Finite Group Databasebeta

← C107×#29099 #41055063

Subgroups — C107×#29099 #41055063

Order 27392.

726 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2511C211yesmaximal, characteristic, complemented
2C107×#2452C211yesmaximal, characteristic
3C107×#2088C211yesmaximal, characteristic, complemented
4C107×#2071C211yesmaximal, characteristic
5C107×#2055C211yesmaximal, characteristic
6C107×#2024C211yesmaximal, characteristic, complemented
7C107×#1990C211yesmaximal, characteristic, complemented
8C107×#1968C211yesmaximal, characteristic
9C107×#1936C211yesmaximal, characteristic
10C107×#1935C211yesmaximal, characteristic, complemented
11C107×#1935C211yesmaximal, characteristic, complemented
12C107×#1920C211yesmaximal, characteristic, complemented
13C107×#1877C211yesmaximal, characteristic
14C107×#1771C211yesmaximal, characteristic, complemented
15C107×#1762C211yesmaximal, characteristic
16C22×SD16×C107C2211yescharacteristic
17C2×C4⋊Q8×C107C2211yescharacteristic
18C2×C22⋊Q8×C107—21no—
19C2×C4×D4×C107C2211yescharacteristic
20C2×#106×C107C2211yescharacteristic
21C2×C4⋊C8×C107C2211yescharacteristic
22C2×#103×C107C2211yescharacteristic
23C2×#103×C107C2211yescharacteristic
24C2×#103×C107C2211yescharacteristic
25C2×#102×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×#97×C107C2211yescharacteristic
29C2×#97×C107C2211yescharacteristic
30C2×C4×C8×C107C2211yescharacteristic
31#400×C107—21no—
32#400×C107—21no—
33#396×C107—21no—
34#393×C107—21no—
35#391×C107C2211yescharacteristic
36#391×C107C2211yescharacteristic
37#391×C107C2211yescharacteristic
38#390×C107C2211yescharacteristic
39#390×C107C2211yescharacteristic
40#389×C107C2211yescharacteristic
41#389×C107C2211yescharacteristic
42#389×C107C2211yescharacteristic
43#387×C107—21no—
44#387×C107—21no—
45#385×C107—21no—
46#384×C107C2211yescharacteristic
47C4×C4⋊C4×C107C2211yescharacteristic
48C4×C4⋊C4×C107C2211yescharacteristic
49#340×C107C2211yescharacteristic
50#340×C107C2211yescharacteristic
51#340×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59C22×Q8×C107—21no—
60C22×Q8×C107C2311yescharacteristic
61C22×D4×C107C2311yescharacteristic
62C23×C4×C107—21no—
63C2×SD16×C107—22no—
64C2×SD16×C107—22no—
65C2×SD16×C107—41no—
66C22×C8×C107C2311yescharacteristic
67C22×C8×C107C2311yescharacteristic
68C22×C8×C107C2311yescharacteristic
69C22×C8×C107C2311yescharacteristic
70C4⋊Q8×C107—22no—
71C4⋊Q8×C107—41no—
72C22⋊Q8×C107—44no—
73C4×D4×C107—22no—
74C4×D4×C107—41no—
75C2×C4⋊C4×C107—21no—
76C2×C4⋊C4×C107—21no—
77C2×C4⋊C4×C107—21no—
78C2×C4⋊C4×C107—21no—
79C2×C4⋊C4×C107—21no—
80C2×C4⋊C4×C107—21no—
81C2×C4⋊C4×C107D411yescharacteristic
82C2×C4⋊C4×C107D411yescharacteristic
83C2×C4⋊C4×C107C2311yescharacteristic
84C2×C4⋊C4×C107C2311yescharacteristic
85C2×C4⋊C4×C107C2311yescharacteristic
86C2×C4⋊C4×C107C2311yescharacteristic
87C2×C4⋊C4×C107C2311yescharacteristic
88C2×C4⋊C4×C107C2311yescharacteristic
89C2×C22⋊C4×C107—21no—
90C2×C22⋊C4×C107—21no—
91C2×C22⋊C4×C107—21no—
92C2×C22⋊C4×C107—21no—
93C2×C22⋊C4×C107—21no—
94C2×C42×C107—21no—
95C2×C42×C107C2311yescharacteristic
96C2×C42×C107C2311yescharacteristic
97C2×C42×C107C2311yescharacteristic
98#106×C107—22no—
99C4⋊C8×C107—22no—
100#103×C107—22no—
101#103×C107—22no—
102#103×C107—41no—
103#102×C107—22no—
104#102×C107—22no—
105#102×C107—22no—
106#97×C107—22no—
107#97×C107—41no—
108C4×C8×C107—41no—
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×C107—21no—
