Finite Group Databasebeta

← C109×#25587 #42143581

Subgroups — C109×#25587 #42143581

Order 27904.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3505C211yesmaximal, characteristic, complemented
2C109×#2561C211yesmaximal, characteristic, complemented
3C109×#2539C211yesmaximal, characteristic, complemented
4C109×#2534C211yesmaximal, characteristic, complemented
5C109×#2022C212yesmaximal, complemented
6C109×#2021C212yesmaximal, complemented
7C109×#1996C211yesmaximal, characteristic, complemented
8C109×#1964C211yesmaximal, characteristic, complemented
9C109×#1890C212yesmaximal, complemented
10C109×#1889C212yesmaximal, complemented
11C4×#99×C109C211yesmaximal, characteristic, complemented
12#553×C109—22no—
13#553×C109—21no—
14#552×C109—21no—
15#551×C109—22no—
16#548×C109—21no—
17#546×C109—21no—
18#539×C109—21no—
19#538×C109—21no—
20#534×C109C2212yes—
21#529×C109—21no—
22#525×C109—21no—
23C2×#123×C109C2212yes—
24C2×#123×C109C2211yescharacteristic
25C2×C22⋊Q8×C109C2211yescharacteristic
26C2×#121×C109C2211yescharacteristic
27C2×#120×C109C2212yes—
28C2×#120×C109C2211yescharacteristic
29#518×C109C2212yes—
30C2×C4×D4×C109C2211yescharacteristic
31C22×C22⋊C4×C109C2211yescharacteristic
32C2×#99×C109C2212yes—
33C2×#99×C109C2212yes—
34C2×#99×C109C2212yes—
35#399×C109—21no—
36#397×C109—21no—
37#396×C109—21no—
38#394×C109—21no—
39#393×C109—21no—
40#392×C109—21no—
41#390×C109—22no—
42#388×C109—22no—
43#388×C109—21no—
44#386×C109—21no—
45#381×C109C2212yes—
46#381×C109C2211yescharacteristic
47#380×C109C2211yescharacteristic
48#379×C109C2212yes—
49#379×C109C2211yescharacteristic
50C4×C22⋊C4×C109C2211yescharacteristic
51C4×C22⋊C4×C109C2211yescharacteristic
52#342×C109C2212yes—
53#342×C109C2212yes—
54#342×C109C2212yes—
55C25×C109C2311yescharacteristic
56C2×#41×C109—21no—
57C22×Q8×C109D411yescharacteristic, complemented
58C22×D4×C109—21no—
59C22×D4×C109—22no—
60C22×D4×C109D411yescharacteristic, complemented
61C22×D4×C109C2311yescharacteristic
62C22×D4×C109C2312yes—
63C23×C4×C109D411yescharacteristic, complemented
64C23×C4×C109C2311yescharacteristic
65C23×C4×C109C2311yescharacteristic
66#126×C109—22no—
67#126×C109—22no—
68#126×C109—22no—
69#125×C109—21no—
70#125×C109—22no—
71#124×C109—21no—
72#124×C109—22no—
73#123×C109—22no—
74#123×C109—22no—
75#123×C109—22no—
76#123×C109—22no—
77#123×C109—22no—
78#123×C109—24no—
79#123×C109—42no—
80#123×C109—42no—
81C22⋊Q8×C109—21no—
82C22⋊Q8×C109—22no—
83C22⋊Q8×C109—21no—
84C22⋊Q8×C109—21no—
85C22⋊Q8×C109—21no—
86C22⋊Q8×C109—21no—
87#121×C109—21no—
88#121×C109—22no—
89#121×C109—21no—
90#121×C109—21no—
91#121×C109—21no—
92#121×C109—21no—
93#121×C109—22no—
94#121×C109—22no—
95#120×C109—22no—
96#120×C109—22no—
97#120×C109—24no—
98#120×C109—42no—
99#120×C109—42no—
100C4×Q8×C109—21no—
101C4×D4×C109—22no—
102C4×D4×C109—21no—
103C4×D4×C109—21no—
104C4×D4×C109—21no—
105C4×D4×C109—21no—
106C4×D4×C109—21no—
107C4×D4×C109—22no—
108C4×D4×C109—22no—
109C4×D4×C109—22no—
110C4×D4×C109—22no—
111#117×C109—21no—
112#117×C109—22no—
113#117×C109—22no—
114C2×C4⋊C4×C109—21no—
