Finite Group Databasebeta

← C107×#9241 #41035205

Subgroups — C107×#9241 #41035205

Order 27392.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C107C211yesmaximal, characteristic
2C107×#2880C211yesmaximal, characteristic, complemented
3C107×#1789C211yesmaximal, characteristic, complemented
4C107×#1507C211yesmaximal, characteristic, complemented
5C107×#1471C211yesmaximal, characteristic, complemented
6C107×#1293C211yesmaximal, characteristic, complemented
7C107×#1282C211yesmaximal, characteristic, complemented
8C22×#41×C107C2211yescharacteristic
9C22×SD16×C107C411yescharacteristic, complemented
10C22×D8×C107C411yescharacteristic, complemented
11C2×#131×C107—21no—
12C2×#121×C107C2211yescharacteristic
13#449×C107—21no—
14#449×C107—21no—
15#449×C107—21no—
16#449×C107—21no—
17C2×#104×C107—21no—
18C2×#104×C107—21no—
19C2×#103×C107C411yescharacteristic, complemented
20C2×#102×C107C411yescharacteristic, complemented
21#408×C107—21no—
22#408×C107—22no—
23#407×C107—21no—
24#407×C107C2211yescharacteristic
25#407×C107C2211yescharacteristic
26C2×C22⋊C8×C107—21no—
27C2×C22⋊C8×C107C2211yescharacteristic
28C2×C22⋊C8×C107C2211yescharacteristic
29C4×C22⋊C4×C107C2211yescharacteristic
30#327×C107—22no—
31#323×C107—21no—
32#323×C107—21no—
33C2×#41×C107—21no—
34C2×#41×C107—21no—
35C2×#41×C107—42no—
36C2×#41×C107—42no—
37C2×#41×C107D411yescharacteristic
38C2×#41×C107D411yescharacteristic
39C2×#41×C107D411yescharacteristic
40C2×#41×C107D411yescharacteristic
41C22×Q8×C107C2×C411yescharacteristic
42C22×D4×C107—21no—
43C22×D4×C107—21no—
44C22×D4×C107C2×C411yescharacteristic
45C22×D4×C107C2×C411yescharacteristic
46C23×C4×C107—21no—
47C23×C4×C107C2311yescharacteristic
48C2×SD16×C107—21no—
49C2×SD16×C107—21no—
50C2×SD16×C107—42no—
51C2×D8×C107—21no—
52C2×D8×C107—21no—
53C2×D8×C107—42no—
54#131×C107—42no—
55#131×C107—42no—
56C2×M16×C107—22no—
57C2×M16×C107—21no—
58C2×M16×C107—21no—
59C22×C8×C107—22no—
60C22×C8×C107—21no—
61C22×C8×C107C2×C411yescharacteristic
62C22×C8×C107C2×C411yescharacteristic
63#121×C107—21no—
64#121×C107—21no—
65#121×C107—21no—
66#121×C107—21no—
67C2×C4⋊C4×C107C2×C411yescharacteristic
68C2×C22⋊C4×C107—21no—
69C2×C22⋊C4×C107—21no—
70C2×C42×C107—21no—
71#104×C107—42no—
72#104×C107—42no—
73#103×C107—21no—
74#103×C107—21no—
75#102×C107—21no—
76#102×C107—21no—
77C22⋊C8×C107—22no—
78C22⋊C8×C107—22no—
79C22⋊C8×C107—21no—
80C22⋊C8×C107—21no—
81C22⋊C8×C107—21no—
82C22⋊C8×C107—21no—
83C22⋊C8×C107—21no—
84C22⋊C8×C107—21no—
85C22⋊C8×C107D411yescharacteristic
86C22⋊C8×C107D411yescharacteristic
87C22⋊C8×C107D412yes—
88#95×C107—21no—
89C24×C107—21no—
90C24×C107—21no—
91C24×C107#4111yescharacteristic
92#41×C107—22no—
93#41×C107—22no—
94#41×C107—22no—
95#41×C107—22no—
96#41×C107—41no—
97#41×C107—41no—
98#41×C107—41no—
99#41×C107—41no—
100#41×C107—44no—
101#41×C107—44no—
102C2×Q8×C107—21no—
103C2×Q8×C107—22no—
104C2×Q8×C107—41no—
105C2×Q8×C107C22⋊C411yescharacteristic
106C2×Q8×C107C22⋊C411yescharacteristic
107C2×D4×C107—21no—
108C2×D4×C107—22no—
109C2×D4×C107—21no—
110C2×D4×C107—21no—
111C2×D4×C107—21no—
112C2×D4×C107—21no—
113C2×D4×C107—21no—
114C2×D4×C107—21no—
115C2×D4×C107—41no—
116C2×D4×C107—41no—
117C2×D4×C107—41no—
118C2×D4×C107—44no—
119C2×D4×C107—41no—
120C2×D4×C107—41no—
121C2×D4×C107—82no—
122C2×D4×C107C22⋊C411yescharacteristic
123C2×D4×C107C22⋊C411yescharacteristic
124C22×C4×C107—21no—
125C22×C4×C107—21no—
126C22×C4×C107—21no—
127C22×C4×C107—21no—
128C22×C4×C107—21no—
129C22×C4×C107—21no—
130C22×C4×C107—41no—
131C22×C4×C107—41no—
132C22×C4×C107—44no—
133C22×C4×C107—41no—
134C22×C4×C107C22×C411yescharacteristic
135C22×C4×C107C2×D411yescharacteristic
136C22×C4×C107C2×D411yescharacteristic
137C22×C4×C107C2×D411yescharacteristic
138C22×C4×C107C2×D411yescharacteristic
