Finite Group Databasebeta

← C107×#18516 #41044480

Subgroups — C107×#18516 #41044480

Order 27392.

1258 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#41×C107C211yesmaximal, characteristic, complemented
2C107×#3169C211yesmaximal, characteristic, complemented
3C107×#3100C211yesmaximal, characteristic, complemented
4C107×#3035C211yesmaximal, characteristic, complemented
5C107×#1649C211yesmaximal, characteristic, complemented
6C107×#1647C211yesmaximal, characteristic, complemented
7C107×#1641C211yesmaximal, characteristic, complemented
8C107×#1639C211yesmaximal, characteristic, complemented
9C107×#1627C211yesmaximal, characteristic, complemented
10C107×#1625C211yesmaximal, characteristic, complemented
11C107×#1621C211yesmaximal, characteristic, complemented
12C107×#1619C211yesmaximal, characteristic, complemented
13C107×#1540C211yesmaximal, characteristic, complemented
14C107×#1476C211yesmaximal, characteristic, complemented
15C2×D4⋊C8×C107C211yesmaximal, characteristic, complemented
16C22×#41×C107—21no—
17C2×#135×C107—21no—
18#550×C107C2211yescharacteristic
19D4×Q8×C107C2211yescharacteristic
20#548×C107—21no—
21#547×C107—21no—
22#547×C107C2211yescharacteristic
23#546×C107—22no—
24#546×C107—21no—
25D42×C107—21no—
26D42×C107C2211yescharacteristic
27#532×C107—21no—
28#532×C107C2211yescharacteristic
29#532×C107C2211yescharacteristic, complemented
30#525×C107—22no—
31#525×C107—21no—
32C4×#41×C107C2211yescharacteristic
33C2×C4×D4×C107—21no—
34C2×C4×D4×C107C2211yescharacteristic
35#500×C107C2211yescharacteristic, complemented
36#493×C107C2211yescharacteristic, complemented
37#486×C107C2211yescharacteristic, complemented
38#486×C107C2211yescharacteristic, complemented
39#480×C107—21no—
40#474×C107C2211yescharacteristic
41#474×C107C2211yescharacteristic, complemented
42#466×C107—22no—
43#464×C107—21no—
44#463×C107—21no—
45#462×C107C2211yescharacteristic, complemented
46#461×C107C2211yescharacteristic, complemented
47#460×C107C2211yescharacteristic, complemented
48#459×C107C2211yescharacteristic
49#459×C107C2211yescharacteristic, complemented
50#459×C107C2211yescharacteristic, complemented
51#447×C107—21no—
52C4×D8×C107—22no—
53C4×D8×C107—21no—
54C4×D8×C107—21no—
55#431×C107C2211yescharacteristic, complemented
56C2×C4⋊C8×C107C2211yescharacteristic, complemented
57#416×C107—21no—
58C2×C4×C8×C107C2211yescharacteristic, complemented
59#332×C107C2211yescharacteristic, complemented
60#332×C107C2211yescharacteristic, complemented
61#331×C107C2211yescharacteristic, complemented
62#331×C107C2211yescharacteristic, complemented
63Q8⋊C8×C107C2211yescharacteristic, complemented
64Q8⋊C8×C107C2211yescharacteristic, complemented
65D4⋊C8×C107C2211yescharacteristic
66D4⋊C8×C107C2211yescharacteristic
67D4⋊C8×C107C2211yescharacteristic, complemented
68D4⋊C8×C107C2211yescharacteristic, complemented
69D4⋊C8×C107C2211yescharacteristic, complemented
70D4⋊C8×C107C2211yescharacteristic, complemented
71C2×#41×C107—22no—
72C2×#41×C107—22no—
73C2×#41×C107—21no—
74C2×#41×C107—21no—
75C2×#41×C107—21no—
