Finite Group Databasebeta

← C109×#18192 #42136186

Subgroups — C109×#18192 #42136186

Order 27904.

1334 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3490C211yesmaximal, characteristic, complemented
2C109×#3002C212yesmaximal, complemented
3C109×#2404C211yesmaximal, characteristic, complemented
4C109×#1606C212yesmaximal, complemented
5C109×#1602C211yesmaximal, characteristic, complemented
6C109×#1601C211yesmaximal, characteristic, complemented
7C109×#1600C212yesmaximal, complemented
8C109×#1596C211yesmaximal, characteristic, complemented
9C109×#1595C211yesmaximal, characteristic, complemented
10C109×#1516C212yesmaximal, complemented
11C2×#323×C109C211yesmaximal, characteristic, complemented
12C22×#41×C109C2211yescharacteristic, complemented
13C2×#135×C109—22no—
14#551×C109—22no—
15#551×C109—22no—
16#546×C109—22no—
17#546×C109—22no—
18#543×C109C2211yescharacteristic
19#538×C109—21no—
20#538×C109C2212yes—
21#534×C109C2211yescharacteristic
22#525×C109—21no—
23#525×C109C2212yes—
24C2×#120×C109—21no—
25C2×#120×C109—21no—
26#518×C109—21no—
27C22×C22⋊C4×C109C2211yescharacteristic
28#452×C109—22no—
29#451×C109C2212yescomplemented
30#450×C109C2212yescomplemented
31#449×C109—22no—
32#448×C109C2212yescomplemented
33#447×C109C2212yescomplemented
34#416×C109—22no—
35C2×C22⋊C8×C109C2212yescomplemented
36#393×C109C2211yescharacteristic
37#393×C109C2211yescharacteristic, complemented
38#392×C109C2211yescharacteristic
39#392×C109C2211yescharacteristic, complemented
40#386×C109—21no—
41#386×C109—21no—
42#386×C109—21no—
43#381×C109C2211yescharacteristic, complemented
44#328×C109C2212yescomplemented
45#328×C109C2212yescomplemented
46#327×C109C2212yescomplemented
47#327×C109C2212yescomplemented
48#323×C109C2211yescharacteristic
49#323×C109C2211yescharacteristic
50#323×C109C2212yescomplemented
51C25×C109D411yescharacteristic
52C2×#41×C109—21no—
53C2×#41×C109—22no—
54C2×#41×C109—22no—
55C2×#41×C109—44no—
56C2×#41×C109D412yescomplemented
57C22×Q8×C109C2311yescharacteristic
58C22×D4×C109—21no—
59C22×D4×C109—21no—
60C22×D4×C109—21no—
61C22×D4×C109—21no—
62C22×D4×C109—21no—
63C22×D4×C109—21no—
64C22×D4×C109C2311yescharacteristic
65C23×C4×C109—21no—
66C23×C4×C109D411yescharacteristic
67C23×C4×C109C2311yescharacteristic
68#135×C109—48no—
69C2×Q16×C109—22no—
70C2×SD16×C109—22no—
71C2×SD16×C109—22no—
72C2×D8×C109—22no—
73C22×C8×C109—22no—
74#126×C109—22no—
75#126×C109—22no—
76#124×C109—22no—
77#124×C109—22no—
78#123×C109—22no—
79#123×C109—22no—
80#123×C109—22no—
81#123×C109—22no—
82#123×C109—22no—
83C22⋊Q8×C109—21no—
84C22⋊Q8×C109—22no—
85C22⋊Q8×C109—21no—
86C22⋊Q8×C109—22no—
87C22⋊Q8×C109D412yescomplemented
88C22⋊Q8×C109C2312yes—
89#121×C109—21no—
90#121×C109—22no—
91#121×C109—22no—
92#121×C109—21no—
93#121×C109D412yescomplemented
94#121×C109C2312yes—
95#120×C109—22no—
96#120×C109—22no—
97#120×C109—22no—
98#120×C109—22no—
99#120×C109—22no—
100#120×C109—44no—
101C4×D4×C109—22no—
102C4×D4×C109—22no—
103C4×D4×C109—22no—
104C4×D4×C109—22no—
105C4×D4×C109—22no—
106C4×D4×C109—22no—
107#117×C109—22no—
108#117×C109—21no—
109#117×C109D412yescomplemented
110C2×C22⋊C4×C109—22no—
111C2×C22⋊C4×C109—21no—
112C2×C22⋊C4×C109—21no—
113C2×C22⋊C4×C109—21no—
114C2×C22⋊C4×C109—22no—
115C2×C22⋊C4×C109—22no—
116C2×C22⋊C4×C109—21no—
117C2×C22⋊C4×C109—21no—
