Finite Group Databasebeta

← C107×#18228 #41044192

Subgroups — C107×#18228 #41044192

Order 27392.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3537C211yesmaximal, characteristic, complemented
2C107×#3006C211yesmaximal, characteristic, complemented
3C107×#3002C211yesmaximal, characteristic, complemented
4C107×#2615C211yesmaximal, characteristic, complemented
5C107×#1606C212yesmaximal, complemented
6C107×#1601C212yesmaximal, complemented
7C107×#1600C212yesmaximal, complemented
8C107×#1595C212yesmaximal, complemented
9C107×#1519C211yesmaximal, characteristic, complemented
10C107×#1513C211yesmaximal, characteristic, complemented
11C107×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C107C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C107—21no—
14C2×#135×C107—21no—
15#560×C107—22no—
16#553×C107—21no—
17#553×C107—21no—
18D42×C107—22no—
19D42×C107—21no—
20D42×C107—21no—
21#540×C107—21no—
22#538×C107—21no—
23#538×C107C2212yes—
24#535×C107—21no—
25#534×C107—21no—
26#534×C107C2212yes—
27#525×C107C2211yescharacteristic
28C2×#121×C107—21no—
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic
31#452×C107—21no—
32#451×C107C2211yescharacteristic, complemented
33#450×C107C2211yescharacteristic, complemented
34#449×C107—21no—
35#449×C107—22no—
36#448×C107C2212yescomplemented
37#448×C107C2211yescharacteristic, complemented
38#447×C107C2211yescharacteristic, complemented
39#447×C107C2212yescomplemented
40#417×C107—21no—
41#416×C107—21no—
42#407×C107C2211yescharacteristic, complemented
43C2×C22⋊C8×C107C2211yescharacteristic, complemented
44#393×C107C2212yescomplemented
45#392×C107—22no—
46#392×C107C2212yescomplemented
47#380×C107—21no—
48#380×C107C2211yescharacteristic, complemented
49#328×C107C2212yescomplemented
50#327×C107C2212yescomplemented
51#327×C107C2212yescomplemented
52#327×C107C2212yescomplemented
53#323×C107C2212yescomplemented
54#323×C107C2212yescomplemented
55C2×#41×C107—21no—
56C2×#41×C107—21no—
57C2×#41×C107—21no—
58C2×#41×C107—21no—
59C2×#41×C107—44no—
60C2×#41×C107D411yescharacteristic, complemented
61C22×Q8×C107C2311yescharacteristic
62C22×D4×C107—22no—
63C22×D4×C107—21no—
64C22×D4×C107—21no—
65C22×D4×C107—22no—
66C22×D4×C107—21no—
67C22×D4×C107—22no—
68C22×D4×C107D411yescharacteristic
69C22×D4×C107D412yes—
70C22×D4×C107D411yescharacteristic, complemented
71C22×D4×C107C2311yescharacteristic
72C23×C4×C107—21no—
73C23×C4×C107C2311yescharacteristic
74AGL(1,ℤ/8)×C107—44no—
75#135×C107—44no—
76C2×Q16×C107—21no—
77C2×SD16×C107—21no—
78C2×SD16×C107—21no—
79C2×SD16×C107—22no—
80C2×D8×C107—21no—
81C2×D8×C107—22no—
82C2×M16×C107—21no—
83C22×C8×C107—21no—
84#127×C107—22no—
85#127×C107—21no—
86#126×C107—22no—
87#126×C107—22no—
88#125×C107—21no—
89#124×C107—22no—
90#123×C107—22no—
91#123×C107—21no—
92#123×C107—22no—
93#123×C107—22no—
94#123×C107—22no—
95C22⋊Q8×C107D411yescharacteristic, complemented
96C22⋊Q8×C107C2311yescharacteristic
97#121×C107—22no—
98#121×C107—21no—
99#121×C107—21no—
100#121×C107—22no—
101#121×C107—22no—
102#121×C107—22no—
103#121×C107—22no—
104#121×C107—21no—
105#121×C107—21no—
106#121×C107—21no—
107#121×C107—21no—
108#121×C107—21no—
109#121×C107—21no—
110#121×C107—22no—
