Finite Group Databasebeta

← C107×#24662 #41050626

Subgroups — C107×#24662 #41050626

Order 27392.

970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C107C211yesmaximal, characteristic, complemented
2C2×#433×C107C211yesmaximal, characteristic, complemented
3C107×#2619C211yesmaximal, characteristic, complemented
4C107×#2324C211yesmaximal, characteristic, complemented
5C107×#2034C211yesmaximal, characteristic, complemented
6C107×#2033C211yesmaximal, characteristic, complemented
7C107×#1999C211yesmaximal, characteristic, complemented
8C107×#1999C211yesmaximal, characteristic, complemented
9C107×#1982C211yesmaximal, characteristic, complemented
10C107×#1972C211yesmaximal, characteristic, complemented
11C107×#1970C211yesmaximal, characteristic, complemented
12C107×#1949C211yesmaximal, characteristic, complemented
13C107×#1936C211yesmaximal, characteristic, complemented
14C107×#1934C211yesmaximal, characteristic, complemented
15C107×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C2×#127×C107C2211yescharacteristic
19C2×#121×C107C2211yescharacteristic
20C2×#121×C107C2211yescharacteristic
21C2×#121×C107C2211yescharacteristic
22C2×C4×D4×C107C2211yescharacteristic
23C2×#117×C107C2211yescharacteristic
24#459×C107—24no—
25#433×C107—24no—
26C2×#107×C107C2211yescharacteristic
27C2×#106×C107C2211yescharacteristic
28C2×C4⋊C8×C107C2211yescharacteristic
29C2×C4⋊C8×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×C22⋊C8×C107C2211yescharacteristic
39C2×C22⋊C8×C107C2211yescharacteristic
40C2×#97×C107C2211yescharacteristic
41C2×C4×C8×C107C2211yescharacteristic
42#394×C107—21no—
43#394×C107—21no—
44#392×C107—21no—
45#392×C107—21no—
46#390×C107—21no—
47#390×C107C2211yescharacteristic
48#390×C107C2211yescharacteristic
49#390×C107C2211yescharacteristic
50#389×C107C2211yescharacteristic
51#388×C107—21no—
52#386×C107—21no—
53#385×C107—21no—
54#382×C107C2211yescharacteristic
55#380×C107C2211yescharacteristic
56C4×C4⋊C4×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61C22×D4×C107—21no—
62C22×D4×C107—21no—
63C22×D4×C107—21no—
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107C2311yescharacteristic
67C22×D4×C107C2311yescharacteristic
68C22×D4×C107C2311yescharacteristic
69C23×C4×C107—21no—
70C23×C4×C107C2311yescharacteristic
71C2×D8×C107—22no—
72C2×D8×C107—22no—
73C2×D8×C107—22no—
74C2×D8×C107—22no—
75C2×D8×C107—41no—
76C2×D8×C107—41no—
77C22×C8×C107C2311yescharacteristic
78C22×C8×C107C2311yescharacteristic
79C22×C8×C107C2311yescharacteristic
80C22×C8×C107C2311yescharacteristic
81#127×C107—22no—
82#127×C107—22no—
83#121×C107—22no—
84#121×C107—22no—
85#121×C107—41no—
86#121×C107—41no—
87#121×C107—41no—
88#121×C107—41no—
89C4×D4×C107—22no—
90C4×D4×C107—22no—
91#117×C107—22no—
92#117×C107—22no—
93C2×C4⋊C4×C107—21no—
94C2×C4⋊C4×C107D411yescharacteristic
95C2×C4⋊C4×C107D411yescharacteristic
96C2×C4⋊C4×C107C2311yescharacteristic
97C2×C4⋊C4×C107C2311yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C4⋊C4×C107C2311yescharacteristic
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—21no—
105C2×C22⋊C4×C107—21no—
106C2×C22⋊C4×C107—21no—
107C2×C22⋊C4×C107—21no—
108C2×C22⋊C4×C107—21no—
109C2×C22⋊C4×C107—21no—
110C2×C22⋊C4×C107—21no—