76C2×#41×C107—21no—
77C2×#41×C107—44no—
78C2×#41×C107—44no—
79C2×#41×C107D411yescharacteristic
80C22×Q8×C107—21no—
81C22×D4×C107—22no—
82C22×D4×C107—21no—
83C22×D4×C107—21no—
84C22×D4×C107D411yescharacteristic
85C23×C4×C107—22no—
86C23×C4×C107—21no—
87#135×C107—44no—
88C2×Q16×C107—21no—
89C2×SD16×C107—21no—
90C2×SD16×C107—21no—
91C2×D8×C107—21no—
92C2×D8×C107—21no—
93C2×D8×C107—22no—
94C2×D8×C107—21no—
95C22×C8×C107—21no—
96C22×C8×C107—21no—
97C4⋊Q8×C107—21no—
98C4⋊Q8×C107C2311yescharacteristic
99C4⋊Q8×C107C2311yescharacteristic
100#127×C107—21no—
101#127×C107C2311yescharacteristic
102#127×C107C2311yescharacteristic
103#124×C107—22no—
104#124×C107—21no—
105#124×C107—21no—
106#123×C107—22no—
107#123×C107—22no—
108#123×C107—22no—
109C22⋊Q8×C107—22no—
110C22⋊Q8×C107—21no—
111C22⋊Q8×C107—22no—
112C22⋊Q8×C107—21no—
113#121×C107—22no—
114#121×C107—22no—
115#121×C107—22no—
116#121×C107—21no—
117#121×C107—21no—
118#121×C107—21no—
119#121×C107—21no—
120#121×C107—21no—
121#121×C107—21no—
122#121×C107—21no—
123#121×C107D412yes—
124#120×C107—22no—
125#120×C107—22no—
126#120×C107—22no—
127C4×Q8×C107D411yescharacteristic
128C4×Q8×C107C2311yescharacteristic
129C4×D4×C107—22no—
130C4×D4×C107—22no—
131C4×D4×C107—22no—
132C4×D4×C107—21no—
133C4×D4×C107—21no—
134C4×D4×C107—21no—
135C4×D4×C107—21no—
136C4×D4×C107—21no—
137C4×D4×C107—21no—
138C4×D4×C107—21no—
139C4×D4×C107—21no—
140C4×D4×C107—21no—
141C4×D4×C107D411yescharacteristic
142C4×D4×C107D411yescharacteristic
143C4×D4×C107D412yes—
144C4×D4×C107D411yescharacteristic
145C4×D4×C107C2311yescharacteristic
146C4×D4×C107C2311yescharacteristic
147C4×D4×C107C2311yescharacteristic
148#117×C107—21no—
149#117×C107D411yescharacteristic
150C2×C4⋊C4×C107—21no—
151C2×C4⋊C4×C107D411yescharacteristic
152C2×C22⋊C4×C107—22no—
153C2×C22⋊C4×C107—21no—
154C2×C42×C107—21no—
155C2×C42×C107C2311yescharacteristic
156#107×C107—22no—
157#107×C107—21no—
158#107×C107—21no—
159C4⋊C8×C107—21no—
160C4⋊C8×C107C2311yescharacteristic
161C4⋊C8×C107C2311yescharacteristic
162C4⋊C8×C107C2311yescharacteristic
163C4⋊C8×C107C2311yescharacteristic
164#103×C107—21no—
165#103×C107—21no—
166#102×C107—21no—
167#102×C107—21no—
168#102×C107—22no—
169#102×C107—21no—
170#102×C107—21no—
171#102×C107—21no—
172#102×C107—21no—
173#102×C107—22no—
174C22⋊C8×C107—21no—
175C4×C8×C107—21no—
176C4×C8×C107—21no—
177C4×C8×C107C2311yescharacteristic
178C4×C8×C107C2311yescharacteristic
179C24×C107—22no—
180C24×C107—21no—
181#41×C107—22no—
182#41×C107—48no—
183#41×C107—48no—
184#41×C107—42no—
185#41×C107—42no—
186#41×C107—42no—
187#41×C107—42no—
188#41×C107—42no—
189#41×C107—42no—
190#41×C107—42no—
191#41×C107—42no—
192#41×C107D814yescomplemented
193C2×Q8×C107—22no—
194C2×Q8×C107—21no—
195C2×Q8×C107—21no—
196C2×Q8×C107—42no—
197C2×Q8×C107—42no—
198C2×Q8×C107C2×D411yescharacteristic
199C2×D4×C107—21no—
200C2×D4×C107—22no—
201C2×D4×C107—22no—
202C2×D4×C107—22no—
203C2×D4×C107—22no—
204C2×D4×C107—22no—
205C2×D4×C107—22no—
206C2×D4×C107—22no—
207C2×D4×C107—21no—
208C2×D4×C107—21no—
209C2×D4×C107—21no—