111#121×C107—44no—
112#121×C107D412yescomplemented
113#121×C107D411yescharacteristic, complemented
114#121×C107C2312yes—
115#121×C107C2311yescharacteristic
116#120×C107—22no—
117#120×C107—22no—
118#120×C107—22no—
119#120×C107—21no—
120#120×C107—22no—
121#120×C107—22no—
122#120×C107—22no—
123C4×D4×C107—22no—
124C4×D4×C107—21no—
125C4×D4×C107—21no—
126C4×D4×C107—21no—
127C4×D4×C107—21no—
128C4×D4×C107—22no—
129#117×C107—21no—
130#117×C107D411yescharacteristic, complemented
131C2×C4⋊C4×C107—21no—
132C2×C4⋊C4×C107D411yescharacteristic
133C2×C4⋊C4×C107D411yescharacteristic, complemented
134C2×C22⋊C4×C107—21no—
135C2×C22⋊C4×C107—22no—
136C2×C22⋊C4×C107—21no—
137C2×C22⋊C4×C107—22no—
138C2×C22⋊C4×C107C2312yes—
139#103×C107—21no—
140#103×C107—21no—
141#103×C107—22no—
142#102×C107—21no—
143#102×C107—21no—
144#102×C107—22no—
145C22⋊C8×C107—21no—
146C22⋊C8×C107—21no—
147C22⋊C8×C107C2311yescharacteristic
148C22⋊C8×C107C2311yescharacteristic
149C22⋊C8×C107C2312yes—
150#95×C107—22no—
151#95×C107C2312yes—
152C24×C107—22no—
153C24×C107—21no—
154C24×C107—21no—
155C24×C107C2×D412yes—
156C24×C107C2×D411yescharacteristic
157#41×C107—24no—
158#41×C107—24no—
159#41×C107—42no—
160#41×C107—42no—
161#41×C107—42no—
162#41×C107—42no—
163#41×C107—42no—
164#41×C107—42no—
165#41×C107—42no—
166C2×Q8×C107—21no—
167C2×Q8×C107—21no—
168C2×Q8×C107—42no—
169C2×Q8×C107C2×D411yescharacteristic
170C2×D4×C107—22no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—22no—
174C2×D4×C107—22no—
175C2×D4×C107—22no—
176C2×D4×C107—22no—
177C2×D4×C107—22no—
178C2×D4×C107—22no—
179C2×D4×C107—21no—
180C2×D4×C107—22no—
181C2×D4×C107—22no—
182C2×D4×C107—21no—
183C2×D4×C107—21no—
184C2×D4×C107—21no—
185C2×D4×C107—21no—
186C2×D4×C107—21no—
187C2×D4×C107—42no—
188C2×D4×C107—42no—
189C2×D4×C107—42no—
190C2×D4×C107—42no—
191C2×D4×C107—42no—
192C2×D4×C107—41no—
193C2×D4×C107—41no—
194C2×D4×C107—44no—
195C2×D4×C107—82no—
196C2×D4×C107—82no—
197C2×D4×C107—82no—
198C2×D4×C107—82no—
199C2×D4×C107—81no—
200C2×D4×C107—81no—
201C2×D4×C107—82no—
202C2×D4×C107—82no—
203C2×D4×C107—84no—
204C2×D4×C107C2×D411yescharacteristic
205C2×D4×C107C2×D412yes—
206C22×C4×C107—24no—
207C22×C4×C107—21no—
208C22×C4×C107—22no—
209C22×C4×C107—22no—
210C22×C4×C107—21no—
211C22×C4×C107—21no—
212C22×C4×C107—22no—
213C22×C4×C107—42no—
214C22×C4×C107—42no—
215C22×C4×C107—41no—
216C22×C4×C107—41no—
217C22×C4×C107C2×D411yescharacteristic
218C22×C4×C107C2×D411yescharacteristic
219C22×C4×C107C2×D411yescharacteristic
220C22×C4×C107C2×D412yes—
221C22×C4×C107C2×D411yescharacteristic
222C22×C4×C107C2×D411yescharacteristic
223C22×C4×C107C2411yescharacteristic
224Q16×C107—42no—
225SD16×C107—42no—
226SD16×C107—42no—
227SD16×C107—44no—
228D8×C107—42no—
229D8×C107—44no—
230M16×C107—42no—
231C2×C8×C107—21no—
232C2×C8×C107—21no—
233C2×C8×C107—22no—
234C2×C8×C107—42no—
235C4⋊C4×C107—22no—
236C4⋊C4×C107—22no—
237C4⋊C4×C107—21no—
238C4⋊C4×C107—21no—
239C4⋊C4×C107—21no—
240C4⋊C4×C107—21no—
241C4⋊C4×C107—21no—
242C4⋊C4×C107—42no—
243C4⋊C4×C107C2×D412yes—
244C4⋊C4×C107C2×D411yescharacteristic
245C4⋊C4×C107C2×D411yescharacteristic
246C22⋊C4×C107—22no—
247C22⋊C4×C107—22no—
248C22⋊C4×C107—22no—
249C22⋊C4×C107—22no—
