Finite Group Databasebeta

← C107×#24397 #41050361

Subgroups — C107×#24397 #41050361

Order 27392.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C107C211yesmaximal, characteristic, complemented
2C2×#469×C107C211yesmaximal, characteristic, complemented
3C2×#465×C107C211yesmaximal, characteristic, complemented
4C2×#449×C107C211yesmaximal, characteristic, complemented
5C2×#408×C107C211yesmaximal, characteristic, complemented
6C107×#2615C211yesmaximal, characteristic, complemented
7C107×#2035C211yesmaximal, characteristic, complemented
8C107×#2034C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1894C211yesmaximal, characteristic, complemented
12C107×#1893C211yesmaximal, characteristic, complemented
13C107×#1874C211yesmaximal, characteristic, complemented
14C107×#1853C211yesmaximal, characteristic, complemented
15C107×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×D8×C107C2211yescharacteristic
20C22×M16×C107C2211yescharacteristic
21C23×C8×C107C2211yescharacteristic
22#537×C107—24no—
23#537×C107—24no—
24C2×C22⋊Q8×C107—21no—
25C2×C22⋊Q8×C107C2211yescharacteristic
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×#121×C107—21no—
28C2×#121×C107—21no—
29C2×#121×C107—21no—
30C2×#121×C107C2211yescharacteristic
31C2×#121×C107C2211yescharacteristic
32C2×#121×C107C2211yescharacteristic
33C2×#121×C107C2211yescharacteristic
34C2×#121×C107C2211yescharacteristic
35C22×C4⋊C4×C107C2211yescharacteristic
36#469×C107—24no—
37#465×C107—24no—
38#449×C107—24no—
39C2×#106×C107C2211yescharacteristic
40C2×#106×C107C2211yescharacteristic
41C2×#103×C107C2211yescharacteristic
42C2×#103×C107C2211yescharacteristic
43C2×#103×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49#408×C107—24no—
50C2×C22⋊C8×C107C2211yescharacteristic
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic
54#393×C107—21no—
55#392×C107—21no—
56#392×C107—21no—
57#392×C107—21no—
58#380×C107C2211yescharacteristic
59#380×C107C2211yescharacteristic
60#380×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63#340×C107C2211yescharacteristic
64#340×C107C2211yescharacteristic
65C2×#41×C107—22no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—22no—
71C2×#41×C107—22no—
72C2×#41×C107—22no—
73C2×#41×C107—41no—
74C2×#41×C107—41no—
75C2×#41×C107—41no—
76C2×#41×C107—41no—
77C22×Q8×C107D411yescharacteristic
78C22×Q8×C107C2311yescharacteristic
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—21no—
83C22×D4×C107—21no—
84C22×D4×C107—21no—
85C22×D4×C107D411yescharacteristic
86C22×D4×C107D411yescharacteristic
87C22×D4×C107D411yescharacteristic
88C22×D4×C107C2311yescharacteristic
89C22×D4×C107C2311yescharacteristic
90C23×C4×C107—21no—
91C23×C4×C107—21no—
92C23×C4×C107C2311yescharacteristic
93C23×C4×C107C2311yescharacteristic
94C23×C4×C107C2311yescharacteristic
95C2×SD16×C107—22no—
96C2×SD16×C107—22no—
97C2×SD16×C107—41no—
98C2×D8×C107—22no—
99C2×D8×C107—22no—
100C2×D8×C107—41no—
101C2×M16×C107—22no—
102C2×M16×C107—22no—
103C2×M16×C107—41no—
104C22×C8×C107—22no—
105C22×C8×C107—22no—
106C22×C8×C107—41no—
107C22×C8×C107C2311yescharacteristic
108C22×C8×C107C2311yescharacteristic
109C22×C8×C107C2311yescharacteristic
110C22×C8×C107C2311yescharacteristic
111C22⋊Q8×C107—28no—
112C22⋊Q8×C107—22no—
113C22⋊Q8×C107—22no—
114C22⋊Q8×C107—22no—
115C22⋊Q8×C107D414yescomplemented
116#121×C107—28no—
117#121×C107—28no—
118#121×C107—28no—
119#121×C107—22no—
120#121×C107—22no—
121#121×C107—22no—
122#121×C107—22no—
123#121×C107—22no—
124#121×C107—22no—
125#121×C107—22no—
126#121×C107—41no—
