Finite Group Databasebeta

← C107×#19278 #41045242

Subgroups — C107×#19278 #41045242

Order 27392.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3131C211yesmaximal, characteristic, complemented
2C107×#3116C211yesmaximal, characteristic, complemented
3C107×#3115C211yesmaximal, characteristic
4C8×#41×C107C211yesmaximal, characteristic, complemented
5C107×#1684C211yesmaximal, characteristic, complemented
6C107×#1683C211yesmaximal, characteristic, complemented
7C107×#1682C211yesmaximal, characteristic, complemented
8C107×#1681C211yesmaximal, characteristic, complemented
9C107×#1680C211yesmaximal, characteristic, complemented
10C107×#1679C211yesmaximal, characteristic, complemented
11C107×#1678C211yesmaximal, characteristic, complemented
12C107×#1677C211yesmaximal, characteristic, complemented
13C107×#1568C211yesmaximal, characteristic, complemented
14C107×#1554C211yesmaximal, characteristic, complemented
15C107×#1553C211yesmaximal, characteristic, complemented
16#533×C107C2211yescharacteristic
17#532×C107C2211yescharacteristic
18C4×#41×C107C2211yescharacteristic
19#488×C107—21no—
20#488×C107—21no—
21#487×C107C2211yescharacteristic
22#487×C107C2211yescharacteristic
23#486×C107C2211yescharacteristic
24#486×C107C2211yescharacteristic
25#485×C107—21no—
26#482×C107—21no—
27#477×C107C2211yescharacteristic
28#476×C107C2211yescharacteristic
29#475×C107C2211yescharacteristic
30#474×C107C2211yescharacteristic
31#462×C107C2211yescharacteristic
32#461×C107C2211yescharacteristic
33#460×C107C2211yescharacteristic
34#459×C107C2211yescharacteristic
35#452×C107—21no—
36#449×C107—21no—
37C8×Q8×C107C2211yescharacteristic
38C8×Q8×C107C2211yescharacteristic
39#442×C107—21no—
40#441×C107—21no—
41#440×C107—21no—
42#440×C107—21no—
43C8×D4×C107—21no—
44C8×D4×C107—21no—
45C8×D4×C107C2211yescharacteristic
46C8×D4×C107C2211yescharacteristic
47#432×C107C2211yescharacteristic
48#432×C107C2211yescharacteristic
49#431×C107—21no—
50#431×C107C2211yescharacteristic
51#416×C107—21no—
52#416×C107—21no—
53C2×C4×C8×C107—21no—
54C2×C4×C8×C107C2211yescharacteristic
55#335×C107C2211yescharacteristic
56#335×C107C2211yescharacteristic
57#334×C107C2211yescharacteristic
58#334×C107C2211yescharacteristic
59#333×C107C2211yescharacteristic
60#333×C107C2211yescharacteristic
61#332×C107C2211yescharacteristic
62#332×C107C2211yescharacteristic
63#332×C107C2211yescharacteristic
64#332×C107C2211yescharacteristic
65#331×C107C2211yescharacteristic
66#331×C107C2211yescharacteristic
67C2×#41×C107—21no—
68C2×#41×C107D411yescharacteristic
69C2×Q16×C107—21no—
70C2×SD16×C107—21no—
71C2×SD16×C107—21no—
72C2×D8×C107—21no—
73C22×C8×C107—21no—
74C22×C8×C107—21no—
75C22×C8×C107D411yescharacteristic
76C22×C8×C107D411yescharacteristic
77C4⋊Q8×C107C2311yescharacteristic
78C4⋊Q8×C107C2311yescharacteristic
79C4⋊Q8×C107C2311yescharacteristic
80#127×C107C2311yescharacteristic
81#125×C107—21no—
82#124×C107—21no—
83C22⋊Q8×C107—21no—
84C22⋊Q8×C107—21no—
85#121×C107—21no—
86#121×C107—21no—
87C4×Q8×C107—21no—
88C4×Q8×C107—21no—
89C4×Q8×C107D411yescharacteristic
90C4×Q8×C107C2311yescharacteristic
91C4×D4×C107—21no—
92C4×D4×C107—21no—
93C4×D4×C107—21no—
94C4×D4×C107—21no—
95C4×D4×C107D411yescharacteristic
96C4×D4×C107C2311yescharacteristic
97#117×C107—21no—
98#117×C107—21no—
99#117×C107D411yescharacteristic
100C2×C42×C107—21no—
101C2×C42×C107C2311yescharacteristic
102#107×C107—21no—
103#107×C107—21no—
104#106×C107—21no—
105#106×C107—21no—
106C4⋊C8×C107—21no—
107C4⋊C8×C107—21no—
108C4⋊C8×C107C2311yescharacteristic