115C2×C4⋊C4×C109—22no—
116C2×C4⋊C4×C109—21no—
117C2×C4⋊C4×C109D411yescharacteristic, complemented
118C2×C4⋊C4×C109D411yescharacteristic, complemented
119C2×C4⋊C4×C109D412yescomplemented
120C2×C4⋊C4×C109D411yescharacteristic, complemented
121C2×C22⋊C4×C109—22no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—22no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109—21no—
129C2×C22⋊C4×C109—21no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—22no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—22no—
134C2×C22⋊C4×C109—21no—
135C2×C22⋊C4×C109—22no—
136C2×C22⋊C4×C109D411yescharacteristic, complemented
137C2×C22⋊C4×C109D412yescomplemented
138C2×C22⋊C4×C109C2311yescharacteristic
139C2×C22⋊C4×C109C2311yescharacteristic
140C2×C22⋊C4×C109C2312yes—
141C2×C22⋊C4×C109C2311yescharacteristic
142C2×C22⋊C4×C109C2312yes—
143C2×C22⋊C4×C109C2312yes—
144C2×C42×C109—21no—
145C2×C42×C109—21no—
146C2×C42×C109D411yescharacteristic, complemented
147#99×C109—24no—
148#99×C109—42no—
149#99×C109—42no—
150#95×C109—21no—
151#95×C109—21no—
152#95×C109—21no—
153#95×C109—21no—
154#95×C109—22no—
155#95×C109—21no—
156#95×C109—22no—
157C24×C109—21no—
158C24×C109—21no—
159C24×C109—21no—
160C24×C109—22no—
161C24×C109—22no—
162C24×C109—42no—
163C24×C109—81no—
164C24×C109C2×D412yes—
165C24×C109C2×D411yescharacteristic
166C24×C109C2411yescharacteristic
167#41×C109—82no—
168C2×Q8×C109—21no—
169C2×Q8×C109—21no—
170C2×Q8×C109—81no—
171C2×D4×C109—21no—
172C2×D4×C109—22no—
173C2×D4×C109—21no—
174C2×D4×C109—22no—
175C2×D4×C109—22no—
176C2×D4×C109—22no—
177C2×D4×C109—22no—
178C2×D4×C109—22no—
179C2×D4×C109—22no—
180C2×D4×C109—22no—
181C2×D4×C109—22no—
182C2×D4×C109—22no—
183C2×D4×C109—21no—
184C2×D4×C109—21no—
185C2×D4×C109—44no—
186C2×D4×C109—42no—
187C2×D4×C109—44no—
188C2×D4×C109—42no—
189C2×D4×C109—81no—
190C2×D4×C109—82no—
191C2×D4×C109—81no—
192C22×C4×C109—22no—
193C22×C4×C109—22no—
194C22×C4×C109—22no—
195C22×C4×C109—21no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—22no—
199C22×C4×C109—21no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—22no—
204C22×C4×C109—22no—
205C22×C4×C109—81no—
206C22×C4×C109—81no—
207C22×C4×C109C2×D411yescharacteristic
208C22×C4×C109C2×D412yes—
209C22×C4×C109C2×D411yescharacteristic
210C22×C4×C109C2×D412yes—
211C22×C4×C109C2×D411yescharacteristic
212C22×C4×C109C2×D412yes—
213C22×C4×C109C2×D411yescharacteristic
214C22×C4×C109C2×D411yescharacteristic
215C22×C4×C109C2×D411yescharacteristic
216C22×C4×C109C2×D411yescharacteristic
217C22×C4×C109C2×D411yescharacteristic
218C22×C4×C109C2×D411yescharacteristic
219C4⋊C4×C109—22no—
220C4⋊C4×C109—22no—
221C4⋊C4×C109—22no—
222C4⋊C4×C109—22no—
223C4⋊C4×C109—21no—
224C4⋊C4×C109—22no—
225C4⋊C4×C109—21no—
226C4⋊C4×C109—21no—
227C4⋊C4×C109—21no—
228C4⋊C4×C109—21no—
229C4⋊C4×C109—22no—
230C4⋊C4×C109—21no—
231C4⋊C4×C109—44no—
232C4⋊C4×C109—42no—
233C4⋊C4×C109—81no—
234C22⋊C4×C109—22no—
235C22⋊C4×C109—22no—
236C22⋊C4×C109—22no—
237C22⋊C4×C109—22no—
238C22⋊C4×C109—22no—
239C22⋊C4×C109—22no—
240C22⋊C4×C109—21no—
241C22⋊C4×C109—22no—