111C2×C22⋊C4×C107—21no—
112C2×C22⋊C4×C107D411yescharacteristic
113C2×C22⋊C4×C107D411yescharacteristic
114C2×C42×C107—21no—
115C2×C42×C107C2311yescharacteristic
116C2×C42×C107C2311yescharacteristic
117#107×C107—41no—
118#106×C107—41no—
119C4⋊C8×C107—22no—
120C4⋊C8×C107D414yescomplemented
121#102×C107—22no—
122#102×C107—22no—
123#102×C107—22no—
124#102×C107—22no—
125#102×C107—41no—
126#102×C107—41no—
127#102×C107—41no—
128#102×C107—41no—
129C22⋊C8×C107—22no—
130C22⋊C8×C107—22no—
131#97×C107—22no—
132C4×C8×C107—22no—
133#95×C107—21no—
134#95×C107—21no—
135#95×C107—21no—
136#95×C107—21no—
137#95×C107—21no—
138C24×C107—21no—
139C24×C107—21no—
140C24×C107—21no—
141C24×C107C2×D411yescharacteristic
142C2×D4×C107—24no—
143C2×D4×C107—21no—
144C2×D4×C107—21no—
145C2×D4×C107—21no—
146C2×D4×C107—21no—
147C2×D4×C107—21no—
148C2×D4×C107—21no—
149C2×D4×C107—21no—
150C2×D4×C107—21no—
151C2×D4×C107—21no—
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—21no—
156C2×D4×C107—21no—
157C2×D4×C107—21no—
158C2×D4×C107—21no—
159C2×D4×C107—21no—
160C2×D4×C107—42no—
161C2×D4×C107—42no—
162C2×D4×C107—42no—
163C2×D4×C107—42no—
164C2×D4×C107—81no—
165C2×D4×C107—81no—
166C2×D4×C107—81no—
167C2×D4×C107—81no—
168C2×D4×C107—81no—
169C2×D4×C107—81no—
170C2×D4×C107—81no—
171C2×D4×C107—81no—
172C2×D4×C107—81no—
173C2×D4×C107—81no—
174C2×D4×C107#4112yes—
175C22×C4×C107—21no—
176C22×C4×C107—21no—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—42no—
187C22×C4×C107—81no—
188C22×C4×C107—81no—
189C22×C4×C107C2×D411yescharacteristic
190C22×C4×C107C2×D411yescharacteristic
191C22×C4×C107C2×D411yescharacteristic
192C22×C4×C107C2×D411yescharacteristic
193C22×C4×C107C2×D411yescharacteristic
194C22×C4×C107C2411yescharacteristic
195D8×C107—44no—
196D8×C107—44no—
197C2×C8×C107—21no—
198C2×C8×C107—21no—
199C2×C8×C107—21no—
200C2×C8×C107—21no—
201C2×C8×C107—21no—
202C2×C8×C107—21no—
203C2×C8×C107—21no—
204C2×C8×C107—21no—
205C2×C8×C107—21no—
206C2×C8×C107—21no—
207C2×C8×C107C2×D412yes—
208C2×C8×C107C2×D412yes—
209C4⋊C4×C107—22no—
210C4⋊C4×C107—22no—
211C4⋊C4×C107—21no—
212C4⋊C4×C107—21no—
213C4⋊C4×C107—21no—
214C4⋊C4×C107—21no—
215C4⋊C4×C107—21no—
216C4⋊C4×C107—21no—
217C4⋊C4×C107—21no—
218C4⋊C4×C107—21no—
219C4⋊C4×C107—21no—
220C4⋊C4×C107—81no—
221C4⋊C4×C107#4112yes—
222C22⋊C4×C107—24no—
223C22⋊C4×C107—22no—
224C22⋊C4×C107—22no—
225C22⋊C4×C107—42no—
226C22⋊C4×C107—42no—
227C22⋊C4×C107—42no—
228C22⋊C4×C107—81no—
229C22⋊C4×C107—81no—
230C22⋊C4×C107—81no—
231C22⋊C4×C107—81no—
232C22⋊C4×C107—81no—
233C22⋊C4×C107—81no—
234C22⋊C4×C107—81no—
235C42×C107—21no—
236C42×C107—21no—
237C42×C107—81no—
238C42×C107C2×D412yes—
239C42×C107#4112yes—
240C23×C107—21no—
241C23×C107—22no—
242C23×C107—21no—
243C23×C107—21no—
244C23×C107—21no—
245C23×C107—21no—
246C23×C107—21no—
247C23×C107—21no—
248C23×C107—41no—
249C23×C107—41no—
250C23×C107—41no—
251C23×C107—41no—
252C23×C107—41no—
253C23×C107—41no—
254C23×C107—41no—
255C23×C107—41no—
256C23×C107—41no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107—41no—
260C23×C107—41no—
261C23×C107—41no—
262C23×C107—41no—
263C23×C107—41no—
264C23×C107—41no—
265C23×C107—41no—
266C23×C107—41no—
267C23×C107—41no—
