Finite Group Databasebeta

← C107×#18414 #41044378

Subgroups — C107×#18414 #41044378

Order 27392.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3534C211yesmaximal, characteristic, complemented
2C107×#3194C211yesmaximal, characteristic, complemented
3C107×#3186C211yesmaximal, characteristic, complemented
4C107×#2661C211yesmaximal, characteristic, complemented
5C107×#1612C211yesmaximal, characteristic, complemented
6C107×#1610C211yesmaximal, characteristic, complemented
7C107×#1609C211yesmaximal, characteristic, complemented
8C107×#1607C211yesmaximal, characteristic, complemented
9C107×#1600C211yesmaximal, characteristic, complemented
10C107×#1598C211yesmaximal, characteristic, complemented
11C107×#1597C211yesmaximal, characteristic, complemented
12C107×#1595C211yesmaximal, characteristic, complemented
13C107×#1507C211yesmaximal, characteristic, complemented
14C107×#1501C211yesmaximal, characteristic, complemented
15C107×#1468C211yesmaximal, characteristic, complemented
16#562×C107—21no—
17#560×C107—21no—
18#553×C107—21no—
19#551×C107—21no—
20#546×C107—21no—
21#546×C107—21no—
22#546×C107—21no—
23D42×C107—21no—
24#540×C107—21no—
25#539×C107—21no—
26#539×C107C2211yescharacteristic
27#538×C107—21no—
28#538×C107C2211yescharacteristic
29#537×C107C2211yescharacteristic
30#534×C107—21no—
31#534×C107C2211yescharacteristic
32#525×C107C2211yescharacteristic
33C2×#123×C107C2211yescharacteristic
34C2×#121×C107C2211yescharacteristic
35C2×#121×C107C2211yescharacteristic, complemented
36#483×C107C2211yescharacteristic, complemented
37#482×C107—21no—
38#480×C107—21no—
39#480×C107C2211yescharacteristic
40#480×C107C2211yescharacteristic, complemented
41#480×C107C2211yescharacteristic, complemented
42#469×C107—21no—
43#468×C107—21no—
44#466×C107—21no—
45#466×C107—21no—
46#450×C107C2211yescharacteristic, complemented
47#449×C107—21no—
48#447×C107—21no—
49#447×C107C2211yescharacteristic
50#447×C107C2211yescharacteristic, complemented
51#447×C107C2211yescharacteristic, complemented
52#407×C107C2211yescharacteristic, complemented
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54#398×C107C2211yescharacteristic, complemented
55#397×C107C2211yescharacteristic, complemented
56#394×C107—21no—
57#394×C107C2211yescharacteristic, complemented
58#392×C107—21no—
59#392×C107C2211yescharacteristic, complemented
60#390×C107—21no—
61#388×C107—21no—
62C4×C22⋊C4×C107C2211yescharacteristic, complemented
63#328×C107C2211yescharacteristic, complemented
64#328×C107C2211yescharacteristic, complemented
65#327×C107C2211yescharacteristic
66#327×C107C2211yescharacteristic
67#327×C107C2211yescharacteristic, complemented
68#327×C107C2211yescharacteristic, complemented
69#327×C107C2211yescharacteristic, complemented
70#327×C107C2211yescharacteristic, complemented
71#324×C107C2211yescharacteristic, complemented
72#324×C107C2211yescharacteristic, complemented
73#323×C107C2211yescharacteristic, complemented
