Finite Group Databasebeta

← C107×#25587 #41051551

Subgroups — C107×#25587 #41051551

Order 27392.

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
1C107×#3505C211yesmaximal, characteristic, complemented
2C107×#2561C211yesmaximal, characteristic, complemented
3C107×#2539C211yesmaximal, characteristic, complemented
4C107×#2534C211yesmaximal, characteristic, complemented
5C107×#2022C212yesmaximal, complemented
6C107×#2021C212yesmaximal, complemented
7C107×#1996C211yesmaximal, characteristic, complemented
8C107×#1964C211yesmaximal, characteristic, complemented
9C107×#1890C212yesmaximal, complemented
10C107×#1889C212yesmaximal, complemented
11C4×#99×C107C211yesmaximal, characteristic, complemented
12#553×C107—22no—
13#553×C107—21no—
14#552×C107—21no—
15#551×C107—22no—
16#548×C107—21no—
17#546×C107—21no—
18#539×C107—21no—
19#538×C107—21no—
20#534×C107C2212yes—
21#529×C107—21no—
22#525×C107—21no—
23C2×#123×C107C2212yes—
24C2×#123×C107C2211yescharacteristic
25C2×C22⋊Q8×C107C2211yescharacteristic
26C2×#121×C107C2211yescharacteristic
27C2×#120×C107C2212yes—
28C2×#120×C107C2211yescharacteristic
29#518×C107C2212yes—
30C2×C4×D4×C107C2211yescharacteristic
31C22×C22⋊C4×C107C2211yescharacteristic
32C2×#99×C107C2212yes—
33C2×#99×C107C2212yes—
34C2×#99×C107C2212yes—
35#399×C107—21no—
36#397×C107—21no—
37#396×C107—21no—
38#394×C107—21no—
39#393×C107—21no—
40#392×C107—21no—
41#390×C107—22no—
42#388×C107—22no—
43#388×C107—21no—
44#386×C107—21no—
45#381×C107C2211yescharacteristic
46#381×C107C2212yes—
47#380×C107C2211yescharacteristic
48#379×C107C2211yescharacteristic
49#379×C107C2212yes—
50C4×C22⋊C4×C107C2211yescharacteristic
51C4×C22⋊C4×C107C2211yescharacteristic
52#342×C107C2212yes—
53#342×C107C2212yes—
54#342×C107C2212yes—
55C25×C107C2311yescharacteristic
56C2×#41×C107—21no—
57C22×Q8×C107D411yescharacteristic, complemented
58C22×D4×C107—21no—
59C22×D4×C107—22no—
60C22×D4×C107D411yescharacteristic, complemented
61C22×D4×C107C2311yescharacteristic
62C22×D4×C107C2312yes—
63C23×C4×C107D411yescharacteristic, complemented
64C23×C4×C107C2311yescharacteristic
65C23×C4×C107C2311yescharacteristic
66#126×C107—22no—
67#126×C107—22no—
68#126×C107—22no—
69#125×C107—21no—
70#125×C107—22no—
71#124×C107—21no—
72#124×C107—22no—
73#123×C107—22no—
74#123×C107—22no—
75#123×C107—22no—
76#123×C107—22no—
77#123×C107—22no—
78#123×C107—24no—
79#123×C107—42no—
80#123×C107—42no—
81C22⋊Q8×C107—21no—
82C22⋊Q8×C107—22no—
83C22⋊Q8×C107—21no—
84C22⋊Q8×C107—21no—
85C22⋊Q8×C107—21no—
86C22⋊Q8×C107—21no—
87#121×C107—21no—
88#121×C107—22no—
89#121×C107—21no—
90#121×C107—21no—
91#121×C107—21no—
92#121×C107—21no—
93#121×C107—22no—
94#121×C107—22no—
95#120×C107—22no—
96#120×C107—22no—
97#120×C107—24no—
98#120×C107—42no—
99#120×C107—42no—
100C4×Q8×C107—21no—
101C4×D4×C107—22no—
102C4×D4×C107—21no—
103C4×D4×C107—21no—
104C4×D4×C107—21no—
105C4×D4×C107—21no—
106C4×D4×C107—21no—
107C4×D4×C107—22no—
108C4×D4×C107—22no—
109C4×D4×C107—22no—
110C4×D4×C107—22no—
111#117×C107—21no—
112#117×C107—22no—
113#117×C107—22no—