250C22⋊C4×C107—22no—
251C22⋊C4×C107—21no—
252C22⋊C4×C107—21no—
253C22⋊C4×C107—21no—
254C22⋊C4×C107—22no—
255C22⋊C4×C107—21no—
256C22⋊C4×C107—22no—
257C22⋊C4×C107—22no—
258C22⋊C4×C107—22no—
259C22⋊C4×C107—21no—
260C22⋊C4×C107—44no—
261C22⋊C4×C107—81no—
262C22⋊C4×C107—82no—
263C42×C107—22no—
264C42×C107—21no—
265C23×C107—21no—
266C23×C107—21no—
267C23×C107—22no—
268C23×C107—22no—
269C23×C107—22no—
270C23×C107—21no—
271C23×C107—22no—
272C23×C107—22no—
273C23×C107—41no—
274C23×C107—41no—
275C23×C107—41no—
276C23×C107—41no—
277C23×C107—41no—
278C23×C107—42no—
279C23×C107—42no—
280C23×C107—42no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—81no—
285C23×C107—81no—
286C23×C107—82no—
287C23×C107—82no—
288C23×C107—82no—
289C23×C107#12011yescharacteristic
290C23×C107#12011yescharacteristic
291C23×C107C22×D411yescharacteristic
292Q8×C107—22no—
293Q8×C107—22no—
294Q8×C107—41no—
295Q8×C107—41no—
296Q8×C107—41no—
297D4×C107—22no—
298D4×C107—22no—
299D4×C107—42no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—41no—
303D4×C107—44no—
304D4×C107—42no—
305D4×C107—44no—
306D4×C107—44no—
307D4×C107—42no—
308D4×C107—41no—
309D4×C107—42no—
310D4×C107—41no—
311D4×C107—42no—
312D4×C107—42no—
313D4×C107—81no—
314D4×C107—82no—
315D4×C107—82no—
316D4×C107—81no—
317D4×C107—82no—
318D4×C107—82no—
319D4×C107—82no—
320D4×C107—82no—
321D4×C107—82no—
322D4×C107—88no—
323C2×C4×C107—22no—
324C2×C4×C107—22no—
325C2×C4×C107—22no—
326C2×C4×C107—22no—
327C2×C4×C107—21no—
328C2×C4×C107—22no—
329C2×C4×C107—22no—
330C2×C4×C107—21no—
331C2×C4×C107—21no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—44no—
336C2×C4×C107—41no—
337C2×C4×C107—41no—
338C2×C4×C107—44no—
339C2×C4×C107—42no—
340C2×C4×C107—42no—
341C2×C4×C107—42no—
342C2×C4×C107—42no—
343C2×C4×C107—42no—
344C2×C4×C107—81no—
345C2×C4×C107—82no—
346C2×C4×C107—82no—
347C2×C4×C107#12011yescharacteristic
348C2×C4×C107#12011yescharacteristic
349C2×C4×C107C22×D411yescharacteristic
350C2×C4×C107C22×D411yescharacteristic
351C8×C107—41no—
352C8×C107—41no—
353C8×C107—42no—
354C22×C107—21no—
355C22×C107—21no—
356C22×C107—21no—
357C22×C107—21no—
358C22×C107—21no—
359C22×C107—21no—
360C22×C107—21no—
361C22×C107—21no—
362C22×C107—42no—
363C22×C107—42no—
364C22×C107—42no—
365C22×C107—42no—
366C22×C107—41no—
367C22×C107—42no—
368C22×C107—42no—
369C22×C107—41no—
370C22×C107—42no—
371C22×C107—41no—
372C22×C107—42no—
373C22×C107—42no—
374C22×C107—81no—
375C22×C107—81no—
376C22×C107—82no—
377C22×C107—82no—
378C22×C107—81no—
379C22×C107—81no—
380C22×C107—81no—
381C22×C107—81no—
382C22×C107—162no—
383C22×C107—164no—
384C22×C107C2×#12011yescharacteristic
385C22×C107#57611yescharacteristic
386C22×C107#57711yescharacteristic
387C4×C107—21no—
388C4×C107—21no—
389C4×C107—21no—
390C4×C107—42no—
391C4×C107—41no—
392C4×C107—42no—
393C4×C107—41no—
394C4×C107—42no—
395C4×C107—41no—
396C4×C107—82no—
397C4×C107B(4,𝔽2)12yes—
398#18228C10711yesmaximal, characteristic, direct product factor, Sylow
399C2×C107—21no—
400C2×C107—21no—
401C2×C107—41no—
402C2×C107—41no—
403C2×C107—82no—
404C2×C107—82no—
405C2×C107—82no—
406C2×C107—81no—
407C2×C107#301211yescharacteristic
408C2×C107#301911yescharacteristic