242C22⋊C4×C109—21no—
243C22⋊C4×C109—22no—
244C22⋊C4×C109—22no—
245C22⋊C4×C109—22no—
246C22⋊C4×C109—21no—
247C22⋊C4×C109—21no—
248C22⋊C4×C109—22no—
249C22⋊C4×C109—22no—
250C22⋊C4×C109—22no—
251C22⋊C4×C109—22no—
252C22⋊C4×C109—22no—
253C22⋊C4×C109—44no—
254C22⋊C4×C109—44no—
255C22⋊C4×C109—42no—
256C22⋊C4×C109—44no—
257C22⋊C4×C109—42no—
258C22⋊C4×C109—42no—
259C22⋊C4×C109—41no—
260C22⋊C4×C109—41no—
261C22⋊C4×C109—41no—
262C22⋊C4×C109—41no—
263C22⋊C4×C109—81no—
264C22⋊C4×C109—82no—
265C22⋊C4×C109#4114yescomplemented
266C42×C109—22no—
267C42×C109—22no—
268C42×C109—21no—
269C42×C109—21no—
270C42×C109—81no—
271C42×C109—81no—
272C23×C109—22no—
273C23×C109—22no—
274C23×C109—22no—
275C23×C109—22no—
276C23×C109—21no—
277C23×C109—21no—
278C23×C109—21no—
279C23×C109—22no—
280C23×C109—22no—
281C23×C109—41no—
282C23×C109—41no—
283C23×C109—41no—
284C23×C109—41no—
285C23×C109—42no—
286C23×C109—41no—
287C23×C109—41no—
288C23×C109—42no—
289C23×C109—41no—
290C23×C109—41no—
291C23×C109—41no—
292C23×C109—42no—
293C23×C109—42no—
294C23×C109—41no—
295C23×C109—41no—
296C23×C109—41no—
297C23×C109—42no—
298C23×C109—42no—
299C23×C109—84no—
300C23×C109—84no—
301C23×C109C22×D411yescharacteristic
302C23×C109C22×D411yescharacteristic
303C23×C109C22×D411yescharacteristic
304C23×C109C2×#4112yes—
305C23×C109H(5,𝔽2)12yes—
306Q8×C109—42no—
307Q8×C109—81no—
308D4×C109—42no—
309D4×C109—42no—
310D4×C109—42no—
311D4×C109—42no—
312D4×C109—42no—
313D4×C109—42no—
314D4×C109—42no—
315D4×C109—81no—
316D4×C109—82no—
317D4×C109—82no—
318D4×C109—88no—
319D4×C109—84no—
320C2×C4×C109—21no—
321C2×C4×C109—22no—
322C2×C4×C109—21no—
323C2×C4×C109—21no—
324C2×C4×C109—22no—
325C2×C4×C109—22no—
326C2×C4×C109—21no—
327C2×C4×C109—21no—
328C2×C4×C109—24no—
329C2×C4×C109—22no—
330C2×C4×C109—22no—
331C2×C4×C109—41no—
332C2×C4×C109—41no—
333C2×C4×C109—41no—
334C2×C4×C109—41no—
335C2×C4×C109—41no—
336C2×C4×C109—41no—
337C2×C4×C109—42no—
338C2×C4×C109—42no—
339C2×C4×C109—42no—
340C2×C4×C109—41no—
341C2×C4×C109—42no—
342C2×C4×C109—41no—
343C2×C4×C109—42no—
344C2×C4×C109—42no—
345C2×C4×C109—42no—
346C2×C4×C109—41no—
347C2×C4×C109—41no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—41no—
351C2×C4×C109—41no—
352C2×C4×C109—41no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—42no—
356C2×C4×C109—42no—
357C2×C4×C109—42no—
358C2×C4×C109—81no—
359C2×C4×C109—82no—
360C2×C4×C109—82no—
361C2×C4×C109#12011yescharacteristic
362C2×C4×C109#12011yescharacteristic
363C2×C4×C109#12011yescharacteristic
364C2×C4×C109#12011yescharacteristic
365C22×C109—21no—
366C22×C109—21no—
367C22×C109—21no—
368C22×C109—21no—
369C22×C109—21no—
370C22×C109—21no—
371C22×C109—42no—
372C22×C109—42no—
373C22×C109—42no—
374C22×C109—44no—
375C22×C109—42no—
376C22×C109—44no—
377C22×C109—42no—
378C22×C109—41no—
379C22×C109—42no—
380C22×C109—42no—
381C22×C109—41no—
382C22×C109—42no—
383C22×C109—41no—
384C22×C109—42no—
385C22×C109—82no—
386C22×C109—82no—
387C22×C109—81no—
388C22×C109—82no—
389C22×C109—81no—
390C22×C109—82no—
391C22×C109—81no—
392C22×C109—81no—
393C22×C109—81no—