118C2×C22⋊C4×C109—21no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109D411yescharacteristic
122C2×C22⋊C4×C109D411yescharacteristic
123C2×C22⋊C4×C109C2311yescharacteristic
124C2×C22⋊C4×C109C2311yescharacteristic
125#103×C109—22no—
126#103×C109—22no—
127#102×C109—22no—
128#102×C109—22no—
129C22⋊C8×C109—22no—
130C22⋊C8×C109C2312yes—
131C22⋊C8×C109C2312yes—
132#95×C109—21no—
133#95×C109—21no—
134#95×C109—21no—
135#95×C109C2311yescharacteristic
136#95×C109C2311yescharacteristic
137C24×C109—21no—
138C24×C109—21no—
139C24×C109—21no—
140C24×C109—21no—
141C24×C109—22no—
142C24×C109—41no—
143C24×C109—42no—
144C24×C109—81no—
145C24×C109C2×D411yescharacteristic
146C24×C109C2×D411yescharacteristic
147C24×C109C2×D411yescharacteristic
148#41×C109—28no—
149#41×C109—44no—
150#41×C109—44no—
151#41×C109—44no—
152#41×C109—44no—
153#41×C109—82no—
154C2×Q8×C109—21no—
155C2×Q8×C109—22no—
156C2×Q8×C109—42no—
157C2×Q8×C109C2×D412yes—
158C2×D4×C109—22no—
159C2×D4×C109—24no—
160C2×D4×C109—22no—
161C2×D4×C109—22no—
162C2×D4×C109—22no—
163C2×D4×C109—21no—
164C2×D4×C109—22no—
165C2×D4×C109—22no—
166C2×D4×C109—22no—
167C2×D4×C109—42no—
168C2×D4×C109—42no—
169C2×D4×C109—42no—
170C2×D4×C109—41no—
171C2×D4×C109—41no—
172C2×D4×C109—42no—
173C2×D4×C109—42no—
174C2×D4×C109—42no—
175C2×D4×C109—42no—
176C2×D4×C109—42no—
177C2×D4×C109—81no—
178C2×D4×C109—81no—
179C2×D4×C109—82no—
180C2×D4×C109—82no—
181C2×D4×C109C2×D412yes—
182C22×C4×C109—21no—
183C22×C4×C109—21no—
184C22×C4×C109—21no—
185C22×C4×C109—21no—
186C22×C4×C109—21no—
187C22×C4×C109—22no—
188C22×C4×C109—21no—
189C22×C4×C109—22no—
190C22×C4×C109—21no—
191C22×C4×C109—21no—
192C22×C4×C109—42no—
193C22×C4×C109—42no—
194C22×C4×C109—42no—
195C22×C4×C109—42no—
196C22×C4×C109—81no—
197C22×C4×C109C2×D412yes—
198C22×C4×C109C2×D411yescharacteristic
199C22×C4×C109C2×D411yescharacteristic
200C22×C4×C109C2×D411yescharacteristic
201C22×C4×C109C2×D412yes—
202C22×C4×C109C2411yescharacteristic
203Q16×C109—44no—
204SD16×C109—44no—
205SD16×C109—44no—
206D8×C109—44no—
207C2×C8×C109—22no—
208C2×C8×C109—22no—
209C2×C8×C109—44no—
210C4⋊C4×C109—22no—
211C4⋊C4×C109—21no—
212C4⋊C4×C109—21no—
213C4⋊C4×C109—22no—
214C4⋊C4×C109—22no—
215C4⋊C4×C109—22no—
216C4⋊C4×C109C2×D412yes—
217C4⋊C4×C109C2×D412yes—
218C22⋊C4×C109—22no—
219C22⋊C4×C109—22no—
220C22⋊C4×C109—22no—
221C22⋊C4×C109—22no—
222C22⋊C4×C109—22no—
223C22⋊C4×C109—22no—
224C22⋊C4×C109—22no—
225C22⋊C4×C109—22no—
226C22⋊C4×C109—22no—
227C22⋊C4×C109—22no—
228C22⋊C4×C109—22no—
229C22⋊C4×C109—22no—
230C22⋊C4×C109—22no—
231C22⋊C4×C109—22no—
232C22⋊C4×C109—42no—
233C22⋊C4×C109—42no—
234C22⋊C4×C109—42no—
235C22⋊C4×C109—81no—
236C22⋊C4×C109—81no—
237C42×C109—22no—
238C42×C109—22no—
239C23×C109—21no—
240C23×C109—21no—
241C23×C109—21no—
242C23×C109—22no—
243C23×C109—21no—
244C23×C109—22no—
245C23×C109—21no—
246C23×C109—22no—
247C23×C109—21no—
248C23×C109—21no—
249C23×C109—41no—
250C23×C109—42no—
251C23×C109—42no—
252C23×C109—41no—
253C23×C109—41no—
254C23×C109—41no—
255C23×C109—41no—
256C23×C109—41no—
257C23×C109—41no—
258C23×C109—41no—
259C23×C109—42no—
260C23×C109—42no—
261C23×C109—41no—
262C23×C109—41no—
263C23×C109—41no—
264C23×C109—42no—
265C23×C109—81no—
266C23×C109—81no—
267C23×C109—81no—
268C23×C109—81no—
269C23×C109—84no—
270C23×C109—84no—
271C23×C109#12011yescharacteristic
