Finite Group Databasebeta

← C107×#18669 #41044633

Subgroups — C107×#18669 #41044633

Order 27392.

882 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3507C211yesmaximal, characteristic
2C107×#3246C211yesmaximal, characteristic
3C107×#3170C211yesmaximal, characteristic, complemented
4C107×#3078C211yesmaximal, characteristic, complemented
5C107×#1650C212yesmaximal, complemented
6C107×#1643C212yesmaximal, complemented
7C107×#1638C212yesmaximal, complemented
8C107×#1632C212yesmaximal, complemented
9C107×#1550C211yesmaximal, characteristic, complemented
10C107×#1492C211yesmaximal, characteristic
11C2×Q8⋊C8×C107C211yesmaximal, characteristic, complemented
12#559×C107—21no—
13#557×C107—21no—
14#556×C107—22no—
15#556×C107C2212yes—
16#554×C107C2212yes—
17#552×C107—22no—
18#539×C107—22no—
19#536×C107—21no—
20#533×C107C2211yescharacteristic
21#533×C107C2211yescharacteristic
22#532×C107C2211yescharacteristic
23#529×C107—22no—
24#520×C107—21no—
25C2×C4×Q8×C107C2211yescharacteristic
26#500×C107C2211yescharacteristic
27#494×C107C2211yescharacteristic
28#487×C107C2211yescharacteristic
29#487×C107C2211yescharacteristic
30#479×C107—22no—
31#477×C107C2212yes—
32#476×C107C2212yes—
33#475×C107—21no—
34#475×C107C2212yes—
35#467×C107—22no—
36#465×C107—22no—
37#461×C107C2212yes—
38#460×C107—21no—
39C4×Q16×C107—22no—
40#428×C107—21no—
41#423×C107C2211yescharacteristic
42C2×C4⋊C8×C107C2211yescharacteristic
43#419×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—
52C22×Q8×C107D411yescharacteristic
53C2×Q16×C107—22no—
54C2×SD16×C107—22no—
55C2×M16×C107—21no—
56C22×C8×C107—21no—
57C22×C8×C107—21no—
58C4⋊Q8×C107—22no—
59C4⋊Q8×C107D411yescharacteristic
60C4⋊Q8×C107C2311yescharacteristic
61C4⋊Q8×C107C2311yescharacteristic
62C4⋊Q8×C107C2311yescharacteristic
63C4⋊Q8×C107C2311yescharacteristic
64#127×C107D411yescharacteristic
65#126×C107—24no—
66#126×C107—24no—
67#125×C107—24no—
68#125×C107—22no—
69#125×C107—21no—
70#125×C107—21no—
71#124×C107—22no—
72#124×C107—22no—
73#124×C107—21no—
74#123×C107—24no—
75#123×C107—24no—
76C22⋊Q8×C107—22no—
77C22⋊Q8×C107—22no—
78C22⋊Q8×C107—24no—
79C22⋊Q8×C107—21no—
80C22⋊Q8×C107—21no—
81C22⋊Q8×C107—21no—
82C22⋊Q8×C107D412yes—
83#121×C107—21no—
84#121×C107D412yes—
85C4×Q8×C107—22no—
86C4×Q8×C107—22no—
87C4×Q8×C107—21no—
88C4×Q8×C107—21no—
89C4×Q8×C107—21no—
90C4×Q8×C107—21no—
91C4×Q8×C107—21no—
92C4×Q8×C107D412yes—
93C4×Q8×C107D412yes—
94C4×Q8×C107C2312yes—
95C4×D4×C107—24no—
96C4×D4×C107—22no—
97C4×D4×C107—22no—
98C4×D4×C107—21no—
99C4×D4×C107C2312yes—
100#117×C107—24no—
101#117×C107—21no—
102#117×C107—22no—
103#117×C107—21no—
104C2×C4⋊C4×C107—21no—
105C2×C4⋊C4×C107—22no—
106C2×C4⋊C4×C107D411yescharacteristic
107C2×C42×C107—21no—
108C2×C42×C107C2311yescharacteristic
109#107×C107—22no—
110#107×C107—22no—
111#106×C107—22no—
112#106×C107—22no—
113C4⋊C8×C107—21no—
114C4⋊C8×C107—21no—
115C4⋊C8×C107C2312yes—
116C4⋊C8×C107C2312yes—
117#103×C107—22no—
