Finite Group Databasebeta

← C107×#23075 #41049039

Subgroups — C107×#23075 #41049039

Order 27392.

806 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C107C211yesmaximal, characteristic
2C107×#2365C211yesmaximal, characteristic, complemented
3C107×#2357C211yesmaximal, characteristic
4C107×#1993C211yesmaximal, characteristic, complemented
5C107×#1949C211yesmaximal, characteristic, complemented
6C107×#1936C211yesmaximal, characteristic
7C107×#1934C211yesmaximal, characteristic
8C107×#1926C211yesmaximal, characteristic
9C107×#1925C211yesmaximal, characteristic
10C107×#1920C211yesmaximal, characteristic, complemented
11C107×#1919C211yesmaximal, characteristic, complemented
12C107×#1776C211yesmaximal, characteristic, complemented
13C4×#106×C107C211yesmaximal, characteristic, complemented
14C107×#1771C211yesmaximal, characteristic, complemented
15C107×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C107C2211yescharacteristic
17C2×C4×Q8×C107—21no—
18C2×C4×D4×C107C2211yescharacteristic
19#476×C107C418yescomplemented
20C2×#107×C107C2211yescharacteristic
21C2×#106×C107C2211yescharacteristic
22C2×#106×C107C2211yescharacteristic
23C2×#106×C107C2211yescharacteristic
24C2×C4⋊C8×C107C2211yescharacteristic
25C2×#102×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×#102×C107C2211yescharacteristic
29C2×#97×C107C2211yescharacteristic
30C2×#97×C107C2211yescharacteristic
31C2×C4×C8×C107C2211yescharacteristic
32#391×C107—21no—
33#390×C107C2211yescharacteristic
34#390×C107C2211yescharacteristic
35#389×C107C2211yescharacteristic
36#389×C107C2211yescharacteristic
37#388×C107—21no—
38#388×C107—21no—
39#387×C107—21no—
40#387×C107—21no—
41#382×C107C2211yescharacteristic
42#381×C107—21no—
43C4×C4⋊C4×C107C2211yescharacteristic
44C4×C4⋊C4×C107C2211yescharacteristic
45C4×C4⋊C4×C107C2211yescharacteristic
46C4×C4⋊C4×C107C2211yescharacteristic
47C4×C4⋊C4×C107C2211yescharacteristic
48C4×C4⋊C4×C107C2211yescharacteristic
49C4×C22⋊C4×C107—21no—
50#340×C107C2211yescharacteristic
51#340×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60C22×Q8×C107—21no—
61C22×D4×C107C2311yescharacteristic
62C23×C4×C107—21no—
63C22×C8×C107C2311yescharacteristic
64C22×C8×C107C2311yescharacteristic
65C22×C8×C107C2311yescharacteristic
66C22×C8×C107C2311yescharacteristic
67C4⋊Q8×C107—22no—
68C4⋊Q8×C107C2×C414yes—
69C4×Q8×C107—44no—
70C4×D4×C107—22no—
71C4×D4×C107C2×C414yes—
72C2×C4⋊C4×C107—21no—
73C2×C4⋊C4×C107—21no—
74C2×C4⋊C4×C107—21no—
75C2×C4⋊C4×C107D411yescharacteristic
76C2×C4⋊C4×C107D411yescharacteristic
77C2×C4⋊C4×C107C2311yescharacteristic
78C2×C4⋊C4×C107C2311yescharacteristic
79C2×C4⋊C4×C107C2311yescharacteristic
80C2×C4⋊C4×C107C2311yescharacteristic
81C2×C4⋊C4×C107C2311yescharacteristic
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C4⋊C4×C107C2311yescharacteristic
84C2×C22⋊C4×C107—21no—
85C2×C22⋊C4×C107—21no—