268C23×C107C22×D411yescharacteristic
269D4×C107—22no—
270D4×C107—22no—
271D4×C107—41no—
272D4×C107—41no—
273D4×C107—41no—
274D4×C107—41no—
275D4×C107—41no—
276D4×C107—41no—
277D4×C107—41no—
278D4×C107—41no—
279D4×C107—41no—
280D4×C107—41no—
281D4×C107—84no—
282D4×C107—84no—
283D4×C107—84no—
284D4×C107—84no—
285D4×C107—84no—
286C2×C4×C107—21no—
287C2×C4×C107—21no—
288C2×C4×C107—21no—
289C2×C4×C107—21no—
290C2×C4×C107—21no—
291C2×C4×C107—21no—
292C2×C4×C107—21no—
293C2×C4×C107—21no—
294C2×C4×C107—22no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—21no—
298C2×C4×C107—21no—
299C2×C4×C107—21no—
300C2×C4×C107—41no—
301C2×C4×C107—41no—
302C2×C4×C107—41no—
303C2×C4×C107—41no—
304C2×C4×C107—41no—
305C2×C4×C107—41no—
306C2×C4×C107—41no—
307C2×C4×C107—41no—
308C2×C4×C107—41no—
309C2×C4×C107—41no—
310C2×C4×C107—41no—
311C2×C4×C107—41no—
312C2×C4×C107—41no—
313C2×C4×C107—41no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—84no—
319C2×C4×C107#12112yes—
320C2×C4×C107#12112yes—
321C2×C4×C107C22×D411yescharacteristic
322C2×C4×C107C2×#4111yescharacteristic
323C2×C4×C107C2×#4111yescharacteristic
324C2×C4×C107C2×#4111yescharacteristic
325C2×C4×C107H(5,𝔽2)11yescharacteristic
326C2×C4×C107H(5,𝔽2)11yescharacteristic
327C8×C107—22no—
328C8×C107—22no—
329C8×C107—41no—
330C8×C107—41no—
331C22×C107—41no—
332C22×C107—42no—
333C22×C107—41no—
334C22×C107—42no—
335C22×C107—41no—
336C22×C107—42no—
337C22×C107—41no—
338C22×C107—41no—
339C22×C107—41no—
340C22×C107—41no—
341C22×C107—81no—
342C22×C107—81no—
343C22×C107—81no—
344C22×C107—81no—
345C22×C107—81no—
346C22×C107—81no—
347C22×C107—81no—
348C22×C107—81no—
349C22×C107—81no—
350C22×C107—81no—
351C22×C107—81no—
352C22×C107—81no—
353C22×C107—81no—
354C22×C107—81no—
355C22×C107—81no—
356C22×C107—81no—
357C22×C107—81no—
358C22×C107—81no—
359C22×C107C2×#12111yescharacteristic
360C22×C107#52511yescharacteristic
361C22×C107#53511yescharacteristic
362C22×C107#57611yescharacteristic
363C22×C107#57611yescharacteristic
364C22×C107#57611yescharacteristic
365C22×C107#57711yescharacteristic
366C4×C107—22no—
367C4×C107—22no—
368C4×C107—42no—
369C4×C107—41no—
370C4×C107—41no—
371C4×C107—41no—
372C4×C107—81no—
373C4×C107—81no—
374C4×C107—81no—
375C4×C107—81no—
376C4×C107#54611yescharacteristic
377C4×C107#55011yescharacteristic
378C4×C107#55311yescharacteristic
379C4×C107#55511yescharacteristic
380#24662C10711yesmaximal, characteristic, direct product factor, Sylow
381C2×C107—81no—
382C2×C107—82no—
383C2×C107—161no—
384C2×C107—161no—
385C2×C107#241411yescharacteristic
386C2×C107#305811yescharacteristic
387C2×C107#306211yescharacteristic
388C2×C107#311911yescharacteristic
389C2×C107#312211yescharacteristic
390C2×C107#322011yescharacteristic
391C2×C107#322411yescharacteristic
392C2×#459C2×C10711yescharacteristic, complemented
393C2×#433C2×C10711yescharacteristic, complemented
394#2619C2×C10711yescharacteristic, complemented
395#2324C2×C10711yescharacteristic, complemented
396#2034C2×C10711yescharacteristic, complemented
397#2033C2×C10711yescharacteristic, complemented
398#1999C2×C10711yescharacteristic, complemented
399#1999C2×C10711yescharacteristic, complemented
400#1982C2×C10711yescharacteristic, complemented