272C23×C109#12011yescharacteristic
273C23×C109#13512yescomplemented
274C23×C109C22×D411yescharacteristic
275Q8×C109—24no—
276Q8×C109—42no—
277Q8×C109—42no—
278Q8×C109—81no—
279D4×C109—24no—
280D4×C109—42no—
281D4×C109—42no—
282D4×C109—44no—
283D4×C109—44no—
284D4×C109—44no—
285D4×C109—42no—
286D4×C109—42no—
287D4×C109—44no—
288D4×C109—44no—
289D4×C109—82no—
290D4×C109—82no—
291D4×C109—81no—
292D4×C109—84no—
293D4×C109—84no—
294C2×C4×C109—24no—
295C2×C4×C109—22no—
296C2×C4×C109—22no—
297C2×C4×C109—21no—
298C2×C4×C109—22no—
299C2×C4×C109—22no—
300C2×C4×C109—21no—
301C2×C4×C109—41no—
302C2×C4×C109—42no—
303C2×C4×C109—41no—
304C2×C4×C109—48no—
305C2×C4×C109—41no—
306C2×C4×C109—42no—
307C2×C4×C109—42no—
308C2×C4×C109—41no—
309C2×C4×C109—41no—
310C2×C4×C109—41no—
311C2×C4×C109—41no—
312C2×C4×C109—41no—
313C2×C4×C109—41no—
314C2×C4×C109—41no—
315C2×C4×C109—41no—
316C2×C4×C109—41no—
317C2×C4×C109—82no—
318C2×C4×C109—81no—
319C2×C4×C109—81no—
320C2×C4×C109—81no—
321C2×C4×C109—82no—
322C2×C4×C109#12012yes—
323C2×C4×C109C22×D412yes—
324C8×C109—42no—
325C8×C109—42no—
326C22×C109—21no—
327C22×C109—21no—
328C22×C109—21no—
329C22×C109—21no—
330C22×C109—22no—
331C22×C109—21no—
332C22×C109—21no—
333C22×C109—21no—
334C22×C109—42no—
335C22×C109—42no—
336C22×C109—42no—
337C22×C109—42no—
338C22×C109—42no—
339C22×C109—42no—
340C22×C109—41no—
341C22×C109—41no—
342C22×C109—42no—
343C22×C109—41no—
344C22×C109—42no—
345C22×C109—41no—
346C22×C109—42no—
347C22×C109—42no—
348C22×C109—41no—
349C22×C109—81no—
350C22×C109—84no—
351C22×C109—81no—
352C22×C109—81no—
353C22×C109—81no—
354C22×C109—84no—
355C22×C109—81no—
356C22×C109—81no—
357C22×C109—162no—
358C22×C109B(4,𝔽2)12yes—
359C22×C109C2×#12011yescharacteristic
360C22×C109C2×#13511yescharacteristic
361C22×C109#57511yescharacteristic
362C4×C109—22no—
363C4×C109—22no—
364C4×C109—42no—
365C4×C109—41no—
366C4×C109—41no—
367C4×C109—42no—
368C4×C109—42no—
369C4×C109—42no—
370C4×C109—81no—
371C4×C109—81no—
372#18192C10911yesmaximal, characteristic, direct product factor, Sylow
373C2×C109—21no—
374C2×C109—21no—
375C2×C109—22no—
376C2×C109—41no—
377C2×C109—42no—
378C2×C109—81no—
379C2×C109—82no—
380C2×C109—82no—
381C2×C109#300211yescharacteristic
382C2×C109#301911yescharacteristic
383C2×C109C2×B(4,𝔽2)11yescharacteristic
384#3490C2×C10911yescharacteristic, complemented
385#3002C2×C10912yescomplemented
386#2404C2×C10911yescharacteristic, complemented
387#1606C2×C10912yescomplemented
388#1602C2×C10911yescharacteristic, complemented
389#1601C2×C10911yescharacteristic, complemented
390#1600C2×C10912yescomplemented
391#1596C2×C10911yescharacteristic, complemented
392#1595C2×C10911yescharacteristic, complemented
393#1516C2×C10912yescomplemented
394C2×#323C2×C10911yescharacteristic, complemented
395C109#1819211yescharacteristic, direct product factor, Sylow
396C22×#41C22×C10911yescharacteristic, complemented
397C2×#135—22no—
398#551—22no—
399#551—22no—
400#546—22no—
401#546—22no—
402#543C22×C10911yescharacteristic
403#538—21no—
404#538C22×C10912yes—
405#534C22×C10911yescharacteristic
406#525—21no—
407#525C22×C10912yes—
408C2×#120—21no—
409C2×#120—21no—
410#518—21no—
411C22×C22⋊C4C22×C10911yescharacteristic
412#452—22no—
413#451C22×C10912yescomplemented
414#450C22×C10912yescomplemented
415#449—22no—
416#448C22×C10912yescomplemented
