Finite Group Databasebeta

← C109×#24142 #42142136

Subgroups — C109×#24142 #42142136

Order 27904.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3505C211yesmaximal, characteristic, complemented
2C109×#2626C211yesmaximal, characteristic, complemented
3C109×#2617C211yesmaximal, characteristic, complemented
4C109×#2321C211yesmaximal, characteristic, complemented
5C109×#2044C212yesmaximal, complemented
6C109×#2021C212yesmaximal, complemented
7C109×#1996C211yesmaximal, characteristic, complemented
8C109×#1964C211yesmaximal, characteristic, complemented
9C109×#1889C212yesmaximal, complemented
10C109×#1867C212yesmaximal, complemented
11C109×#1799C211yesmaximal, 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×C22⋊Q8×C109C2211yescharacteristic
24C2×#121×C109C2211yescharacteristic
25C2×#120×C109C2211yescharacteristic
26C2×#120×C109C2212yes—
27#518×C109C2212yes—
28C2×C4×D4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2211yescharacteristic
30C2×#99×C109C2212yes—
31C2×#99×C109C2212yes—
32C2×#99×C109C2212yes—
33#399×C109—21no—
34#397×C109—21no—
35#396×C109—22no—
36#394×C109—22no—
37#393×C109—21no—
38#392×C109—21no—
39#390×C109—21no—
40#388×C109—21no—
41#388×C109—21no—
42#386×C109—21no—
43#386×C109C2211yescharacteristic
44#386×C109C2212yes—
45#385×C109C2212yes—
46#385×C109C2211yescharacteristic
47#380×C109C2211yescharacteristic
48#380×C109C2211yescharacteristic
49#379×C109C2212yes—
50#379×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—
78C22⋊Q8×C109—21no—
79C22⋊Q8×C109—22no—
80C22⋊Q8×C109—21no—
81C22⋊Q8×C109—21no—
82C22⋊Q8×C109—21no—
83C22⋊Q8×C109—21no—
84#121×C109—21no—
85#121×C109—22no—
86#121×C109—21no—
87#121×C109—21no—
88#121×C109—21no—
89#121×C109—21no—
90#121×C109—22no—
91#121×C109—22no—
92#120×C109—22no—
93#120×C109—22no—
94#120×C109—22no—
95#120×C109—22no—
96#120×C109—24no—
97#120×C109—42no—
98C4×Q8×C109—21no—
99C4×D4×C109—22no—
100C4×D4×C109—21no—
101C4×D4×C109—21no—
102C4×D4×C109—21no—
103C4×D4×C109—21no—
104C4×D4×C109—21no—
105C4×D4×C109—22no—
106C4×D4×C109—22no—
107C4×D4×C109—22no—
108C4×D4×C109—22no—
109#117×C109—21no—
110#117×C109—22no—
111#117×C109—22no—
112C2×C4⋊C4×C109—21no—
113C2×C4⋊C4×C109—21no—
114C2×C4⋊C4×C109—21no—
115C2×C4⋊C4×C109—22no—
116C2×C4⋊C4×C109D411yescharacteristic, complemented
117C2×C4⋊C4×C109D411yescharacteristic, complemented
118C2×C4⋊C4×C109D412yescomplemented
119C2×C4⋊C4×C109D411yescharacteristic, complemented
120C2×C22⋊C4×C109—22no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109—22no—
129C2×C22⋊C4×C109—21no—
130C2×C22⋊C4×C109—22no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—22no—
134C2×C22⋊C4×C109—22no—
135C2×C22⋊C4×C109D411yescharacteristic, complemented
136C2×C22⋊C4×C109D412yescomplemented
137C2×C22⋊C4×C109C2312yes—
138C2×C22⋊C4×C109C2311yescharacteristic
139C2×C22⋊C4×C109C2312yes—
140C2×C22⋊C4×C109C2311yescharacteristic
141C2×C22⋊C4×C109C2312yes—
142C2×C22⋊C4×C109C2311yescharacteristic
