Finite Group Databasebeta

← C107×#18668 #41044632

Subgroups — C107×#18668 #41044632

Order 27392.

936 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3507C211yesmaximal, characteristic, complemented
2C107×#3245C211yesmaximal, characteristic
3C107×#3167C211yesmaximal, characteristic, complemented
4C107×#3037C211yesmaximal, characteristic, complemented
5C107×#1652C212yesmaximal, complemented
6C107×#1644C212yesmaximal, complemented
7C107×#1628C212yesmaximal, complemented
8C107×#1622C212yesmaximal, complemented
9C107×#1550C211yesmaximal, characteristic, complemented
10C107×#1492C211yesmaximal, characteristic, complemented
11C2×Q8⋊C8×C107C211yesmaximal, characteristic, complemented
12C2×#137×C107—21no—
13#559×C107—21no—
14#557×C107—21no—
15#556×C107—22no—
16#556×C107C2212yes—
17#554×C107C2212yes—
18#552×C107—22no—
19#539×C107—22no—
20#536×C107—21no—
21#533×C107C2211yescharacteristic
22#532×C107C2211yescharacteristic
23#532×C107C2211yescharacteristic
24#529×C107—22no—
25#520×C107—21no—
26C2×C4×Q8×C107C2211yescharacteristic
27#498×C107C2211yescharacteristic
28#492×C107C2211yescharacteristic
29#487×C107C2211yescharacteristic
30#486×C107C2211yescharacteristic
31#474×C107—21no—
32#474×C107C2212yes—
33#466×C107—22no—
34#465×C107—22no—
35#464×C107—22no—
36#462×C107C2212yes—
37#460×C107C2212yes—
38#459×C107—21no—
39#459×C107C2212yes—
40C4×SD16×C107—22no—
41#423×C107C2211yescharacteristic
42C2×C4⋊C8×C107C2211yescharacteristic
43#417×C107—21no—
44C2×C4×C8×C107C2211yescharacteristic
45#333×C107C2212yes—
46#332×C107C2212yes—
47Q8⋊C8×C107C2212yes—
48Q8⋊C8×C107C2212yes—
49D4⋊C8×C107C2212yes—
50D4⋊C8×C107C2212yes—
51C2×#41×C107—21no—
52C2×#41×C107—21no—
53C22×Q8×C107D411yescharacteristic
54#137×C107—44no—
55C2×Q16×C107—22no—
56C2×SD16×C107—22no—
57C2×SD16×C107—22no—
58C2×D8×C107—22no—
59C2×M16×C107—21no—
60C22×C8×C107—21no—
61C22×C8×C107—21no—
62C4⋊Q8×C107—22no—
63C4⋊Q8×C107D411yescharacteristic
64C4⋊Q8×C107C2311yescharacteristic
65C4⋊Q8×C107C2311yescharacteristic
66C4⋊Q8×C107C2311yescharacteristic
67#127×C107D411yescharacteristic
68#127×C107C2311yescharacteristic
69#126×C107—24no—
70#126×C107—24no—
71#125×C107—24no—
72#125×C107—22no—
73#125×C107—21no—
74#124×C107—22no—
75#124×C107—22no—
76#124×C107—21no—
77#124×C107—21no—
78#123×C107—24no—
79#123×C107—24no—
80C22⋊Q8×C107—22no—
81C22⋊Q8×C107—22no—
82C22⋊Q8×C107—24no—
83C22⋊Q8×C107—21no—
84C22⋊Q8×C107D412yes—
85#121×C107—21no—
86#121×C107—21no—
87#121×C107—21no—
88#121×C107D412yes—
89C4×Q8×C107—22no—
90C4×Q8×C107—22no—
91C4×Q8×C107—21no—
92C4×Q8×C107—21no—
93C4×Q8×C107—21no—
94C4×Q8×C107D412yes—
95C4×Q8×C107D412yes—
96C4×Q8×C107C2312yes—
97C4×D4×C107—24no—
98C4×D4×C107—22no—
99C4×D4×C107—22no—
100C4×D4×C107—21no—
101C4×D4×C107—21no—
102C4×D4×C107—21no—
103C4×D4×C107C2312yes—
104#117×C107—24no—
105#117×C107—21no—
106#117×C107—22no—
107C2×C4⋊C4×C107—21no—
108C2×C4⋊C4×C107—22no—
109C2×C4⋊C4×C107D411yescharacteristic
110C2×C42×C107—21no—
111C2×C42×C107C2311yescharacteristic
112#107×C107—22no—
113#106×C107—22no—
114C4⋊C8×C107—21no—
115C4⋊C8×C107—21no—
116C4⋊C8×C107C2312yes—
117C4⋊C8×C107C2312yes—
118#103×C107—22no—
119#103×C107—22no—
120#102×C107—22no—