109C4⋊C8×C107C2311yescharacteristic
110C4⋊C8×C107C2311yescharacteristic
111C4⋊C8×C107C2311yescharacteristic
112C4⋊C8×C107C2311yescharacteristic
113C4⋊C8×C107C2311yescharacteristic
114#103×C107—21no—
115#103×C107—21no—
116#103×C107—21no—
117#103×C107—21no—
118#103×C107—21no—
119#103×C107—21no—
120#103×C107—21no—
121#103×C107—21no—
122#102×C107—21no—
123#102×C107—21no—
124#102×C107—21no—
125#102×C107—21no—
126#102×C107—21no—
127#102×C107—21no—
128#102×C107—21no—
129#102×C107—21no—
130C22⋊C8×C107—21no—
131C22⋊C8×C107—21no—
132C22⋊C8×C107—21no—
133C22⋊C8×C107—21no—
134C22⋊C8×C107—21no—
135#97×C107—21no—
136#97×C107—21no—
137C4×C8×C107—21no—
138C4×C8×C107—21no—
139C4×C8×C107—21no—
140C4×C8×C107D411yescharacteristic
141C4×C8×C107D411yescharacteristic
142C4×C8×C107C2311yescharacteristic
143C4×C8×C107C2311yescharacteristic
144#41×C107—22no—
145#41×C107—22no—
146#41×C107—42no—
147#41×C107—42no—
148C2×Q8×C107—21no—
149C2×Q8×C107—21no—
150C2×Q8×C107—21no—
151C2×Q8×C107C2×D411yescharacteristic
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—21no—
156C2×D4×C107—41no—
157C2×D4×C107C2×D411yescharacteristic
158C22×C4×C107—21no—
159C22×C4×C107—21no—
160C22×C4×C107—21no—
161C22×C4×C107—41no—
162C22×C4×C107C2×D411yescharacteristic
163C22×C4×C107C2×D411yescharacteristic
164C22×C4×C107#4111yescharacteristic
165Q16×C107—42no—
166SD16×C107—42no—
167SD16×C107—42no—
168D8×C107—42no—
169C2×C8×C107—21no—
170C2×C8×C107—21no—
171C2×C8×C107—21no—
172C2×C8×C107—21no—
173C2×C8×C107—21no—
174C2×C8×C107—21no—
175C2×C8×C107—41no—
176C2×C8×C107—41no—
177C2×C8×C107—42no—
178C2×C8×C107—42no—
179C2×C8×C107C2×D411yescharacteristic
180C2×C8×C107C2×D411yescharacteristic
181C2×C8×C107C2×D411yescharacteristic
182C2×C8×C107C2×D411yescharacteristic
183C4⋊C4×C107—21no—
184C4⋊C4×C107—21no—
185C4⋊C4×C107—21no—
186C4⋊C4×C107—21no—
187C4⋊C4×C107—21no—
188C4⋊C4×C107—21no—
189C4⋊C4×C107—21no—
190C4⋊C4×C107—21no—
191C4⋊C4×C107—41no—
192C4⋊C4×C107—41no—
193C4⋊C4×C107C2×D411yescharacteristic
194C4⋊C4×C107C2×D411yescharacteristic
195C22⋊C4×C107—21no—
196C22⋊C4×C107—21no—
197C22⋊C4×C107—21no—
198C22⋊C4×C107—41no—
199C22⋊C4×C107—41no—
200C22⋊C4×C107—41no—
201C42×C107—21no—
202C42×C107—21no—
203C42×C107—21no—
204C42×C107—41no—
205C42×C107C2×D411yescharacteristic
206C42×C107C2×D411yescharacteristic
207C42×C107#4111yescharacteristic
208C42×C107C2411yescharacteristic
209C23×C107—21no—
210C23×C107—41no—
211C23×C107#12111yescharacteristic
212Q8×C107—21no—
213Q8×C107—41no—
214Q8×C107—41no—
215Q8×C107—41no—
216Q8×C107—41no—
217Q8×C107—81no—
218Q8×C107#13512yes—
219D4×C107—24no—
220D4×C107—21no—
221D4×C107—41no—
222D4×C107—41no—
223D4×C107—41no—
224D4×C107—41no—
225D4×C107—81no—
226D4×C107—82no—
227D4×C107#13512yes—
228C2×C4×C107—24no—
229C2×C4×C107—21no—
230C2×C4×C107—21no—
231C2×C4×C107—21no—
232C2×C4×C107—21no—
233C2×C4×C107—21no—
234C2×C4×C107—21no—
235C2×C4×C107—21no—
236C2×C4×C107—41no—
237C2×C4×C107—42no—
238C2×C4×C107—41no—
239C2×C4×C107—41no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—82no—
244C2×C4×C107#12111yescharacteristic
245C2×C4×C107#12111yescharacteristic
246C2×C4×C107#12111yescharacteristic
247C2×C4×C107C22×D411yescharacteristic
248C2×C4×C107C22×D411yescharacteristic
249C2×C4×C107C2×#4111yescharacteristic
250C8×C107—21no—
251C8×C107—21no—
252C8×C107—21no—
253C8×C107—21no—
254C8×C107—41no—
255C8×C107—41no—
256C8×C107—41no—
257C8×C107—41no—
258C8×C107—41no—
259C8×C107—41no—
260C22×C107—21no—
261C22×C107—21no—
262C22×C107—22no—
263C22×C107—21no—
264C22×C107—41no—
265C22×C107—41no—
266C22×C107—81no—
267C22×C107—81no—