127#121×C107—41no—
128#121×C107D414yescomplemented
129C2×C4⋊C4×C107—21no—
130C2×C4⋊C4×C107—21no—
131C2×C4⋊C4×C107—21no—
132C2×C4⋊C4×C107—22no—
133C2×C4⋊C4×C107—22no—
134C2×C4⋊C4×C107C2311yescharacteristic
135C2×C4⋊C4×C107C2311yescharacteristic
136C2×C4⋊C4×C107C2311yescharacteristic
137C2×C4⋊C4×C107C2311yescharacteristic
138C2×C4⋊C4×C107C2311yescharacteristic
139C2×C22⋊C4×C107—21no—
140C2×C22⋊C4×C107—21no—
141C2×C22⋊C4×C107—21no—
142C2×C22⋊C4×C107—21no—
143C2×C22⋊C4×C107—21no—
144C2×C22⋊C4×C107—21no—
145C2×C22⋊C4×C107—21no—
146C2×C22⋊C4×C107—21no—
147C2×C22⋊C4×C107—21no—
148C2×C22⋊C4×C107—21no—
149#106×C107—22no—
150#106×C107—22no—
151#103×C107—22no—
152#103×C107—22no—
153#103×C107—41no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—22no—
157#102×C107—22no—
158#102×C107—41no—
159C22⋊C8×C107—22no—
160C22⋊C8×C107—22no—
161C22⋊C8×C107—22no—
162C22⋊C8×C107D414yescomplemented
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—21no—
167C24×C107—21no—
168C24×C107C2×D411yescharacteristic
169C24×C107C2×D411yescharacteristic
170C24×C107C2×D411yescharacteristic
171#41×C107—44no—
172#41×C107—44no—
173#41×C107—44no—
174#41×C107—44no—
175#41×C107—44no—
176#41×C107—44no—
177#41×C107—44no—
178#41×C107—44no—
179C2×Q8×C107—22no—
180C2×Q8×C107—22no—
181C2×Q8×C107—21no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—41no—
187C2×Q8×C107C2×D412yes—
188C2×D4×C107—24no—
189C2×D4×C107—22no—
190C2×D4×C107—22no—
191C2×D4×C107—22no—
192C2×D4×C107—22no—
193C2×D4×C107—24no—
194C2×D4×C107—24no—
195C2×D4×C107—22no—
196C2×D4×C107—22no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—21no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—21no—
208C2×D4×C107—41no—
209C2×D4×C107—41no—
210C2×D4×C107—41no—
211C2×D4×C107—42no—
212C2×D4×C107—42no—
213C2×D4×C107—42no—
214C2×D4×C107—42no—
215C2×D4×C107—42no—
216C2×D4×C107—81no—
217C2×D4×C107—81no—
218C2×D4×C107—81no—
219C2×D4×C107—81no—
220C2×D4×C107—81no—
221C2×D4×C107—81no—
222C2×D4×C107—81no—
223C2×D4×C107—81no—
224C2×D4×C107—81no—
225C2×D4×C107—81no—
226C2×D4×C107C2×D412yes—
227C22×C4×C107—21no—
228C22×C4×C107—21no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—21no—
232C22×C4×C107—21no—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—24no—
236C22×C4×C107—21no—
237C22×C4×C107—21no—
238C22×C4×C107—21no—
239C22×C4×C107—24no—
240C22×C4×C107—21no—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—21no—
249C22×C4×C107—42no—
250C22×C4×C107—42no—
251C22×C4×C107—81no—
252C22×C4×C107—81no—
253C22×C4×C107C2×D411yescharacteristic
254C22×C4×C107C2×D411yescharacteristic
255C22×C4×C107C2×D412yes—
256C22×C4×C107C2×D412yes—
257C22×C4×C107C2×D411yescharacteristic
258C22×C4×C107C2×D412yes—
259C22×C4×C107#4112yes—
260C22×C4×C107C2411yescharacteristic
261SD16×C107—44no—
262D8×C107—44no—
263M16×C107—44no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107—21no—
267C2×C8×C107—21no—
268C2×C8×C107—21no—
269C2×C8×C107—21no—
270C2×C8×C107—21no—
271C2×C8×C107—21no—
272C2×C8×C107—21no—
273C2×C8×C107—21no—
274C2×C8×C107—44no—
275C2×C8×C107C2×D412yes—
276C2×C8×C107C2×D412yes—
277C4⋊C4×C107—24no—
278C4⋊C4×C107—24no—
279C4⋊C4×C107—24no—
280C4⋊C4×C107—21no—
281C4⋊C4×C107—21no—
282C4⋊C4×C107—21no—
283C4⋊C4×C107—21no—
284C4⋊C4×C107—21no—
285C4⋊C4×C107—21no—
286C4⋊C4×C107—21no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107C2×D412yes—
289C4⋊C4×C107C2×D412yes—
290C22⋊C4×C107—24no—
291C22⋊C4×C107—24no—
292C22⋊C4×C107—24no—
293C22⋊C4×C107—24no—
294C22⋊C4×C107—42no—
295C22⋊C4×C107—42no—
296C22⋊C4×C107—42no—
297C22⋊C4×C107—81no—