118#103×C107—22no—
119#103×C107—22no—
120#103×C107—22no—
121#103×C107—22no—
122#102×C107—22no—
123C4×C8×C107—21no—
124C4×C8×C107C2311yescharacteristic
125C4×C8×C107C2311yescharacteristic
126#41×C107—42no—
127#41×C107—42no—
128C2×Q8×C107—21no—
129C2×Q8×C107—21no—
130C2×Q8×C107—21no—
131C2×Q8×C107—22no—
132C2×Q8×C107—22no—
133C2×Q8×C107—21no—
134C2×Q8×C107—21no—
135C2×Q8×C107C2×D412yes—
136C2×Q8×C107C2×D412yes—
137C2×D4×C107—22no—
138C2×D4×C107—21no—
139C2×D4×C107—21no—
140C2×D4×C107C2×D412yes—
141C22×C4×C107—21no—
142C22×C4×C107—24no—
143C22×C4×C107—21no—
144C22×C4×C107—22no—
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107C2×D411yescharacteristic
147C22×C4×C107C2×D411yescharacteristic
148Q16×C107—44no—
149SD16×C107—82no—
150M16×C107—42no—
151C2×C8×C107—21no—
152C2×C8×C107—21no—
153C2×C8×C107—22no—
154C2×C8×C107—22no—
155C2×C8×C107—42no—
156C2×C8×C107—81no—
157C4⋊C4×C107—24no—
158C4⋊C4×C107—24no—
159C4⋊C4×C107—24no—
160C4⋊C4×C107—22no—
161C4⋊C4×C107—21no—
162C4⋊C4×C107—22no—
163C4⋊C4×C107—21no—
164C4⋊C4×C107—22no—
165C4⋊C4×C107—21no—
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—41no—
174C4⋊C4×C107—41no—
175C4⋊C4×C107C2×D412yes—
176C4⋊C4×C107C2×D412yes—
177C4⋊C4×C107C2×D412yes—
178C22⋊C4×C107—24no—
179C22⋊C4×C107—24no—
180C22⋊C4×C107—24no—
181C22⋊C4×C107—22no—
182C22⋊C4×C107—22no—
183C22⋊C4×C107—22no—
184C22⋊C4×C107—41no—
185C42×C107—24no—
186C42×C107—22no—
187C42×C107—22no—
188C42×C107—22no—
189C42×C107—41no—
190C42×C107C2×D411yescharacteristic
191C42×C107C2×D411yescharacteristic
192C42×C107C2×D411yescharacteristic
193C42×C107C2411yescharacteristic
194C23×C107—22no—
195C23×C107#12011yescharacteristic
196Q8×C107—22no—
197Q8×C107—22no—
198Q8×C107—42no—
199Q8×C107—42no—
200Q8×C107—41no—
201Q8×C107—41no—
202Q8×C107—42no—
203Q8×C107—42no—
204Q8×C107—41no—
205Q8×C107—41no—
206D4×C107—22no—
207D4×C107—22no—
208D4×C107—44no—
209D4×C107—42no—
210D4×C107—81no—
211C2×C4×C107—21no—
212C2×C4×C107—21no—
213C2×C4×C107—22no—
214C2×C4×C107—22no—
215C2×C4×C107—22no—
216C2×C4×C107—22no—
217C2×C4×C107—22no—
218C2×C4×C107—41no—
219C2×C4×C107—42no—
220C2×C4×C107—42no—
221C2×C4×C107—42no—
222C2×C4×C107—41no—
223C2×C4×C107—41no—
224C2×C4×C107—81no—
225C2×C4×C107—84no—
226C2×C4×C107#12011yescharacteristic
227C2×C4×C107#12011yescharacteristic
228C2×C4×C107#12011yescharacteristic
229C2×C4×C107#13512yes—
230C2×C4×C107#13712yes—
231C2×C4×C107C22×D411yescharacteristic
232C2×C4×C107C22×D411yescharacteristic
233C2×C4×C107C22×D411yescharacteristic
234C8×C107—22no—
235C8×C107—41no—
236C8×C107—42no—
237C8×C107—42no—
238C22×C107—21no—
239C22×C107—21no—
240C22×C107—42no—
241C22×C107—42no—
242C22×C107—42no—
243C22×C107#45212yes—
244C22×C107C2×#12011yescharacteristic
245C4×C107—21no—
246C4×C107—21no—
247C4×C107—21no—
248C4×C107—42no—
249C4×C107—42no—
250C4×C107—42no—
251C4×C107—42no—
252C4×C107—42no—
253C4×C107—81no—
254C4×C107—81no—
255C4×C107#45212yes—
