Finite Group Databasebeta

← C107×#24142 #41050106

Subgroups — C107×#24142 #41050106

Order 27392.

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
1C107×#3505C211yesmaximal, characteristic, complemented
2C107×#2626C211yesmaximal, characteristic, complemented
3C107×#2617C211yesmaximal, characteristic, complemented
4C107×#2321C211yesmaximal, characteristic, complemented
5C107×#2044C212yesmaximal, complemented
6C107×#2021C212yesmaximal, complemented
7C107×#1996C211yesmaximal, characteristic, complemented
8C107×#1964C211yesmaximal, characteristic, complemented
9C107×#1889C212yesmaximal, complemented
10C107×#1867C212yesmaximal, complemented
11C107×#1799C211yesmaximal, 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×C22⋊Q8×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C2×#120×C107C2211yescharacteristic
26C2×#120×C107C2212yes—
27#518×C107C2212yes—
28C2×C4×D4×C107C2211yescharacteristic
29C22×C22⋊C4×C107C2211yescharacteristic
30C2×#99×C107C2212yes—
31C2×#99×C107C2212yes—
32C2×#99×C107C2212yes—
33#399×C107—21no—
34#397×C107—21no—
35#396×C107—22no—
36#394×C107—22no—
37#393×C107—21no—
38#392×C107—21no—
39#390×C107—21no—
40#388×C107—21no—
41#388×C107—21no—
42#386×C107—21no—
43#386×C107C2212yes—
44#386×C107C2211yescharacteristic
45#385×C107C2211yescharacteristic
46#385×C107C2212yes—
47#380×C107C2211yescharacteristic
48#380×C107C2211yescharacteristic
49#379×C107C2211yescharacteristic
50#379×C107C2212yes—
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—
78C22⋊Q8×C107—21no—
79C22⋊Q8×C107—22no—
80C22⋊Q8×C107—21no—
81C22⋊Q8×C107—21no—
82C22⋊Q8×C107—21no—
83C22⋊Q8×C107—21no—
84#121×C107—21no—
85#121×C107—22no—
86#121×C107—21no—
87#121×C107—21no—
88#121×C107—21no—
89#121×C107—21no—
90#121×C107—22no—
91#121×C107—22no—
92#120×C107—22no—
93#120×C107—22no—
94#120×C107—22no—
95#120×C107—22no—
96#120×C107—24no—
97#120×C107—42no—
98C4×Q8×C107—21no—
99C4×D4×C107—22no—
100C4×D4×C107—21no—
101C4×D4×C107—21no—
102C4×D4×C107—21no—
103C4×D4×C107—21no—
104C4×D4×C107—21no—
105C4×D4×C107—22no—
106C4×D4×C107—22no—
107C4×D4×C107—22no—
108C4×D4×C107—22no—
109#117×C107—21no—
110#117×C107—22no—
111#117×C107—22no—
112C2×C4⋊C4×C107—21no—
113C2×C4⋊C4×C107—21no—
114C2×C4⋊C4×C107—21no—
115C2×C4⋊C4×C107—22no—
116C2×C4⋊C4×C107D411yescharacteristic, complemented
117C2×C4⋊C4×C107D412yescomplemented
118C2×C4⋊C4×C107D411yescharacteristic, complemented
119C2×C4⋊C4×C107D411yescharacteristic, complemented
120C2×C22⋊C4×C107—22no—
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—22no—
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—22no—
134C2×C22⋊C4×C107—22no—
135C2×C22⋊C4×C107D411yescharacteristic, complemented
136C2×C22⋊C4×C107D412yescomplemented
137C2×C22⋊C4×C107C2312yes—
138C2×C22⋊C4×C107C2311yescharacteristic
139C2×C22⋊C4×C107C2312yes—
140C2×C22⋊C4×C107C2311yescharacteristic
141C2×C22⋊C4×C107C2312yes—
142C2×C22⋊C4×C107C2311yescharacteristic