298C22⋊C4×C107—81no—
299C22⋊C4×C107—81no—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—21no—
303C23×C107—21no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—21no—
311C23×C107—21no—
312C23×C107—21no—
313C23×C107—22no—
314C23×C107—21no—
315C23×C107—21no—
316C23×C107—21no—
317C23×C107—21no—
318C23×C107—21no—
319C23×C107—21no—
320C23×C107—41no—
321C23×C107—41no—
322C23×C107—41no—
323C23×C107—41no—
324C23×C107—41no—
325C23×C107—41no—
326C23×C107—41no—
327C23×C107—41no—
328C23×C107—41no—
329C23×C107—41no—
330C23×C107—41no—
331C23×C107—41no—
332C23×C107—41no—
333C23×C107#12012yes—
334C23×C107#12112yes—
335C23×C107C22×D411yescharacteristic
336Q8×C107—22no—
337Q8×C107—22no—
338Q8×C107—44no—
339Q8×C107—41no—
340Q8×C107—41no—
341D4×C107—22no—
342D4×C107—22no—
343D4×C107—44no—
344D4×C107—44no—
345D4×C107—44no—
346D4×C107—48no—
347D4×C107—41no—
348D4×C107—41no—
349D4×C107—41no—
350D4×C107—41no—
351D4×C107—41no—
352D4×C107—41no—
353D4×C107—84no—
354D4×C107—84no—
355D4×C107—84no—
356D4×C107—84no—
357D4×C107—84no—
358C2×C4×C107—21no—
359C2×C4×C107—21no—
360C2×C4×C107—21no—
361C2×C4×C107—21no—
362C2×C4×C107—22no—
363C2×C4×C107—22no—
364C2×C4×C107—22no—
365C2×C4×C107—22no—
366C2×C4×C107—22no—
367C2×C4×C107—22no—
368C2×C4×C107—22no—
369C2×C4×C107—22no—
370C2×C4×C107—22no—
371C2×C4×C107—22no—
372C2×C4×C107—22no—
373C2×C4×C107—21no—
374C2×C4×C107—21no—
375C2×C4×C107—21no—
376C2×C4×C107—48no—
377C2×C4×C107—41no—
378C2×C4×C107—41no—
379C2×C4×C107—41no—
380C2×C4×C107—41no—
381C2×C4×C107—41no—
382C2×C4×C107—41no—
383C2×C4×C107—41no—
384C2×C4×C107—41no—
385C2×C4×C107—41no—
386C2×C4×C107—41no—
387C2×C4×C107—41no—
388C2×C4×C107—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107—41no—
395C2×C4×C107—41no—
396C2×C4×C107—84no—
397C2×C4×C107#12012yes—
398C2×C4×C107#12112yes—
399C2×C4×C107C22×D411yescharacteristic
400C2×C4×C107C22×D411yescharacteristic
401C2×C4×C107C22×D411yescharacteristic
402C2×C4×C107C2×#4111yescharacteristic
403C2×C4×C107H(5,𝔽2)11yescharacteristic
404C2×C4×C107H(5,𝔽2)11yescharacteristic
405C8×C107—22no—
406C8×C107—22no—
407C8×C107—41no—
408C8×C107—41no—
409C22×C107—22no—
410C22×C107—22no—
411C22×C107—22no—
412C22×C107—22no—
413C22×C107—22no—
414C22×C107—22no—
415C22×C107—41no—
416C22×C107—41no—
417C22×C107—41no—
418C22×C107—41no—
419C22×C107—41no—
420C22×C107—41no—
421C22×C107—41no—
422C22×C107—41no—
423C22×C107—42no—
424C22×C107—41no—
425C22×C107—41no—
426C22×C107—41no—
427C22×C107—41no—
428C22×C107—42no—
429C22×C107—41no—
430C22×C107—42no—
431C22×C107—41no—
432C22×C107—41no—
433C22×C107—81no—
434C22×C107—81no—
435C22×C107—81no—
436C22×C107—81no—
437C22×C107—81no—
438C22×C107—81no—
439C22×C107—81no—
440C22×C107—81no—
441C22×C107—81no—
442C22×C107—81no—
443C22×C107—81no—
444C22×C107C2×#12011yescharacteristic
445C22×C107C2×#12111yescharacteristic
446C22×C107#53411yescharacteristic
447C22×C107#57611yescharacteristic
448C22×C107#57711yescharacteristic
449C22×C107#57711yescharacteristic
450C22×C107#57711yescharacteristic
451C4×C107—22no—
452C4×C107—22no—
453C4×C107—41no—
454C4×C107—42no—
455C4×C107—42no—
456C4×C107—42no—
457C4×C107—81no—
458C4×C107—81no—
459C4×C107—81no—
460C4×C107D4211yescharacteristic
461C4×C107D4211yescharacteristic
462C4×C107#54611yescharacteristic
463C4×C107#54611yescharacteristic
464#24397C10711yesmaximal, characteristic, direct product factor, Sylow
465C2×C107—42no—
466C2×C107—42no—
467C2×C107—81no—
468C2×C107—82no—
469C2×C107—161no—
470C2×C107#241011yescharacteristic
471C2×C107#301011yescharacteristic