114C2×C4⋊C4×C107—21no—
115C2×C4⋊C4×C107—22no—
116C2×C4⋊C4×C107—21no—
117C2×C4⋊C4×C107D412yescomplemented
118C2×C4⋊C4×C107D411yescharacteristic, complemented
119C2×C4⋊C4×C107D411yescharacteristic, complemented
120C2×C4⋊C4×C107D411yescharacteristic, complemented
121C2×C22⋊C4×C107—22no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—22no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—22no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107—21no—
130C2×C22⋊C4×C107—22no—
131C2×C22⋊C4×C107—21no—
132C2×C22⋊C4×C107—21no—
133C2×C22⋊C4×C107—21no—
134C2×C22⋊C4×C107—21no—
135C2×C22⋊C4×C107—22no—
136C2×C22⋊C4×C107D412yescomplemented
137C2×C22⋊C4×C107D411yescharacteristic, complemented
138C2×C22⋊C4×C107C2311yescharacteristic
139C2×C22⋊C4×C107C2311yescharacteristic
140C2×C22⋊C4×C107C2312yes—
141C2×C22⋊C4×C107C2311yescharacteristic
142C2×C22⋊C4×C107C2312yes—
143C2×C22⋊C4×C107C2312yes—
144C2×C42×C107—21no—
145C2×C42×C107—21no—
146C2×C42×C107D411yescharacteristic, complemented
147#99×C107—24no—
148#99×C107—42no—
149#99×C107—42no—
150#95×C107—21no—
151#95×C107—21no—
152#95×C107—21no—
153#95×C107—21no—
154#95×C107—22no—
155#95×C107—21no—
156#95×C107—22no—
157C24×C107—21no—
158C24×C107—21no—
159C24×C107—21no—
160C24×C107—22no—
161C24×C107—22no—
162C24×C107—42no—
163C24×C107—81no—
164C24×C107C2×D412yes—
165C24×C107C2×D411yescharacteristic
166C24×C107C2411yescharacteristic
167#41×C107—82no—
168C2×Q8×C107—21no—
169C2×Q8×C107—21no—
170C2×Q8×C107—81no—
171C2×D4×C107—21no—
172C2×D4×C107—22no—
173C2×D4×C107—21no—
174C2×D4×C107—22no—
175C2×D4×C107—22no—
176C2×D4×C107—22no—
177C2×D4×C107—22no—
178C2×D4×C107—22no—
179C2×D4×C107—22no—
180C2×D4×C107—22no—
181C2×D4×C107—22no—
182C2×D4×C107—22no—
183C2×D4×C107—21no—
184C2×D4×C107—21no—
185C2×D4×C107—44no—
186C2×D4×C107—42no—
187C2×D4×C107—44no—
188C2×D4×C107—42no—
189C2×D4×C107—81no—
190C2×D4×C107—82no—
191C2×D4×C107—81no—
192C22×C4×C107—22no—
193C22×C4×C107—22no—
194C22×C4×C107—22no—
195C22×C4×C107—21no—
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—22no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—22no—
204C22×C4×C107—22no—
205C22×C4×C107—81no—
206C22×C4×C107—81no—
207C22×C4×C107C2×D411yescharacteristic
208C22×C4×C107C2×D412yes—
209C22×C4×C107C2×D411yescharacteristic
210C22×C4×C107C2×D412yes—
211C22×C4×C107C2×D411yescharacteristic
212C22×C4×C107C2×D412yes—
213C22×C4×C107C2×D411yescharacteristic
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2×D411yescharacteristic
217C22×C4×C107C2×D411yescharacteristic
218C22×C4×C107C2×D411yescharacteristic
219C4⋊C4×C107—22no—
220C4⋊C4×C107—22no—
221C4⋊C4×C107—22no—
222C4⋊C4×C107—22no—
223C4⋊C4×C107—21no—
224C4⋊C4×C107—22no—
225C4⋊C4×C107—21no—
226C4⋊C4×C107—21no—
227C4⋊C4×C107—21no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—22no—
230C4⋊C4×C107—21no—
231C4⋊C4×C107—44no—
232C4⋊C4×C107—42no—
233C4⋊C4×C107—81no—
234C22⋊C4×C107—22no—
235C22⋊C4×C107—22no—
236C22⋊C4×C107—22no—
237C22⋊C4×C107—22no—
238C22⋊C4×C107—22no—
239C22⋊C4×C107—22no—
240C22⋊C4×C107—21no—
