Finite Group Databasebeta

← C107×#33754 #41059718

Subgroups — C107×#33754 #41059718

Order 27392.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3050C211yesmaximal, characteristic, complemented
2C2×#466×C107C211yesmaximal, characteristic, complemented
3C107×#2236C211yesmaximal, characteristic, complemented
4C107×#2234C212yesmaximal, complemented
5C107×#2233C211yesmaximal, characteristic, complemented
6C107×#2217C212yesmaximal, complemented
7C107×#2215C212yesmaximal, complemented
8C107×#2187C211yesmaximal, characteristic, complemented
9C107×#2186C212yesmaximal, complemented
10C107×#2184C211yesmaximal, characteristic, complemented
11C2×C22⋊C16×C107C211yesmaximal, characteristic, complemented
12C2×#135×C107C2211yescharacteristic, complemented
13C22×D8×C107C2211yescharacteristic
14C23×C8×C107C2211yescharacteristic
15#525×C107—21no—
16C2×#121×C107—21no—
17C2×SD32×C107C2212yescomplemented
18C2×D16×C107C2212yescomplemented
19C22×C16×C107C2212yescomplemented
20#467×C107C2211yescharacteristic
21#467×C107C2211yescharacteristic, complemented
22#466×C107—21no—
23#466×C107—21no—
24#466×C107C2211yescharacteristic
25#466×C107C2212yes—
26#466×C107C2212yes—
27#466×C107C2211yescharacteristic, complemented
28#465×C107—21no—
29#465×C107—21no—
30#427×C107C2211yescharacteristic, complemented
31C2×#107×C107C2211yescharacteristic
32#416×C107—21no—
33C2×#102×C107—21no—
34#367×C107C2212yescomplemented
35#366×C107C2212yescomplemented
36#358×C107C2212yescomplemented
37#357×C107C2212yescomplemented
38#357×C107C2212yescomplemented
39#357×C107C2212yescomplemented
40C22⋊C16×C107C2211yescharacteristic
41C22⋊C16×C107C2211yescharacteristic
42C22⋊C16×C107C2212yescomplemented
43C2×#41×C107—21no—
44C22×D4×C107—21no—
45C22×D4×C107—41no—
46C23×C4×C107D411yescharacteristic
47#135×C107—42no—
48C2×Q16×C107C2311yescharacteristic
49C2×SD16×C107—21no—
50C2×D8×C107—21no—
51C2×D8×C107—42no—
52C2×D8×C107C2312yes—
53C2×D8×C107C2311yescharacteristic
54C22×C8×C107—42no—
55C22×C8×C107D411yescharacteristic
56C22×C8×C107D411yescharacteristic
57C22×C8×C107D411yescharacteristic
58C22×C8×C107C2311yescharacteristic
59C22×C8×C107C2311yescharacteristic
60C22×C8×C107C2311yescharacteristic
61#123×C107—41no—
62C22⋊Q8×C107—21no—
63C22⋊Q8×C107—21no—
64#121×C107—21no—
65#121×C107—21no—
66#121×C107—22no—
67#121×C107—22no—
68#121×C107—41no—
69#121×C107—41no—
70#120×C107—41no—
71C4×D4×C107—41no—
72C4×D4×C107—41no—
73#117×C107—21no—
74C2×C4⋊C4×C107—21no—
75C2×C22⋊C4×C107—41no—
76SD32×C107—42no—
77D16×C107—42no—
78C2×C16×C107—42no—
79C2×C16×C107C2312yes—
80C2×C16×C107C2312yes—
81#107×C107—21no—
82#107×C107C2311yescharacteristic
83#107×C107C2311yescharacteristic
84#107×C107C2312yes—
85#106×C107—21no—
86#103×C107—21no—
87#103×C107—21no—
88#102×C107—22no—
89#102×C107—22no—
90#102×C107—21no—
91#102×C107—21no—