409C2×C107C2×B(4,𝔽2)11yescharacteristic
410#3537C2×C10711yescharacteristic, complemented
411#3006C2×C10711yescharacteristic, complemented
412#3002C2×C10711yescharacteristic, complemented
413#2615C2×C10711yescharacteristic, complemented
414#1606C2×C10712yescomplemented
415#1601C2×C10712yescomplemented
416#1600C2×C10712yescomplemented
417#1595C2×C10712yescomplemented
418#1519C2×C10711yescharacteristic, complemented
419#1513C2×C10711yescharacteristic, complemented
420#1471C2×C10711yescharacteristic, complemented
421C107#1822811yescharacteristic, direct product factor, Sylow
422C22×#41C22×C10711yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424C2×#135—21no—
425#560—22no—
426#553—21no—
427#553—21no—
428D42—22no—
429D42—21no—
430D42—21no—
431#540—21no—
432#538—21no—
433#538C22×C10712yes—
434#535—21no—
435#534—21no—
436#534C22×C10712yes—
437#525C22×C10711yescharacteristic
438C2×#121—21no—
439C2×#121C22×C10711yescharacteristic
440C2×#121C22×C10711yescharacteristic
441#452—21no—
442#451C22×C10711yescharacteristic, complemented
443#450C22×C10711yescharacteristic, complemented
444#449—21no—
445#449—22no—
446#448C22×C10711yescharacteristic, complemented
447#448C22×C10712yescomplemented
448#447C22×C10711yescharacteristic, complemented
449#447C22×C10712yescomplemented
450#417—21no—
451#416—21no—
452#407C22×C10711yescharacteristic, complemented
453C2×C22⋊C8C22×C10711yescharacteristic, complemented
454#393C22×C10712yescomplemented
455#392—22no—
456#392C22×C10712yescomplemented
457#380—21no—
458#380C22×C10711yescharacteristic, complemented
459#328C22×C10712yescomplemented
460#327C22×C10712yescomplemented
461#327C22×C10712yescomplemented
462#327C22×C10712yescomplemented
463#323C22×C10712yescomplemented
464#323C22×C10712yescomplemented
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C10711yescharacteristic, complemented
471C22×Q8C23×C10711yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C10711yescharacteristic
479C22×D4D4×C10712yes—
480C22×D4D4×C10711yescharacteristic, complemented
481C22×D4C23×C10711yescharacteristic
482C23×C4—21no—
483C23×C4C23×C10711yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C10711yescharacteristic, complemented
506C22⋊Q8C23×C10711yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C10712yescomplemented
523#121D4×C10711yescharacteristic, complemented
524#121C23×C10712yes—
525#121C23×C10711yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C10711yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C10711yescharacteristic
543C2×C4⋊C4D4×C10711yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C10712yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C10711yescharacteristic
558C22⋊C8C23×C10711yescharacteristic
559C22⋊C8C23×C10712yes—
560#95—22no—
561#95C23×C10712yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C10712yes—
566C24C2×D4×C10711yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C10711yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C10711yescharacteristic
615C2×D4C2×D4×C10712yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C10711yescharacteristic
628C22×C4C2×D4×C10711yescharacteristic
629C22×C4C2×D4×C10711yescharacteristic
630C22×C4C2×D4×C10712yes—