241C22⋊C4×C107—22no—
242C22⋊C4×C107—21no—
243C22⋊C4×C107—22no—
244C22⋊C4×C107—22no—
245C22⋊C4×C107—22no—
246C22⋊C4×C107—21no—
247C22⋊C4×C107—21no—
248C22⋊C4×C107—22no—
249C22⋊C4×C107—22no—
250C22⋊C4×C107—22no—
251C22⋊C4×C107—22no—
252C22⋊C4×C107—22no—
253C22⋊C4×C107—44no—
254C22⋊C4×C107—44no—
255C22⋊C4×C107—42no—
256C22⋊C4×C107—44no—
257C22⋊C4×C107—42no—
258C22⋊C4×C107—42no—
259C22⋊C4×C107—41no—
260C22⋊C4×C107—41no—
261C22⋊C4×C107—41no—
262C22⋊C4×C107—41no—
263C22⋊C4×C107—81no—
264C22⋊C4×C107—82no—
265C22⋊C4×C107#4114yescomplemented
266C42×C107—22no—
267C42×C107—22no—
268C42×C107—21no—
269C42×C107—21no—
270C42×C107—81no—
271C42×C107—81no—
272C23×C107—22no—
273C23×C107—22no—
274C23×C107—22no—
275C23×C107—22no—
276C23×C107—21no—
277C23×C107—21no—
278C23×C107—21no—
279C23×C107—22no—
280C23×C107—22no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107—42no—
286C23×C107—41no—
287C23×C107—41no—
288C23×C107—42no—
289C23×C107—41no—
290C23×C107—41no—
291C23×C107—41no—
292C23×C107—42no—
293C23×C107—42no—
294C23×C107—41no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—42no—
298C23×C107—42no—
299C23×C107—84no—
300C23×C107—84no—
301C23×C107C22×D411yescharacteristic
302C23×C107C22×D411yescharacteristic
303C23×C107C22×D411yescharacteristic
304C23×C107C2×#4112yes—
305C23×C107H(5,𝔽2)12yes—
306Q8×C107—42no—
307Q8×C107—81no—
308D4×C107—42no—
309D4×C107—42no—
310D4×C107—42no—
311D4×C107—42no—
312D4×C107—42no—
313D4×C107—42no—
314D4×C107—42no—
315D4×C107—81no—
316D4×C107—82no—
317D4×C107—82no—
318D4×C107—88no—
319D4×C107—84no—
320C2×C4×C107—21no—
321C2×C4×C107—22no—
322C2×C4×C107—21no—
323C2×C4×C107—21no—
324C2×C4×C107—22no—
325C2×C4×C107—22no—
326C2×C4×C107—21no—
327C2×C4×C107—21no—
328C2×C4×C107—24no—
329C2×C4×C107—22no—
330C2×C4×C107—22no—
331C2×C4×C107—41no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—41no—
336C2×C4×C107—41no—
337C2×C4×C107—42no—
338C2×C4×C107—42no—
339C2×C4×C107—42no—
340C2×C4×C107—41no—
341C2×C4×C107—42no—
342C2×C4×C107—41no—
343C2×C4×C107—42no—
344C2×C4×C107—42no—
345C2×C4×C107—42no—
346C2×C4×C107—41no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—41no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—41no—
354C2×C4×C107—41no—
355C2×C4×C107—42no—
356C2×C4×C107—42no—
357C2×C4×C107—42no—
358C2×C4×C107—81no—
359C2×C4×C107—82no—
360C2×C4×C107—82no—
361C2×C4×C107#12011yescharacteristic
362C2×C4×C107#12011yescharacteristic
363C2×C4×C107#12011yescharacteristic
364C2×C4×C107#12011yescharacteristic
365C22×C107—21no—
366C22×C107—21no—
367C22×C107—21no—
368C22×C107—21no—
369C22×C107—21no—
370C22×C107—21no—
371C22×C107—42no—
372C22×C107—42no—
373C22×C107—42no—
374C22×C107—44no—
375C22×C107—42no—
376C22×C107—44no—
377C22×C107—42no—
378C22×C107—41no—
379C22×C107—42no—
380C22×C107—42no—
381C22×C107—41no—
382C22×C107—42no—
383C22×C107—41no—
384C22×C107—42no—
385C22×C107—82no—
386C22×C107—82no—
387C22×C107—81no—
388C22×C107—82no—
389C22×C107—81no—
390C22×C107—82no—
391C22×C107—81no—
392C22×C107—81no—
393C22×C107—81no—