268C22×C107—81no—
269C22×C107C2×#12111yescharacteristic
270C4×C107—21no—
271C4×C107—21no—
272C4×C107—22no—
273C4×C107—21no—
274C4×C107—21no—
275C4×C107—41no—
276C4×C107—41no—
277C4×C107—81no—
278C4×C107—81no—
279C4×C107—81no—
280C4×C107C2×#13511yescharacteristic
281C4×C107C2×#13511yescharacteristic
282C4×C107#57511yescharacteristic
283C4×C107#57511yescharacteristic
284#19278C10711yesmaximal, characteristic, direct product factor, Sylow
285C2×C107—41no—
286C2×C107—42no—
287C2×C107—161no—
288C2×C107#304011yescharacteristic
289C2×C107#305011yescharacteristic
290C2×C107#306711yescharacteristic
291#3131C2×C10711yescharacteristic, complemented
292#3116C2×C10711yescharacteristic, complemented
293#3115C2×C10711yescharacteristic
294C8×#41C2×C10711yescharacteristic, complemented
295#1684C2×C10711yescharacteristic, complemented
296#1683C2×C10711yescharacteristic, complemented
297#1682C2×C10711yescharacteristic, complemented
298#1681C2×C10711yescharacteristic, complemented
299#1680C2×C10711yescharacteristic, complemented
300#1679C2×C10711yescharacteristic, complemented
301#1678C2×C10711yescharacteristic, complemented
302#1677C2×C10711yescharacteristic, complemented
303#1568C2×C10711yescharacteristic, complemented
304#1554C2×C10711yescharacteristic, complemented
305#1553C2×C10711yescharacteristic, complemented
306C107#1927811yescharacteristic, direct product factor, Sylow
307#533C22×C10711yescharacteristic
308#532C22×C10711yescharacteristic
309C4×#41C22×C10711yescharacteristic
310#488—21no—
311#488—21no—
312#487C22×C10711yescharacteristic
313#487C22×C10711yescharacteristic
314#486C22×C10711yescharacteristic
315#486C22×C10711yescharacteristic
316#485—21no—
317#482—21no—
318#477C22×C10711yescharacteristic
319#476C22×C10711yescharacteristic
320#475C22×C10711yescharacteristic
321#474C22×C10711yescharacteristic
322#462C22×C10711yescharacteristic
323#461C22×C10711yescharacteristic
324#460C22×C10711yescharacteristic
325#459C22×C10711yescharacteristic
326#452—21no—
327#449—21no—
328C8×Q8C22×C10711yescharacteristic
329C8×Q8C22×C10711yescharacteristic
330#442—21no—
331#441—21no—
332#440—21no—
333#440—21no—
334C8×D4—21no—
335C8×D4—21no—
336C8×D4C22×C10711yescharacteristic
337C8×D4C22×C10711yescharacteristic
338#432C22×C10711yescharacteristic
339#432C22×C10711yescharacteristic
340#431—21no—
341#431C22×C10711yescharacteristic
342#416—21no—
343#416—21no—
344C2×C4×C8—21no—
345C2×C4×C8C22×C10711yescharacteristic
346#335C22×C10711yescharacteristic
347#335C22×C10711yescharacteristic
348#334C22×C10711yescharacteristic
349#334C22×C10711yescharacteristic
350#333C22×C10711yescharacteristic
351#333C22×C10711yescharacteristic
352#332C22×C10711yescharacteristic
353#332C22×C10711yescharacteristic
354#332C22×C10711yescharacteristic
355#332C22×C10711yescharacteristic
356#331C22×C10711yescharacteristic
357#331C22×C10711yescharacteristic
358C2×#41—21no—
359C2×#41D4×C10711yescharacteristic
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×D8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8D4×C10711yescharacteristic
367C22×C8D4×C10711yescharacteristic
368C4⋊Q8C23×C10711yescharacteristic
369C4⋊Q8C23×C10711yescharacteristic
370C4⋊Q8C23×C10711yescharacteristic
371#127C23×C10711yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8D4×C10711yescharacteristic
381C4×Q8C23×C10711yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4D4×C10711yescharacteristic
387C4×D4C23×C10711yescharacteristic
388#117—21no—
389#117—21no—
390#117D4×C10711yescharacteristic
391C2×C42—21no—