74#323×C107C2211yescharacteristic, complemented
75C2×#41×C107—21no—
76C2×#41×C107D411yescharacteristic, complemented
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107D411yescharacteristic
83C22×D4×C107D411yescharacteristic, complemented
84C22×D4×C107C2311yescharacteristic
85C23×C4×C107C2311yescharacteristic
86C2×SD16×C107—21no—
87C2×D8×C107—21no—
88C2×D8×C107—21no—
89C2×D8×C107—21no—
90C2×M16×C107—21no—
91C22×C8×C107—21no—
92#127×C107—21no—
93#126×C107—21no—
94#126×C107—21no—
95#126×C107—21no—
96#126×C107—21no—
97#125×C107—21no—
98#125×C107—21no—
99#124×C107—21no—
100#124×C107—21no—
101#124×C107—21no—
102#123×C107—21no—
103#123×C107—21no—
104#123×C107—21no—
105#123×C107—21no—
106#123×C107—21no—
107#123×C107—21no—
108#123×C107—21no—
109#123×C107—21no—
110#123×C107—21no—
111#123×C107—21no—
112#123×C107—21no—
113#123×C107—21no—
114#123×C107—21no—
115#123×C107—21no—
116C22⋊Q8×C107—21no—
117C22⋊Q8×C107—21no—
118C22⋊Q8×C107—21no—
119C22⋊Q8×C107—21no—
120C22⋊Q8×C107—21no—
121C22⋊Q8×C107D411yescharacteristic, complemented
122C22⋊Q8×C107C2311yescharacteristic
123#121×C107—21no—
124#121×C107—21no—
125#121×C107—21no—
126#121×C107—21no—
127#121×C107—21no—
128#121×C107—21no—
129#121×C107—21no—
130#121×C107—21no—
131#121×C107—21no—
132#121×C107—21no—
133#121×C107—21no—
134#121×C107—21no—
135#121×C107—21no—
136#121×C107—21no—
137#121×C107—21no—
138#121×C107—21no—
139#121×C107—21no—
140#121×C107—21no—
141#121×C107—21no—
142#121×C107D411yescharacteristic, complemented
143#121×C107D411yescharacteristic, complemented
144#121×C107D411yescharacteristic, complemented
145#121×C107C2311yescharacteristic
146#121×C107C2311yescharacteristic
147#121×C107C2311yescharacteristic
148#120×C107—21no—
149#120×C107—21no—
150#120×C107—21no—
151#120×C107—21no—
152#120×C107—21no—
153#120×C107—21no—
154#120×C107—21no—
155#120×C107—21no—
156C4×D4×C107—21no—
157C4×D4×C107—21no—
158C4×D4×C107—21no—
159C4×D4×C107—21no—
160C4×D4×C107—21no—
161C4×D4×C107—21no—
162C4×D4×C107—21no—
163C4×D4×C107—21no—
164#117×C107—21no—
165#117×C107D411yescharacteristic, complemented
166C2×C4⋊C4×C107—21no—
167C2×C4⋊C4×C107D411yescharacteristic
168C2×C4⋊C4×C107D411yescharacteristic, complemented
169C2×C4⋊C4×C107C2311yescharacteristic
170C2×C4⋊C4×C107C2311yescharacteristic
171C2×C22⋊C4×C107—21no—
172C2×C22⋊C4×C107—21no—
173C2×C22⋊C4×C107—21no—
174C2×C22⋊C4×C107—21no—
175C2×C22⋊C4×C107—21no—
176C2×C22⋊C4×C107—21no—
177C2×C22⋊C4×C107—21no—
178C2×C22⋊C4×C107—21no—
179C2×C22⋊C4×C107—21no—
180C2×C22⋊C4×C107D411yescharacteristic
181C2×C22⋊C4×C107D411yescharacteristic
182C2×C22⋊C4×C107C2311yescharacteristic
183C2×C42×C107—21no—
184#107×C107—21no—
185#107×C107—21no—
186#107×C107—21no—
187#106×C107—21no—
188#103×C107—21no—
189#102×C107—21no—
190#102×C107—21no—
191#102×C107—21no—
192#102×C107—21no—
193#102×C107—21no—
194#102×C107—21no—
195#102×C107—21no—
196C22⋊C8×C107—21no—
197C22⋊C8×C107—21no—
198C22⋊C8×C107C2311yescharacteristic