86C2×C22⋊C4×C107—21no—
87C2×C22⋊C4×C107—21no—
88C2×C22⋊C4×C107—21no—
89C2×C42×C107—21no—
90C2×C42×C107—21no—
91C2×C42×C107—21no—
92C2×C42×C107—21no—
93C2×C42×C107—21no—
94C2×C42×C107C2311yescharacteristic
95C2×C42×C107C2311yescharacteristic
96C2×C42×C107C2311yescharacteristic
97#107×C107—22no—
98#106×C107—22no—
99#106×C107C2×C414yes—
100#106×C107C2×C414yes—
101C4⋊C8×C107C2×C414yes—
102#102×C107—22no—
103#102×C107—22no—
104#102×C107C2×C414yes—
105#102×C107C2×C414yes—
106#97×C107—22no—
107#97×C107—22no—
108C4×C8×C107—22no—
109#95×C107—21no—
110#95×C107—21no—
111#95×C107—21no—
112#95×C107—21no—
113#95×C107—21no—
114#95×C107—21no—
115#95×C107—21no—
116#95×C107—21no—
117#95×C107—21no—
118#95×C107D411yescharacteristic
119#95×C107D411yescharacteristic
120C24×C107—21no—
121C2×Q8×C107—24no—
122C2×Q8×C107—42no—
123C2×Q8×C107—42no—
124C2×D4×C107—21no—
125C2×D4×C107—21no—
126C2×D4×C107—21no—
127C2×D4×C107—21no—
128C2×D4×C107—21no—
129C2×D4×C107C22×C412yes—
130C22×C4×C107—21no—
131C22×C4×C107—21no—
132C22×C4×C107—21no—
133C22×C4×C107—21no—
134C22×C4×C107—24no—
135C22×C4×C107—21no—
136C22×C4×C107—21no—
137C22×C4×C107—21no—
138C22×C4×C107—81no—
139C22×C4×C107—81no—
140C22×C4×C107C2×D411yescharacteristic
141C22×C4×C107C2×D411yescharacteristic
142C22×C4×C107C2×D411yescharacteristic
143C22×C4×C107C2×D411yescharacteristic
144C22×C4×C107C2×D411yescharacteristic
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107C2411yescharacteristic
147C2×C8×C107—21no—
148C2×C8×C107—21no—
149C2×C8×C107—21no—
150C2×C8×C107—21no—
151C2×C8×C107—21no—
152C2×C8×C107—21no—
153C2×C8×C107—21no—
154C2×C8×C107—21no—
155C2×C8×C107—21no—
156C2×C8×C107C22×C412yes—
157C2×C8×C107C22×C412yes—
158C2×C8×C107#4112yes—
159C4⋊C4×C107—24no—
160C4⋊C4×C107—22no—
161C4⋊C4×C107—21no—
162C4⋊C4×C107—21no—
163C4⋊C4×C107—21no—
164C4⋊C4×C107—21no—
165C4⋊C4×C107—21no—
166C4⋊C4×C107—21no—
167C4⋊C4×C107—21no—
168C4⋊C4×C107—21no—
169C4⋊C4×C107—21no—
170C4⋊C4×C107—21no—
171C4⋊C4×C107—41no—
172C4⋊C4×C107—42no—
173C4⋊C4×C107—42no—
174C4⋊C4×C107C22×C412yes—
175C4⋊C4×C107C22×C412yes—
176C4⋊C4×C107C22×C412yes—
177C4⋊C4×C107#4112yes—
178C22⋊C4×C107—24no—
179C22⋊C4×C107—42no—
180C22⋊C4×C107—42no—
181C22⋊C4×C107—81no—
182C22⋊C4×C107—81no—
183C42×C107—21no—
184C42×C107—21no—
185C42×C107—21no—
186C42×C107—21no—
187C42×C107—42no—
188C42×C107—42no—
189C42×C107—42no—
190C42×C107—81no—
191C42×C107—81no—
192C42×C107C22×C412yes—
193C42×C107#4112yes—
194C23×C107—22no—
195C23×C107—41no—
196C23×C107—41no—
197C23×C107—41no—
198C23×C107—41no—
199C23×C107—41no—
200C23×C107—41no—
201C23×C107C22×D411yescharacteristic
202Q8×C107—48no—
203D4×C107—22no—
204D4×C107—22no—
205D4×C107—41no—
206D4×C107—41no—
207C2×C4×C107—21no—
208C2×C4×C107—21no—
209C2×C4×C107—21no—
210C2×C4×C107—21no—
211C2×C4×C107—21no—
212C2×C4×C107—21no—
213C2×C4×C107—22no—
214C2×C4×C107—22no—
