Finite Group Databasebeta

← C107×#26708 #41052672

Subgroups — C107×#26708 #41052672

Order 27392.

710 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2447C211yesmaximal, characteristic
2C107×#2369C211yesmaximal, characteristic, complemented
3C107×#2086C211yesmaximal, characteristic, complemented
4C107×#2042C211yesmaximal, characteristic
5C107×#2024C211yesmaximal, characteristic, complemented
6C107×#2023C211yesmaximal, characteristic
7C107×#1983C211yesmaximal, characteristic
8C107×#1935C211yesmaximal, characteristic, complemented
9C107×#1928C211yesmaximal, characteristic, complemented
10C107×#1927C211yesmaximal, characteristic, complemented
11C107×#1926C211yesmaximal, characteristic
12C107×#1920C211yesmaximal, characteristic, complemented
13C107×#1917C211yesmaximal, characteristic, complemented
14C107×#1862C211yesmaximal, characteristic
15C107×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C107C2211yescharacteristic
17C2×#124×C107C2211yescharacteristic
18C2×C4×D4×C107C2211yescharacteristic
19C2×#107×C107C2211yescharacteristic
20C2×#106×C107C2211yescharacteristic
21C2×C4⋊C8×C107C2211yescharacteristic
22C2×#103×C107C2211yescharacteristic
23C2×#103×C107C2211yescharacteristic
24C2×#103×C107C2211yescharacteristic
25C2×#103×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×#102×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#97×C107C2211yescharacteristic
31#397×C107—21no—
32#397×C107—21no—
33#391×C107—21no—
34#391×C107—21no—
35#391×C107C2211yescharacteristic
36#391×C107C2211yescharacteristic
37#390×C107C2211yescharacteristic
38#389×C107—21no—
39#389×C107C2211yescharacteristic
40#389×C107C2211yescharacteristic
41#389×C107C2211yescharacteristic
42#385×C107—21no—
43#381×C107—21no—
44C4×C4⋊C4×C107—21no—
45C4×C4⋊C4×C107C2211yescharacteristic
46C4×C4⋊C4×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#336×C107C2211yescharacteristic
56#336×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59C22×Q8×C107—21no—
60C22×Q8×C107C2311yescharacteristic
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×C107—22no—
69#124×C107—22no—
70#124×C107—41no—
71C4×D4×C107—22no—
72C4×D4×C107—41no—
73C2×C4⋊C4×C107—21no—
74C2×C4⋊C4×C107—21no—
75C2×C4⋊C4×C107—21no—
76C2×C4⋊C4×C107—21no—
77C2×C4⋊C4×C107D411yescharacteristic
78C2×C4⋊C4×C107D411yescharacteristic
79C2×C4⋊C4×C107C2311yescharacteristic
80C2×C4⋊C4×C107C2311yescharacteristic
81C2×C4⋊C4×C107C2311yescharacteristic
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C4⋊C4×C107C2311yescharacteristic
84C2×C4⋊C4×C107C2311yescharacteristic
85C2×C22⋊C4×C107—21no—
86C2×C22⋊C4×C107—21no—
87C2×C22⋊C4×C107—21no—
88C2×C22⋊C4×C107—21no—
89C2×C22⋊C4×C107—21no—
90C2×C42×C107—21no—
91C2×C42×C107—21no—
92C2×C42×C107—21no—
93C2×C42×C107C2311yescharacteristic
94C2×C42×C107C2311yescharacteristic
95C2×C42×C107C2311yescharacteristic
96#107×C107—41no—
97#106×C107—22no—
98C4⋊C8×C107—41no—
99#103×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#102×C107—22no—
107#97×C107—41no—
108#95×C107—21no—
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—21no—
123C2×Q8×C107—21no—
124C2×Q8×C107—21no—
125C2×Q8×C107—21no—
126C2×Q8×C107—21no—
127C2×Q8×C107—21no—
128C2×Q8×C107—81no—
129C2×Q8×C107—81no—
130C2×D4×C107—21no—
131C2×D4×C107—21no—
132C2×D4×C107—21no—
133C2×D4×C107—21no—
134C2×D4×C107—21no—
135C2×D4×C107#4112yes—
136C22×C4×C107—21no—
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—42no—
144C22×C4×C107—42no—
145C22×C4×C107—81no—
146C22×C4×C107C2×D411yescharacteristic
147C22×C4×C107C2×D411yescharacteristic
148C22×C4×C107C2×D411yescharacteristic
149C22×C4×C107C2×D411yescharacteristic
150C22×C4×C107C2×D411yescharacteristic
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2411yescharacteristic
153C2×C8×C107—21no—
154C2×C8×C107—21no—
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—
165C4⋊C4×C107—24no—
166C4⋊C4×C107—22no—
167C4⋊C4×C107—21no—
168C4⋊C4×C107—21no—
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—41no—
177C4⋊C4×C107—81no—
178C4⋊C4×C107—81no—
179C4⋊C4×C107—81no—
180C4⋊C4×C107#4112yes—
181C4⋊C4×C107#4112yes—
182C4⋊C4×C107#4112yes—
183C22⋊C4×C107—42no—
184C22⋊C4×C107—42no—
185C22⋊C4×C107—42no—