417#447C22×C10912yescomplemented
418#416—22no—
419C2×C22⋊C8C22×C10912yescomplemented
420#393C22×C10911yescharacteristic
421#393C22×C10911yescharacteristic, complemented
422#392C22×C10911yescharacteristic
423#392C22×C10911yescharacteristic, complemented
424#386—21no—
425#386—21no—
426#386—21no—
427#381C22×C10911yescharacteristic, complemented
428#328C22×C10912yescomplemented
429#328C22×C10912yescomplemented
430#327C22×C10912yescomplemented
431#327C22×C10912yescomplemented
432#323C22×C10911yescharacteristic
433#323C22×C10911yescharacteristic
434#323C22×C10912yescomplemented
435C25D4×C10911yescharacteristic
436C2×#41—21no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—44no—
440C2×#41D4×C10912yescomplemented
441C22×Q8C23×C10911yescharacteristic
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C23×C10911yescharacteristic
449C23×C4—21no—
450C23×C4D4×C10911yescharacteristic
451C23×C4C23×C10911yescharacteristic
452#135—48no—
453C2×Q16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×D8—22no—
457C22×C8—22no—
458#126—22no—
459#126—22no—
460#124—22no—
461#124—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—21no—
470C22⋊Q8—22no—
471C22⋊Q8D4×C10912yescomplemented
472C22⋊Q8C23×C10912yes—
473#121—21no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121D4×C10912yescomplemented
478#121C23×C10912yes—
479#120—22no—
480#120—22no—
481#120—22no—
482#120—22no—
483#120—22no—
484#120—44no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491#117—22no—
492#117—21no—
493#117D4×C10912yescomplemented
494C2×C22⋊C4—22no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C10911yescharacteristic
506C2×C22⋊C4D4×C10911yescharacteristic
507C2×C22⋊C4C23×C10911yescharacteristic
508C2×C22⋊C4C23×C10911yescharacteristic
509#103—22no—
510#103—22no—
511#102—22no—
512#102—22no—
513C22⋊C8—22no—
514C22⋊C8C23×C10912yes—
515C22⋊C8C23×C10912yes—
516#95—21no—
517#95—21no—
518#95—21no—
519#95C23×C10911yescharacteristic
520#95C23×C10911yescharacteristic
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—41no—
527C24—42no—
528C24—81no—
529C24C2×D4×C10911yescharacteristic
530C24C2×D4×C10911yescharacteristic
531C24C2×D4×C10911yescharacteristic
532#41—28no—
533#41—44no—
534#41—44no—
535#41—44no—
536#41—44no—
537#41—82no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—42no—
541C2×Q8C2×D4×C10912yes—
542C2×D4—22no—
543C2×D4—24no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—82no—
565C2×D4C2×D4×C10912yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—81no—
581C22×C4C2×D4×C10912yes—
582C22×C4C2×D4×C10911yescharacteristic
583C22×C4C2×D4×C10911yescharacteristic
584C22×C4C2×D4×C10911yescharacteristic
585C22×C4C2×D4×C10912yes—
586C22×C4C24×C10911yescharacteristic
587Q16—44no—
588SD16—44no—
589SD16—44no—
590D8—44no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—44no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4C2×D4×C10912yes—
601C4⋊C4C2×D4×C10912yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—81no—
620C22⋊C4—81no—
621C42—22no—
622C42—22no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—21no—
628C23—22no—
629C23—21no—
630C23—22no—
631C23—21no—
632C23—21no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—42no—
649C23—81no—
650C23—81no—
651C23—81no—
652C23—81no—
653C23—84no—
654C23—84no—
655C23#120×C10911yescharacteristic