401#1972C2×C10711yescharacteristic, complemented
402#1970C2×C10711yescharacteristic, complemented
403#1949C2×C10711yescharacteristic, complemented
404#1936C2×C10711yescharacteristic, complemented
405#1934C2×C10711yescharacteristic, complemented
406#1804C2×C10711yescharacteristic, complemented
407C107#2466211yescharacteristic, direct product factor, Sylow
408C22×D8C22×C10711yescharacteristic
409C22×D8C22×C10711yescharacteristic
410C2×#127C22×C10711yescharacteristic
411C2×#121C22×C10711yescharacteristic
412C2×#121C22×C10711yescharacteristic
413C2×#121C22×C10711yescharacteristic
414C2×C4×D4C22×C10711yescharacteristic
415C2×#117C22×C10711yescharacteristic
416#459—24no—
417#433—24no—
418C2×#107C22×C10711yescharacteristic
419C2×#106C22×C10711yescharacteristic
420C2×C4⋊C8C22×C10711yescharacteristic
421C2×C4⋊C8C22×C10711yescharacteristic
422C2×#102C22×C10711yescharacteristic
423C2×#102C22×C10711yescharacteristic
424C2×#102C22×C10711yescharacteristic
425C2×#102C22×C10711yescharacteristic
426C2×#102C22×C10711yescharacteristic
427C2×#102C22×C10711yescharacteristic
428C2×#102C22×C10711yescharacteristic
429C2×#102C22×C10711yescharacteristic
430C2×C22⋊C8C22×C10711yescharacteristic
431C2×C22⋊C8C22×C10711yescharacteristic
432C2×#97C22×C10711yescharacteristic
433C2×C4×C8C22×C10711yescharacteristic
434#394—21no—
435#394—21no—
436#392—21no—
437#392—21no—
438#390—21no—
439#390C22×C10711yescharacteristic
440#390C22×C10711yescharacteristic
441#390C22×C10711yescharacteristic
442#389C22×C10711yescharacteristic
443#388—21no—
444#386—21no—
445#385—21no—
446#382C22×C10711yescharacteristic
447#380C22×C10711yescharacteristic
448C4×C4⋊C4C22×C10711yescharacteristic
449#340C22×C10711yescharacteristic
450#340C22×C10711yescharacteristic
451#340C22×C10711yescharacteristic
452#340C22×C10711yescharacteristic
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C23×C10711yescharacteristic
459C22×D4C23×C10711yescharacteristic
460C22×D4C23×C10711yescharacteristic
461C23×C4—21no—
462C23×C4C23×C10711yescharacteristic
463C2×D8—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—41no—
468C2×D8—41no—
469C22×C8C23×C10711yescharacteristic
470C22×C8C23×C10711yescharacteristic
471C22×C8C23×C10711yescharacteristic
472C22×C8C23×C10711yescharacteristic
473#127—22no—
474#127—22no—
475#121—22no—
476#121—22no—
477#121—41no—
478#121—41no—
479#121—41no—
480#121—41no—
481C4×D4—22no—
482C4×D4—22no—
483#117—22no—
484#117—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4D4×C10711yescharacteristic
487C2×C4⋊C4D4×C10711yescharacteristic
488C2×C4⋊C4C23×C10711yescharacteristic
489C2×C4⋊C4C23×C10711yescharacteristic
490C2×C4⋊C4C23×C10711yescharacteristic
491C2×C4⋊C4C23×C10711yescharacteristic
492C2×C4⋊C4C23×C10711yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C10711yescharacteristic
505C2×C22⋊C4D4×C10711yescharacteristic
506C2×C42—21no—
507C2×C42C23×C10711yescharacteristic
508C2×C42C23×C10711yescharacteristic
509#107—41no—
510#106—41no—
511C4⋊C8—22no—
512C4⋊C8D4×C10714yescomplemented
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518#102—41no—
519#102—41no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—22no—
524C4×C8—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C2×D4×C10711yescharacteristic