186C22⋊C4×C107—42no—
187C22⋊C4×C107—81no—
188C42×C107—21no—
189C42×C107—21no—
190C42×C107—21no—
191C42×C107—21no—
192C42×C107—21no—
193C42×C107—21no—
194C42×C107—42no—
195C42×C107—81no—
196C42×C107—81no—
197C23×C107—22no—
198C23×C107—41no—
199C23×C107—41no—
200C23×C107—41no—
201C23×C107—41no—
202C23×C107—41no—
203C23×C107—41no—
204C23×C107C22×D411yescharacteristic
205Q8×C107—41no—
206Q8×C107—41no—
207Q8×C107—41no—
208Q8×C107—41no—
209Q8×C107—84no—
210D4×C107—22no—
211D4×C107—22no—
212D4×C107—41no—
213D4×C107—41no—
214C2×C4×C107—21no—
215C2×C4×C107—21no—
216C2×C4×C107—21no—
217C2×C4×C107—22no—
218C2×C4×C107—22no—
219C2×C4×C107—21no—
220C2×C4×C107—21no—
221C2×C4×C107—21no—
222C2×C4×C107—21no—
223C2×C4×C107—22no—
224C2×C4×C107—21no—
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—21no—
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—84no—
253C2×C4×C107#13712yes—
254C2×C4×C107C2×#4111yescharacteristic
255C2×C4×C107C2×#4111yescharacteristic
256C2×C4×C107C2×#4111yescharacteristic
257C2×C4×C107C2×#4111yescharacteristic
258C2×C4×C107H(5,𝔽2)11yescharacteristic
259C2×C4×C1072−1+411yescharacteristic
260C8×C107—41no—
261C8×C107—41no—
262C8×C107—41no—
263C8×C107—41no—
264C22×C107—42no—
265C22×C107—42no—
266C22×C107—42no—
267C22×C107—81no—
268C22×C107—81no—
269C22×C107—81no—
270C22×C107—81no—
271C22×C107#52511yescharacteristic
272C22×C107#54611yescharacteristic
273C22×C107#54811yescharacteristic
274C22×C107C2×#13711yescharacteristic
275C22×C107#57511yescharacteristic
276C22×C107#57611yescharacteristic
277C22×C107#57711yescharacteristic
278C4×C107—22no—
279C4×C107—41no—
280C4×C107—41no—
281C4×C107—41no—
282C4×C107—42no—
283C4×C107—42no—
284C4×C107—42no—
285C4×C107—41no—
286C4×C107—41no—
287C4×C107—81no—
288C4×C107—81no—
289C4×C107—81no—
290C4×C107—81no—
291C4×C107#52911yescharacteristic
292C4×C107#54211yescharacteristic
293C4×C107#55211yescharacteristic
294C4×C107#55911yescharacteristic
295#26708C10711yesmaximal, characteristic, direct product factor, Sylow
296C2×C107—82no—
297C2×C107#245811yescharacteristic
298C2×C107#311711yescharacteristic
299C2×C107#311811yescharacteristic
300C2×C107#331911yescharacteristic
301C2×C107#333111yescharacteristic
302C2×C107#337511yescharacteristic
303C2×C107#337611yescharacteristic
304#2447C2×C10711yescharacteristic
305#2369C2×C10711yescharacteristic, complemented
306#2086C2×C10711yescharacteristic, complemented
307#2042C2×C10711yescharacteristic
308#2024C2×C10711yescharacteristic, complemented
309#2023C2×C10711yescharacteristic
310#1983C2×C10711yescharacteristic
311#1935C2×C10711yescharacteristic, complemented
312#1928C2×C10711yescharacteristic, complemented
313#1927C2×C10711yescharacteristic, complemented
314#1926C2×C10711yescharacteristic
315#1920C2×C10711yescharacteristic, complemented
316#1917C2×C10711yescharacteristic, complemented
317#1862C2×C10711yescharacteristic
318#1762C2×C10711yescharacteristic
319C107#2670811yescharacteristic, direct product factor, Sylow
320C2×C4⋊Q8C22×C10711yescharacteristic
321C2×#124C22×C10711yescharacteristic
322C2×C4×D4C22×C10711yescharacteristic
323C2×#107C22×C10711yescharacteristic
324C2×#106C22×C10711yescharacteristic
325C2×C4⋊C8C22×C10711yescharacteristic
326C2×#103C22×C10711yescharacteristic
327C2×#103C22×C10711yescharacteristic
328C2×#103C22×C10711yescharacteristic
329C2×#103C22×C10711yescharacteristic
330C2×#102C22×C10711yescharacteristic
331C2×#102C22×C10711yescharacteristic
332C2×#102C22×C10711yescharacteristic
333C2×#102C22×C10711yescharacteristic
334C2×#97C22×C10711yescharacteristic
335#397—21no—
336#397—21no—
337#391—21no—
338#391—21no—
339#391C22×C10711yescharacteristic
340#391C22×C10711yescharacteristic
341#390C22×C10711yescharacteristic
342#389—21no—
343#389C22×C10711yescharacteristic
344#389C22×C10711yescharacteristic
345#389C22×C10711yescharacteristic
346#385—21no—
347#381—21no—
348C4×C4⋊C4—21no—
349C4×C4⋊C4C22×C10711yescharacteristic
350C4×C4⋊C4C22×C10711yescharacteristic
351C4×C4⋊C4C22×C10711yescharacteristic
352C4×C4⋊C4C22×C10711yescharacteristic
353#340C22×C10711yescharacteristic
354#340C22×C10711yescharacteristic
355#340C22×C10711yescharacteristic
356#340C22×C10711yescharacteristic