656C23#120×C10911yescharacteristic
657C23#135×C10912yescomplemented
658C23C22×D4×C10911yescharacteristic
659Q8—24no—
660Q8—42no—
661Q8—42no—
662Q8—81no—
663D4—24no—
664D4—42no—
665D4—42no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—42no—
670D4—42no—
671D4—44no—
672D4—44no—
673D4—82no—
674D4—82no—
675D4—81no—
676D4—84no—
677D4—84no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—48no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
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—41no—
701C2×C4—82no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—82no—
706C2×C4#120×C10912yes—
707C2×C4C22×D4×C10912yes—
708C8—42no—
709C8—42no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—41no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—81no—
734C22—84no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—84no—
739C22—81no—
740C22—81no—
741C22—162no—
742C22B(4,𝔽2)×C10912yes—
743C22C2×#120×C10911yescharacteristic
744C22C2×#135×C10911yescharacteristic
745C22#575×C10911yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—41no—
750C4—41no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—81no—
755C4—81no—
756C2—21no—
757C2—21no—
758C2—22no—
759C2—41no—
760C2—42no—
761C2—81no—
762C2—82no—
763C2—82no—
764C2C109×#300211yescharacteristic
765C2C109×#301911yescharacteristic
766C2C2×B(4,𝔽2)×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3490C2semidirect
2. C109×#3002C2semidirect
3. C109×#2404C2semidirect
4. C109×#1606C2semidirect
5. C109×#1602C2semidirect
6. C109×#1601C2semidirect
7. C109×#1600C2semidirect
8. C109×#1596C2semidirect
9. C109×#1595C2semidirect
10. C109×#1516C2semidirect
11. C2×#323×C109C2semidirect
12. C22×#41×C109C22semidirect
29. #451×C109C22semidirect
30. #450×C109C22semidirect
32. #448×C109C22semidirect
33. #447×C109C22semidirect
35. C2×C22⋊C8×C109C22semidirect
37. #393×C109C22semidirect
39. #392×C109C22semidirect
43. #381×C109C22semidirect
44. #328×C109C22semidirect
45. #328×C109C22semidirect
46. #327×C109C22semidirect
47. #327×C109C22semidirect
50. #323×C109C22semidirect
56. C2×#41×C109D4semidirect
87. C22⋊Q8×C109D4semidirect
93. #121×C109D4semidirect
109. #117×C109D4semidirect
273. C23×C109#135semidirect
372. #18192C109direct (N × H)
384. #3490C2×C109semidirect
385. #3002C2×C109semidirect
386. #2404C2×C109semidirect
387. #1606C2×C109semidirect
388. #1602C2×C109semidirect
389. #1601C2×C109semidirect
390. #1600C2×C109semidirect
391. #1596C2×C109semidirect
392. #1595C2×C109semidirect
393. #1516C2×C109semidirect
394. C2×#323C2×C109semidirect
395. C109#18192direct (N × H)
396. C22×#41C22×C109semidirect
413. #451C22×C109semidirect
414. #450C22×C109semidirect
416. #448C22×C109semidirect
417. #447C22×C109semidirect
419. C2×C22⋊C8C22×C109semidirect
421. #393C22×C109semidirect
423. #392C22×C109semidirect
427. #381C22×C109semidirect
428. #328C22×C109semidirect
429. #328C22×C109semidirect
430. #327C22×C109semidirect
431. #327C22×C109semidirect
434. #323C22×C109semidirect
440. C2×#41D4×C109semidirect
471. C22⋊Q8D4×C109semidirect
477. #121D4×C109semidirect
493. #117D4×C109semidirect
657. C23#135×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#34902
C109×#30022
C109×#24042
C109×#16062
C109×#16022
C109×#16012
C109×#16002
C109×#15962
C109×#15952
C109×#15162
C2×#323×C1092
#18192109