143C2×C42×C107—21no—
144C2×C42×C107D411yescharacteristic, complemented
145#99×C107—24no—
146#99×C107—42no—
147#99×C107—42no—
148#95×C107—21no—
149#95×C107—21no—
150#95×C107—21no—
151#95×C107—21no—
152#95×C107—22no—
153#95×C107—21no—
154#95×C107—22no—
155C24×C107—21no—
156C24×C107—21no—
157C24×C107—21no—
158C24×C107—21no—
159C24×C107—21no—
160C24×C107—21no—
161C24×C107—81no—
162C24×C107—81no—
163C24×C107C2×D412yes—
164C24×C107C2×D411yescharacteristic
165C24×C107#4112yescomplemented
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—21no—
177C2×D4×C107—21no—
178C2×D4×C107—22no—
179C2×D4×C107—21no—
180C2×D4×C107—22no—
181C2×D4×C107—21no—
182C2×D4×C107—22no—
183C2×D4×C107—22no—
184C2×D4×C107—22no—
185C2×D4×C107—24no—
186C2×D4×C107—21no—
187C2×D4×C107—21no—
188C2×D4×C107—44no—
189C2×D4×C107—81no—
190C2×D4×C107—81no—
191C2×D4×C107—81no—
192C2×D4×C107—82no—
193C2×D4×C107—82no—
194C22×C4×C107—21no—
195C22×C4×C107—22no—
196C22×C4×C107—22no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—22no—
203C22×C4×C107—22no—
204C22×C4×C107—21no—
205C22×C4×C107—81no—
206C22×C4×C107—81no—
207C22×C4×C107—81no—
208C22×C4×C107C2×D411yescharacteristic
209C22×C4×C107C2×D412yes—
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D412yes—
212C22×C4×C107C2×D411yescharacteristic
213C22×C4×C107C2×D412yes—
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2×D411yescharacteristic
217C22×C4×C107C2×D411yescharacteristic
218C22×C4×C107C2×D411yescharacteristic
219C22×C4×C107C2×D411yescharacteristic
220C4⋊C4×C107—22no—
221C4⋊C4×C107—22no—
222C4⋊C4×C107—22no—
223C4⋊C4×C107—22no—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—22no—
226C4⋊C4×C107—21no—
227C4⋊C4×C107—21no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—21no—
230C4⋊C4×C107—22no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—81no—
233C4⋊C4×C107—81no—
234C4⋊C4×C107—81no—
235C4⋊C4×C107—82no—
236C22⋊C4×C107—22no—
237C22⋊C4×C107—22no—
238C22⋊C4×C107—24no—
239C22⋊C4×C107—22no—
240C22⋊C4×C107—22no—
241C22⋊C4×C107—22no—
242C22⋊C4×C107—22no—
243C22⋊C4×C107—21no—
244C22⋊C4×C107—22no—
245C22⋊C4×C107—21no—
246C22⋊C4×C107—22no—
247C22⋊C4×C107—21no—
248C22⋊C4×C107—22no—
249C22⋊C4×C107—21no—
250C22⋊C4×C107—21no—
251C22⋊C4×C107—22no—
252C22⋊C4×C107—22no—
253C22⋊C4×C107—22no—
254C22⋊C4×C107—21no—
255C22⋊C4×C107—22no—
256C22⋊C4×C107—22no—
257C22⋊C4×C107—21no—
258C22⋊C4×C107—44no—
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—81no—
266C22⋊C4×C107—82no—
267C22⋊C4×C107—81no—
268C22⋊C4×C107—82no—
269C22⋊C4×C107#4112yescomplemented
270C42×C107—22no—
271C42×C107—22no—
272C42×C107—21no—
273C42×C107—21no—
274C42×C107—81no—
275C23×C107—21no—
276C23×C107—22no—
277C23×C107—22no—
278C23×C107—21no—
279C23×C107—22no—
280C23×C107—22no—
281C23×C107—21no—
282C23×C107—22no—
283C23×C107—22no—
284C23×C107—41no—
285C23×C107—41no—
286C23×C107—41no—
287C23×C107—41no—
288C23×C107—42no—
289C23×C107—41no—
