Finite Group Databasebeta

← C107×#18415 #41044379

Subgroups — C107×#18415 #41044379

Order 27392.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3534C211yesmaximal, characteristic
2C107×#3196C211yesmaximal, characteristic, complemented
3C107×#3187C211yesmaximal, characteristic, complemented
4C107×#2663C211yesmaximal, characteristic, complemented
5C107×#1618C211yesmaximal, characteristic, complemented
6C107×#1616C211yesmaximal, characteristic, complemented
7C107×#1615C211yesmaximal, characteristic, complemented
8C107×#1613C211yesmaximal, characteristic, complemented
9C107×#1606C211yesmaximal, characteristic, complemented
10C107×#1604C211yesmaximal, characteristic, complemented
11C107×#1603C211yesmaximal, characteristic, complemented
12C107×#1601C211yesmaximal, 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×C22⋊Q8×C107C2211yescharacteristic, complemented
35C2×#121×C107C2211yescharacteristic
36#485×C107—21no—
37#484×C107C2211yescharacteristic, complemented
38#483×C107—21no—
39#481×C107C2211yescharacteristic
40#481×C107C2211yescharacteristic, complemented
41#481×C107C2211yescharacteristic, complemented
42#470×C107—21no—
43#468×C107—21no—
44#465×C107—21no—
45#465×C107—21no—
46#452×C107—21no—
47#451×C107C2211yescharacteristic, complemented
48#450×C107—21no—
49#448×C107C2211yescharacteristic
50#448×C107C2211yescharacteristic, complemented
51#448×C107C2211yescharacteristic, complemented
52#407×C107C2211yescharacteristic, complemented
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54#400×C107C2211yescharacteristic, complemented
55#399×C107C2211yescharacteristic, complemented
56#397×C107—21no—
57#395×C107C2211yescharacteristic, complemented
58#394×C107—21no—
59#393×C107C2211yescharacteristic, complemented
60#389×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
77C22×Q8×C107C2311yescharacteristic
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107D411yescharacteristic
82C22×D4×C107D411yescharacteristic
83C23×C4×C107C2311yescharacteristic
84C2×Q16×C107—21no—
85C2×SD16×C107—21no—
86C2×SD16×C107—21no—
87C2×SD16×C107—21no—
88C2×M16×C107—21no—
89C22×C8×C107—21no—
90#127×C107—21no—
91#126×C107—21no—
92#126×C107—21no—
93#126×C107—21no—
94#126×C107—21no—
95#125×C107—21no—
96#125×C107—21no—
97#124×C107—21no—
98#124×C107—21no—
99#124×C107—21no—
100#123×C107—21no—
101#123×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—
114C22⋊Q8×C107—21no—
115C22⋊Q8×C107—21no—
116C22⋊Q8×C107—21no—
117C22⋊Q8×C107—21no—
118C22⋊Q8×C107—21no—
119C22⋊Q8×C107—21no—
120C22⋊Q8×C107—21no—
121C22⋊Q8×C107—21no—
122C22⋊Q8×C107—21no—
123C22⋊Q8×C107D411yescharacteristic
124C22⋊Q8×C107C2311yescharacteristic
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×C107D411yescharacteristic
141#121×C107D411yescharacteristic
142#121×C107D411yescharacteristic
143#121×C107C2311yescharacteristic
144#121×C107C2311yescharacteristic
145#121×C107C2311yescharacteristic
146#120×C107—21no—
147#120×C107—21no—
148#120×C107—21no—
149#120×C107—21no—
150#120×C107—21no—
151#120×C107—21no—
152#120×C107—21no—
153#120×C107—21no—
154C4×D4×C107—21no—
155C4×D4×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—
162#117×C107—21no—
163#117×C107D411yescharacteristic
164C2×C4⋊C4×C107—21no—
165C2×C4⋊C4×C107—21no—
166C2×C4⋊C4×C107—21no—
167C2×C4⋊C4×C107D411yescharacteristic