210C2×D4×C107—21no—
211C2×D4×C107—21no—
212C2×D4×C107—21no—
213C2×D4×C107—41no—
214C2×D4×C107—42no—
215C2×D4×C107—48no—
216C2×D4×C107—42no—
217C2×D4×C107—42no—
218C2×D4×C107—42no—
219C2×D4×C107—41no—
220C2×D4×C107C2×D411yescharacteristic
221C2×D4×C107C2×D411yescharacteristic
222C2×D4×C107C2×D411yescharacteristic
223C2×D4×C107C2×D412yes—
224C22×C4×C107—21no—
225C22×C4×C107—22no—
226C22×C4×C107—22no—
227C22×C4×C107—22no—
228C22×C4×C107—21no—
229C22×C4×C107—21no—
230C22×C4×C107—22no—
231C22×C4×C107—21no—
232C22×C4×C107—21no—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—21no—
236C22×C4×C107—48no—
237C22×C4×C107—42no—
238C22×C4×C107—42no—
239C22×C4×C107—41no—
240C22×C4×C107C2×D411yescharacteristic
241C22×C4×C107C2×D411yescharacteristic
242C22×C4×C107C2×D411yescharacteristic
243Q16×C107—42no—
244SD16×C107—42no—
245SD16×C107—42no—
246D8×C107—44no—
247D8×C107—42no—
248D8×C107—42no—
249D8×C107—42no—
250C2×C8×C107—21no—
251C2×C8×C107—21no—
252C2×C8×C107—21no—
253C2×C8×C107—21no—
254C2×C8×C107—21no—
255C2×C8×C107—21no—
256C2×C8×C107—42no—
257C2×C8×C107—42no—
258C4⋊C4×C107—22no—
259C4⋊C4×C107—22no—
260C4⋊C4×C107—21no—
261C4⋊C4×C107—21no—
262C4⋊C4×C107—21no—
263C4⋊C4×C107—21no—
264C4⋊C4×C107—21no—
265C4⋊C4×C107—21no—
266C4⋊C4×C107C2×D411yescharacteristic
267C4⋊C4×C107C2×D411yescharacteristic
268C4⋊C4×C107C2×D411yescharacteristic
269C4⋊C4×C107C2×D411yescharacteristic
270C4⋊C4×C107C2×D412yes—
271C22⋊C4×C107—22no—
272C22⋊C4×C107—22no—
273C22⋊C4×C107—22no—
274C22⋊C4×C107—22no—
275C22⋊C4×C107—21no—
276C22⋊C4×C107—21no—
277C22⋊C4×C107—22no—
278C22⋊C4×C107—21no—
279C22⋊C4×C107—21no—
280C22⋊C4×C107—22no—
281C22⋊C4×C107—21no—
282C22⋊C4×C107—21no—
283C22⋊C4×C107—21no—
284C22⋊C4×C107—41no—
285C22⋊C4×C107—41no—
286C42×C107—21no—
287C42×C107—21no—
288C42×C107—21no—
289C42×C107C2×D411yescharacteristic
290C42×C107C2×D411yescharacteristic
291C42×C107C2×D411yescharacteristic
292C42×C107C2411yescharacteristic
293C23×C107—21no—
294C23×C107—21no—
295C23×C107—21no—
296C23×C107—22no—
297C23×C107—42no—
298C23×C107—44no—
299C23×C107—44no—
300C23×C107—42no—
301C23×C107—41no—
302C23×C107—81no—
303C23×C107—82no—
304C23×C107#12011yescharacteristic
305Q8×C107—21no—
306Q8×C107—44no—
307Q8×C107—41no—
308Q8×C107—41no—
309Q8×C107—41no—
310Q8×C107—41no—
311Q8×C107C2×D812yes—
312D4×C107—24no—
313D4×C107—21no—
314D4×C107—21no—
315D4×C107—21no—
316D4×C107—21no—
317D4×C107—42no—
318D4×C107—42no—
319D4×C107—44no—
320D4×C107—42no—
321D4×C107—44no—
322D4×C107—44no—
323D4×C107—44no—
324D4×C107—44no—
325D4×C107—41no—
326D4×C107—41no—
327D4×C107—41no—
328D4×C107—41no—
329D4×C107—41no—
330D4×C107—41no—
331D4×C107—41no—
332D4×C107—41no—
333D4×C107—82no—
334D4×C107—82no—
335D4×C107C2×D812yes—
336D4×C107#13512yescomplemented
337C2×C4×C107—21no—
338C2×C4×C107—21no—
339C2×C4×C107—21no—
340C2×C4×C107—24no—
341C2×C4×C107—21no—
342C2×C4×C107—21no—
343C2×C4×C107—21no—
344C2×C4×C107—22no—
345C2×C4×C107—21no—
346C2×C4×C107—41no—
347C2×C4×C107—44no—
348C2×C4×C107—44no—
349C2×C4×C107—44no—
350C2×C4×C107—42no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—41no—