119#95×C107D411yescharacteristic
120#95×C107D411yescharacteristic
121C24×C107—21no—
122C2×Q8×C107—21no—
123C2×Q8×C107—21no—
124C2×Q8×C107—21no—
125C2×Q8×C107—21no—
126C2×Q8×C107—21no—
127C2×Q8×C107—21no—
128C2×Q8×C107—42no—
129C2×Q8×C107—42no—
130C2×Q8×C107—81no—
131C2×D4×C107—21no—
132C2×D4×C107—21no—
133C2×D4×C107—21no—
134C2×D4×C107—21no—
135C2×D4×C107—21no—
136C2×D4×C107#4112yes—
137C22×C4×C107—21no—
138C22×C4×C107—21no—
139C22×C4×C107—21no—
140C22×C4×C107—21no—
141C22×C4×C107—21no—
142C22×C4×C107—21no—
143C22×C4×C107—21no—
144C22×C4×C107—42no—
145C22×C4×C107—42no—
146C22×C4×C107—81no—
147C22×C4×C107C2×D411yescharacteristic
148C22×C4×C107C2×D411yescharacteristic
149C22×C4×C107C2×D411yescharacteristic
150C22×C4×C107C2×D411yescharacteristic
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107C2411yescharacteristic
154SD16×C107—44no—
155C2×C8×C107—21no—
156C2×C8×C107—21no—
157C2×C8×C107—21no—
158C2×C8×C107—21no—
159C2×C8×C107—21no—
160C2×C8×C107—21no—
161C2×C8×C107—21no—
162C2×C8×C107—21no—
163C2×C8×C107—21no—
164C2×C8×C107—21no—
165C2×C8×C107#4112yes—
166C2×C8×C107#4112yes—
167C4⋊C4×C107—22no—
168C4⋊C4×C107—22no—
169C4⋊C4×C107—21no—
170C4⋊C4×C107—21no—
171C4⋊C4×C107—21no—
172C4⋊C4×C107—21no—
173C4⋊C4×C107—21no—
174C4⋊C4×C107—21no—
175C4⋊C4×C107—21no—
176C4⋊C4×C107—21no—
177C4⋊C4×C107—21no—
178C4⋊C4×C107—21no—
179C4⋊C4×C107—21no—
180C4⋊C4×C107—42no—
181C4⋊C4×C107—42no—
182C4⋊C4×C107—42no—
183C4⋊C4×C107—42no—
184C4⋊C4×C107—81no—
185C4⋊C4×C107—81no—
186C4⋊C4×C107#4112yes—
187C22⋊C4×C107—42no—
188C22⋊C4×C107—42no—
189C22⋊C4×C107—42no—
190C22⋊C4×C107—42no—
191C22⋊C4×C107—81no—
192C42×C107—21no—
193C42×C107—21no—
194C42×C107—21no—
195C42×C107—21no—
196C42×C107—21no—
197C42×C107—21no—
198C42×C107—81no—
199C23×C107—22no—
200C23×C107—41no—
201C23×C107—41no—
202C23×C107—41no—
203C23×C107—41no—
204C23×C107—41no—
205C23×C107—41no—
206C23×C107C22×D411yescharacteristic
207Q8×C107—41no—
208Q8×C107—41no—
209Q8×C107—41no—
210Q8×C107—41no—
211Q8×C107—84no—
212D4×C107—22no—
213D4×C107—22no—
214D4×C107—41no—
215D4×C107—41no—
216C2×C4×C107—21no—
217C2×C4×C107—21no—
218C2×C4×C107—21no—
219C2×C4×C107—21no—
220C2×C4×C107—21no—
221C2×C4×C107—21no—
222C2×C4×C107—21no—
223C2×C4×C107—21no—
224C2×C4×C107—22no—
225C2×C4×C107—21no—
226C2×C4×C107—21no—
227C2×C4×C107—21no—
228C2×C4×C107—21no—
229C2×C4×C107—21no—
230C2×C4×C107—21no—
231C2×C4×C107—21no—
232C2×C4×C107—21no—
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—41no—
244C2×C4×C107—41no—
245C2×C4×C107—41no—
246C2×C4×C107—41no—
247C2×C4×C107—41no—
248C2×C4×C107—41no—
249C2×C4×C107—41no—
250C2×C4×C107—41no—
251C2×C4×C107—41no—
252C2×C4×C107—41no—
253C2×C4×C107—84no—
254C2×C4×C107AGL(1,ℤ/8)12yes—
255C2×C4×C107#13712yes—
256C2×C4×C107C2×#4111yescharacteristic
257C2×C4×C107C2×#4111yescharacteristic
258C2×C4×C107C2×#4111yescharacteristic
259C2×C4×C107C2×#4111yescharacteristic
260C2×C4×C107H(5,𝔽2)11yescharacteristic
261C2×C4×C1072−1+411yescharacteristic
262C8×C107—22no—
263C8×C107—22no—
264C8×C107—41no—
265C8×C107—41no—
266C22×C107—42no—
267C22×C107—42no—
268C22×C107—42no—
269C22×C107—81no—
270C22×C107—81no—
271C22×C107—81no—
272C22×C107—81no—
273C22×C107#53211yescharacteristic
274C22×C107#54611yescharacteristic
275C22×C107#54811yescharacteristic
276C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C107C2×#13711yescharacteristic
278C22×C107#57711yescharacteristic
279C22×C107#57711yescharacteristic
280C4×C107—22no—