199C22⋊C8×C107C2311yescharacteristic
200C22⋊C8×C107C2311yescharacteristic
201C22⋊C8×C107C2311yescharacteristic
202#95×C107—21no—
203#95×C107—21no—
204#95×C107C2311yescharacteristic
205#95×C107C2311yescharacteristic
206C24×C107—21no—
207C24×C107—21no—
208C24×C107—21no—
209C24×C107C2×D411yescharacteristic
210C24×C107C2×D411yescharacteristic
211#41×C107—81no—
212#41×C107—81no—
213#41×C107—81no—
214C2×Q8×C107—21no—
215C2×Q8×C107C2×D411yescharacteristic
216C2×D4×C107—21no—
217C2×D4×C107—21no—
218C2×D4×C107—21no—
219C2×D4×C107—21no—
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—21no—
223C2×D4×C107—21no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—21no—
229C2×D4×C107—21no—
230C2×D4×C107—21no—
231C2×D4×C107—21no—
232C2×D4×C107—21no—
233C2×D4×C107—21no—
234C2×D4×C107—21no—
235C2×D4×C107—42no—
236C2×D4×C107—41no—
237C2×D4×C107—41no—
238C2×D4×C107—81no—
239C2×D4×C107—81no—
240C2×D4×C107—81no—
241C2×D4×C107—81no—
242C2×D4×C107—81no—
243C2×D4×C107—81no—
244C2×D4×C107—81no—
245C2×D4×C107—81no—
246C2×D4×C107—81no—
247C2×D4×C107—81no—
248C2×D4×C107—81no—
249C2×D4×C107—82no—
250C2×D4×C107C2×D411yescharacteristic
251C2×D4×C107C2×D411yescharacteristic
252C2×D4×C107C2×D411yescharacteristic
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—21no—
259C22×C4×C107—21no—
260C22×C4×C107—21no—
261C22×C4×C107—21no—
262C22×C4×C107—21no—
263C22×C4×C107—81no—
264C22×C4×C107C2×D411yescharacteristic
265C22×C4×C107C2×D411yescharacteristic
266C22×C4×C107C2×D411yescharacteristic
267C22×C4×C107C2×D411yescharacteristic
268C22×C4×C107C2×D411yescharacteristic
269C22×C4×C107C2×D411yescharacteristic
270C22×C4×C107C2×D411yescharacteristic
271C22×C4×C107C2×D411yescharacteristic
272C22×C4×C107C2411yescharacteristic
273SD16×C107—81no—
274D8×C107—81no—
275D8×C107—81no—
276D8×C107—81no—
277M16×C107—81no—
278C2×C8×C107—21no—
279C2×C8×C107—21no—
280C2×C8×C107—21no—
281C2×C8×C107—21no—
282C2×C8×C107—81no—
283C4⋊C4×C107—21no—
284C4⋊C4×C107—21no—
285C4⋊C4×C107—21no—
286C4⋊C4×C107—21no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107—21no—
289C4⋊C4×C107—21no—
290C4⋊C4×C107—21no—
291C4⋊C4×C107—21no—
292C4⋊C4×C107—21no—
293C4⋊C4×C107—21no—
294C4⋊C4×C107—21no—
295C4⋊C4×C107—21no—
296C4⋊C4×C107—21no—
297C4⋊C4×C107—21no—
298C4⋊C4×C107—81no—
299C4⋊C4×C107C2×D411yescharacteristic
300C4⋊C4×C107C2×D411yescharacteristic
301C4⋊C4×C107C2×D411yescharacteristic
302C4⋊C4×C107C2×D411yescharacteristic
303C22⋊C4×C107—21no—
304C22⋊C4×C107—21no—
305C22⋊C4×C107—21no—
306C22⋊C4×C107—21no—
307C22⋊C4×C107—21no—
308C22⋊C4×C107—21no—
309C22⋊C4×C107—21no—
310C22⋊C4×C107—21no—
311C22⋊C4×C107—21no—
312C22⋊C4×C107—21no—
313C22⋊C4×C107—21no—
314C22⋊C4×C107—21no—
315C22⋊C4×C107—21no—
316C22⋊C4×C107—21no—
317C22⋊C4×C107—21no—
318C22⋊C4×C107—21no—
319C22⋊C4×C107—21no—
320C22⋊C4×C107—21no—
321C22⋊C4×C107—21no—
322C22⋊C4×C107—21no—
323C22⋊C4×C107—21no—
324C22⋊C4×C107—21no—
325C22⋊C4×C107—21no—
326C22⋊C4×C107—21no—
327C22⋊C4×C107—21no—
328C22⋊C4×C107—42no—