139C22×C4×C107#4111yescharacteristic
140SD16×C107—42no—
141SD16×C107—42no—
142D8×C107—42no—
143D8×C107—42no—
144M16×C107—44no—
145M16×C107—41no—
146M16×C107—41no—
147M16×C107—41no—
148M16×C107—41no—
149C2×C8×C107—21no—
150C2×C8×C107—21no—
151C2×C8×C107—21no—
152C2×C8×C107—22no—
153C2×C8×C107—21no—
154C2×C8×C107—44no—
155C2×C8×C107—41no—
156C2×C8×C107—41no—
157C2×C8×C107—41no—
158C2×C8×C107—41no—
159C2×C8×C107—41no—
160C4⋊C4×C107—21no—
161C4⋊C4×C107—21no—
162C22⋊C4×C107—22no—
163C22⋊C4×C107—41no—
164C22⋊C4×C107—41no—
165C22⋊C4×C107—41no—
166C42×C107—41no—
167C42×C107—41no—
168C23×C107—21no—
169C23×C107—21no—
170C23×C107—21no—
171C23×C107—21no—
172C23×C107—41no—
173C23×C107—41no—
174C23×C107—42no—
175C23×C107—41no—
176C23×C107—41no—
177C23×C107—41no—
178C23×C107—41no—
179C23×C107—41no—
180C23×C107—81no—
181C23×C107—81no—
182C23×C107—81no—
183C23×C107C4×D411yescharacteristic
184C23×C107#12111yescharacteristic
185C23×C107#12311yescharacteristic
186Q8×C107—21no—
187Q8×C107—21no—
188Q8×C107—21no—
189Q8×C107—42no—
190Q8×C107#9912yes—
191D4×C107—24no—
192D4×C107—21no—
193D4×C107—21no—
194D4×C107—21no—
195D4×C107—42no—
196D4×C107—42no—
197D4×C107—42no—
198D4×C107—42no—
199D4×C107—41no—
200D4×C107—41no—
201D4×C107—81no—
202D4×C107—82no—
203D4×C107—82no—
204D4×C107#9912yes—
205C2×C4×C107—24no—
206C2×C4×C107—21no—
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—21no—
214C2×C4×C107—41no—
215C2×C4×C107—41no—
216C2×C4×C107—41no—
217C2×C4×C107—42no—
218C2×C4×C107—42no—
219C2×C4×C107—42no—
220C2×C4×C107—42no—
221C2×C4×C107—42no—
222C2×C4×C107—41no—
223C2×C4×C107—81no—
224C2×C4×C107—81no—
225C2×C4×C107—81no—
226C2×C4×C107C2×C22⋊C411yescharacteristic
227C2×C4×C107C4×D411yescharacteristic
228C2×C4×C107#12011yescharacteristic
229C2×C4×C107#12111yescharacteristic
230C8×C107—41no—
231C8×C107—42no—
232C8×C107—41no—
233C8×C107—41no—
234C8×C107—41no—
235C8×C107—81no—
236C22×C107—21no—
237C22×C107—21no—
238C22×C107—21no—
239C22×C107—21no—
240C22×C107—21no—
241C22×C107—21no—
242C22×C107—22no—
243C22×C107—21no—
244C22×C107—21no—
245C22×C107—41no—
246C22×C107—41no—
247C22×C107—41no—
248C22×C107—41no—
249C22×C107—41no—
250C22×C107—81no—
251C22×C107—81no—
252C22×C107—82no—
253C22×C107—82no—
254C22×C107—81no—
255C22×C107—81no—
256C22×C107—81no—
257C22×C107—161no—
258C22×C107—161no—
259C22×C107#38611yescharacteristic
260C22×C107#44311yescharacteristic
261C22×C107#44411yescharacteristic
262C4×C107—21no—
263C4×C107—21no—
264C4×C107—22no—
265C4×C107—21no—
266C4×C107—41no—
267C4×C107—82no—
268C4×C107—81no—
269C4×C107C2×#9911yescharacteristic
270C4×C107C2×#9911yescharacteristic
271#9241C10711yesmaximal, characteristic, direct product factor, Sylow
272C2×C107—21no—
273C2×C107—21no—
274C2×C107—41no—
275C2×C107—41no—
276C2×C107—42no—
277C2×C107—81no—
278C2×C107—161no—
279C2×C107#187611yescharacteristic
280C2×C107#189811yescharacteristic
281C2×C107#190311yescharacteristic
282C2×#449C2×C10711yescharacteristic
283#2880C2×C10711yescharacteristic, complemented
284#1789C2×C10711yescharacteristic, complemented
285#1507C2×C10711yescharacteristic, complemented
286#1471C2×C10711yescharacteristic, complemented
287#1293C2×C10711yescharacteristic, complemented
288#1282C2×C10711yescharacteristic, complemented
289C107#924111yescharacteristic, direct product factor, Sylow
290C22×#41C22×C10711yescharacteristic
291C22×SD16C4×C10711yescharacteristic, complemented
292C22×D8C4×C10711yescharacteristic, complemented
293C2×#131—21no—
294C2×#121C22×C10711yescharacteristic
295#449—21no—
296#449—21no—
297#449—21no—
298#449—21no—
299C2×#104—21no—
300C2×#104—21no—
301C2×#103C4×C10711yescharacteristic, complemented
302C2×#102C4×C10711yescharacteristic, complemented
303#408—21no—
304#408—22no—
305#407—21no—
306#407C22×C10711yescharacteristic