281C4×C107—22no—
282C4×C107—41no—
283C4×C107—41no—
284C4×C107—41no—
285C4×C107—42no—
286C4×C107—41no—
287C4×C107—81no—
288C4×C107—81no—
289C4×C107—81no—
290C4×C107—81no—
291C4×C107—81no—
292C4×C107—81no—
293C4×C107#52911yescharacteristic
294C4×C107#53911yescharacteristic
295C4×C107#55111yescharacteristic
296C4×C107#55611yescharacteristic
297#29099C10711yesmaximal, characteristic, direct product factor, Sylow
298C2×C107—82no—
299C2×C107#256011yescharacteristic
300C2×C107#317311yescharacteristic
301C2×C107#318211yescharacteristic
302C2×C107#331011yescharacteristic
303C2×C107#331611yescharacteristic
304C2×C107#337211yescharacteristic
305C2×C107#337311yescharacteristic
306#2511C2×C10711yescharacteristic, complemented
307#2452C2×C10711yescharacteristic
308#2088C2×C10711yescharacteristic, complemented
309#2071C2×C10711yescharacteristic
310#2055C2×C10711yescharacteristic
311#2024C2×C10711yescharacteristic, complemented
312#1990C2×C10711yescharacteristic, complemented
313#1968C2×C10711yescharacteristic
314#1936C2×C10711yescharacteristic
315#1935C2×C10711yescharacteristic, complemented
316#1935C2×C10711yescharacteristic, complemented
317#1920C2×C10711yescharacteristic, complemented
318#1877C2×C10711yescharacteristic
319#1771C2×C10711yescharacteristic, complemented
320#1762C2×C10711yescharacteristic
321C107#2909911yescharacteristic, direct product factor, Sylow
322C22×SD16C22×C10711yescharacteristic
323C2×C4⋊Q8C22×C10711yescharacteristic
324C2×C22⋊Q8—21no—
325C2×C4×D4C22×C10711yescharacteristic
326C2×#106C22×C10711yescharacteristic
327C2×C4⋊C8C22×C10711yescharacteristic
328C2×#103C22×C10711yescharacteristic
329C2×#103C22×C10711yescharacteristic
330C2×#103C22×C10711yescharacteristic
331C2×#102C22×C10711yescharacteristic
332C2×#102C22×C10711yescharacteristic
333C2×#102C22×C10711yescharacteristic
334C2×#97C22×C10711yescharacteristic
335C2×#97C22×C10711yescharacteristic
336C2×C4×C8C22×C10711yescharacteristic
337#400—21no—
338#400—21no—
339#396—21no—
340#393—21no—
341#391C22×C10711yescharacteristic
342#391C22×C10711yescharacteristic
343#391C22×C10711yescharacteristic
344#390C22×C10711yescharacteristic
345#390C22×C10711yescharacteristic
346#389C22×C10711yescharacteristic
347#389C22×C10711yescharacteristic
348#389C22×C10711yescharacteristic
349#387—21no—
350#387—21no—
351#385—21no—
352#384C22×C10711yescharacteristic
353C4×C4⋊C4C22×C10711yescharacteristic
354C4×C4⋊C4C22×C10711yescharacteristic
355#340C22×C10711yescharacteristic
356#340C22×C10711yescharacteristic
357#340C22×C10711yescharacteristic
358#340C22×C10711yescharacteristic
359#340C22×C10711yescharacteristic
360#340C22×C10711yescharacteristic
361#340C22×C10711yescharacteristic
362#340C22×C10711yescharacteristic
363#336C22×C10711yescharacteristic
364#336C22×C10711yescharacteristic
365C22×Q8—21no—
366C22×Q8C23×C10711yescharacteristic
367C22×D4C23×C10711yescharacteristic
368C23×C4—21no—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16—41no—
372C22×C8C23×C10711yescharacteristic
373C22×C8C23×C10711yescharacteristic
374C22×C8C23×C10711yescharacteristic
375C22×C8C23×C10711yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—41no—
378C22⋊Q8—44no—
379C4×D4—22no—
380C4×D4—41no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4D4×C10711yescharacteristic
388C2×C4⋊C4D4×C10711yescharacteristic
389C2×C4⋊C4C23×C10711yescharacteristic
390C2×C4⋊C4C23×C10711yescharacteristic
391C2×C4⋊C4C23×C10711yescharacteristic