168C2×C4⋊C4×C107D411yescharacteristic
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×C107D411yescharacteristic
179C2×C22⋊C4×C107D411yescharacteristic
180C2×C22⋊C4×C107C2311yescharacteristic
181C2×C42×C107—21no—
182#107×C107—21no—
183#106×C107—21no—
184#106×C107—21no—
185#106×C107—21no—
186#103×C107—21no—
187#103×C107—21no—
188#103×C107—21no—
189#103×C107—21no—
190#103×C107—21no—
191#102×C107—21no—
192#102×C107—21no—
193#102×C107—21no—
194C22⋊C8×C107—21no—
195C22⋊C8×C107—21no—
196C22⋊C8×C107C2311yescharacteristic
197C22⋊C8×C107C2311yescharacteristic
198C22⋊C8×C107C2311yescharacteristic
199C22⋊C8×C107C2311yescharacteristic
200#95×C107—21no—
201#95×C107—21no—
202#95×C107—21no—
203#95×C107—21no—
204#95×C107C2311yescharacteristic
205#95×C107C2311yescharacteristic
206C24×C107—21no—
207C24×C107—21no—
208C24×C107C2×D411yescharacteristic
209C24×C107C2×D411yescharacteristic
210#41×C107—81no—
211#41×C107—81no—
212#41×C107—81no—
213C2×Q8×C107—21no—
214C2×Q8×C107—21no—
215C2×Q8×C107—21no—
216C2×Q8×C107—81no—
217C2×Q8×C107C2×D411yescharacteristic
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—81no—
236C2×D4×C107—81no—
237C2×D4×C107—81no—
238C2×D4×C107—81no—
239C2×D4×C107—81no—
240C2×D4×C107—81no—
241C2×D4×C107—82no—
242C2×D4×C107C2×D411yescharacteristic
243C2×D4×C107C2×D411yescharacteristic
244C2×D4×C107C2×D411yescharacteristic
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—21no—
249C22×C4×C107—21no—
250C22×C4×C107—21no—
251C22×C4×C107—21no—
252C22×C4×C107—21no—
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—81no—
257C22×C4×C107C2×D411yescharacteristic
258C22×C4×C107C2×D411yescharacteristic
259C22×C4×C107C2×D411yescharacteristic
260C22×C4×C107C2×D411yescharacteristic
261C22×C4×C107C2×D411yescharacteristic
262C22×C4×C107C2×D411yescharacteristic
263C22×C4×C107C2×D411yescharacteristic
264C22×C4×C107C2×D411yescharacteristic
265C22×C4×C107C2411yescharacteristic
266Q16×C107—81no—
267SD16×C107—81no—
268SD16×C107—81no—
269SD16×C107—81no—
270M16×C107—81no—
271C2×C8×C107—21no—
272C2×C8×C107—21no—
273C2×C8×C107—21no—
274C2×C8×C107—21no—
275C2×C8×C107—81no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—21no—
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×C107—21no—
289C4⋊C4×C107—21no—
290C4⋊C4×C107—21no—
291C4⋊C4×C107—42no—
292C4⋊C4×C107—41no—
293C4⋊C4×C107—41no—
294C4⋊C4×C107—81no—
295C4⋊C4×C107C2×D411yescharacteristic
296C4⋊C4×C107C2×D411yescharacteristic
297C4⋊C4×C107C2×D411yescharacteristic
298C4⋊C4×C107C2×D411yescharacteristic
299C22⋊C4×C107—21no—
300C22⋊C4×C107—21no—
301C22⋊C4×C107—21no—
302C22⋊C4×C107—21no—
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—42no—
325C22⋊C4×C107—42no—
326C22⋊C4×C107—41no—
327C22⋊C4×C107—41no—
328C22⋊C4×C107—81no—
329C42×C107—21no—
330C42×C107—21no—
331C42×C107—21no—
332C42×C107—81no—
333C23×C107—21no—
334C23×C107—21no—
335C23×C107—21no—
336C23×C107—21no—
337C23×C107—21no—
338C23×C107—21no—
339C23×C107—21no—
340C23×C107—21no—
341C23×C107—41no—
342C23×C107—41no—
343C23×C107—42no—
344C23×C107—41no—
345C23×C107—41no—
346C23×C107—81no—
347C23×C107—81no—
348C23×C107—81no—
349C23×C107—81no—
350C23×C107—81no—
351C23×C107#12011yescharacteristic
352C23×C107#12011yescharacteristic
353C23×C107C22×D411yescharacteristic
354Q8×C107—41no—
355Q8×C107—41no—
356Q8×C107—41no—
357Q8×C107—41no—
358Q8×C107—41no—
359Q8×C107—81no—