215C2×C4×C107—22no—
216C2×C4×C107—21no—
217C2×C4×C107—21no—
218C2×C4×C107—21no—
219C2×C4×C107—22no—
220C2×C4×C107—21no—
221C2×C4×C107—21no—
222C2×C4×C107—21no—
223C2×C4×C107—21no—
224C2×C4×C107—21no—
225C2×C4×C107—21no—
226C2×C4×C107—41no—
227C2×C4×C107—41no—
228C2×C4×C107—41no—
229C2×C4×C107—41no—
230C2×C4×C107—41no—
231C2×C4×C107—41no—
232C2×C4×C107—41no—
233C2×C4×C107—41no—
234C2×C4×C107—41no—
235C2×C4×C107—41no—
236C2×C4×C107—41no—
237C2×C4×C107—41no—
238C2×C4×C107—41no—
239C2×C4×C107—41no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—84no—
244C2×C4×C107C4×D412yes—
245C2×C4×C107C4×D412yes—
246C2×C4×C107AGL(1,ℤ/8)12yes—
247C2×C4×C107C23×C411yescharacteristic
248C2×C4×C107C2×#4111yescharacteristic
249C2×C4×C107C2×#4111yescharacteristic
250C2×C4×C107C2×#4111yescharacteristic
251C2×C4×C1072−1+411yescharacteristic
252C2×C4×C1072−1+411yescharacteristic
253C8×C107—22no—
254C8×C107—22no—
255C8×C107—22no—
256C8×C107—41no—
257C22×C107—42no—
258C22×C107—42no—
259C22×C107—42no—
260C22×C107—81no—
261C22×C107—81no—
262C22×C107—81no—
263C22×C107—81no—
264C22×C107C2×C4×D411yescharacteristic
265C22×C107#54711yescharacteristic
266C22×C107#54811yescharacteristic
267C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C107#57511yescharacteristic
269C22×C107#57711yescharacteristic
270C22×C107#57711yescharacteristic
271C4×C107—22no—
272C4×C107—22no—
273C4×C107—22no—
274C4×C107—41no—
275C4×C107—41no—
276C4×C107—41no—
277C4×C107—42no—
278C4×C107—42no—
279C4×C107—42no—
280C4×C107—42no—
281C4×C107—81no—
282C4×C107—81no—
283C4×C107—81no—
284C4×C107C4×#4111yescharacteristic
285C4×C107#51911yescharacteristic
286C4×C107#55211yescharacteristic
287C4×C107#55611yescharacteristic
288#23075C10711yesmaximal, characteristic, direct product factor, Sylow
289C2×C107—82no—
290C2×C107#236211yescharacteristic
291C2×C107C4×AGL(1,ℤ/8)11yescharacteristic
292C2×C107#294911yescharacteristic
293C2×C107#334511yescharacteristic
294C2×C107#335011yescharacteristic
295C2×C107#337111yescharacteristic
296C2×C107#337311yescharacteristic
297C2×#476C2×C10711yescharacteristic
298#2365C2×C10711yescharacteristic, complemented
299#2357C2×C10711yescharacteristic
300#1993C2×C10711yescharacteristic, complemented
301#1949C2×C10711yescharacteristic, complemented
302#1936C2×C10711yescharacteristic
303#1934C2×C10711yescharacteristic
304#1926C2×C10711yescharacteristic
305#1925C2×C10711yescharacteristic
306#1920C2×C10711yescharacteristic, complemented
307#1919C2×C10711yescharacteristic, complemented
308#1776C2×C10711yescharacteristic, complemented
309C4×#106C2×C10711yescharacteristic, complemented
310#1771C2×C10711yescharacteristic, complemented
311#1762C2×C10711yescharacteristic
312C107#2307511yescharacteristic, direct product factor, Sylow
313C2×C4⋊Q8C22×C10711yescharacteristic
314C2×C4×Q8—21no—
315C2×C4×D4C22×C10711yescharacteristic