256C4×C107C2×#13511yescharacteristic
257C4×C107C2×#13711yescharacteristic
258C4×C107#57711yescharacteristic
259C4×C107#57811yescharacteristic
260#18669C10711yesmaximal, characteristic, direct product factor, Sylow
261C2×C107—22no—
262C2×C107—82no—
263C2×C107C2×#45211yescharacteristic
264C2×C107#301311yescharacteristic
265C2×C107#301811yescharacteristic
266#3507C2×C10711yescharacteristic
267#3246C2×C10711yescharacteristic
268#3170C2×C10711yescharacteristic, complemented
269#3078C2×C10711yescharacteristic, complemented
270#1650C2×C10712yescomplemented
271#1643C2×C10712yescomplemented
272#1638C2×C10712yescomplemented
273#1632C2×C10712yescomplemented
274#1550C2×C10711yescharacteristic, complemented
275#1492C2×C10711yescharacteristic
276C2×Q8⋊C8C2×C10711yescharacteristic, complemented
277C107#1866911yescharacteristic, direct product factor, Sylow
278#559—21no—
279#557—21no—
280#556—22no—
281#556C22×C10712yes—
282#554C22×C10712yes—
283#552—22no—
284#539—22no—
285#536—21no—
286#533C22×C10711yescharacteristic
287#533C22×C10711yescharacteristic
288#532C22×C10711yescharacteristic
289#529—22no—
290#520—21no—
291C2×C4×Q8C22×C10711yescharacteristic
292#500C22×C10711yescharacteristic
293#494C22×C10711yescharacteristic
294#487C22×C10711yescharacteristic
295#487C22×C10711yescharacteristic
296#479—22no—
297#477C22×C10712yes—
298#476C22×C10712yes—
299#475—21no—
300#475C22×C10712yes—
301#467—22no—
302#465—22no—
303#461C22×C10712yes—
304#460—21no—
305C4×Q16—22no—
306#428—21no—
307#423C22×C10711yescharacteristic
308C2×C4⋊C8C22×C10711yescharacteristic
309#419—21no—
310C2×C4×C8C22×C10711yescharacteristic
311#333C22×C10712yes—
312#332C22×C10712yes—
313Q8⋊C8C22×C10712yes—
314Q8⋊C8C22×C10712yes—
315D4⋊C8C22×C10712yes—
316D4⋊C8C22×C10712yes—
317C2×#41—21no—
318C22×Q8D4×C10711yescharacteristic
319C2×Q16—22no—
320C2×SD16—22no—
321C2×M16—21no—
322C22×C8—21no—
323C22×C8—21no—
324C4⋊Q8—22no—
325C4⋊Q8D4×C10711yescharacteristic
326C4⋊Q8C23×C10711yescharacteristic
327C4⋊Q8C23×C10711yescharacteristic
328C4⋊Q8C23×C10711yescharacteristic
329C4⋊Q8C23×C10711yescharacteristic
330#127D4×C10711yescharacteristic
331#126—24no—
332#126—24no—
333#125—24no—
334#125—22no—
335#125—21no—
336#125—21no—
337#124—22no—
338#124—22no—
339#124—21no—
340#123—24no—
341#123—24no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—24no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8D4×C10712yes—
349#121—21no—
350#121D4×C10712yes—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8D4×C10712yes—
359C4×Q8D4×C10712yes—
360C4×Q8C23×C10712yes—
361C4×D4—24no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4C23×C10712yes—
366#117—24no—
367#117—21no—
368#117—22no—
369#117—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4D4×C10711yescharacteristic
373C2×C42—21no—
374C2×C42C23×C10711yescharacteristic
375#107—22no—
376#107—22no—
377#106—22no—
378#106—22no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8C23×C10712yes—