143C2×C42×C109—21no—
144C2×C42×C109D411yescharacteristic, complemented
145#99×C109—24no—
146#99×C109—42no—
147#99×C109—42no—
148#95×C109—21no—
149#95×C109—21no—
150#95×C109—21no—
151#95×C109—21no—
152#95×C109—22no—
153#95×C109—21no—
154#95×C109—22no—
155C24×C109—21no—
156C24×C109—21no—
157C24×C109—21no—
158C24×C109—21no—
159C24×C109—21no—
160C24×C109—21no—
161C24×C109—81no—
162C24×C109—81no—
163C24×C109C2×D412yes—
164C24×C109C2×D411yescharacteristic
165C24×C109#4112yescomplemented
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—21no—
177C2×D4×C109—21no—
178C2×D4×C109—22no—
179C2×D4×C109—21no—
180C2×D4×C109—22no—
181C2×D4×C109—21no—
182C2×D4×C109—22no—
183C2×D4×C109—22no—
184C2×D4×C109—22no—
185C2×D4×C109—24no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—44no—
189C2×D4×C109—81no—
190C2×D4×C109—81no—
191C2×D4×C109—81no—
192C2×D4×C109—82no—
193C2×D4×C109—82no—
194C22×C4×C109—21no—
195C22×C4×C109—22no—
196C22×C4×C109—22no—
197C22×C4×C109—21no—
198C22×C4×C109—21no—
199C22×C4×C109—21no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—22no—
203C22×C4×C109—22no—
204C22×C4×C109—21no—
205C22×C4×C109—81no—
206C22×C4×C109—81no—
207C22×C4×C109—81no—
208C22×C4×C109C2×D411yescharacteristic
209C22×C4×C109C2×D412yes—
210C22×C4×C109C2×D411yescharacteristic
211C22×C4×C109C2×D412yes—
212C22×C4×C109C2×D411yescharacteristic
213C22×C4×C109C2×D412yes—
214C22×C4×C109C2×D411yescharacteristic
215C22×C4×C109C2×D411yescharacteristic
216C22×C4×C109C2×D411yescharacteristic
217C22×C4×C109C2×D411yescharacteristic
218C22×C4×C109C2×D411yescharacteristic
219C22×C4×C109C2×D411yescharacteristic
220C4⋊C4×C109—22no—
221C4⋊C4×C109—22no—
222C4⋊C4×C109—22no—
223C4⋊C4×C109—22no—
224C4⋊C4×C109—21no—
225C4⋊C4×C109—22no—
226C4⋊C4×C109—21no—
227C4⋊C4×C109—21no—
228C4⋊C4×C109—21no—
229C4⋊C4×C109—21no—
230C4⋊C4×C109—22no—
231C4⋊C4×C109—21no—
232C4⋊C4×C109—81no—
233C4⋊C4×C109—81no—
234C4⋊C4×C109—81no—
235C4⋊C4×C109—82no—
236C22⋊C4×C109—22no—
237C22⋊C4×C109—22no—
238C22⋊C4×C109—24no—
239C22⋊C4×C109—22no—
240C22⋊C4×C109—22no—
241C22⋊C4×C109—22no—
242C22⋊C4×C109—22no—
243C22⋊C4×C109—21no—
244C22⋊C4×C109—22no—
245C22⋊C4×C109—21no—
246C22⋊C4×C109—22no—
247C22⋊C4×C109—21no—
248C22⋊C4×C109—22no—
249C22⋊C4×C109—21no—
250C22⋊C4×C109—21no—
251C22⋊C4×C109—22no—
252C22⋊C4×C109—22no—
253C22⋊C4×C109—22no—
254C22⋊C4×C109—21no—
255C22⋊C4×C109—22no—
256C22⋊C4×C109—22no—
257C22⋊C4×C109—21no—
258C22⋊C4×C109—44no—
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—81no—
266C22⋊C4×C109—82no—
267C22⋊C4×C109—81no—
268C22⋊C4×C109—82no—
269C22⋊C4×C109#4112yescomplemented
270C42×C109—22no—
271C42×C109—22no—
272C42×C109—21no—
273C42×C109—21no—
274C42×C109—81no—
275C23×C109—21no—
276C23×C109—22no—
277C23×C109—22no—
278C23×C109—21no—
279C23×C109—22no—
280C23×C109—22no—
281C23×C109—21no—
282C23×C109—22no—
283C23×C109—22no—
284C23×C109—41no—
285C23×C109—41no—
286C23×C109—41no—
287C23×C109—41no—