357#340C22×C10711yescharacteristic
358#340C22×C10711yescharacteristic
359#336C22×C10711yescharacteristic
360#336C22×C10711yescharacteristic
361#336C22×C10711yescharacteristic
362#336C22×C10711yescharacteristic
363C22×Q8—21no—
364C22×Q8C23×C10711yescharacteristic
365C22×D4C23×C10711yescharacteristic
366C23×C4—21no—
367C22×C8C23×C10711yescharacteristic
368C22×C8C23×C10711yescharacteristic
369C22×C8C23×C10711yescharacteristic
370C22×C8C23×C10711yescharacteristic
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373#124—22no—
374#124—41no—
375C4×D4—22no—
376C4×D4—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4D4×C10711yescharacteristic
382C2×C4⋊C4D4×C10711yescharacteristic
383C2×C4⋊C4C23×C10711yescharacteristic
384C2×C4⋊C4C23×C10711yescharacteristic
385C2×C4⋊C4C23×C10711yescharacteristic
386C2×C4⋊C4C23×C10711yescharacteristic
387C2×C4⋊C4C23×C10711yescharacteristic
388C2×C4⋊C4C23×C10711yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C10711yescharacteristic
398C2×C42C23×C10711yescharacteristic
399C2×C42C23×C10711yescharacteristic
400#107—41no—
401#106—22no—
402C4⋊C8—41no—
403#103—22no—
404#103—22no—
405#103—22no—
406#103—41no—
407#102—22no—
408#102—22no—
409#102—22no—
410#102—22no—
411#97—41no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95D4×C10711yescharacteristic
423#95D4×C10711yescharacteristic
424C24—21no—
425C2×Q8—24no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—81no—
433C2×Q8—81no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4#41×C10712yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—81no—
450C22×C4C2×D4×C10711yescharacteristic
451C22×C4C2×D4×C10711yescharacteristic
452C22×C4C2×D4×C10711yescharacteristic
453C22×C4C2×D4×C10711yescharacteristic
454C22×C4C2×D4×C10711yescharacteristic
455C22×C4C2×D4×C10711yescharacteristic
456C22×C4C24×C10711yescharacteristic
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4#41×C10712yes—
485C4⋊C4#41×C10712yes—
486C4⋊C4#41×C10712yes—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—81no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—42no—
499C42—81no—
500C42—81no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C22×D4×C10711yescharacteristic
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—84no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
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—84no—
557C2×C4#137×C10712yes—
558C2×C4C2×#41×C10711yescharacteristic
559C2×C4C2×#41×C10711yescharacteristic
560C2×C4C2×#41×C10711yescharacteristic
561C2×C4C2×#41×C10711yescharacteristic
562C2×C4H(5,𝔽2)×C10711yescharacteristic
563C2×C42−1+4×C10711yescharacteristic
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#525×C10711yescharacteristic
576C22#546×C10711yescharacteristic
577C22#548×C10711yescharacteristic
578C22C2×#137×C10711yescharacteristic
579C22#575×C10711yescharacteristic
580C22#576×C10711yescharacteristic
581C22#577×C10711yescharacteristic
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4#529×C10711yescharacteristic
596C4#542×C10711yescharacteristic
597C4#552×C10711yescharacteristic
598C4#559×C10711yescharacteristic
599C2—82no—
600C2C107×#245811yescharacteristic
601C2C107×#311711yescharacteristic
602C2C107×#311811yescharacteristic
603C2C107×#331911yescharacteristic
604C2C107×#333111yescharacteristic
605C2C107×#337511yescharacteristic
606C2C107×#337611yescharacteristic
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
2. C107×#2369C2semidirect
3. C107×#2086C2semidirect
5. C107×#2024C2semidirect
8. C107×#1935C2semidirect
9. C107×#1928C2semidirect
10. C107×#1927C2semidirect
12. C107×#1920C2semidirect
13. C107×#1917C2semidirect
295. #26708C107direct (N × H)
305. #2369C2×C107semidirect
306. #2086C2×C107semidirect
308. #2024C2×C107semidirect
311. #1935C2×C107semidirect
312. #1928C2×C107semidirect
313. #1927C2×C107semidirect
315. #1920C2×C107semidirect
316. #1917C2×C107semidirect
319. C107#26708direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#24472
C107×#23692
C107×#20862
C107×#20422
C107×#20242
C107×#20232
C107×#19832
C107×#19352
C107×#19282
C107×#19272
C107×#19262
C107×#19202
C107×#19172
C107×#18622
C107×#17622
#26708107