394C22×C109C2×#12011yescharacteristic
395C22×C109#53211yescharacteristic
396C22×C109#53511yescharacteristic
397C22×C109#54612yes—
398C22×C109#55012yes—
399C4×C109—21no—
400C4×C109—21no—
401C4×C109—21no—
402C4×C109—21no—
403C4×C109—44no—
404C4×C109—41no—
405C4×C109—42no—
406C4×C109—41no—
407C4×C109—42no—
408C4×C109—41no—
409C4×C109—42no—
410C4×C109—81no—
411C4×C109—82no—
412C4×C109—81no—
413C4×C109—81no—
414#25587C10911yesmaximal, characteristic, direct product factor, Sylow
415C2×C109—22no—
416C2×C109—21no—
417C2×C109—22no—
418C2×C109—21no—
419C2×C109—82no—
420C2×C109—81no—
421C2×C109—82no—
422C2×C109#243111yescharacteristic
423C2×C109#302511yescharacteristic
424C2×C109#302611yescharacteristic
425#3505C2×C10911yescharacteristic, complemented
426#2561C2×C10911yescharacteristic, complemented
427#2539C2×C10911yescharacteristic, complemented
428#2534C2×C10911yescharacteristic, complemented
429#2022C2×C10912yescomplemented
430#2021C2×C10912yescomplemented
431#1996C2×C10911yescharacteristic, complemented
432#1964C2×C10911yescharacteristic, complemented
433#1890C2×C10912yescomplemented
434#1889C2×C10912yescomplemented
435C4×#99C2×C10911yescharacteristic, complemented
436C109#2558711yescharacteristic, direct product factor, Sylow
437#553—22no—
438#553—21no—
439#552—21no—
440#551—22no—
441#548—21no—
442#546—21no—
443#539—21no—
444#538—21no—
445#534C22×C10912yes—
446#529—21no—
447#525—21no—
448C2×#123C22×C10912yes—
449C2×#123C22×C10911yescharacteristic
450C2×C22⋊Q8C22×C10911yescharacteristic
451C2×#121C22×C10911yescharacteristic
452C2×#120C22×C10912yes—
453C2×#120C22×C10911yescharacteristic
454#518C22×C10912yes—
455C2×C4×D4C22×C10911yescharacteristic
456C22×C22⋊C4C22×C10911yescharacteristic
457C2×#99C22×C10912yes—
458C2×#99C22×C10912yes—
459C2×#99C22×C10912yes—
460#399—21no—
461#397—21no—
462#396—21no—
463#394—21no—
464#393—21no—
465#392—21no—
466#390—22no—
467#388—22no—
468#388—21no—
469#386—21no—
470#381C22×C10912yes—
471#381C22×C10911yescharacteristic
472#380C22×C10911yescharacteristic
473#379C22×C10912yes—
474#379C22×C10911yescharacteristic
475C4×C22⋊C4C22×C10911yescharacteristic
476C4×C22⋊C4C22×C10911yescharacteristic
477#342C22×C10912yes—
478#342C22×C10912yes—
479#342C22×C10912yes—
480C25C23×C10911yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C10911yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C10911yescharacteristic, complemented
486C22×D4C23×C10911yescharacteristic
487C22×D4C23×C10912yes—
488C23×C4D4×C10911yescharacteristic, complemented
489C23×C4C23×C10911yescharacteristic
490C23×C4C23×C10911yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C10911yescharacteristic, complemented
543C2×C4⋊C4D4×C10911yescharacteristic, complemented
544C2×C4⋊C4D4×C10912yescomplemented
545C2×C4⋊C4D4×C10911yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C10911yescharacteristic, complemented
562C2×C22⋊C4D4×C10912yescomplemented
563C2×C22⋊C4C23×C10911yescharacteristic
564C2×C22⋊C4C23×C10911yescharacteristic
565C2×C22⋊C4C23×C10912yes—
566C2×C22⋊C4C23×C10911yescharacteristic