329C22⋊C4×C107—42no—
330C22⋊C4×C107—41no—
331C22⋊C4×C107—41no—
332C22⋊C4×C107—81no—
333C22⋊C4×C107—81no—
334C22⋊C4×C107—81no—
335C42×C107—21no—
336C42×C107—21no—
337C42×C107—21no—
338C42×C107—81no—
339C23×C107—21no—
340C23×C107—21no—
341C23×C107—21no—
342C23×C107—21no—
343C23×C107—21no—
344C23×C107—21no—
345C23×C107—21no—
346C23×C107—21no—
347C23×C107—41no—
348C23×C107—41no—
349C23×C107—42no—
350C23×C107—41no—
351C23×C107—41no—
352C23×C107—41no—
353C23×C107—41no—
354C23×C107—41no—
355C23×C107—41no—
356C23×C107—41no—
357C23×C107—41no—
358C23×C107—41no—
359C23×C107—81no—
360C23×C107—81no—
361C23×C107—81no—
362C23×C107—81no—
363C23×C107—81no—
364C23×C107#12011yescharacteristic
365C23×C107#12011yescharacteristic
366C23×C107C22×D411yescharacteristic
367Q8×C107—41no—
368Q8×C107—81no—
369D4×C107—41no—
370D4×C107—41no—
371D4×C107—41no—
372D4×C107—41no—
373D4×C107—41no—
374D4×C107—41no—
375D4×C107—41no—
376D4×C107—42no—
377D4×C107—42no—
378D4×C107—41no—
379D4×C107—41no—
380D4×C107—41no—
381D4×C107—41no—
382D4×C107—41no—
383D4×C107—41no—
384D4×C107—81no—
385D4×C107—81no—
386D4×C107—81no—
387D4×C107—81no—
388D4×C107—81no—
389D4×C107—81no—
390D4×C107—81no—
391D4×C107—81no—
392D4×C107—81no—
393D4×C107—81no—
394D4×C107—81no—
395D4×C107—81no—
396D4×C107—84no—
397D4×C107—82no—
398D4×C107—82no—
399C2×C4×C107—22no—
400C2×C4×C107—21no—
401C2×C4×C107—21no—
402C2×C4×C107—21no—
403C2×C4×C107—21no—
404C2×C4×C107—21no—
405C2×C4×C107—21no—
406C2×C4×C107—21no—
407C2×C4×C107—21no—
408C2×C4×C107—21no—
409C2×C4×C107—21no—
410C2×C4×C107—41no—
411C2×C4×C107—41no—
412C2×C4×C107—41no—
413C2×C4×C107—41no—
414C2×C4×C107—41no—
415C2×C4×C107—41no—
416C2×C4×C107—41no—
417C2×C4×C107—41no—
418C2×C4×C107—41no—
419C2×C4×C107—41no—
420C2×C4×C107—41no—
421C2×C4×C107—41no—
422C2×C4×C107—41no—
423C2×C4×C107—41no—
424C2×C4×C107—41no—
425C2×C4×C107—41no—
426C2×C4×C107—81no—
427C2×C4×C107—81no—
428C2×C4×C107—81no—
429C2×C4×C107—81no—
430C2×C4×C107—81no—
431C2×C4×C107—81no—
432C2×C4×C107—81no—
433C2×C4×C107#12011yescharacteristic
434C2×C4×C107#12011yescharacteristic
435C2×C4×C107C22×D411yescharacteristic
436C2×C4×C107C22×D411yescharacteristic
437C8×C107—41no—
438C8×C107—41no—
439C8×C107—41no—
440C8×C107—41no—
441C22×C107—21no—
442C22×C107—21no—
443C22×C107—21no—
444C22×C107—21no—
445C22×C107—21no—
446C22×C107—21no—
447C22×C107—21no—
448C22×C107—21no—
449C22×C107—41no—
450C22×C107—41no—
451C22×C107—41no—
452C22×C107—41no—
453C22×C107—41no—
454C22×C107—41no—
455C22×C107—41no—
456C22×C107—41no—
457C22×C107—41no—
458C22×C107—41no—
459C22×C107—41no—
460C22×C107—41no—
461C22×C107—81no—
462C22×C107—81no—
463C22×C107—81no—
464C22×C107—81no—
465C22×C107—81no—
466C22×C107—81no—
467C22×C107—81no—
468C22×C107—81no—
469C22×C107—81no—
470C22×C107—81no—
471C22×C107—81no—
472C22×C107—162no—
473C22×C107—162no—
474C22×C107C2×#12011yescharacteristic
475C22×C107#57611yescharacteristic
476C22×C107#57611yescharacteristic
477C4×C107—21no—