472C2×C107#301211yescharacteristic
473C2×C107#306011yescharacteristic
474C2×C107#306211yescharacteristic
475C2×C107#319811yescharacteristic
476C2×C107#320411yescharacteristic
477C2×#537C2×C10711yescharacteristic, complemented
478C2×#469C2×C10711yescharacteristic, complemented
479C2×#465C2×C10711yescharacteristic, complemented
480C2×#449C2×C10711yescharacteristic, complemented
481C2×#408C2×C10711yescharacteristic, complemented
482#2615C2×C10711yescharacteristic, complemented
483#2035C2×C10711yescharacteristic, complemented
484#2034C2×C10711yescharacteristic, complemented
485#2000C2×C10711yescharacteristic, complemented
486#1999C2×C10711yescharacteristic, complemented
487#1894C2×C10711yescharacteristic, complemented
488#1893C2×C10711yescharacteristic, complemented
489#1874C2×C10711yescharacteristic, complemented
490#1853C2×C10711yescharacteristic, complemented
491#1788C2×C10711yescharacteristic, complemented
492C107#2439711yescharacteristic, direct product factor, Sylow
493C22×#41C22×C10711yescharacteristic
494C22×#41C22×C10711yescharacteristic
495C22×SD16C22×C10711yescharacteristic
496C22×D8C22×C10711yescharacteristic
497C22×M16C22×C10711yescharacteristic
498C23×C8C22×C10711yescharacteristic
499#537—24no—
500#537—24no—
501C2×C22⋊Q8—21no—
502C2×C22⋊Q8C22×C10711yescharacteristic
503C2×C22⋊Q8C22×C10711yescharacteristic
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—21no—
507C2×#121C22×C10711yescharacteristic
508C2×#121C22×C10711yescharacteristic
509C2×#121C22×C10711yescharacteristic
510C2×#121C22×C10711yescharacteristic
511C2×#121C22×C10711yescharacteristic
512C22×C4⋊C4C22×C10711yescharacteristic
513#469—24no—
514#465—24no—
515#449—24no—
516C2×#106C22×C10711yescharacteristic
517C2×#106C22×C10711yescharacteristic
518C2×#103C22×C10711yescharacteristic
519C2×#103C22×C10711yescharacteristic
520C2×#103C22×C10711yescharacteristic
521C2×#102C22×C10711yescharacteristic
522C2×#102C22×C10711yescharacteristic
523C2×#102C22×C10711yescharacteristic
524C2×#102C22×C10711yescharacteristic
525C2×#102C22×C10711yescharacteristic
526#408—24no—
527C2×C22⋊C8C22×C10711yescharacteristic
528C2×C22⋊C8C22×C10711yescharacteristic
529C2×C22⋊C8C22×C10711yescharacteristic
530C2×C22⋊C8C22×C10711yescharacteristic
531#393—21no—
532#392—21no—
533#392—21no—
534#392—21no—
535#380C22×C10711yescharacteristic
536#380C22×C10711yescharacteristic
537#380C22×C10711yescharacteristic
538#340C22×C10711yescharacteristic
539#340C22×C10711yescharacteristic
540#340C22×C10711yescharacteristic
541#340C22×C10711yescharacteristic
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C10711yescharacteristic
555C22×Q8C23×C10711yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4D4×C10711yescharacteristic
563C22×D4D4×C10711yescharacteristic
564C22×D4D4×C10711yescharacteristic
565C22×D4C23×C10711yescharacteristic
566C22×D4C23×C10711yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C10711yescharacteristic
570C23×C4C23×C10711yescharacteristic
571C23×C4C23×C10711yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C10711yescharacteristic
585C22×C8C23×C10711yescharacteristic
586C22×C8C23×C10711yescharacteristic
587C22×C8C23×C10711yescharacteristic
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C10714yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121D4×C10714yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4C23×C10711yescharacteristic
612C2×C4⋊C4C23×C10711yescharacteristic
613C2×C4⋊C4C23×C10711yescharacteristic
614C2×C4⋊C4C23×C10711yescharacteristic