360D4×C107—41no—
361D4×C107—41no—
362D4×C107—41no—
363D4×C107—42no—
364D4×C107—42no—
365D4×C107—41no—
366D4×C107—41no—
367D4×C107—41no—
368D4×C107—41no—
369D4×C107—41no—
370D4×C107—41no—
371D4×C107—81no—
372D4×C107—81no—
373D4×C107—81no—
374D4×C107—81no—
375D4×C107—81no—
376D4×C107—81no—
377D4×C107—81no—
378D4×C107—81no—
379D4×C107—81no—
380D4×C107—81no—
381D4×C107—81no—
382D4×C107—81no—
383C2×C4×C107—22no—
384C2×C4×C107—21no—
385C2×C4×C107—21no—
386C2×C4×C107—21no—
387C2×C4×C107—21no—
388C2×C4×C107—21no—
389C2×C4×C107—21no—
390C2×C4×C107—21no—
391C2×C4×C107—21no—
392C2×C4×C107—21no—
393C2×C4×C107—21no—
394C2×C4×C107—41no—
395C2×C4×C107—41no—
396C2×C4×C107—41no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—41no—
402C2×C4×C107—41no—
403C2×C4×C107—41no—
404C2×C4×C107—41no—
405C2×C4×C107—41no—
406C2×C4×C107—41no—
407C2×C4×C107—41no—
408C2×C4×C107—41no—
409C2×C4×C107—41no—
410C2×C4×C107—41no—
411C2×C4×C107—41no—
412C2×C4×C107—41no—
413C2×C4×C107—81no—
414C2×C4×C107—81no—
415C2×C4×C107—81no—
416C2×C4×C107—81no—
417C2×C4×C107—81no—
418C2×C4×C107—81no—
419C2×C4×C107—81no—
420C2×C4×C107#12011yescharacteristic
421C2×C4×C107#12011yescharacteristic
422C2×C4×C107C22×D411yescharacteristic
423C2×C4×C107C22×D411yescharacteristic
424C8×C107—41no—
425C8×C107—41no—
426C8×C107—41no—
427C8×C107—41no—
428C22×C107—21no—
429C22×C107—21no—
430C22×C107—21no—
431C22×C107—21no—
432C22×C107—21no—
433C22×C107—21no—
434C22×C107—21no—
435C22×C107—21no—
436C22×C107—41no—
437C22×C107—41no—
438C22×C107—41no—
439C22×C107—41no—
440C22×C107—41no—
441C22×C107—41no—
442C22×C107—41no—
443C22×C107—41no—
444C22×C107—41no—
445C22×C107—41no—
446C22×C107—41no—
447C22×C107—41no—
448C22×C107—81no—
449C22×C107—81no—
450C22×C107—81no—
451C22×C107—81no—
452C22×C107—162no—
453C22×C107—162no—
454C22×C107C2×#12011yescharacteristic
455C22×C107#57711yescharacteristic
456C22×C107#57711yescharacteristic
457C4×C107—21no—
458C4×C107—21no—
459C4×C107—21no—
460C4×C107—21no—
461C4×C107—42no—
462C4×C107—41no—
463C4×C107—41no—
464C4×C107—41no—
465C4×C107—41no—
466C4×C107—41no—
467C4×C107—41no—
468C4×C107—41no—
469C4×C107—41no—
470C4×C107—81no—
471C4×C107—81no—
472C4×C107—81no—
473#18415C10711yesmaximal, characteristic, direct product factor, Sylow
474C2×C107—21no—
475C2×C107—21no—
476C2×C107—41no—
477C2×C107—41no—
478C2×C107—81no—
479C2×C107—81no—
480C2×C107—81no—
481C2×C107—81no—
482C2×C107#300911yescharacteristic
483C2×C107#301811yescharacteristic
484C2×C107#302611yescharacteristic
485#3534C2×C10711yescharacteristic
486#3196C2×C10711yescharacteristic, complemented
487#3187C2×C10711yescharacteristic, complemented
488#2663C2×C10711yescharacteristic, complemented
489#1618C2×C10711yescharacteristic, complemented
490#1616C2×C10711yescharacteristic, complemented
491#1615C2×C10711yescharacteristic, complemented
492#1613C2×C10711yescharacteristic, complemented
493#1606C2×C10711yescharacteristic, complemented
494#1604C2×C10711yescharacteristic, complemented
495#1603C2×C10711yescharacteristic, complemented
496#1601C2×C10711yescharacteristic, complemented
497#1507C2×C10711yescharacteristic, complemented
498#1501C2×C10711yescharacteristic, complemented
499#1468C2×C10711yescharacteristic, complemented
500C107#1841511yescharacteristic, direct product factor, Sylow
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C10711yescharacteristic