121#102×C107—22no—
122#102×C107—22no—
123#102×C107—22no—
124C4×C8×C107—21no—
125C4×C8×C107C2311yescharacteristic
126C4×C8×C107C2311yescharacteristic
127#41×C107—42no—
128#41×C107—42no—
129#41×C107—42no—
130#41×C107—42no—
131C2×Q8×C107—21no—
132C2×Q8×C107—21no—
133C2×Q8×C107—21no—
134C2×Q8×C107—22no—
135C2×Q8×C107—22no—
136C2×Q8×C107—21no—
137C2×Q8×C107C2×D412yes—
138C2×Q8×C107C2×D412yes—
139C2×D4×C107—22no—
140C2×D4×C107—21no—
141C2×D4×C107—21no—
142C2×D4×C107—21no—
143C2×D4×C107—21no—
144C2×D4×C107—21no—
145C2×D4×C107—41no—
146C2×D4×C107C2×D412yes—
147C22×C4×C107—21no—
148C22×C4×C107—24no—
149C22×C4×C107—21no—
150C22×C4×C107—22no—
151C22×C4×C107—41no—
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107C2×D411yescharacteristic
154C22×C4×C107C2×D411yescharacteristic
155Q16×C107—44no—
156SD16×C107—44no—
157SD16×C107—44no—
158D8×C107—82no—
159M16×C107—42no—
160C2×C8×C107—21no—
161C2×C8×C107—21no—
162C2×C8×C107—22no—
163C2×C8×C107—22no—
164C2×C8×C107—42no—
165C2×C8×C107—81no—
166C4⋊C4×C107—24no—
167C4⋊C4×C107—24no—
168C4⋊C4×C107—24no—
169C4⋊C4×C107—22no—
170C4⋊C4×C107—21no—
171C4⋊C4×C107—22no—
172C4⋊C4×C107—21no—
173C4⋊C4×C107—22no—
174C4⋊C4×C107—21no—
175C4⋊C4×C107—22no—
176C4⋊C4×C107—21no—
177C4⋊C4×C107—21no—
178C4⋊C4×C107—21no—
179C4⋊C4×C107—21no—
180C4⋊C4×C107C2×D412yes—
181C4⋊C4×C107C2×D412yes—
182C4⋊C4×C107C2×D412yes—
183C22⋊C4×C107—24no—
184C22⋊C4×C107—24no—
185C22⋊C4×C107—24no—
186C22⋊C4×C107—22no—
187C22⋊C4×C107—22no—
188C22⋊C4×C107—22no—
189C22⋊C4×C107—41no—
190C22⋊C4×C107—41no—
191C42×C107—24no—
192C42×C107—22no—
193C42×C107—22no—
194C42×C107—22no—
195C42×C107C2×D411yescharacteristic
196C42×C107C2×D411yescharacteristic
197C42×C107C2×D411yescharacteristic
198C42×C107C2411yescharacteristic
199C23×C107—22no—
200C23×C107—41no—
201C23×C107#12011yescharacteristic
202Q8×C107—22no—
203Q8×C107—22no—
204Q8×C107—42no—
205Q8×C107—41no—
206Q8×C107—41no—
207Q8×C107—42no—
208Q8×C107—42no—
209Q8×C107—41no—
210Q8×C107—41no—
211D4×C107—22no—
212D4×C107—22no—
213D4×C107—42no—
214D4×C107—44no—
215D4×C107—41no—
216D4×C107—41no—
217D4×C107—41no—
218D4×C107—41no—
219D4×C107—42no—
220D4×C107—81no—
221D4×C107—82no—
222C2×C4×C107—21no—
223C2×C4×C107—21no—
224C2×C4×C107—22no—
225C2×C4×C107—22no—
226C2×C4×C107—22no—
227C2×C4×C107—22no—
228C2×C4×C107—22no—
229C2×C4×C107—41no—
230C2×C4×C107—42no—
231C2×C4×C107—42no—
232C2×C4×C107—42no—
233C2×C4×C107—41no—
234C2×C4×C107—81no—
235C2×C4×C107—84no—
236C2×C4×C107—82no—
237C2×C4×C107#12011yescharacteristic
238C2×C4×C107#12011yescharacteristic
239C2×C4×C107#12011yescharacteristic
240C2×C4×C107#13512yes—
241C2×C4×C107AGL(1,ℤ/8)12yes—
242C2×C4×C107C22×D411yescharacteristic
243C2×C4×C107C22×D411yescharacteristic
244C2×C4×C107C22×D411yescharacteristic
245C8×C107—22no—
246C8×C107—41no—
247C8×C107—42no—
248C8×C107—42no—
249C22×C107—21no—
250C22×C107—21no—
251C22×C107—42no—
252C22×C107—42no—
253C22×C107—42no—
254C22×C107—81no—
255C22×C107—81no—
256C22×C107—81no—
257C22×C107#44912yes—
258C22×C107C2×#12011yescharacteristic
259C4×C107—21no—
260C4×C107—21no—
261C4×C107—21no—
262C4×C107—42no—
263C4×C107—42no—
264C4×C107—42no—
265C4×C107—42no—
266C4×C107—42no—