354C2×C4×C107—41no—
355C2×C4×C107—41no—
356C2×C4×C107—41no—
357C2×C4×C107—42no—
358C2×C4×C107—44no—
359C2×C4×C107—42no—
360C2×C4×C107—41no—
361C2×C4×C107—81no—
362C2×C4×C107—82no—
363C2×C4×C107#12011yescharacteristic
364C2×C4×C107#12011yescharacteristic
365C2×C4×C107#12011yescharacteristic
366C2×C4×C107C2×D812yes—
367C2×C4×C107AGL(1,ℤ/8)12yes—
368C2×C4×C107C22×D411yescharacteristic
369C2×C4×C107C22×D411yescharacteristic
370C2×C4×C107C22×D411yescharacteristic
371C8×C107—22no—
372C8×C107—41no—
373C8×C107—41no—
374C8×C107—41no—
375C8×C107—41no—
376C8×C107—41no—
377C22×C107—21no—
378C22×C107—21no—
379C22×C107—22no—
380C22×C107—22no—
381C22×C107—41no—
382C22×C107—41no—
383C22×C107—41no—
384C22×C107—41no—
385C22×C107—42no—
386C22×C107—41no—
387C22×C107—41no—
388C22×C107—42no—
389C22×C107—42no—
390C22×C107—41no—
391C22×C107—84no—
392C22×C107—88no—
393C22×C107—81no—
394C22×C107—81no—
395C22×C107—81no—
396C22×C107#44712yes—
397C22×C107C2×#12011yescharacteristic
398C4×C107—22no—
399C4×C107—21no—
400C4×C107—21no—
401C4×C107—21no—
402C4×C107—41no—
403C4×C107—42no—
404C4×C107—41no—
405C4×C107—41no—
406C4×C107—41no—
407C4×C107—81no—
408C4×C107#44712yes—
409C4×C107C22×D811yescharacteristic
410C4×C107C2×#13511yescharacteristic
411C4×C107C2×AGL(1,ℤ/8)11yescharacteristic
412C4×C107#57511yescharacteristic
413#18516C10711yesmaximal, characteristic, direct product factor, Sylow
414C2×C107—22no—
415C2×C107—42no—
416C2×C107—42no—
417C2×C107—81no—
418C2×C107—82no—
419C2×C107—161no—
420C2×C107C2×#44711yescharacteristic
421C2×C107#300211yescharacteristic
422C2×C107#301811yescharacteristic
423D4×#41C2×C10711yescharacteristic, complemented
424#3169C2×C10711yescharacteristic, complemented
425#3100C2×C10711yescharacteristic, complemented
426#3035C2×C10711yescharacteristic, complemented
427#1649C2×C10711yescharacteristic, complemented
428#1647C2×C10711yescharacteristic, complemented
429#1641C2×C10711yescharacteristic, complemented
430#1639C2×C10711yescharacteristic, complemented
431#1627C2×C10711yescharacteristic, complemented
432#1625C2×C10711yescharacteristic, complemented
433#1621C2×C10711yescharacteristic, complemented
434#1619C2×C10711yescharacteristic, complemented
435#1540C2×C10711yescharacteristic, complemented
436#1476C2×C10711yescharacteristic, complemented
437C2×D4⋊C8C2×C10711yescharacteristic, complemented
438C107#1851611yescharacteristic, direct product factor, Sylow
439C22×#41—21no—
440C2×#135—21no—
441#550C22×C10711yescharacteristic
442D4×Q8C22×C10711yescharacteristic
443#548—21no—
444#547—21no—
445#547C22×C10711yescharacteristic
446#546—22no—
447#546—21no—
448D42—21no—
449D42C22×C10711yescharacteristic
450#532—21no—
451#532C22×C10711yescharacteristic
452#532C22×C10711yescharacteristic, complemented
453#525—22no—
454#525—21no—
455C4×#41C22×C10711yescharacteristic
456C2×C4×D4—21no—
457C2×C4×D4C22×C10711yescharacteristic
458#500C22×C10711yescharacteristic, complemented
459#493C22×C10711yescharacteristic, complemented
460#486C22×C10711yescharacteristic, complemented