382C4⋊C8C23×C10712yes—
383#103—22no—
384#103—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389C4×C8—21no—
390C4×C8C23×C10711yescharacteristic
391C4×C8C23×C10711yescharacteristic
392#41—42no—
393#41—42no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8C2×D4×C10712yes—
402C2×Q8C2×D4×C10712yes—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4C2×D4×C10712yes—
407C22×C4—21no—
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4C2×D4×C10711yescharacteristic
412C22×C4C2×D4×C10711yescharacteristic
413C22×C4C2×D4×C10711yescharacteristic
414Q16—44no—
415SD16—82no—
416M16—42no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—42no—
422C2×C8—81no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4C2×D4×C10712yes—
442C4⋊C4C2×D4×C10712yes—
443C4⋊C4C2×D4×C10712yes—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—41no—
451C42—24no—
452C42—22no—
453C42—22no—
454C42—22no—
455C42—41no—
456C42C2×D4×C10711yescharacteristic
457C42C2×D4×C10711yescharacteristic
458C42C2×D4×C10711yescharacteristic
459C42C24×C10711yescharacteristic
460C23—22no—
461C23#120×C10711yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—42no—
465Q8—42no—
466Q8—42no—
467Q8—42no—
468Q8—41no—
469Q8—41no—
470Q8—41no—
471Q8—41no—
472D4—22no—
473D4—22no—
474D4—44no—
475D4—42no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—81no—
491C2×C4—84no—
492C2×C4#120×C10711yescharacteristic
493C2×C4#120×C10711yescharacteristic
494C2×C4#120×C10711yescharacteristic
495C2×C4#135×C10712yes—
496C2×C4#137×C10712yes—
497C2×C4C22×D4×C10711yescharacteristic
498C2×C4C22×D4×C10711yescharacteristic
499C2×C4C22×D4×C10711yescharacteristic
500C8—22no—
501C8—41no—
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22#452×C10712yes—
510C22C2×#120×C10711yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—81no—
520C4—81no—
521C4#452×C10712yes—
522C4C2×#135×C10711yescharacteristic
523C4C2×#137×C10711yescharacteristic
524C4#577×C10711yescharacteristic
525C4#578×C10711yescharacteristic
526C2—22no—
527C2—82no—
528C2C2×#452×C10711yescharacteristic
529C2C107×#301311yescharacteristic
530C2C107×#301811yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC42C24×C107
prime radical#532×C107C22
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×#3170C2semidirect
4. C107×#3078C2semidirect
5. C107×#1650C2semidirect
6. C107×#1643C2semidirect
7. C107×#1638C2semidirect
8. C107×#1632C2semidirect
9. C107×#1550C2semidirect
11. C2×Q8⋊C8×C107C2semidirect
260. #18669C107direct (N × H)
268. #3170C2×C107semidirect
269. #3078C2×C107semidirect
270. #1650C2×C107semidirect
271. #1643C2×C107semidirect
272. #1638C2×C107semidirect
273. #1632C2×C107semidirect
274. #1550C2×C107semidirect
276. C2×Q8⋊C8C2×C107semidirect
277. C107#18669direct (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×#32462
C107×#31702
C107×#30782
C107×#16502
C107×#16432
C107×#16382
C107×#16322
C107×#15502
C107×#14922
C2×Q8⋊C8×C1072
#18669107