290C23×C107—42no—
291C23×C107—41no—
292C23×C107—41no—
293C23×C107—42no—
294C23×C107—41no—
295C23×C107—42no—
296C23×C107—42no—
297C23×C107—42no—
298C23×C107—41no—
299C23×C107—41no—
300C23×C107—41no—
301C23×C107—41no—
302C23×C107—82no—
303C23×C107—82no—
304C23×C107—82no—
305C23×C107—82no—
306C23×C107C22×D411yescharacteristic
307C23×C107C22×D411yescharacteristic
308C23×C107C22×D411yescharacteristic
309C23×C107C2×#4111yescharacteristic
310C23×C107C2×#4111yescharacteristic
311C23×C107H(5,𝔽2)11yescharacteristic
312C23×C1072−1+411yescharacteristic
313Q8×C107—42no—
314Q8×C107—81no—
315D4×C107—42no—
316D4×C107—42no—
317D4×C107—42no—
318D4×C107—41no—
319D4×C107—41no—
320D4×C107—41no—
321D4×C107—42no—
322D4×C107—42no—
323D4×C107—41no—
324D4×C107—81no—
325D4×C107—82no—
326D4×C107—84no—
327D4×C107—82no—
328D4×C107—88no—
329C2×C4×C107—21no—
330C2×C4×C107—22no—
331C2×C4×C107—21no—
332C2×C4×C107—21no—
333C2×C4×C107—22no—
334C2×C4×C107—22no—
335C2×C4×C107—21no—
336C2×C4×C107—22no—
337C2×C4×C107—21no—
338C2×C4×C107—22no—
339C2×C4×C107—22no—
340C2×C4×C107—41no—
341C2×C4×C107—41no—
342C2×C4×C107—41no—
343C2×C4×C107—41no—
344C2×C4×C107—41no—
345C2×C4×C107—41no—
346C2×C4×C107—42no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—42no—
351C2×C4×C107—41no—
352C2×C4×C107—42no—
353C2×C4×C107—41no—
354C2×C4×C107—41no—
355C2×C4×C107—42no—
356C2×C4×C107—42no—
357C2×C4×C107—41no—
358C2×C4×C107—42no—
359C2×C4×C107—42no—
360C2×C4×C107—42no—
361C2×C4×C107—41no—
362C2×C4×C107—42no—
363C2×C4×C107—41no—
364C2×C4×C107—41no—
365C2×C4×C107—42no—
366C2×C4×C107—42no—
367C2×C4×C107—81no—
368C2×C4×C107—82no—
369C2×C4×C107—82no—
370C2×C4×C107#12011yescharacteristic
371C2×C4×C107#12011yescharacteristic
372C2×C4×C107#12011yescharacteristic
373C2×C4×C107#12011yescharacteristic
374C22×C107—21no—
375C22×C107—21no—
376C22×C107—21no—
377C22×C107—21no—
378C22×C107—21no—
379C22×C107—21no—
380C22×C107—41no—
381C22×C107—41no—
382C22×C107—41no—
383C22×C107—41no—
384C22×C107—42no—
385C22×C107—42no—
386C22×C107—44no—
387C22×C107—42no—
388C22×C107—44no—
389C22×C107—41no—
390C22×C107—42no—
391C22×C107—42no—
392C22×C107—41no—
393C22×C107—42no—
394C22×C107—42no—
395C22×C107—41no—
396C22×C107—82no—
397C22×C107—81no—
398C22×C107—82no—
399C22×C107—82no—
400C22×C107—81no—
401C22×C107—81no—
402C22×C107—82no—
403C22×C107—81no—
404C22×C107—81no—
405C22×C107C2×#12011yescharacteristic
406C22×C107#52511yescharacteristic
407C22×C107#53711yescharacteristic
408C22×C107#54611yescharacteristic
409C22×C107#54711yescharacteristic
410C22×C107#54811yescharacteristic
411C22×C107#55011yescharacteristic
412C4×C107—21no—
413C4×C107—21no—
414C4×C107—21no—
415C4×C107—21no—
416C4×C107—42no—
417C4×C107—41no—
418C4×C107—42no—
419C4×C107—41no—
420C4×C107—42no—
421C4×C107—41no—
422C4×C107—42no—
423C4×C107—82no—
424C4×C107—81no—
425C4×C107—82no—
426C4×C107—81no—
427#24142C10711yesmaximal, characteristic, direct product factor, Sylow
