Finite Group Databasebeta

← C107×#19379 #41045343

Subgroups — C107×#19379 #41045343

Order 27392.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3252C211yesmaximal, characteristic
2C107×#3238C211yesmaximal, characteristic
3C107×#3165C211yesmaximal, characteristic, complemented
4C107×#2969C211yesmaximal, characteristic
5C107×#1696C211yesmaximal, characteristic, complemented
6C107×#1695C211yesmaximal, characteristic, complemented
7C107×#1692C211yesmaximal, characteristic, complemented
8C107×#1691C211yesmaximal, characteristic, complemented
9C107×#1676C211yesmaximal, characteristic, complemented
10C107×#1675C211yesmaximal, characteristic, complemented
11C107×#1672C211yesmaximal, characteristic, complemented
12C107×#1671C211yesmaximal, characteristic, complemented
13C107×#1569C211yesmaximal, characteristic, complemented
14C107×#1554C211yesmaximal, characteristic, complemented
15C107×#1548C211yesmaximal, characteristic, complemented
16#533×C107C2211yescharacteristic
17C2×C4⋊Q8×C107C2211yescharacteristic
18#529×C107C2211yescharacteristic
19#501×C107—21no—
20#501×C107—21no—
21#501×C107—21no—
22#500×C107C2211yescharacteristic
23#500×C107C2211yescharacteristic
24#498×C107C2211yescharacteristic
25#498×C107C2211yescharacteristic
26#489×C107—21no—
27#483×C107—21no—
28#480×C107—21no—
29#479×C107—21no—
30#477×C107C2211yescharacteristic
31#477×C107C2211yescharacteristic
32#477×C107C2211yescharacteristic
33#476×C107C2211yescharacteristic
34#476×C107C2211yescharacteristic
35#476×C107C2211yescharacteristic
36#470×C107—21no—
37#468×C107—21no—
38#464×C107—21no—
39#462×C107C2211yescharacteristic
40#461×C107C2211yescharacteristic
41#446×C107C2211yescharacteristic
42C8×Q8×C107C2211yescharacteristic
43#436×C107—21no—
44#436×C107C2211yescharacteristic
45#435×C107—21no—
46C8×D4×C107C2211yescharacteristic
47#433×C107—21no—
48#432×C107C2211yescharacteristic
49#431×C107C2211yescharacteristic
50#428×C107—21no—
51#428×C107—21no—
52#423×C107C2211yescharacteristic
53#405×C107—21no—
54C4×M16×C107C2211yescharacteristic
55#335×C107C2211yescharacteristic
56#335×C107C2211yescharacteristic
57#334×C107C2211yescharacteristic
58#334×C107C2211yescharacteristic
59#333×C107C2211yescharacteristic
60#333×C107C2211yescharacteristic
61#333×C107C2211yescharacteristic
62#333×C107C2211yescharacteristic
63#333×C107C2211yescharacteristic
64#333×C107C2211yescharacteristic
65#332×C107C2211yescharacteristic
66#332×C107C2211yescharacteristic
67C22×Q8×C107—21no—
68C2×Q16×C107—21no—
69C2×SD16×C107—21no—
70C2×M16×C107—21no—
71C2×M16×C107—21no—
72C2×M16×C107D411yescharacteristic
73C2×M16×C107D411yescharacteristic
74C22×C8×C107—21no—
75C4⋊Q8×C107—21no—
76C4⋊Q8×C107—21no—
77C4⋊Q8×C107—21no—
78C4⋊Q8×C107C2311yescharacteristic
79C4⋊Q8×C107C2311yescharacteristic
80C4⋊Q8×C107C2311yescharacteristic
81C4⋊Q8×C107C2311yescharacteristic
82#126×C107—21no—
83#125×C107—21no—
84#125×C107D411yescharacteristic
85#124×C107D411yescharacteristic
86#123×C107—21no—
87C22⋊Q8×C107—21no—
88C22⋊Q8×C107—21no—
89C22⋊Q8×C107D411yescharacteristic
90#121×C107D411yescharacteristic
91C4×Q8×C107—21no—
92C4×Q8×C107—21no—
93C4×Q8×C107C2311yescharacteristic
94C4×D4×C107—21no—
95C4×D4×C107C2311yescharacteristic
96#117×C107—21no—
97#117×C107—21no—
98C2×C4⋊C4×C107—21no—
99C2×C4⋊C4×C107—21no—
100C2×C42×C107C2311yescharacteristic
101#107×C107—21no—
102#107×C107—21no—
103#107×C107—21no—
104#107×C107—21no—
105#107×C107—21no—