512#538—21no—
513#538C22×C10711yescharacteristic
514#537C22×C10711yescharacteristic
515#534—21no—
516#534C22×C10711yescharacteristic
517#525C22×C10711yescharacteristic
518C2×#123C22×C10711yescharacteristic
519C2×C22⋊Q8C22×C10711yescharacteristic, complemented
520C2×#121C22×C10711yescharacteristic
521#485—21no—
522#484C22×C10711yescharacteristic, complemented
523#483—21no—
524#481C22×C10711yescharacteristic
525#481C22×C10711yescharacteristic, complemented
526#481C22×C10711yescharacteristic, complemented
527#470—21no—
528#468—21no—
529#465—21no—
530#465—21no—
531#452—21no—
532#451C22×C10711yescharacteristic, complemented
533#450—21no—
534#448C22×C10711yescharacteristic
535#448C22×C10711yescharacteristic, complemented
536#448C22×C10711yescharacteristic, complemented
537#407C22×C10711yescharacteristic, complemented
538C2×C22⋊C8C22×C10711yescharacteristic, complemented
539#400C22×C10711yescharacteristic, complemented
540#399C22×C10711yescharacteristic, complemented
541#397—21no—
542#395C22×C10711yescharacteristic, complemented
543#394—21no—
544#393C22×C10711yescharacteristic, complemented
545#389—21no—
546#388—21no—
547C4×C22⋊C4C22×C10711yescharacteristic, complemented
548#328C22×C10711yescharacteristic, complemented
549#328C22×C10711yescharacteristic, complemented
550#327C22×C10711yescharacteristic
551#327C22×C10711yescharacteristic
552#327C22×C10711yescharacteristic, complemented
553#327C22×C10711yescharacteristic, complemented
554#327C22×C10711yescharacteristic, complemented
555#327C22×C10711yescharacteristic, complemented
556#324C22×C10711yescharacteristic, complemented
557#324C22×C10711yescharacteristic, complemented
558#323C22×C10711yescharacteristic, complemented
559#323C22×C10711yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C10711yescharacteristic
562C22×Q8C23×C10711yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C10711yescharacteristic
567C22×D4D4×C10711yescharacteristic
568C23×C4C23×C10711yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C10711yescharacteristic
609C22⋊Q8C23×C10711yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C10711yescharacteristic
626#121D4×C10711yescharacteristic
627#121D4×C10711yescharacteristic
628#121C23×C10711yescharacteristic
629#121C23×C10711yescharacteristic
630#121C23×C10711yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C10711yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C10711yescharacteristic
653C2×C4⋊C4D4×C10711yescharacteristic
654C2×C4⋊C4C23×C10711yescharacteristic
655C2×C4⋊C4C23×C10711yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C10711yescharacteristic
664C2×C22⋊C4D4×C10711yescharacteristic
665C2×C22⋊C4C23×C10711yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C10711yescharacteristic
682C22⋊C8C23×C10711yescharacteristic
683C22⋊C8C23×C10711yescharacteristic
684C22⋊C8C23×C10711yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C10711yescharacteristic
690#95C23×C10711yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C10711yescharacteristic
694C24C2×D4×C10711yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C10711yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C10711yescharacteristic
728C2×D4C2×D4×C10711yescharacteristic
729C2×D4C2×D4×C10711yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C10711yescharacteristic