567C2×C22⋊C4C23×C10912yes—
568C2×C22⋊C4C23×C10912yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C10911yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C10912yes—
590C24C2×D4×C10911yescharacteristic
591C24C24×C10911yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C10911yescharacteristic
633C22×C4C2×D4×C10912yes—
634C22×C4C2×D4×C10911yescharacteristic
635C22×C4C2×D4×C10912yes—
636C22×C4C2×D4×C10911yescharacteristic
637C22×C4C2×D4×C10912yes—
638C22×C4C2×D4×C10911yescharacteristic
639C22×C4C2×D4×C10911yescharacteristic
640C22×C4C2×D4×C10911yescharacteristic
641C22×C4C2×D4×C10911yescharacteristic
642C22×C4C2×D4×C10911yescharacteristic
643C22×C4C2×D4×C10911yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C10914yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C10911yescharacteristic
727C23C22×D4×C10911yescharacteristic
728C23C22×D4×C10911yescharacteristic
729C23C2×#41×C10912yes—
730C23H(5,𝔽2)×C10912yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C10911yescharacteristic
787C2×C4#120×C10911yescharacteristic
788C2×C4#120×C10911yescharacteristic
789C2×C4#120×C10911yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C10911yescharacteristic
820C22#532×C10911yescharacteristic
821C22#535×C10911yescharacteristic
822C22#546×C10912yes—
823C22#550×C10912yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C109×#243111yescharacteristic
847C2C109×#302511yescharacteristic
848C2C109×#302611yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC24C24×C109
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3505C2semidirect
2. C109×#2561C2semidirect
3. C109×#2539C2semidirect
4. C109×#2534C2semidirect
5. C109×#2022C2semidirect
6. C109×#2021C2semidirect
7. C109×#1996C2semidirect
8. C109×#1964C2semidirect
9. C109×#1890C2semidirect
10. C109×#1889C2semidirect
11. C4×#99×C109C2semidirect
57. C22×Q8×C109D4semidirect
60. C22×D4×C109D4semidirect
63. C23×C4×C109D4semidirect
117. C2×C4⋊C4×C109D4semidirect
118. C2×C4⋊C4×C109D4semidirect
119. C2×C4⋊C4×C109D4semidirect
120. C2×C4⋊C4×C109D4semidirect
136. C2×C22⋊C4×C109D4semidirect
137. C2×C22⋊C4×C109D4semidirect
146. C2×C42×C109D4semidirect
265. C22⋊C4×C109#41semidirect
414. #25587C109direct (N × H)
425. #3505C2×C109semidirect
426. #2561C2×C109semidirect
427. #2539C2×C109semidirect
428. #2534C2×C109semidirect
429. #2022C2×C109semidirect
430. #2021C2×C109semidirect
431. #1996C2×C109semidirect
432. #1964C2×C109semidirect
433. #1890C2×C109semidirect
434. #1889C2×C109semidirect
435. C4×#99C2×C109semidirect
436. C109#25587direct (N × H)
482. C22×Q8D4×C109semidirect
485. C22×D4D4×C109semidirect
488. C23×C4D4×C109semidirect
542. C2×C4⋊C4D4×C109semidirect
543. C2×C4⋊C4D4×C109semidirect
544. C2×C4⋊C4D4×C109semidirect
545. C2×C4⋊C4D4×C109semidirect
561. C2×C22⋊C4D4×C109semidirect
562. C2×C22⋊C4D4×C109semidirect
571. C2×C42D4×C109semidirect
690. C22⋊C4#41×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35052
C109×#25612
C109×#25392
C109×#25342
C109×#20222
C109×#20212
C109×#19962
C109×#19642
C109×#18902
C109×#18892
C4×#99×C1092
#25587109