461#486C22×C10711yescharacteristic, complemented
462#480—21no—
463#474C22×C10711yescharacteristic
464#474C22×C10711yescharacteristic, complemented
465#466—22no—
466#464—21no—
467#463—21no—
468#462C22×C10711yescharacteristic, complemented
469#461C22×C10711yescharacteristic, complemented
470#460C22×C10711yescharacteristic, complemented
471#459C22×C10711yescharacteristic
472#459C22×C10711yescharacteristic, complemented
473#459C22×C10711yescharacteristic, complemented
474#447—21no—
475C4×D8—21no—
476C4×D8—21no—
477C4×D8—22no—
478#431C22×C10711yescharacteristic, complemented
479C2×C4⋊C8C22×C10711yescharacteristic, complemented
480#416—21no—
481C2×C4×C8C22×C10711yescharacteristic, complemented
482#332C22×C10711yescharacteristic, complemented
483#332C22×C10711yescharacteristic, complemented
484#331C22×C10711yescharacteristic, complemented
485#331C22×C10711yescharacteristic, complemented
486Q8⋊C8C22×C10711yescharacteristic, complemented
487Q8⋊C8C22×C10711yescharacteristic, complemented
488D4⋊C8C22×C10711yescharacteristic
489D4⋊C8C22×C10711yescharacteristic
490D4⋊C8C22×C10711yescharacteristic, complemented
491D4⋊C8C22×C10711yescharacteristic, complemented
492D4⋊C8C22×C10711yescharacteristic, complemented
493D4⋊C8C22×C10711yescharacteristic, complemented
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—44no—
501C2×#41—44no—
502C2×#41D4×C10711yescharacteristic
503C22×Q8—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4D4×C10711yescharacteristic
508C23×C4—22no—
509C23×C4—21no—
510#135—44no—
511C2×Q16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×D8—21no—
515C2×D8—21no—
516C2×D8—21no—
517C2×D8—22no—
518C22×C8—21no—
519C22×C8—21no—
520C4⋊Q8—21no—
521C4⋊Q8C23×C10711yescharacteristic
522C4⋊Q8C23×C10711yescharacteristic
523#127—21no—
524#127C23×C10711yescharacteristic
525#127C23×C10711yescharacteristic
526#124—22no—
527#124—21no—
528#124—21no—
529#123—22no—
530#123—22no—
531#123—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—22no—
535C22⋊Q8—21no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121D4×C10712yes—
547#120—22no—
548#120—22no—
549#120—22no—
550C4×Q8D4×C10711yescharacteristic
551C4×Q8C23×C10711yescharacteristic
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4D4×C10711yescharacteristic
565C4×D4D4×C10711yescharacteristic
566C4×D4D4×C10711yescharacteristic
567C4×D4D4×C10712yes—
568C4×D4C23×C10711yescharacteristic
569C4×D4C23×C10711yescharacteristic
570C4×D4C23×C10711yescharacteristic
571#117—21no—
572#117D4×C10711yescharacteristic
573C2×C4⋊C4—21no—
574C2×C4⋊C4D4×C10711yescharacteristic
575C2×C22⋊C4—22no—
576C2×C22⋊C4—21no—
577C2×C42—21no—
578C2×C42C23×C10711yescharacteristic
579#107—22no—
580#107—21no—
581#107—21no—
582C4⋊C8—21no—
583C4⋊C8C23×C10711yescharacteristic
584C4⋊C8C23×C10711yescharacteristic
585C4⋊C8C23×C10711yescharacteristic
586C4⋊C8C23×C10711yescharacteristic
587#103—21no—
588#103—21no—
589#102—21no—
590#102—21no—
591#102—22no—
592#102—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—22no—
597C22⋊C8—21no—
598C4×C8—21no—