478C4×C107—21no—
479C4×C107—21no—
480C4×C107—21no—
481C4×C107—42no—
482C4×C107—41no—
483C4×C107—41no—
484C4×C107—41no—
485C4×C107—41no—
486C4×C107—41no—
487C4×C107—41no—
488C4×C107—41no—
489C4×C107—41no—
490C4×C107—81no—
491C4×C107—81no—
492#18414C10711yesmaximal, characteristic, direct product factor, Sylow
493C2×C107—21no—
494C2×C107—21no—
495C2×C107—41no—
496C2×C107—41no—
497C2×C107—81no—
498C2×C107—81no—
499C2×C107—81no—
500C2×C107—81no—
501C2×C107—161no—
502C2×C107#300811yescharacteristic
503C2×C107#301811yescharacteristic
504C2×C107#302611yescharacteristic
505#3534C2×C10711yescharacteristic, complemented
506#3194C2×C10711yescharacteristic, complemented
507#3186C2×C10711yescharacteristic, complemented
508#2661C2×C10711yescharacteristic, complemented
509#1612C2×C10711yescharacteristic, complemented
510#1610C2×C10711yescharacteristic, complemented
511#1609C2×C10711yescharacteristic, complemented
512#1607C2×C10711yescharacteristic, complemented
513#1600C2×C10711yescharacteristic, complemented
514#1598C2×C10711yescharacteristic, complemented
515#1597C2×C10711yescharacteristic, complemented
516#1595C2×C10711yescharacteristic, complemented
517#1507C2×C10711yescharacteristic, complemented
518#1501C2×C10711yescharacteristic, complemented
519#1468C2×C10711yescharacteristic, complemented
520C107#1841411yescharacteristic, direct product factor, Sylow
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C10711yescharacteristic
532#538—21no—
533#538C22×C10711yescharacteristic
534#537C22×C10711yescharacteristic
535#534—21no—
536#534C22×C10711yescharacteristic
537#525C22×C10711yescharacteristic
538C2×#123C22×C10711yescharacteristic
539C2×#121C22×C10711yescharacteristic
540C2×#121C22×C10711yescharacteristic, complemented
541#483C22×C10711yescharacteristic, complemented
542#482—21no—
543#480—21no—
544#480C22×C10711yescharacteristic
545#480C22×C10711yescharacteristic, complemented
546#480C22×C10711yescharacteristic, complemented
547#469—21no—
548#468—21no—
549#466—21no—
550#466—21no—
551#450C22×C10711yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C10711yescharacteristic
555#447C22×C10711yescharacteristic, complemented
556#447C22×C10711yescharacteristic, complemented
557#407C22×C10711yescharacteristic, complemented
558C2×C22⋊C8C22×C10711yescharacteristic, complemented
559#398C22×C10711yescharacteristic, complemented
560#397C22×C10711yescharacteristic, complemented
561#394—21no—
562#394C22×C10711yescharacteristic, complemented
563#392—21no—
564#392C22×C10711yescharacteristic, complemented
565#390—21no—
566#388—21no—
567C4×C22⋊C4C22×C10711yescharacteristic, complemented
568#328C22×C10711yescharacteristic, complemented
569#328C22×C10711yescharacteristic, complemented
570#327C22×C10711yescharacteristic
571#327C22×C10711yescharacteristic
572#327C22×C10711yescharacteristic, complemented
573#327C22×C10711yescharacteristic, complemented
574#327C22×C10711yescharacteristic, complemented