288C23×C109—42no—
289C23×C109—41no—
290C23×C109—42no—
291C23×C109—41no—
292C23×C109—41no—
293C23×C109—42no—
294C23×C109—41no—
295C23×C109—42no—
296C23×C109—42no—
297C23×C109—42no—
298C23×C109—41no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109—41no—
302C23×C109—82no—
303C23×C109—82no—
304C23×C109—82no—
305C23×C109—82no—
306C23×C109C22×D411yescharacteristic
307C23×C109C22×D411yescharacteristic
308C23×C109C22×D411yescharacteristic
309C23×C109C2×#4111yescharacteristic
310C23×C109C2×#4111yescharacteristic
311C23×C109H(5,𝔽2)11yescharacteristic
312C23×C1092−1+411yescharacteristic
313Q8×C109—42no—
314Q8×C109—81no—
315D4×C109—42no—
316D4×C109—42no—
317D4×C109—42no—
318D4×C109—41no—
319D4×C109—41no—
320D4×C109—41no—
321D4×C109—42no—
322D4×C109—42no—
323D4×C109—41no—
324D4×C109—81no—
325D4×C109—82no—
326D4×C109—84no—
327D4×C109—82no—
328D4×C109—88no—
329C2×C4×C109—21no—
330C2×C4×C109—22no—
331C2×C4×C109—21no—
332C2×C4×C109—21no—
333C2×C4×C109—22no—
334C2×C4×C109—22no—
335C2×C4×C109—21no—
336C2×C4×C109—22no—
337C2×C4×C109—21no—
338C2×C4×C109—22no—
339C2×C4×C109—22no—
340C2×C4×C109—41no—
341C2×C4×C109—41no—
342C2×C4×C109—41no—
343C2×C4×C109—41no—
344C2×C4×C109—41no—
345C2×C4×C109—41no—
346C2×C4×C109—42no—
347C2×C4×C109—41no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—42no—
351C2×C4×C109—41no—
352C2×C4×C109—42no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—42no—
356C2×C4×C109—42no—
357C2×C4×C109—41no—
358C2×C4×C109—42no—
359C2×C4×C109—42no—
360C2×C4×C109—42no—
361C2×C4×C109—41no—
362C2×C4×C109—42no—
363C2×C4×C109—41no—
364C2×C4×C109—41no—
365C2×C4×C109—42no—
366C2×C4×C109—42no—
367C2×C4×C109—81no—
368C2×C4×C109—82no—
369C2×C4×C109—82no—
370C2×C4×C109#12011yescharacteristic
371C2×C4×C109#12011yescharacteristic
372C2×C4×C109#12011yescharacteristic
373C2×C4×C109#12011yescharacteristic
374C22×C109—21no—
375C22×C109—21no—
376C22×C109—21no—
377C22×C109—21no—
378C22×C109—21no—
379C22×C109—21no—
380C22×C109—41no—
381C22×C109—41no—
382C22×C109—41no—
383C22×C109—41no—
384C22×C109—42no—
385C22×C109—42no—
386C22×C109—44no—
387C22×C109—42no—
388C22×C109—44no—
389C22×C109—41no—
390C22×C109—42no—
391C22×C109—42no—
392C22×C109—41no—
393C22×C109—42no—
394C22×C109—42no—
395C22×C109—41no—
396C22×C109—82no—
397C22×C109—81no—
398C22×C109—82no—
399C22×C109—82no—
400C22×C109—81no—
401C22×C109—81no—
402C22×C109—82no—
403C22×C109—81no—
404C22×C109—81no—
405C22×C109C2×#12011yescharacteristic
406C22×C109#52511yescharacteristic
407C22×C109#53711yescharacteristic
408C22×C109#54611yescharacteristic
409C22×C109#54711yescharacteristic
410C22×C109#54811yescharacteristic
411C22×C109#55011yescharacteristic
412C4×C109—21no—
413C4×C109—21no—
414C4×C109—21no—
415C4×C109—21no—
416C4×C109—42no—
417C4×C109—41no—
418C4×C109—42no—
419C4×C109—41no—
420C4×C109—42no—
421C4×C109—41no—
422C4×C109—42no—
423C4×C109—82no—
424C4×C109—81no—
425C4×C109—82no—
426C4×C109—81no—