392C2×C4⋊C4C23×C10711yescharacteristic
393C2×C4⋊C4C23×C10711yescharacteristic
394C2×C4⋊C4C23×C10711yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42C23×C10711yescharacteristic
402C2×C42C23×C10711yescharacteristic
403C2×C42C23×C10711yescharacteristic
404#106—22no—
405C4⋊C8—22no—
406#103—22no—
407#103—22no—
408#103—41no—
409#102—22no—
410#102—22no—
411#102—22no—
412#97—22no—
413#97—41no—
414C4×C8—41no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95D4×C10711yescharacteristic
426#95D4×C10711yescharacteristic
427C24—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—81no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4#41×C10712yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—81no—
453C22×C4C2×D4×C10711yescharacteristic
454C22×C4C2×D4×C10711yescharacteristic
455C22×C4C2×D4×C10711yescharacteristic
456C22×C4C2×D4×C10711yescharacteristic
457C22×C4C2×D4×C10711yescharacteristic
458C22×C4C2×D4×C10711yescharacteristic
459C22×C4C24×C10711yescharacteristic
460SD16—44no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8#41×C10712yes—
472C2×C8#41×C10712yes—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4#41×C10712yes—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—81no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—81no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23C22×D4×C10711yescharacteristic
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—84no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—84no—
560C2×C4AGL(1,ℤ/8)×C10712yes—
561C2×C4#137×C10712yes—
562C2×C4C2×#41×C10711yescharacteristic
563C2×C4C2×#41×C10711yescharacteristic
564C2×C4C2×#41×C10711yescharacteristic
565C2×C4C2×#41×C10711yescharacteristic
566C2×C4H(5,𝔽2)×C10711yescharacteristic
567C2×C42−1+4×C10711yescharacteristic
568C8—22no—
569C8—22no—
570C8—41no—
571C8—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22#532×C10711yescharacteristic
580C22#546×C10711yescharacteristic
581C22#548×C10711yescharacteristic
582C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
583C22C2×#137×C10711yescharacteristic
584C22#577×C10711yescharacteristic
585C22#577×C10711yescharacteristic
586C4—22no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4#529×C10711yescharacteristic
600C4#539×C10711yescharacteristic
601C4#551×C10711yescharacteristic
602C4#556×C10711yescharacteristic
603C2—82no—
604C2C107×#256011yescharacteristic
605C2C107×#317311yescharacteristic
606C2C107×#318211yescharacteristic
607C2C107×#331011yescharacteristic
608C2C107×#331611yescharacteristic
609C2C107×#337211yescharacteristic
610C2C107×#337311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C22×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
1. C107×#2511C2semidirect
3. C107×#2088C2semidirect
6. C107×#2024C2semidirect
7. C107×#1990C2semidirect
10. C107×#1935C2semidirect
11. C107×#1935C2semidirect
12. C107×#1920C2semidirect
14. C107×#1771C2semidirect
297. #29099C107direct (N × H)
306. #2511C2×C107semidirect
308. #2088C2×C107semidirect
311. #2024C2×C107semidirect
312. #1990C2×C107semidirect
315. #1935C2×C107semidirect
316. #1935C2×C107semidirect
317. #1920C2×C107semidirect
319. #1771C2×C107semidirect
321. C107#29099direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#25112
C107×#24522
C107×#20882
C107×#20712
C107×#20552
C107×#20242
C107×#19902
C107×#19682
C107×#19362
C107×#19352
C107×#19202
C107×#18772
C107×#17712
C107×#17622
#29099107