575#327C22×C10711yescharacteristic, complemented
576#324C22×C10711yescharacteristic, complemented
577#324C22×C10711yescharacteristic, complemented
578#323C22×C10711yescharacteristic, complemented
579#323C22×C10711yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C10711yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C10711yescharacteristic
588C22×D4D4×C10711yescharacteristic, complemented
589C22×D4C23×C10711yescharacteristic
590C23×C4C23×C10711yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C10711yescharacteristic, complemented
627C22⋊Q8C23×C10711yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C10711yescharacteristic, complemented
648#121D4×C10711yescharacteristic, complemented
649#121D4×C10711yescharacteristic, complemented
650#121C23×C10711yescharacteristic
651#121C23×C10711yescharacteristic
652#121C23×C10711yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C10711yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C10711yescharacteristic
673C2×C4⋊C4D4×C10711yescharacteristic, complemented
674C2×C4⋊C4C23×C10711yescharacteristic
675C2×C4⋊C4C23×C10711yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C10711yescharacteristic
686C2×C22⋊C4D4×C10711yescharacteristic
687C2×C22⋊C4C23×C10711yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C10711yescharacteristic
704C22⋊C8C23×C10711yescharacteristic
705C22⋊C8C23×C10711yescharacteristic
706C22⋊C8C23×C10711yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C10711yescharacteristic
710#95C23×C10711yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C10711yescharacteristic
715C24C2×D4×C10711yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C10711yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C10711yescharacteristic
756C2×D4C2×D4×C10711yescharacteristic
757C2×D4C2×D4×C10711yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C10711yescharacteristic
770C22×C4C2×D4×C10711yescharacteristic
771C22×C4C2×D4×C10711yescharacteristic
772C22×C4C2×D4×C10711yescharacteristic
773C22×C4C2×D4×C10711yescharacteristic
774C22×C4C2×D4×C10711yescharacteristic
775C22×C4C2×D4×C10711yescharacteristic
776C22×C4C2×D4×C10711yescharacteristic
777C22×C4C24×C10711yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C10711yescharacteristic
805C4⋊C4C2×D4×C10711yescharacteristic
806C4⋊C4C2×D4×C10711yescharacteristic
807C4⋊C4C2×D4×C10711yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C10711yescharacteristic
870C23#120×C10711yescharacteristic
871C23C22×D4×C10711yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C10711yescharacteristic
939C2×C4#120×C10711yescharacteristic
940C2×C4C22×D4×C10711yescharacteristic
941C2×C4C22×D4×C10711yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C10711yescharacteristic
980C22#576×C10711yescharacteristic
981C22#576×C10711yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C107×#300811yescharacteristic
1007C2C107×#301811yescharacteristic