428C2×C107—21no—
429C2×C107—21no—
430C2×C107—21no—
431C2×C107—21no—
432C2×C107—21no—
433C2×C107—21no—
434C2×C107—82no—
435C2×C107—81no—
436C2×C107—82no—
437C2×C107#240711yescharacteristic
438C2×C107#302611yescharacteristic
439C2×C107#302711yescharacteristic
440#3505C2×C10711yescharacteristic, complemented
441#2626C2×C10711yescharacteristic, complemented
442#2617C2×C10711yescharacteristic, complemented
443#2321C2×C10711yescharacteristic, complemented
444#2044C2×C10712yescomplemented
445#2021C2×C10712yescomplemented
446#1996C2×C10711yescharacteristic, complemented
447#1964C2×C10711yescharacteristic, complemented
448#1889C2×C10712yescomplemented
449#1867C2×C10712yescomplemented
450#1799C2×C10711yescharacteristic, complemented
451C107#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×C10712yes—
461#529—21no—
462#525—21no—
463C2×C22⋊Q8C22×C10711yescharacteristic
464C2×#121C22×C10711yescharacteristic
465C2×#120C22×C10711yescharacteristic
466C2×#120C22×C10712yes—
467#518C22×C10712yes—
468C2×C4×D4C22×C10711yescharacteristic
469C22×C22⋊C4C22×C10711yescharacteristic
470C2×#99C22×C10712yes—
471C2×#99C22×C10712yes—
472C2×#99C22×C10712yes—
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×C10711yescharacteristic
484#386C22×C10712yes—
485#385C22×C10711yescharacteristic
486#385C22×C10712yes—
487#380C22×C10711yescharacteristic
488#380C22×C10711yescharacteristic
489#379C22×C10711yescharacteristic
490#379C22×C10712yes—
491C4×C22⋊C4C22×C10711yescharacteristic
492#342C22×C10712yes—
493#342C22×C10712yes—
494#342C22×C10712yes—
495C25C23×C10711yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C10711yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C10711yescharacteristic, complemented
501C22×D4C23×C10711yescharacteristic
502C22×D4C23×C10712yes—
503C23×C4D4×C10711yescharacteristic, complemented
504C23×C4C23×C10711yescharacteristic
505C23×C4C23×C10711yescharacteristic
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×C10711yescharacteristic, complemented
557C2×C4⋊C4D4×C10711yescharacteristic, complemented
558C2×C4⋊C4D4×C10712yescomplemented
559C2×C4⋊C4D4×C10711yescharacteristic, 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×C10711yescharacteristic, complemented
576C2×C22⋊C4D4×C10712yescomplemented
577C2×C22⋊C4C23×C10712yes—
578C2×C22⋊C4C23×C10711yescharacteristic
579C2×C22⋊C4C23×C10712yes—
580C2×C22⋊C4C23×C10711yescharacteristic
581C2×C22⋊C4C23×C10712yes—
582C2×C22⋊C4C23×C10711yescharacteristic
583C2×C42—21no—
584C2×C42D4×C10711yescharacteristic, 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×C10712yes—
604C24C2×D4×C10711yescharacteristic
605C24#41×C10712yescomplemented
606C24C24×C10711yescharacteristic
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×C10711yescharacteristic
649C22×C4C2×D4×C10712yes—
650C22×C4C2×D4×C10711yescharacteristic
651C22×C4C2×D4×C10712yes—
652C22×C4C2×D4×C10711yescharacteristic