307#407C22×C10711yescharacteristic
308C2×C22⋊C8—21no—
309C2×C22⋊C8C22×C10711yescharacteristic
310C2×C22⋊C8C22×C10711yescharacteristic
311C4×C22⋊C4C22×C10711yescharacteristic
312#327—22no—
313#323—21no—
314#323—21no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41D4×C10711yescharacteristic
320C2×#41D4×C10711yescharacteristic
321C2×#41D4×C10711yescharacteristic
322C2×#41D4×C10711yescharacteristic
323C22×Q8C2×C4×C10711yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×C4×C10711yescharacteristic
327C22×D4C2×C4×C10711yescharacteristic
328C23×C4—21no—
329C23×C4C23×C10711yescharacteristic
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—42no—
333C2×D8—21no—
334C2×D8—21no—
335C2×D8—42no—
336#131—42no—
337#131—42no—
338C2×M16—22no—
339C2×M16—21no—
340C2×M16—21no—
341C22×C8—22no—
342C22×C8—21no—
343C22×C8C2×C4×C10711yescharacteristic
344C22×C8C2×C4×C10711yescharacteristic
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349C2×C4⋊C4C2×C4×C10711yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353#104—42no—
354#104—42no—
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8D4×C10711yescharacteristic
368C22⋊C8D4×C10711yescharacteristic
369C22⋊C8D4×C10712yes—
370#95—21no—
371C24—21no—
372C24—21no—
373C24#41×C10711yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8C22⋊C4×C10711yescharacteristic
388C2×Q8C22⋊C4×C10711yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—44no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—82no—
404C2×D4C22⋊C4×C10711yescharacteristic
405C2×D4C22⋊C4×C10711yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—41no—
416C22×C4C22×C4×C10711yescharacteristic
417C22×C4C2×D4×C10711yescharacteristic
418C22×C4C2×D4×C10711yescharacteristic
419C22×C4C2×D4×C10711yescharacteristic
420C22×C4C2×D4×C10711yescharacteristic
421C22×C4#41×C10711yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—44no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C42—41no—
449C42—41no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23C4×D4×C10711yescharacteristic
466C23#121×C10711yescharacteristic
467C23#123×C10711yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#99×C10712yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4#99×C10712yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4C2×C22⋊C4×C10711yescharacteristic
509C2×C4C4×D4×C10711yescharacteristic
510C2×C4#120×C10711yescharacteristic
511C2×C4#121×C10711yescharacteristic
512C8—41no—
513C8—42no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—81no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22#386×C10711yescharacteristic
542C22#443×C10711yescharacteristic
543C22#444×C10711yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—81no—
551C4C2×#99×C10711yescharacteristic
552C4C2×#99×C10711yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2C107×#187611yescharacteristic
561C2C107×#189811yescharacteristic
562C2C107×#190311yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC2×#449×C107C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2880C2semidirect
3. C107×#1789C2semidirect
4. C107×#1507C2semidirect
5. C107×#1471C2semidirect
6. C107×#1293C2semidirect
7. C107×#1282C2semidirect
9. C22×SD16×C107C4semidirect
10. C22×D8×C107C4semidirect
19. C2×#103×C107C4semidirect
20. C2×#102×C107C4semidirect
271. #9241C107direct (N × H)
283. #2880C2×C107semidirect
284. #1789C2×C107semidirect
285. #1507C2×C107semidirect
286. #1471C2×C107semidirect
287. #1293C2×C107semidirect
288. #1282C2×C107semidirect
289. C107#9241direct (N × H)
291. C22×SD16C4×C107semidirect
292. C22×D8C4×C107semidirect
301. C2×#103C4×C107semidirect
302. C2×#102C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1072
C107×#28802
C107×#17892
C107×#15072
C107×#14712
C107×#12932
C107×#12822
#9241107