427#24142C10911yesmaximal, characteristic, direct product factor, Sylow
428C2×C109—21no—
429C2×C109—21no—
430C2×C109—21no—
431C2×C109—21no—
432C2×C109—21no—
433C2×C109—21no—
434C2×C109—82no—
435C2×C109—81no—
436C2×C109—82no—
437C2×C109#240711yescharacteristic
438C2×C109#302611yescharacteristic
439C2×C109#302711yescharacteristic
440#3505C2×C10911yescharacteristic, complemented
441#2626C2×C10911yescharacteristic, complemented
442#2617C2×C10911yescharacteristic, complemented
443#2321C2×C10911yescharacteristic, complemented
444#2044C2×C10912yescomplemented
445#2021C2×C10912yescomplemented
446#1996C2×C10911yescharacteristic, complemented
447#1964C2×C10911yescharacteristic, complemented
448#1889C2×C10912yescomplemented
449#1867C2×C10912yescomplemented
450#1799C2×C10911yescharacteristic, complemented
451C109#2414211yescharacteristic, direct product factor, Sylow
452#553—22no—
453#553—21no—
454#552—21no—
455#551—22no—
456#548—21no—
457#546—21no—
458#539—21no—
459#538—21no—
460#534C22×C10912yes—
461#529—21no—
462#525—21no—
463C2×C22⋊Q8C22×C10911yescharacteristic
464C2×#121C22×C10911yescharacteristic
465C2×#120C22×C10911yescharacteristic
466C2×#120C22×C10912yes—
467#518C22×C10912yes—
468C2×C4×D4C22×C10911yescharacteristic
469C22×C22⋊C4C22×C10911yescharacteristic
470C2×#99C22×C10912yes—
471C2×#99C22×C10912yes—
472C2×#99C22×C10912yes—
473#399—21no—
474#397—21no—
475#396—22no—
476#394—22no—
477#393—21no—
478#392—21no—
479#390—21no—
480#388—21no—
481#388—21no—
482#386—21no—
483#386C22×C10911yescharacteristic
484#386C22×C10912yes—
485#385C22×C10911yescharacteristic
486#385C22×C10912yes—
487#380C22×C10911yescharacteristic
488#380C22×C10911yescharacteristic
489#379C22×C10911yescharacteristic
490#379C22×C10912yes—
491C4×C22⋊C4C22×C10911yescharacteristic
492#342C22×C10912yes—
493#342C22×C10912yes—
494#342C22×C10912yes—
495C25C23×C10911yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C10911yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C10911yescharacteristic, complemented
501C22×D4C23×C10911yescharacteristic
502C22×D4C23×C10912yes—
503C23×C4D4×C10911yescharacteristic, complemented
504C23×C4C23×C10911yescharacteristic
505C23×C4C23×C10911yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C10911yescharacteristic, complemented
557C2×C4⋊C4D4×C10911yescharacteristic, complemented
558C2×C4⋊C4D4×C10912yescomplemented
559C2×C4⋊C4D4×C10911yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C10911yescharacteristic, complemented
576C2×C22⋊C4D4×C10912yescomplemented
577C2×C22⋊C4C23×C10912yes—
578C2×C22⋊C4C23×C10911yescharacteristic
579C2×C22⋊C4C23×C10912yes—
580C2×C22⋊C4C23×C10911yescharacteristic
581C2×C22⋊C4C23×C10912yes—
582C2×C22⋊C4C23×C10911yescharacteristic
583C2×C42—21no—
584C2×C42D4×C10911yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C10912yes—
604C24C2×D4×C10911yescharacteristic
605C24#41×C10912yescomplemented
606C24C24×C10911yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C10911yescharacteristic