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4#41×C10712yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C10711yescharacteristic
582C22×C4C2×D4×C10711yescharacteristic
583C22×C4C2×D4×C10711yescharacteristic
584C22×C4C2×D4×C10711yescharacteristic
585C22×C4C2×D4×C10711yescharacteristic
586C22×C4C24×C10711yescharacteristic
587D8—44no—
588D8—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8C2×D4×C10712yes—
600C2×C8C2×D4×C10712yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—81no—
613C4⋊C4#41×C10712yes—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—81no—
630C42C2×D4×C10712yes—
631C42#41×C10712yes—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C22×D4×C10711yescharacteristic
661D4—22no—
662D4—22no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675D4—84no—
676D4—84no—
677D4—84no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—84no—
711C2×C4#121×C10712yes—
712C2×C4#121×C10712yes—
713C2×C4C22×D4×C10711yescharacteristic
714C2×C4C2×#41×C10711yescharacteristic
715C2×C4C2×#41×C10711yescharacteristic
716C2×C4C2×#41×C10711yescharacteristic
717C2×C4H(5,𝔽2)×C10711yescharacteristic
718C2×C4H(5,𝔽2)×C10711yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#121×C10711yescharacteristic
752C22#525×C10711yescharacteristic
753C22#535×C10711yescharacteristic
754C22#576×C10711yescharacteristic
755C22#576×C10711yescharacteristic
756C22#576×C10711yescharacteristic
757C22#577×C10711yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4#546×C10711yescharacteristic
769C4#550×C10711yescharacteristic
770C4#553×C10711yescharacteristic
771C4#555×C10711yescharacteristic
772C2—81no—
773C2—82no—
774C2—161no—
775C2—161no—
776C2C107×#241411yescharacteristic
777C2C107×#305811yescharacteristic
778C2C107×#306211yescharacteristic
779C2C107×#311911yescharacteristic
780C2C107×#312211yescharacteristic
781C2C107×#322011yescharacteristic
782C2C107×#322411yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×#117×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C107C2semidirect
2. C2×#433×C107C2semidirect
3. C107×#2619C2semidirect
4. C107×#2324C2semidirect
5. C107×#2034C2semidirect
6. C107×#2033C2semidirect
7. C107×#1999C2semidirect
8. C107×#1999C2semidirect
9. C107×#1982C2semidirect
10. C107×#1972C2semidirect
11. C107×#1970C2semidirect
12. C107×#1949C2semidirect
13. C107×#1936C2semidirect
14. C107×#1934C2semidirect
15. C107×#1804C2semidirect
120. C4⋊C8×C107D4semidirect
380. #24662C107direct (N × H)
392. C2×#459C2×C107semidirect
393. C2×#433C2×C107semidirect
394. #2619C2×C107semidirect
395. #2324C2×C107semidirect
396. #2034C2×C107semidirect
397. #2033C2×C107semidirect
398. #1999C2×C107semidirect
399. #1999C2×C107semidirect
400. #1982C2×C107semidirect
401. #1972C2×C107semidirect
402. #1970C2×C107semidirect
403. #1949C2×C107semidirect
404. #1936C2×C107semidirect
405. #1934C2×C107semidirect
406. #1804C2×C107semidirect
407. C107#24662direct (N × H)
512. C4⋊C8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1072
C2×#433×C1072
C107×#26192
C107×#23242
C107×#20342
C107×#20332
C107×#19992
C107×#19822
C107×#19722
C107×#19702
C107×#19492
C107×#19362
C107×#19342
C107×#18042
#24662107