106#107×C107—21no—
107#107×C107—21no—
108#106×C107—21no—
109#106×C107—21no—
110#106×C107—21no—
111#106×C107—21no—
112#106×C107—21no—
113#106×C107—21no—
114#106×C107—21no—
115C4⋊C8×C107—21no—
116C4⋊C8×C107—21no—
117C4⋊C8×C107—21no—
118C4⋊C8×C107C2311yescharacteristic
119C4⋊C8×C107C2311yescharacteristic
120C4⋊C8×C107C2311yescharacteristic
121C4⋊C8×C107C2311yescharacteristic
122C4⋊C8×C107C2311yescharacteristic
123C4⋊C8×C107C2311yescharacteristic
124#103×C107—21no—
125#103×C107—21no—
126#103×C107—21no—
127#103×C107—21no—
128#103×C107—21no—
129#102×C107—21no—
130#102×C107—21no—
131#102×C107—21no—
132C22⋊C8×C107—21no—
133C22⋊C8×C107—21no—
134C22⋊C8×C107—21no—
135C22⋊C8×C107—21no—
136#97×C107—21no—
137#97×C107—21no—
138#97×C107D411yescharacteristic
139#97×C107D411yescharacteristic
140C4×C8×C107—21no—
141C4×C8×C107—21no—
142C4×C8×C107C2311yescharacteristic
143C4×C8×C107C2311yescharacteristic
144C2×Q8×C107—21no—
145C2×Q8×C107—21no—
146C2×Q8×C107—21no—
147C2×Q8×C107—21no—
148C2×Q8×C107—41no—
149C2×Q8×C107—82no—
150C2×Q8×C107C2×D411yescharacteristic
151C2×D4×C107—21no—
152C2×D4×C107C2×D411yescharacteristic
153C22×C4×C107—21no—
154C22×C4×C107—41no—
155C22×C4×C107C2×D411yescharacteristic
156C22×C4×C107C2×D411yescharacteristic
157C22×C4×C107#4111yescharacteristic
158Q16×C107—81no—
159SD16×C107—81no—
160M16×C107—22no—
161M16×C107—22no—
162M16×C107—42no—
163M16×C107—81no—
164C2×C8×C107—21no—
165C2×C8×C107—21no—
166C2×C8×C107—21no—
167C2×C8×C107—21no—
168C2×C8×C107—21no—
169C2×C8×C107—21no—
170C2×C8×C107—42no—
171C2×C8×C107C2×D411yescharacteristic
172C2×C8×C107C2×D411yescharacteristic
173C2×C8×C107C2×D411yescharacteristic
174C2×C8×C107C2×D411yescharacteristic
175C4⋊C4×C107—21no—
176C4⋊C4×C107—21no—
177C4⋊C4×C107—21no—
178C4⋊C4×C107—21no—
179C4⋊C4×C107—21no—
180C4⋊C4×C107—21no—
181C4⋊C4×C107—21no—
182C4⋊C4×C107—21no—
183C4⋊C4×C107—21no—
184C4⋊C4×C107—21no—
185C4⋊C4×C107—21no—
186C4⋊C4×C107—21no—
187C4⋊C4×C107—41no—
188C4⋊C4×C107—41no—
189C4⋊C4×C107—41no—
190C4⋊C4×C107—41no—
191C4⋊C4×C107C2×D411yescharacteristic
192C4⋊C4×C107C2×D411yescharacteristic
193C22⋊C4×C107—21no—
194C22⋊C4×C107—21no—
195C22⋊C4×C107—21no—
196C22⋊C4×C107—21no—
197C22⋊C4×C107—21no—
198C22⋊C4×C107—41no—
199C42×C107—21no—
200C42×C107—41no—
201C42×C107C2×D411yescharacteristic
202C42×C107C2×D411yescharacteristic
203C42×C107#4111yescharacteristic
204C42×C107C2411yescharacteristic
205C23×C107—21no—
206C23×C107#12111yescharacteristic
207Q8×C107—21no—
208Q8×C107—21no—
209Q8×C107—41no—
210Q8×C107—41no—
211Q8×C107—81no—
212Q8×C107—81no—
213Q8×C107—81no—
214Q8×C107—82no—
215D4×C107—21no—
216D4×C107—21no—
217D4×C107—81no—
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—21no—
225C2×C4×C107—41no—
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—82no—
233C2×C4×C107#12111yescharacteristic
234C2×C4×C107#12111yescharacteristic
235C2×C4×C107#12111yescharacteristic
236C2×C4×C107C22×D411yescharacteristic
237C2×C4×C107C22×D411yescharacteristic
238C2×C4×C107C2×#4111yescharacteristic
239C8×C107—21no—
240C8×C107—21no—
241C8×C107—41no—
242C8×C107—41no—
243C8×C107—41no—
244C8×C107—41no—
245C8×C107—41no—
246C8×C107—41no—
247C8×C107#13712yes—
248C8×C107#13712yes—
249C22×C107—21no—
250C22×C107—21no—
251C22×C107—21no—
252C22×C107—41no—
253C22×C107—41no—
254C22×C107—41no—
255C22×C107C2×#12111yescharacteristic
256C4×C107—21no—
257C4×C107—21no—
258C4×C107—21no—
259C4×C107—21no—
260C4×C107—41no—
261C4×C107—41no—