316#476C4×C10718yescomplemented
317C2×#107C22×C10711yescharacteristic
318C2×#106C22×C10711yescharacteristic
319C2×#106C22×C10711yescharacteristic
320C2×#106C22×C10711yescharacteristic
321C2×C4⋊C8C22×C10711yescharacteristic
322C2×#102C22×C10711yescharacteristic
323C2×#102C22×C10711yescharacteristic
324C2×#102C22×C10711yescharacteristic
325C2×#102C22×C10711yescharacteristic
326C2×#97C22×C10711yescharacteristic
327C2×#97C22×C10711yescharacteristic
328C2×C4×C8C22×C10711yescharacteristic
329#391—21no—
330#390C22×C10711yescharacteristic
331#390C22×C10711yescharacteristic
332#389C22×C10711yescharacteristic
333#389C22×C10711yescharacteristic
334#388—21no—
335#388—21no—
336#387—21no—
337#387—21no—
338#382C22×C10711yescharacteristic
339#381—21no—
340C4×C4⋊C4C22×C10711yescharacteristic
341C4×C4⋊C4C22×C10711yescharacteristic
342C4×C4⋊C4C22×C10711yescharacteristic
343C4×C4⋊C4C22×C10711yescharacteristic
344C4×C4⋊C4C22×C10711yescharacteristic
345C4×C4⋊C4C22×C10711yescharacteristic
346C4×C22⋊C4—21no—
347#340C22×C10711yescharacteristic
348#340C22×C10711yescharacteristic
349#340C22×C10711yescharacteristic
350#340C22×C10711yescharacteristic
351#340C22×C10711yescharacteristic
352#340C22×C10711yescharacteristic
353#340C22×C10711yescharacteristic
354#340C22×C10711yescharacteristic
355#336C22×C10711yescharacteristic
356#336C22×C10711yescharacteristic
357C22×Q8—21no—
358C22×D4C23×C10711yescharacteristic
359C23×C4—21no—
360C22×C8C23×C10711yescharacteristic
361C22×C8C23×C10711yescharacteristic
362C22×C8C23×C10711yescharacteristic
363C22×C8C23×C10711yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8C2×C4×C10714yes—
366C4×Q8—44no—
367C4×D4—22no—
368C4×D4C2×C4×C10714yes—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4D4×C10711yescharacteristic
373C2×C4⋊C4D4×C10711yescharacteristic
374C2×C4⋊C4C23×C10711yescharacteristic
375C2×C4⋊C4C23×C10711yescharacteristic
376C2×C4⋊C4C23×C10711yescharacteristic
377C2×C4⋊C4C23×C10711yescharacteristic
378C2×C4⋊C4C23×C10711yescharacteristic
379C2×C4⋊C4C23×C10711yescharacteristic
380C2×C4⋊C4C23×C10711yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42C23×C10711yescharacteristic
392C2×C42C23×C10711yescharacteristic
393C2×C42C23×C10711yescharacteristic
394#107—22no—
395#106—22no—
396#106C2×C4×C10714yes—
397#106C2×C4×C10714yes—
398C4⋊C8C2×C4×C10714yes—
399#102—22no—
400#102—22no—
401#102C2×C4×C10714yes—
402#102C2×C4×C10714yes—
403#97—22no—
404#97—22no—
405C4×C8—22no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95D4×C10711yescharacteristic
416#95D4×C10711yescharacteristic
417C24—21no—
418C2×Q8—24no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C22×C4×C10712yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4C2×D4×C10711yescharacteristic
438C22×C4C2×D4×C10711yescharacteristic
439C22×C4C2×D4×C10711yescharacteristic
440C22×C4C2×D4×C10711yescharacteristic