599C4×C8—21no—
600C4×C8C23×C10711yescharacteristic
601C4×C8C23×C10711yescharacteristic
602C24—22no—
603C24—21no—
604#41—22no—
605#41—48no—
606#41—48no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614#41—42no—
615#41D8×C10714yescomplemented
616C2×Q8—22no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—42no—
620C2×Q8—42no—
621C2×Q8C2×D4×C10711yescharacteristic
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—41no—
637C2×D4—48no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—41no—
643C2×D4C2×D4×C10711yescharacteristic
644C2×D4C2×D4×C10711yescharacteristic
645C2×D4C2×D4×C10711yescharacteristic
646C2×D4C2×D4×C10712yes—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—48no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—41no—
663C22×C4C2×D4×C10711yescharacteristic
664C22×C4C2×D4×C10711yescharacteristic
665C22×C4C2×D4×C10711yescharacteristic
666Q16—42no—
667SD16—42no—
668SD16—42no—
669D8—44no—
670D8—42no—
671D8—42no—
672D8—42no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—42no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C10711yescharacteristic
690C4⋊C4C2×D4×C10711yescharacteristic
691C4⋊C4C2×D4×C10711yescharacteristic
692C4⋊C4C2×D4×C10711yescharacteristic
693C4⋊C4C2×D4×C10712yes—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—22no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—22no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—41no—
708C22⋊C4—41no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42C2×D4×C10711yescharacteristic
713C42C2×D4×C10711yescharacteristic
714C42C2×D4×C10711yescharacteristic
715C42C24×C10711yescharacteristic
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—42no—
721C23—44no—
722C23—44no—
723C23—42no—
724C23—41no—
725C23—81no—
726C23—82no—
727C23#120×C10711yescharacteristic
728Q8—21no—
729Q8—44no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8C2×D8×C10712yes—
735D4—24no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—44no—
743D4—42no—
744D4—44no—
745D4—44no—
746D4—44no—
747D4—44no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—82no—
757D4—82no—
758D4C2×D8×C10712yes—
759D4#135×C10712yescomplemented
760C2×C4—21no—
761C2×C4—24no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—41no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—81no—
785C2×C4—82no—
786C2×C4#120×C10711yescharacteristic
787C2×C4#120×C10711yescharacteristic
788C2×C4#120×C10711yescharacteristic
789C2×C4C2×D8×C10712yes—
790C2×C4AGL(1,ℤ/8)×C10712yes—
791C2×C4C22×D4×C10711yescharacteristic
792C2×C4C22×D4×C10711yescharacteristic
793C2×C4C22×D4×C10711yescharacteristic
794C8—22no—
795C8—41no—
796C8—41no—
797C8—41no—
798C8—41no—
799C8—41no—
800C22—21no—
801C22—21no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—84no—
815C22—88no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22#447×C10712yes—
820C22C2×#120×C10711yescharacteristic
821C4—22no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—81no—
831C4#447×C10712yes—
832C4C22×D8×C10711yescharacteristic
833C4C2×#135×C10711yescharacteristic