262C4×C107—41no—
263C4×C107—81no—
264C4×C107—81no—
265C4×C107—81no—
266C4×C107—81no—
267C4×C107C2×#13711yescharacteristic
268C4×C107C2×#13711yescharacteristic
269C4×C107#57711yescharacteristic
270C4×C107#57811yescharacteristic
271#19379C10711yesmaximal, characteristic, direct product factor, Sylow
272C2×C107—41no—
273C2×C107—81no—
274C2×C107#303911yescharacteristic
275C2×C107#306311yescharacteristic
276C2×C107#306811yescharacteristic
277#3252C2×C10711yescharacteristic
278#3238C2×C10711yescharacteristic
279#3165C2×C10711yescharacteristic, complemented
280#2969C2×C10711yescharacteristic
281#1696C2×C10711yescharacteristic, complemented
282#1695C2×C10711yescharacteristic, complemented
283#1692C2×C10711yescharacteristic, complemented
284#1691C2×C10711yescharacteristic, complemented
285#1676C2×C10711yescharacteristic, complemented
286#1675C2×C10711yescharacteristic, complemented
287#1672C2×C10711yescharacteristic, complemented
288#1671C2×C10711yescharacteristic, complemented
289#1569C2×C10711yescharacteristic, complemented
290#1554C2×C10711yescharacteristic, complemented
291#1548C2×C10711yescharacteristic, complemented
292C107#1937911yescharacteristic, direct product factor, Sylow
293#533C22×C10711yescharacteristic
294C2×C4⋊Q8C22×C10711yescharacteristic
295#529C22×C10711yescharacteristic
296#501—21no—
297#501—21no—
298#501—21no—
299#500C22×C10711yescharacteristic
300#500C22×C10711yescharacteristic
301#498C22×C10711yescharacteristic
302#498C22×C10711yescharacteristic
303#489—21no—
304#483—21no—
305#480—21no—
306#479—21no—
307#477C22×C10711yescharacteristic
308#477C22×C10711yescharacteristic
309#477C22×C10711yescharacteristic
310#476C22×C10711yescharacteristic
311#476C22×C10711yescharacteristic
312#476C22×C10711yescharacteristic
313#470—21no—
314#468—21no—
315#464—21no—
316#462C22×C10711yescharacteristic
317#461C22×C10711yescharacteristic
318#446C22×C10711yescharacteristic
319C8×Q8C22×C10711yescharacteristic
320#436—21no—
321#436C22×C10711yescharacteristic
322#435—21no—
323C8×D4C22×C10711yescharacteristic
324#433—21no—
325#432C22×C10711yescharacteristic
326#431C22×C10711yescharacteristic
327#428—21no—
328#428—21no—
329#423C22×C10711yescharacteristic
330#405—21no—
331C4×M16C22×C10711yescharacteristic
332#335C22×C10711yescharacteristic
333#335C22×C10711yescharacteristic
334#334C22×C10711yescharacteristic
335#334C22×C10711yescharacteristic
336#333C22×C10711yescharacteristic
337#333C22×C10711yescharacteristic
338#333C22×C10711yescharacteristic
339#333C22×C10711yescharacteristic
340#333C22×C10711yescharacteristic
341#333C22×C10711yescharacteristic
342#332C22×C10711yescharacteristic
343#332C22×C10711yescharacteristic
344C22×Q8—21no—
345C2×Q16—21no—
346C2×SD16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16D4×C10711yescharacteristic
350C2×M16D4×C10711yescharacteristic
351C22×C8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8C23×C10711yescharacteristic
356C4⋊Q8C23×C10711yescharacteristic
357C4⋊Q8C23×C10711yescharacteristic
358C4⋊Q8C23×C10711yescharacteristic
359#126—21no—
360#125—21no—
361#125D4×C10711yescharacteristic
362#124D4×C10711yescharacteristic
363#123—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8D4×C10711yescharacteristic
367#121D4×C10711yescharacteristic
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C23×C10711yescharacteristic
371C4×D4—21no—
372C4×D4C23×C10711yescharacteristic
373#117—21no—