441C22×C4C2×D4×C10711yescharacteristic
442C22×C4C2×D4×C10711yescharacteristic
443C22×C4C24×C10711yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C22×C4×C10712yes—
454C2×C8C22×C4×C10712yes—
455C2×C8#41×C10712yes—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4C22×C4×C10712yes—
472C4⋊C4C22×C4×C10712yes—
473C4⋊C4C22×C4×C10712yes—
474C4⋊C4#41×C10712yes—
475C22⋊C4—24no—
476C22⋊C4—42no—
477C22⋊C4—42no—
478C22⋊C4—81no—
479C22⋊C4—81no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42—42no—
486C42—42no—
487C42—81no—
488C42—81no—
489C42C22×C4×C10712yes—
490C42#41×C10712yes—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C22×D4×C10711yescharacteristic
499Q8—48no—
500D4—22no—
501D4—22no—
502D4—41no—
503D4—41no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—84no—
541C2×C4C4×D4×C10712yes—
542C2×C4C4×D4×C10712yes—
543C2×C4AGL(1,ℤ/8)×C10712yes—
544C2×C4C23×C4×C10711yescharacteristic
545C2×C4C2×#41×C10711yescharacteristic
546C2×C4C2×#41×C10711yescharacteristic
547C2×C4C2×#41×C10711yescharacteristic
548C2×C42−1+4×C10711yescharacteristic
549C2×C42−1+4×C10711yescharacteristic
550C8—22no—
551C8—22no—
552C8—22no—
553C8—41no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22C2×C4×D4×C10711yescharacteristic
562C22#547×C10711yescharacteristic
563C22#548×C10711yescharacteristic
564C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
565C22#575×C10711yescharacteristic
566C22#577×C10711yescharacteristic
567C22#577×C10711yescharacteristic
568C4—22no—
569C4—22no—
570C4—22no—
571C4—42no—
572C4—42no—
573C4—42no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—42no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C4×#41×C10711yescharacteristic
582C4#519×C10711yescharacteristic
583C4#552×C10711yescharacteristic
584C4#556×C10711yescharacteristic
585C2—82no—
586C2C107×#236211yescharacteristic
587C2C4×AGL(1,ℤ/8)×C10711yescharacteristic
588C2C107×#294911yescharacteristic
589C2C107×#334511yescharacteristic
590C2C107×#335011yescharacteristic
591C2C107×#337111yescharacteristic
592C2C107×#337311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2365C2semidirect
4. C107×#1993C2semidirect
5. C107×#1949C2semidirect
10. C107×#1920C2semidirect
11. C107×#1919C2semidirect
12. C107×#1776C2semidirect
13. C4×#106×C107C2semidirect
14. C107×#1771C2semidirect
19. #476×C107C4semidirect
288. #23075C107direct (N × H)
298. #2365C2×C107semidirect
300. #1993C2×C107semidirect
301. #1949C2×C107semidirect
306. #1920C2×C107semidirect
307. #1919C2×C107semidirect
308. #1776C2×C107semidirect
309. C4×#106C2×C107semidirect
310. #1771C2×C107semidirect
312. C107#23075direct (N × H)
316. #476C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1072
C107×#23652
C107×#23572
C107×#19932
C107×#19492
C107×#19362
C107×#19342
C107×#19262
C107×#19252
C107×#19202
C107×#19192
C107×#17762
C4×#106×C1072
C107×#17712
C107×#17622
#23075107