392C2×C42C23×C10711yescharacteristic
393#107—21no—
394#107—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C10711yescharacteristic
400C4⋊C8C23×C10711yescharacteristic
401C4⋊C8C23×C10711yescharacteristic
402C4⋊C8C23×C10711yescharacteristic
403C4⋊C8C23×C10711yescharacteristic
404C4⋊C8C23×C10711yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427#97—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8D4×C10711yescharacteristic
432C4×C8D4×C10711yescharacteristic
433C4×C8C23×C10711yescharacteristic
434C4×C8C23×C10711yescharacteristic
435#41—22no—
436#41—22no—
437#41—42no—
438#41—42no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C10711yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C10711yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4C2×D4×C10711yescharacteristic
454C22×C4C2×D4×C10711yescharacteristic
455C22×C4#41×C10711yescharacteristic
456Q16—42no—
457SD16—42no—
458SD16—42no—
459D8—42no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—42no—
469C2×C8—42no—
470C2×C8C2×D4×C10711yescharacteristic
471C2×C8C2×D4×C10711yescharacteristic
472C2×C8C2×D4×C10711yescharacteristic
473C2×C8C2×D4×C10711yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C10711yescharacteristic
485C4⋊C4C2×D4×C10711yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42C2×D4×C10711yescharacteristic
497C42C2×D4×C10711yescharacteristic
498C42#41×C10711yescharacteristic
499C42C24×C10711yescharacteristic
500C23—21no—
501C23—41no—
502C23#121×C10711yescharacteristic
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8#135×C10712yes—
510D4—24no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4#135×C10712yes—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4#121×C10711yescharacteristic
536C2×C4#121×C10711yescharacteristic
537C2×C4#121×C10711yescharacteristic
538C2×C4C22×D4×C10711yescharacteristic
539C2×C4C22×D4×C10711yescharacteristic
540C2×C4C2×#41×C10711yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C2×#121×C10711yescharacteristic
561C4—21no—
562C4—21no—
563C4—22no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×#135×C10711yescharacteristic
572C4C2×#135×C10711yescharacteristic
573C4#575×C10711yescharacteristic
574C4#575×C10711yescharacteristic
575C2—41no—
576C2—42no—
577C2—161no—
578C2C107×#304011yescharacteristic
579C2C107×#305011yescharacteristic
580C2C107×#306711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#121
commutator, Frattini, cosocleC42C24×C107
prime radicalC107×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3131C2semidirect
2. C107×#3116C2semidirect
4. C8×#41×C107C2semidirect
5. C107×#1684C2semidirect
6. C107×#1683C2semidirect
7. C107×#1682C2semidirect
8. C107×#1681C2semidirect
9. C107×#1680C2semidirect
10. C107×#1679C2semidirect
11. C107×#1678C2semidirect
12. C107×#1677C2semidirect
13. C107×#1568C2semidirect
14. C107×#1554C2semidirect
15. C107×#1553C2semidirect
284. #19278C107direct (N × H)
291. #3131C2×C107semidirect
292. #3116C2×C107semidirect
294. C8×#41C2×C107semidirect
295. #1684C2×C107semidirect
296. #1683C2×C107semidirect
297. #1682C2×C107semidirect
298. #1681C2×C107semidirect
299. #1680C2×C107semidirect
300. #1679C2×C107semidirect
301. #1678C2×C107semidirect
302. #1677C2×C107semidirect
303. #1568C2×C107semidirect
304. #1554C2×C107semidirect
305. #1553C2×C107semidirect
306. C107#19278direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#31312
C107×#31162
C107×#31152
C8×#41×C1072
C107×#16842
C107×#16832
C107×#16822
C107×#16812
C107×#16802
C107×#16792
C107×#16782
C107×#16772
C107×#15682
C107×#15542
C107×#15532
#19278107