743C22×C4C2×D4×C10711yescharacteristic
744C22×C4C2×D4×C10711yescharacteristic
745C22×C4C2×D4×C10711yescharacteristic
746C22×C4C2×D4×C10711yescharacteristic
747C22×C4C2×D4×C10711yescharacteristic
748C22×C4C2×D4×C10711yescharacteristic
749C22×C4C2×D4×C10711yescharacteristic
750C22×C4C24×C10711yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C10711yescharacteristic
781C4⋊C4C2×D4×C10711yescharacteristic
782C4⋊C4C2×D4×C10711yescharacteristic
783C4⋊C4C2×D4×C10711yescharacteristic
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C10711yescharacteristic
837C23#120×C10711yescharacteristic
838C23C22×D4×C10711yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C10711yescharacteristic
906C2×C4#120×C10711yescharacteristic
907C2×C4C22×D4×C10711yescharacteristic
908C2×C4C22×D4×C10711yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C10711yescharacteristic
940C22#577×C10711yescharacteristic
941C22#577×C10711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C107×#300911yescharacteristic
967C2C107×#301811yescharacteristic
968C2C107×#302611yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3534C2
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
2. C107×#3196C2semidirect
3. C107×#3187C2semidirect
4. C107×#2663C2semidirect
5. C107×#1618C2semidirect
6. C107×#1616C2semidirect
7. C107×#1615C2semidirect
8. C107×#1613C2semidirect
9. C107×#1606C2semidirect
10. C107×#1604C2semidirect
11. C107×#1603C2semidirect
12. C107×#1601C2semidirect
13. C107×#1507C2semidirect
14. C107×#1501C2semidirect
15. C107×#1468C2semidirect
34. C2×C22⋊Q8×C107C22semidirect
37. #484×C107C22semidirect
40. #481×C107C22semidirect
41. #481×C107C22semidirect
47. #451×C107C22semidirect
50. #448×C107C22semidirect
51. #448×C107C22semidirect
52. #407×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
54. #400×C107C22semidirect
55. #399×C107C22semidirect
57. #395×C107C22semidirect
59. #393×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
473. #18415C107direct (N × H)
486. #3196C2×C107semidirect
487. #3187C2×C107semidirect
488. #2663C2×C107semidirect
489. #1618C2×C107semidirect
490. #1616C2×C107semidirect
491. #1615C2×C107semidirect
492. #1613C2×C107semidirect
493. #1606C2×C107semidirect
494. #1604C2×C107semidirect
495. #1603C2×C107semidirect
496. #1601C2×C107semidirect
497. #1507C2×C107semidirect
498. #1501C2×C107semidirect
499. #1468C2×C107semidirect
500. C107#18415direct (N × H)
519. C2×C22⋊Q8C22×C107semidirect
522. #484C22×C107semidirect
525. #481C22×C107semidirect
526. #481C22×C107semidirect
532. #451C22×C107semidirect
535. #448C22×C107semidirect
536. #448C22×C107semidirect
537. #407C22×C107semidirect
538. C2×C22⋊C8C22×C107semidirect
539. #400C22×C107semidirect
540. #399C22×C107semidirect
542. #395C22×C107semidirect
544. #393C22×C107semidirect
547. C4×C22⋊C4C22×C107semidirect
548. #328C22×C107semidirect
549. #328C22×C107semidirect
552. #327C22×C107semidirect
553. #327C22×C107semidirect
554. #327C22×C107semidirect
555. #327C22×C107semidirect
556. #324C22×C107semidirect
557. #324C22×C107semidirect
558. #323C22×C107semidirect
559. #323C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35342
C107×#31962
C107×#31872
C107×#26632
C107×#16182
C107×#16162
C107×#16152
C107×#16132
C107×#16062
C107×#16042
C107×#16032
C107×#16012
C107×#15072
C107×#15012
C107×#14682
#18415107