649C22×C4C2×D4×C10912yes—
650C22×C4C2×D4×C10911yescharacteristic
651C22×C4C2×D4×C10912yes—
652C22×C4C2×D4×C10911yescharacteristic
653C22×C4C2×D4×C10912yes—
654C22×C4C2×D4×C10911yescharacteristic
655C22×C4C2×D4×C10911yescharacteristic
656C22×C4C2×D4×C10911yescharacteristic
657C22×C4C2×D4×C10911yescharacteristic
658C22×C4C2×D4×C10911yescharacteristic
659C22×C4C2×D4×C10911yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C10912yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C10911yescharacteristic
747C23C22×D4×C10911yescharacteristic
748C23C22×D4×C10911yescharacteristic
749C23C2×#41×C10911yescharacteristic
750C23C2×#41×C10911yescharacteristic
751C23H(5,𝔽2)×C10911yescharacteristic
752C232−1+4×C10911yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C10911yescharacteristic
811C2×C4#120×C10911yescharacteristic
812C2×C4#120×C10911yescharacteristic
813C2×C4#120×C10911yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C10911yescharacteristic
846C22#525×C10911yescharacteristic
847C22#537×C10911yescharacteristic
848C22#546×C10911yescharacteristic
849C22#547×C10911yescharacteristic
850C22#548×C10911yescharacteristic
851C22#550×C10911yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C109×#240711yescharacteristic
877C2C109×#302611yescharacteristic
878C2C109×#302711yescharacteristic
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×#2626C2semidirect
3. C109×#2617C2semidirect
4. C109×#2321C2semidirect
5. C109×#2044C2semidirect
6. C109×#2021C2semidirect
7. C109×#1996C2semidirect
8. C109×#1964C2semidirect
9. C109×#1889C2semidirect
10. C109×#1867C2semidirect
11. C109×#1799C2semidirect
57. C22×Q8×C109D4semidirect
60. C22×D4×C109D4semidirect
63. C23×C4×C109D4semidirect
116. C2×C4⋊C4×C109D4semidirect
117. C2×C4⋊C4×C109D4semidirect
118. C2×C4⋊C4×C109D4semidirect
119. C2×C4⋊C4×C109D4semidirect
135. C2×C22⋊C4×C109D4semidirect
136. C2×C22⋊C4×C109D4semidirect
144. C2×C42×C109D4semidirect
165. C24×C109#41semidirect
269. C22⋊C4×C109#41semidirect
427. #24142C109direct (N × H)
440. #3505C2×C109semidirect
441. #2626C2×C109semidirect
442. #2617C2×C109semidirect
443. #2321C2×C109semidirect
444. #2044C2×C109semidirect
445. #2021C2×C109semidirect
446. #1996C2×C109semidirect
447. #1964C2×C109semidirect
448. #1889C2×C109semidirect
449. #1867C2×C109semidirect
450. #1799C2×C109semidirect
451. C109#24142direct (N × H)
497. C22×Q8D4×C109semidirect
500. C22×D4D4×C109semidirect
503. C23×C4D4×C109semidirect
556. C2×C4⋊C4D4×C109semidirect
557. C2×C4⋊C4D4×C109semidirect
558. C2×C4⋊C4D4×C109semidirect
559. C2×C4⋊C4D4×C109semidirect
575. C2×C22⋊C4D4×C109semidirect
576. C2×C22⋊C4D4×C109semidirect
584. C2×C42D4×C109semidirect
605. C24#41×C109semidirect
709. 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×#26262
C109×#26172
C109×#23212
C109×#20442
C109×#20212
C109×#19962
C109×#19642
C109×#18892
C109×#18672
C109×#17992
#24142109