631C22×C4C2×D4×C10711yescharacteristic
632C22×C4C2×D4×C10711yescharacteristic
633C22×C4C24×C10711yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C10712yes—
654C4⋊C4C2×D4×C10711yescharacteristic
655C4⋊C4C2×D4×C10711yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C10711yescharacteristic
700C23#120×C10711yescharacteristic
701C23C22×D4×C10711yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C10711yescharacteristic
758C2×C4#120×C10711yescharacteristic
759C2×C4C22×D4×C10711yescharacteristic
760C2×C4C22×D4×C10711yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C10711yescharacteristic
795C22#576×C10711yescharacteristic
796C22#577×C10711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4B(4,𝔽2)×C10712yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C107×#301211yescharacteristic
817C2C107×#301911yescharacteristic
818C2C2×B(4,𝔽2)×C10711yescharacteristic
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×#3537C2semidirect
2. C107×#3006C2semidirect
3. C107×#3002C2semidirect
4. C107×#2615C2semidirect
5. C107×#1606C2semidirect
6. C107×#1601C2semidirect
7. C107×#1600C2semidirect
8. C107×#1595C2semidirect
9. C107×#1519C2semidirect
10. C107×#1513C2semidirect
11. C107×#1471C2semidirect
12. C22×#41×C107C22semidirect
32. #451×C107C22semidirect
33. #450×C107C22semidirect
36. #448×C107C22semidirect
37. #448×C107C22semidirect
38. #447×C107C22semidirect
39. #447×C107C22semidirect
42. #407×C107C22semidirect
43. C2×C22⋊C8×C107C22semidirect
44. #393×C107C22semidirect
46. #392×C107C22semidirect
48. #380×C107C22semidirect
49. #328×C107C22semidirect
50. #327×C107C22semidirect
51. #327×C107C22semidirect
52. #327×C107C22semidirect
53. #323×C107C22semidirect
54. #323×C107C22semidirect
60. C2×#41×C107D4semidirect
70. C22×D4×C107D4semidirect
95. C22⋊Q8×C107D4semidirect
112. #121×C107D4semidirect
113. #121×C107D4semidirect
130. #117×C107D4semidirect
133. C2×C4⋊C4×C107D4semidirect
398. #18228C107direct (N × H)
410. #3537C2×C107semidirect
411. #3006C2×C107semidirect
412. #3002C2×C107semidirect
413. #2615C2×C107semidirect
414. #1606C2×C107semidirect
415. #1601C2×C107semidirect
416. #1600C2×C107semidirect
417. #1595C2×C107semidirect
418. #1519C2×C107semidirect
419. #1513C2×C107semidirect
420. #1471C2×C107semidirect
421. C107#18228direct (N × H)
422. C22×#41C22×C107semidirect
442. #451C22×C107semidirect
443. #450C22×C107semidirect
446. #448C22×C107semidirect
447. #448C22×C107semidirect
448. #447C22×C107semidirect
449. #447C22×C107semidirect
452. #407C22×C107semidirect
453. C2×C22⋊C8C22×C107semidirect
454. #393C22×C107semidirect
456. #392C22×C107semidirect
458. #380C22×C107semidirect
459. #328C22×C107semidirect
460. #327C22×C107semidirect
461. #327C22×C107semidirect
462. #327C22×C107semidirect
463. #323C22×C107semidirect
464. #323C22×C107semidirect
470. C2×#41D4×C107semidirect
480. C22×D4D4×C107semidirect
505. C22⋊Q8D4×C107semidirect
522. #121D4×C107semidirect
523. #121D4×C107semidirect
540. #117D4×C107semidirect
543. 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×#35372
C107×#30062
C107×#30022
C107×#26152
C107×#16062
C107×#16012
C107×#16002
C107×#15952
C107×#15192
C107×#15132
C107×#14712
#18228107