615C2×C4⋊C4C23×C10711yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626#106—22no—
627#106—22no—
628#103—22no—
629#103—22no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8D4×C10714yescomplemented
640#95—21no—
641#95—21no—
642#95—21no—
643C24—21no—
644C24—21no—
645C24C2×D4×C10711yescharacteristic
646C24C2×D4×C10711yescharacteristic
647C24C2×D4×C10711yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C10712yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C10712yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C10711yescharacteristic
731C22×C4C2×D4×C10711yescharacteristic
732C22×C4C2×D4×C10712yes—
733C22×C4C2×D4×C10712yes—
734C22×C4C2×D4×C10711yescharacteristic
735C22×C4C2×D4×C10712yes—
736C22×C4#41×C10712yes—
737C22×C4C24×C10711yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8C2×D4×C10712yes—
753C2×C8C2×D4×C10712yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C10712yes—
766C4⋊C4C2×D4×C10712yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23#120×C10712yes—
811C23#121×C10712yes—
812C23C22×D4×C10711yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4#120×C10712yes—
875C2×C4#121×C10712yes—
876C2×C4C22×D4×C10711yescharacteristic
877C2×C4C22×D4×C10711yescharacteristic
878C2×C4C22×D4×C10711yescharacteristic
879C2×C4C2×#41×C10711yescharacteristic
880C2×C4H(5,𝔽2)×C10711yescharacteristic
881C2×C4H(5,𝔽2)×C10711yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×#120×C10711yescharacteristic
922C22C2×#121×C10711yescharacteristic
923C22#534×C10711yescharacteristic
924C22#576×C10711yescharacteristic
925C22#577×C10711yescharacteristic
926C22#577×C10711yescharacteristic
927C22#577×C10711yescharacteristic
928C4—22no—
929C4—22no—
930C4—41no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C10711yescharacteristic
938C4D42×C10711yescharacteristic
939C4#546×C10711yescharacteristic
940C4#546×C10711yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C107×#241011yescharacteristic
947C2C107×#301011yescharacteristic
948C2C107×#301211yescharacteristic
949C2C107×#306011yescharacteristic
950C2C107×#306211yescharacteristic
951C2C107×#319811yescharacteristic
952C2C107×#320411yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×#41×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#537×C107C2semidirect
2. C2×#469×C107C2semidirect
3. C2×#465×C107C2semidirect
4. C2×#449×C107C2semidirect
5. C2×#408×C107C2semidirect
6. C107×#2615C2semidirect
7. C107×#2035C2semidirect
8. C107×#2034C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1894C2semidirect
12. C107×#1893C2semidirect
13. C107×#1874C2semidirect
14. C107×#1853C2semidirect
15. C107×#1788C2semidirect
115. C22⋊Q8×C107D4semidirect
128. #121×C107D4semidirect
162. C22⋊C8×C107D4semidirect
464. #24397C107direct (N × H)
477. C2×#537C2×C107semidirect
478. C2×#469C2×C107semidirect
479. C2×#465C2×C107semidirect
480. C2×#449C2×C107semidirect
481. C2×#408C2×C107semidirect
482. #2615C2×C107semidirect
483. #2035C2×C107semidirect
484. #2034C2×C107semidirect
485. #2000C2×C107semidirect
486. #1999C2×C107semidirect
487. #1894C2×C107semidirect
488. #1893C2×C107semidirect
489. #1874C2×C107semidirect
490. #1853C2×C107semidirect
491. #1788C2×C107semidirect
492. C107#24397direct (N × H)
592. C22⋊Q8D4×C107semidirect
605. #121D4×C107semidirect
639. C22⋊C8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1072
C2×#469×C1072
C2×#465×C1072
C2×#449×C1072
C2×#408×C1072
C107×#26152
C107×#20352
C107×#20342
C107×#20002
C107×#19992
C107×#18942
C107×#18932
C107×#18742
C107×#18532
C107×#17882
#24397107