394C22×C107C2×#12011yescharacteristic
395C22×C107#53211yescharacteristic
396C22×C107#53511yescharacteristic
397C22×C107#54612yes—
398C22×C107#55012yes—
399C4×C107—21no—
400C4×C107—21no—
401C4×C107—21no—
402C4×C107—21no—
403C4×C107—44no—
404C4×C107—41no—
405C4×C107—42no—
406C4×C107—41no—
407C4×C107—42no—
408C4×C107—41no—
409C4×C107—42no—
410C4×C107—81no—
411C4×C107—82no—
412C4×C107—81no—
413C4×C107—81no—
414#25587C10711yesmaximal, characteristic, direct product factor, Sylow
415C2×C107—22no—
416C2×C107—21no—
417C2×C107—22no—
418C2×C107—21no—
419C2×C107—82no—
420C2×C107—81no—
421C2×C107—82no—
422C2×C107#243111yescharacteristic
423C2×C107#302511yescharacteristic
424C2×C107#302611yescharacteristic
425#3505C2×C10711yescharacteristic, complemented
426#2561C2×C10711yescharacteristic, complemented
427#2539C2×C10711yescharacteristic, complemented
428#2534C2×C10711yescharacteristic, complemented
429#2022C2×C10712yescomplemented
430#2021C2×C10712yescomplemented
431#1996C2×C10711yescharacteristic, complemented
432#1964C2×C10711yescharacteristic, complemented
433#1890C2×C10712yescomplemented
434#1889C2×C10712yescomplemented
435C4×#99C2×C10711yescharacteristic, complemented
436C107#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×C10712yes—
446#529—21no—
447#525—21no—
448C2×#123C22×C10712yes—
449C2×#123C22×C10711yescharacteristic
450C2×C22⋊Q8C22×C10711yescharacteristic
451C2×#121C22×C10711yescharacteristic
452C2×#120C22×C10712yes—
453C2×#120C22×C10711yescharacteristic
454#518C22×C10712yes—
455C2×C4×D4C22×C10711yescharacteristic
456C22×C22⋊C4C22×C10711yescharacteristic
457C2×#99C22×C10712yes—
458C2×#99C22×C10712yes—
459C2×#99C22×C10712yes—
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×C10712yes—
471#381C22×C10711yescharacteristic
472#380C22×C10711yescharacteristic
473#379C22×C10712yes—
474#379C22×C10711yescharacteristic
475C4×C22⋊C4C22×C10711yescharacteristic
476C4×C22⋊C4C22×C10711yescharacteristic
477#342C22×C10712yes—
478#342C22×C10712yes—
479#342C22×C10712yes—
480C25C23×C10711yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C10711yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C10711yescharacteristic, complemented
486C22×D4C23×C10711yescharacteristic
487C22×D4C23×C10712yes—
488C23×C4D4×C10711yescharacteristic, complemented
489C23×C4C23×C10711yescharacteristic
490C23×C4C23×C10711yescharacteristic
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×C10711yescharacteristic, complemented
543C2×C4⋊C4D4×C10711yescharacteristic, complemented
544C2×C4⋊C4D4×C10712yescomplemented
545C2×C4⋊C4D4×C10711yescharacteristic, 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×C10711yescharacteristic, complemented
562C2×C22⋊C4D4×C10712yescomplemented
563C2×C22⋊C4C23×C10711yescharacteristic
564C2×C22⋊C4C23×C10711yescharacteristic
565C2×C22⋊C4C23×C10712yes—
566C2×C22⋊C4C23×C10711yescharacteristic
567C2×C22⋊C4C23×C10712yes—
568C2×C22⋊C4C23×C10712yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C10711yescharacteristic, 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×C10712yes—