834C4C2×AGL(1,ℤ/8)×C10711yescharacteristic
835C4#575×C10711yescharacteristic
836C2—22no—
837C2—42no—
838C2—42no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C2×#447×C10711yescharacteristic
843C2C107×#300211yescharacteristic
844C2C107×#301811yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutator, Frattini, cosocleC42C24×C107
socleC22×C107C2×#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. D4×#41×C107C2semidirect
2. C107×#3169C2semidirect
3. C107×#3100C2semidirect
4. C107×#3035C2semidirect
5. C107×#1649C2semidirect
6. C107×#1647C2semidirect
7. C107×#1641C2semidirect
8. C107×#1639C2semidirect
9. C107×#1627C2semidirect
10. C107×#1625C2semidirect
11. C107×#1621C2semidirect
12. C107×#1619C2semidirect
13. C107×#1540C2semidirect
14. C107×#1476C2semidirect
15. C2×D4⋊C8×C107C2semidirect
29. #532×C107C22semidirect
35. #500×C107C22semidirect
36. #493×C107C22semidirect
37. #486×C107C22semidirect
38. #486×C107C22semidirect
41. #474×C107C22semidirect
45. #462×C107C22semidirect
46. #461×C107C22semidirect
47. #460×C107C22semidirect
49. #459×C107C22semidirect
50. #459×C107C22semidirect
55. #431×C107C22semidirect
56. C2×C4⋊C8×C107C22semidirect
58. C2×C4×C8×C107C22semidirect
59. #332×C107C22semidirect
60. #332×C107C22semidirect
61. #331×C107C22semidirect
62. #331×C107C22semidirect
63. Q8⋊C8×C107C22semidirect
64. Q8⋊C8×C107C22semidirect
67. D4⋊C8×C107C22semidirect
68. D4⋊C8×C107C22semidirect
69. D4⋊C8×C107C22semidirect
70. D4⋊C8×C107C22semidirect
192. #41×C107D8semidirect
336. D4×C107#135semidirect
413. #18516C107direct (N × H)
423. D4×#41C2×C107semidirect
424. #3169C2×C107semidirect
425. #3100C2×C107semidirect
426. #3035C2×C107semidirect
427. #1649C2×C107semidirect
428. #1647C2×C107semidirect
429. #1641C2×C107semidirect
430. #1639C2×C107semidirect
431. #1627C2×C107semidirect
432. #1625C2×C107semidirect
433. #1621C2×C107semidirect
434. #1619C2×C107semidirect
435. #1540C2×C107semidirect
436. #1476C2×C107semidirect
437. C2×D4⋊C8C2×C107semidirect
438. C107#18516direct (N × H)
452. #532C22×C107semidirect
458. #500C22×C107semidirect
459. #493C22×C107semidirect
460. #486C22×C107semidirect
461. #486C22×C107semidirect
464. #474C22×C107semidirect
468. #462C22×C107semidirect
469. #461C22×C107semidirect
470. #460C22×C107semidirect
472. #459C22×C107semidirect
473. #459C22×C107semidirect
478. #431C22×C107semidirect
479. C2×C4⋊C8C22×C107semidirect
481. C2×C4×C8C22×C107semidirect
482. #332C22×C107semidirect
483. #332C22×C107semidirect
484. #331C22×C107semidirect
485. #331C22×C107semidirect
486. Q8⋊C8C22×C107semidirect
487. Q8⋊C8C22×C107semidirect
490. D4⋊C8C22×C107semidirect
491. D4⋊C8C22×C107semidirect
492. D4⋊C8C22×C107semidirect
493. D4⋊C8C22×C107semidirect
615. #41D8×C107semidirect
759. D4#135×C107semidirect

Maximal subgroups

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

subgroupindex
D4×#41×C1072
C107×#31692
C107×#31002
C107×#30352
C107×#16492
C107×#16472
C107×#16412
C107×#16392
C107×#16272
C107×#16252
C107×#16212
C107×#16192
C107×#15402
C107×#14762
C2×D4⋊C8×C1072
#18516107