267C4×C107—81no—
268C4×C107#44912yes—
269C4×C107C2×#13511yescharacteristic
270C4×C107C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C107#57711yescharacteristic
272C4×C107#57811yescharacteristic
273#18668C10711yesmaximal, characteristic, direct product factor, Sylow
274C2×C107—22no—
275C2×C107—82no—
276C2×C107—161no—
277C2×C107C2×#44911yescharacteristic
278C2×C107#301311yescharacteristic
279C2×C107#301811yescharacteristic
280#3507C2×C10711yescharacteristic, complemented
281#3245C2×C10711yescharacteristic
282#3167C2×C10711yescharacteristic, complemented
283#3037C2×C10711yescharacteristic, complemented
284#1652C2×C10712yescomplemented
285#1644C2×C10712yescomplemented
286#1628C2×C10712yescomplemented
287#1622C2×C10712yescomplemented
288#1550C2×C10711yescharacteristic, complemented
289#1492C2×C10711yescharacteristic, complemented
290C2×Q8⋊C8C2×C10711yescharacteristic, complemented
291C107#1866811yescharacteristic, direct product factor, Sylow
292C2×#137—21no—
293#559—21no—
294#557—21no—
295#556—22no—
296#556C22×C10712yes—
297#554C22×C10712yes—
298#552—22no—
299#539—22no—
300#536—21no—
301#533C22×C10711yescharacteristic
302#532C22×C10711yescharacteristic
303#532C22×C10711yescharacteristic
304#529—22no—
305#520—21no—
306C2×C4×Q8C22×C10711yescharacteristic
307#498C22×C10711yescharacteristic
308#492C22×C10711yescharacteristic
309#487C22×C10711yescharacteristic
310#486C22×C10711yescharacteristic
311#474—21no—
312#474C22×C10712yes—
313#466—22no—
314#465—22no—
315#464—22no—
316#462C22×C10712yes—
317#460C22×C10712yes—
318#459—21no—
319#459C22×C10712yes—
320C4×SD16—22no—
321#423C22×C10711yescharacteristic
322C2×C4⋊C8C22×C10711yescharacteristic
323#417—21no—
324C2×C4×C8C22×C10711yescharacteristic
325#333C22×C10712yes—
326#332C22×C10712yes—
327Q8⋊C8C22×C10712yes—
328Q8⋊C8C22×C10712yes—
329D4⋊C8C22×C10712yes—
330D4⋊C8C22×C10712yes—
331C2×#41—21no—
332C2×#41—21no—
333C22×Q8D4×C10711yescharacteristic
334#137—44no—
335C2×Q16—22no—
336C2×SD16—22no—
337C2×SD16—22no—
338C2×D8—22no—
339C2×M16—21no—
340C22×C8—21no—
341C22×C8—21no—
342C4⋊Q8—22no—
343C4⋊Q8D4×C10711yescharacteristic
344C4⋊Q8C23×C10711yescharacteristic
345C4⋊Q8C23×C10711yescharacteristic
346C4⋊Q8C23×C10711yescharacteristic
347#127D4×C10711yescharacteristic
348#127C23×C10711yescharacteristic
349#126—24no—
350#126—24no—
351#125—24no—
352#125—22no—
353#125—21no—
354#124—22no—
355#124—22no—
356#124—21no—
357#124—21no—
358#123—24no—
359#123—24no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—24no—
363C22⋊Q8—21no—
364C22⋊Q8D4×C10712yes—
365#121—21no—
366#121—21no—
367#121—21no—
368#121D4×C10712yes—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8D4×C10712yes—
375C4×Q8D4×C10712yes—
376C4×Q8C23×C10712yes—
377C4×D4—24no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C10712yes—
384#117—24no—
385#117—21no—
386#117—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4D4×C10711yescharacteristic
390C2×C42—21no—
391C2×C42C23×C10711yescharacteristic
392#107—22no—
393#106—22no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8C23×C10712yes—
397C4⋊C8C23×C10712yes—
398#103—22no—
399#103—22no—
400#102—22no—
401#102—22no—
402#102—22no—