374#117—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C42C23×C10711yescharacteristic
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C10711yescharacteristic
396C4⋊C8C23×C10711yescharacteristic
397C4⋊C8C23×C10711yescharacteristic
398C4⋊C8C23×C10711yescharacteristic
399C4⋊C8C23×C10711yescharacteristic
400C4⋊C8C23×C10711yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413#97—21no—
414#97—21no—
415#97D4×C10711yescharacteristic
416#97D4×C10711yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8C23×C10711yescharacteristic
420C4×C8C23×C10711yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8C2×D4×C10711yescharacteristic
428C2×D4—21no—
429C2×D4C2×D4×C10711yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4C2×D4×C10711yescharacteristic
433C22×C4C2×D4×C10711yescharacteristic
434C22×C4#41×C10711yescharacteristic
435Q16—81no—
436SD16—81no—
437M16—22no—
438M16—22no—
439M16—42no—
440M16—81no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8C2×D4×C10711yescharacteristic
449C2×C8C2×D4×C10711yescharacteristic
450C2×C8C2×D4×C10711yescharacteristic
451C2×C8C2×D4×C10711yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C10711yescharacteristic
469C4⋊C4C2×D4×C10711yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C42—21no—
477C42—41no—
478C42C2×D4×C10711yescharacteristic
479C42C2×D4×C10711yescharacteristic
480C42#41×C10711yescharacteristic
481C42C24×C10711yescharacteristic
482C23—21no—
483C23#121×C10711yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490Q8—81no—
491Q8—82no—
492D4—21no—
493D4—21no—
494D4—81no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—82no—
510C2×C4#121×C10711yescharacteristic
511C2×C4#121×C10711yescharacteristic
512C2×C4#121×C10711yescharacteristic
513C2×C4C22×D4×C10711yescharacteristic
514C2×C4C22×D4×C10711yescharacteristic
515C2×C4C2×#41×C10711yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8#137×C10712yes—
525C8#137×C10712yes—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22C2×#121×C10711yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4C2×#137×C10711yescharacteristic
545C4C2×#137×C10711yescharacteristic
546C4#577×C10711yescharacteristic
547C4#578×C10711yescharacteristic
548C2—41no—
549C2—81no—
550C2C107×#303911yescharacteristic
551C2C107×#306311yescharacteristic
552C2C107×#306811yescharacteristic
subgroupG/H
center, socleC22×C107C2×#121
commutator, Frattini, cosocleC42C24×C107
prime radical#121×C107D4
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
3. C107×#3165C2semidirect
5. C107×#1696C2semidirect
6. C107×#1695C2semidirect
7. C107×#1692C2semidirect
8. C107×#1691C2semidirect
9. C107×#1676C2semidirect
10. C107×#1675C2semidirect
11. C107×#1672C2semidirect
12. C107×#1671C2semidirect
13. C107×#1569C2semidirect
14. C107×#1554C2semidirect
15. C107×#1548C2semidirect
271. #19379C107direct (N × H)
279. #3165C2×C107semidirect
281. #1696C2×C107semidirect
282. #1695C2×C107semidirect
283. #1692C2×C107semidirect
284. #1691C2×C107semidirect
285. #1676C2×C107semidirect
286. #1675C2×C107semidirect
287. #1672C2×C107semidirect
288. #1671C2×C107semidirect
289. #1569C2×C107semidirect
290. #1554C2×C107semidirect
291. #1548C2×C107semidirect
292. C107#19379direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#32522
C107×#32382
C107×#31652
C107×#29692
C107×#16962
C107×#16952
C107×#16922
C107×#16912
C107×#16762
C107×#16752
C107×#16722
C107×#16712
C107×#15692
C107×#15542
C107×#15482
#19379107