C109#1870811yescharacteristic, direct product factor, Sylow
394#562—22no—
395#559—21no—
396#559C22×C10911yescharacteristic
397#557C22×C10911yescharacteristic
398#554—21no—
399#550C22×C10911yescharacteristic
400D4×Q8C22×C10911yescharacteristic
401#548—21no—
402#547—21no—
403#542—21no—
404#542—21no—
405#540—21no—
406#539—22no—
407#536—21no—
408#533C22×C10911yescharacteristic
409#532C22×C10911yescharacteristic
410#532C22×C10911yescharacteristic
411#529C22×C10911yescharacteristic
412#500C22×C10911yescharacteristic
413#497—21no—
414#493C22×C10911yescharacteristic
415#489—21no—
416#486C22×C10911yescharacteristic
417#486C22×C10911yescharacteristic
418#478—21no—
419#475C22×C10911yescharacteristic
420#474C22×C10911yescharacteristic
421#469—21no—
422#468—21no—
423#466—22no—
424#463—21no—
425#462C22×C10911yescharacteristic
426#462C22×C10911yescharacteristic
427#460C22×C10911yescharacteristic
428#460C22×C10911yescharacteristic
429#460C22×C10911yescharacteristic
430#459C22×C10911yescharacteristic
431#452—21no—
432#452—21no—
433C4×D8—22no—
434#432C22×C10911yescharacteristic
435#423C22×C10911yescharacteristic
436C2×C4×C8C22×C10911yescharacteristic
437#332C22×C10911yescharacteristic
438#332C22×C10911yescharacteristic
439#331C22×C10911yescharacteristic
440#331C22×C10911yescharacteristic
441Q8⋊C8C22×C10911yescharacteristic
442Q8⋊C8C22×C10911yescharacteristic
443Q8⋊C8C22×C10911yescharacteristic
444Q8⋊C8C22×C10911yescharacteristic
445Q8⋊C8C22×C10911yescharacteristic
446Q8⋊C8C22×C10911yescharacteristic
447D4⋊C8C22×C10911yescharacteristic
448D4⋊C8C22×C10911yescharacteristic
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C10911yescharacteristic
465C4⋊Q8D4×C10911yescharacteristic
466C4⋊Q8C23×C10911yescharacteristic
467C4⋊Q8C23×C10911yescharacteristic
468#127—21no—
469#127C23×C10911yescharacteristic
470#127C23×C10911yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C10911yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C10911yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C10911yescharacteristic
499C22⋊Q8D4×C10911yescharacteristic
500C22⋊Q8D4×C10911yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C10911yescharacteristic
509#121D4×C10912yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C10911yescharacteristic
514C4×Q8C23×C10911yescharacteristic
515C4×Q8C23×C10911yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C10912yes—
526C4×D4C23×C10911yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C10911yescharacteristic
531#107—22no—
532#107—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C10911yescharacteristic
536C4⋊C8C23×C10911yescharacteristic
537C4⋊C8C23×C10911yescharacteristic
538C4⋊C8C23×C10911yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#102—22no—
543#102—21no—
544#102—22no—
545#102—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
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C10911yescharacteristic
567C2×Q8C2×D4×C10911yescharacteristic
568C2×Q8C2×D4×C10911yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C10911yescharacteristic
580C2×D4C2×D4×C10912yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C10911yescharacteristic
588C22×C4C2×D4×C10911yescharacteristic
589C22×C4C2×D4×C10911yescharacteristic
590Q16—81no—
591Q16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—81no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C10911yescharacteristic
624C4⋊C4C2×D4×C10911yescharacteristic
625C4⋊C4C2×D4×C10911yescharacteristic
626C4⋊C4C2×D4×C10911yescharacteristic
627C4⋊C4C2×D4×C10912yes—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C10911yescharacteristic
649C42C2×D4×C10911yescharacteristic
650C42C2×D4×C10911yescharacteristic
651C42C24×C10911yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C10911yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C10911yescharacteristic
707C2×C4#120×C10911yescharacteristic
708C2×C4#120×C10911yescharacteristic
709C2×C4C22×D4×C10911yescharacteristic
710C2×C4C22×D4×C10911yescharacteristic
711C2×C4C22×D4×C10911yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C10911yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4#576×C10911yescharacteristic
745C4#576×C10911yescharacteristic
746C4#577×C10911yescharacteristic
747C4#578×C10911yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C109×#300811yescharacteristic
753C2C109×#301311yescharacteristic
754C2C109×#301811yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC42C24×C109
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×#3554C2semidirect
2. C109×#3251C2semidirect
3. C109×#3216C2semidirect
4. C109×#3169C2semidirect
5. C109×#1649C2semidirect
6. C109×#1648C2semidirect
7. C109×#1641C2semidirect
8. C109×#1640C2semidirect
9. C109×#1627C2semidirect
10. C109×#1626C2semidirect
11. C109×#1621C2semidirect
12. C109×#1620C2semidirect
13. C109×#1557C2semidirect
14. C109×#1494C2semidirect
15. C109×#1493C2semidirect
370. #18708C109direct (N × H)
378. #3554C2×C109semidirect
379. #3251C2×C109semidirect
380. #3216C2×C109semidirect
381. #3169C2×C109semidirect
382. #1649C2×C109semidirect
383. #1648C2×C109semidirect
384. #1641C2×C109semidirect
385. #1640C2×C109semidirect
386. #1627C2×C109semidirect
387. #1626C2×C109semidirect
388. #1621C2×C109semidirect
389. #1620C2×C109semidirect
390. #1557C2×C109semidirect
391. #1494C2×C109semidirect
392. #1493C2×C109semidirect
393. C109#18708direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#35542
C109×#32512
C109×#32162
C109×#31692
C109×#16492
C109×#16482
C109×#16412
C109×#16402
C109×#16272
C109×#16262
C109×#16212
C109×#16202
C109×#15572
C109×#14942
C109×#14932
#18708109