590C24C2×D4×C10711yescharacteristic
591C24C24×C10711yescharacteristic
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×C10711yescharacteristic
633C22×C4C2×D4×C10712yes—
634C22×C4C2×D4×C10711yescharacteristic
635C22×C4C2×D4×C10712yes—
636C22×C4C2×D4×C10711yescharacteristic
637C22×C4C2×D4×C10712yes—
638C22×C4C2×D4×C10711yescharacteristic
639C22×C4C2×D4×C10711yescharacteristic
640C22×C4C2×D4×C10711yescharacteristic
641C22×C4C2×D4×C10711yescharacteristic
642C22×C4C2×D4×C10711yescharacteristic
643C22×C4C2×D4×C10711yescharacteristic
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—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C10714yescomplemented
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×C10711yescharacteristic
727C23C22×D4×C10711yescharacteristic
728C23C22×D4×C10711yescharacteristic
729C23C2×#41×C10712yes—
730C23H(5,𝔽2)×C10712yes—
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×C10711yescharacteristic
787C2×C4#120×C10711yescharacteristic
788C2×C4#120×C10711yescharacteristic
789C2×C4#120×C10711yescharacteristic
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×C10711yescharacteristic
820C22#532×C10711yescharacteristic
821C22#535×C10711yescharacteristic
822C22#546×C10712yes—
823C22#550×C10712yes—
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—
846C2C107×#243111yescharacteristic
847C2C107×#302511yescharacteristic
848C2C107×#302611yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC24C24×C107
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3505C2semidirect
2. C107×#2561C2semidirect
3. C107×#2539C2semidirect
4. C107×#2534C2semidirect
5. C107×#2022C2semidirect
6. C107×#2021C2semidirect
7. C107×#1996C2semidirect
8. C107×#1964C2semidirect
9. C107×#1890C2semidirect
10. C107×#1889C2semidirect
11. C4×#99×C107C2semidirect
57. C22×Q8×C107D4semidirect
60. C22×D4×C107D4semidirect
63. C23×C4×C107D4semidirect
117. C2×C4⋊C4×C107D4semidirect
118. C2×C4⋊C4×C107D4semidirect
119. C2×C4⋊C4×C107D4semidirect
120. C2×C4⋊C4×C107D4semidirect
136. C2×C22⋊C4×C107D4semidirect
137. C2×C22⋊C4×C107D4semidirect
146. C2×C42×C107D4semidirect
265. C22⋊C4×C107#41semidirect
414. #25587C107direct (N × H)
425. #3505C2×C107semidirect
426. #2561C2×C107semidirect
427. #2539C2×C107semidirect
428. #2534C2×C107semidirect
429. #2022C2×C107semidirect
430. #2021C2×C107semidirect
431. #1996C2×C107semidirect
432. #1964C2×C107semidirect
433. #1890C2×C107semidirect
434. #1889C2×C107semidirect
435. C4×#99C2×C107semidirect
436. C107#25587direct (N × H)
482. C22×Q8D4×C107semidirect
485. C22×D4D4×C107semidirect
488. C23×C4D4×C107semidirect
542. C2×C4⋊C4D4×C107semidirect
543. C2×C4⋊C4D4×C107semidirect
544. C2×C4⋊C4D4×C107semidirect
545. C2×C4⋊C4D4×C107semidirect
561. C2×C22⋊C4D4×C107semidirect
562. C2×C22⋊C4D4×C107semidirect
571. C2×C42D4×C107semidirect
690. C22⋊C4#41×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35052
C107×#25612
C107×#25392
C107×#25342
C107×#20222
C107×#20212
C107×#19962
C107×#19642
C107×#18902
C107×#18892
C4×#99×C1072
#25587107