403#102—22no—
404C4×C8—21no—
405C4×C8C23×C10711yescharacteristic
406C4×C8C23×C10711yescharacteristic
407#41—42no—
408#41—42no—
409#41—42no—
410#41—42no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8C2×D4×C10712yes—
418C2×Q8C2×D4×C10712yes—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—41no—
426C2×D4C2×D4×C10712yes—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—41no—
432C22×C4C2×D4×C10711yescharacteristic
433C22×C4C2×D4×C10711yescharacteristic
434C22×C4C2×D4×C10711yescharacteristic
435Q16—44no—
436SD16—44no—
437SD16—44no—
438D8—82no—
439M16—42no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—42no—
445C2×C8—81no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4C2×D4×C10712yes—
461C4⋊C4C2×D4×C10712yes—
462C4⋊C4C2×D4×C10712yes—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—24no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42C2×D4×C10711yescharacteristic
476C42C2×D4×C10711yescharacteristic
477C42C2×D4×C10711yescharacteristic
478C42C24×C10711yescharacteristic
479C23—22no—
480C23—41no—
481C23#120×C10711yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—42no—
485Q8—42no—
486Q8—42no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491D4—22no—
492D4—22no—
493D4—42no—
494D4—44no—
495D4—42no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—81no—
501D4—82no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—81no—
515C2×C4—84no—
516C2×C4—82no—
517C2×C4#120×C10711yescharacteristic
518C2×C4#120×C10711yescharacteristic
519C2×C4#120×C10711yescharacteristic
520C2×C4#135×C10712yes—
521C2×C4AGL(1,ℤ/8)×C10712yes—
522C2×C4C22×D4×C10711yescharacteristic
523C2×C4C22×D4×C10711yescharacteristic
524C2×C4C22×D4×C10711yescharacteristic
525C8—22no—
526C8—41no—
527C8—42no—
528C8—42no—
529C22—21no—
530C22—21no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22#449×C10712yes—
538C22C2×#120×C10711yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—81no—
548C4#449×C10712yes—
549C4C2×#135×C10711yescharacteristic
550C4C2×AGL(1,ℤ/8)×C10711yescharacteristic
551C4#577×C10711yescharacteristic
552C4#578×C10711yescharacteristic
553C2—22no—
554C2—82no—
555C2—161no—
556C2C2×#449×C10711yescharacteristic
557C2C107×#301311yescharacteristic
558C2C107×#301811yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC42C24×C107
prime radicalC107×#3245C2
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×#3507C2semidirect
3. C107×#3167C2semidirect
4. C107×#3037C2semidirect
5. C107×#1652C2semidirect
6. C107×#1644C2semidirect
7. C107×#1628C2semidirect
8. C107×#1622C2semidirect
9. C107×#1550C2semidirect
10. C107×#1492C2semidirect
11. C2×Q8⋊C8×C107C2semidirect
273. #18668C107direct (N × H)
280. #3507C2×C107semidirect
282. #3167C2×C107semidirect
283. #3037C2×C107semidirect
284. #1652C2×C107semidirect
285. #1644C2×C107semidirect
286. #1628C2×C107semidirect
287. #1622C2×C107semidirect
288. #1550C2×C107semidirect
289. #1492C2×C107semidirect
290. C2×Q8⋊C8C2×C107semidirect
291. C107#18668direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#35072
C107×#32452
C107×#31672
C107×#30372
C107×#16522
C107×#16442
C107×#16282
C107×#16222
C107×#15502
C107×#14922
C2×Q8⋊C8×C1072
#18668107