1008C2C107×#302611yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3534C2semidirect
2. C107×#3194C2semidirect
3. C107×#3186C2semidirect
4. C107×#2661C2semidirect
5. C107×#1612C2semidirect
6. C107×#1610C2semidirect
7. C107×#1609C2semidirect
8. C107×#1607C2semidirect
9. C107×#1600C2semidirect
10. C107×#1598C2semidirect
11. C107×#1597C2semidirect
12. C107×#1595C2semidirect
13. C107×#1507C2semidirect
14. C107×#1501C2semidirect
15. C107×#1468C2semidirect
35. C2×#121×C107C22semidirect
36. #483×C107C22semidirect
40. #480×C107C22semidirect
41. #480×C107C22semidirect
46. #450×C107C22semidirect
50. #447×C107C22semidirect
51. #447×C107C22semidirect
52. #407×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
54. #398×C107C22semidirect
55. #397×C107C22semidirect
57. #394×C107C22semidirect
59. #392×C107C22semidirect
62. C4×C22⋊C4×C107C22semidirect
63. #328×C107C22semidirect
64. #328×C107C22semidirect
67. #327×C107C22semidirect
68. #327×C107C22semidirect
69. #327×C107C22semidirect
70. #327×C107C22semidirect
71. #324×C107C22semidirect
72. #324×C107C22semidirect
73. #323×C107C22semidirect
74. #323×C107C22semidirect
76. C2×#41×C107D4semidirect
83. C22×D4×C107D4semidirect
121. C22⋊Q8×C107D4semidirect
142. #121×C107D4semidirect
143. #121×C107D4semidirect
144. #121×C107D4semidirect
165. #117×C107D4semidirect
168. C2×C4⋊C4×C107D4semidirect
492. #18414C107direct (N × H)
505. #3534C2×C107semidirect
506. #3194C2×C107semidirect
507. #3186C2×C107semidirect
508. #2661C2×C107semidirect
509. #1612C2×C107semidirect
510. #1610C2×C107semidirect
511. #1609C2×C107semidirect
512. #1607C2×C107semidirect
513. #1600C2×C107semidirect
514. #1598C2×C107semidirect
515. #1597C2×C107semidirect
516. #1595C2×C107semidirect
517. #1507C2×C107semidirect
518. #1501C2×C107semidirect
519. #1468C2×C107semidirect
520. C107#18414direct (N × H)
540. C2×#121C22×C107semidirect
541. #483C22×C107semidirect
545. #480C22×C107semidirect
546. #480C22×C107semidirect
551. #450C22×C107semidirect
555. #447C22×C107semidirect
556. #447C22×C107semidirect
557. #407C22×C107semidirect
558. C2×C22⋊C8C22×C107semidirect
559. #398C22×C107semidirect
560. #397C22×C107semidirect
562. #394C22×C107semidirect
564. #392C22×C107semidirect
567. C4×C22⋊C4C22×C107semidirect
568. #328C22×C107semidirect
569. #328C22×C107semidirect
572. #327C22×C107semidirect
573. #327C22×C107semidirect
574. #327C22×C107semidirect
575. #327C22×C107semidirect
576. #324C22×C107semidirect
577. #324C22×C107semidirect
578. #323C22×C107semidirect
579. #323C22×C107semidirect
581. C2×#41D4×C107semidirect
588. C22×D4D4×C107semidirect
626. C22⋊Q8D4×C107semidirect
647. #121D4×C107semidirect
648. #121D4×C107semidirect
649. #121D4×C107semidirect
670. #117D4×C107semidirect
673. C2×C4⋊C4D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35342
C107×#31942
C107×#31862
C107×#26612
C107×#16122
C107×#16102
C107×#16092
C107×#16072
C107×#16002
C107×#15982
C107×#15972
C107×#15952
C107×#15072
C107×#15012
C107×#14682
#18414107