653C22×C4C2×D4×C10712yes—
654C22×C4C2×D4×C10711yescharacteristic
655C22×C4C2×D4×C10711yescharacteristic
656C22×C4C2×D4×C10711yescharacteristic
657C22×C4C2×D4×C10711yescharacteristic
658C22×C4C2×D4×C10711yescharacteristic
659C22×C4C2×D4×C10711yescharacteristic
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×C10712yescomplemented
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×C10711yescharacteristic
747C23C22×D4×C10711yescharacteristic
748C23C22×D4×C10711yescharacteristic
749C23C2×#41×C10711yescharacteristic
750C23C2×#41×C10711yescharacteristic
751C23H(5,𝔽2)×C10711yescharacteristic
752C232−1+4×C10711yescharacteristic
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×C10711yescharacteristic
811C2×C4#120×C10711yescharacteristic
812C2×C4#120×C10711yescharacteristic
813C2×C4#120×C10711yescharacteristic
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—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C10711yescharacteristic
846C22#525×C10711yescharacteristic
847C22#537×C10711yescharacteristic
848C22#546×C10711yescharacteristic
849C22#547×C10711yescharacteristic
850C22#548×C10711yescharacteristic
851C22#550×C10711yescharacteristic
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—
876C2C107×#240711yescharacteristic
877C2C107×#302611yescharacteristic
878C2C107×#302711yescharacteristic
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×#2626C2semidirect
3. C107×#2617C2semidirect
4. C107×#2321C2semidirect
5. C107×#2044C2semidirect
6. C107×#2021C2semidirect
7. C107×#1996C2semidirect
8. C107×#1964C2semidirect
9. C107×#1889C2semidirect
10. C107×#1867C2semidirect
11. C107×#1799C2semidirect
57. C22×Q8×C107D4semidirect
60. C22×D4×C107D4semidirect
63. C23×C4×C107D4semidirect
116. C2×C4⋊C4×C107D4semidirect
117. C2×C4⋊C4×C107D4semidirect
118. C2×C4⋊C4×C107D4semidirect
119. C2×C4⋊C4×C107D4semidirect
135. C2×C22⋊C4×C107D4semidirect
136. C2×C22⋊C4×C107D4semidirect
144. C2×C42×C107D4semidirect
165. C24×C107#41semidirect
269. C22⋊C4×C107#41semidirect
427. #24142C107direct (N × H)
440. #3505C2×C107semidirect
441. #2626C2×C107semidirect
442. #2617C2×C107semidirect
443. #2321C2×C107semidirect
444. #2044C2×C107semidirect
445. #2021C2×C107semidirect
446. #1996C2×C107semidirect
447. #1964C2×C107semidirect
448. #1889C2×C107semidirect
449. #1867C2×C107semidirect
450. #1799C2×C107semidirect
451. C107#24142direct (N × H)
497. C22×Q8D4×C107semidirect
500. C22×D4D4×C107semidirect
503. C23×C4D4×C107semidirect
556. C2×C4⋊C4D4×C107semidirect
557. C2×C4⋊C4D4×C107semidirect
558. C2×C4⋊C4D4×C107semidirect
559. C2×C4⋊C4D4×C107semidirect
575. C2×C22⋊C4D4×C107semidirect
576. C2×C22⋊C4D4×C107semidirect
584. C2×C42D4×C107semidirect
605. C24#41×C107semidirect
709. 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×#26262
C107×#26172
C107×#23212
C107×#20442
C107×#20212
C107×#19962
C107×#19642
C107×#18892
C107×#18672
C107×#17992
#24142107