92C24×C107—41no—
93C24×C107D811yescharacteristic
94#41×C107—42no—
95#41×C107—42no—
96C2×Q8×C107—21no—
97C2×D4×C107—22no—
98C2×D4×C107—21no—
99C2×D4×C107—42no—
100C2×D4×C107—42no—
101C2×D4×C107—41no—
102C2×D4×C107—41no—
103C2×D4×C107—41no—
104C2×D4×C107—42no—
105C2×D4×C107—42no—
106C2×D4×C107—41no—
107C2×D4×C107—84no—
108C22×C4×C107—41no—
109C22×C4×C107—41no—
110C22×C4×C107—41no—
111C22×C4×C107—41no—
112C22×C4×C107D811yescharacteristic
113C22×C4×C107D811yescharacteristic
114C22×C4×C107D811yescharacteristic
115C22×C4×C107C2×D411yescharacteristic
116C22×C4×C107C2×D411yescharacteristic
117C22×C4×C107C2×D411yescharacteristic
118Q16×C107—22no—
119SD16×C107—42no—
120D8×C107—22no—
121D8×C107—22no—
122D8×C107—22no—
123D8×C107—42no—
124C2×C8×C107—22no—
125C2×C8×C107—22no—
126C2×C8×C107—22no—
127C2×C8×C107—41no—
128C2×C8×C107—41no—
129C2×C8×C107—41no—
130C2×C8×C107C2×D411yescharacteristic
131C2×C8×C107C2×D411yescharacteristic
132C2×C8×C107C2×D411yescharacteristic
133C2×C8×C107C2411yescharacteristic
134C4⋊C4×C107—22no—
135C4⋊C4×C107—21no—
136C4⋊C4×C107—21no—
137C4⋊C4×C107—41no—
138C4⋊C4×C107—41no—
139C4⋊C4×C107—41no—
140C22⋊C4×C107—41no—
141C22⋊C4×C107—41no—
142C22⋊C4×C107—41no—
143C22⋊C4×C107—42no—
144C22⋊C4×C107—42no—
145C22⋊C4×C107—41no—
146C22⋊C4×C107—41no—
147C42×C107—41no—
148C16×C107—22no—
149C16×C107—22no—
150C23×C107—22no—
151C23×C107—22no—
152C23×C107—41no—
153C23×C107—41no—
154C23×C107—42no—
155C23×C107—82no—
156C23×C107—82no—
157C23×C107—82no—
158C23×C107C2×D811yescharacteristic
159C23×C107C2×D811yescharacteristic
160C23×C107C2×D811yescharacteristic
161Q8×C107—41no—
162Q8×C107—41no—
163D4×C107—42no—
164D4×C107—41no—
165D4×C107—42no—
166D4×C107—41no—
167D4×C107—82no—
168D4×C107—84no—
169D4×C107—82no—
170D4×C107—82no—
171D4×C107—82no—
172D4×C107—84no—
173C2×C4×C107—21no—
174C2×C4×C107—21no—
175C2×C4×C107—21no—
176C2×C4×C107—21no—
177C2×C4×C107—21no—
178C2×C4×C107—21no—
179C2×C4×C107—41no—
180C2×C4×C107—41no—
181C2×C4×C107—41no—
182C2×C4×C107—41no—
183C2×C4×C107—41no—
184C2×C4×C107—42no—
185C2×C4×C107—41no—
186C2×C4×C107—82no—
187C2×C4×C107—82no—
188C2×C4×C107C2×D811yescharacteristic
189C2×C4×C107C2×D811yescharacteristic
190C2×C4×C107C2×D811yescharacteristic
191C2×C4×C107C22×D411yescharacteristic
192C8×C107—21no—
193C8×C107—21no—
194C8×C107—21no—
195C8×C107H(5,𝔽2)12yes—
196C22×C107—21no—
197C22×C107—21no—
198C22×C107—21no—
199C22×C107—21no—
200C22×C107—21no—
201C22×C107—21no—
202C22×C107—21no—
203C22×C107—44no—
204C22×C107—81no—
205C22×C107—82no—
206C22×C107—82no—
207C22×C107—81no—
208C22×C107—81no—
209C22×C107—82no—
210C22×C107—164no—
211C22×C107#50812yes—
212C22×C107#50912yes—
213C22×C107C22×D811yescharacteristic
214C4×C107—21no—
215C4×C107—21no—
216C4×C107—21no—
217C4×C107—81no—
218C4×C107—82no—
219C4×C107—81no—
220C4×C107—81no—
221C4×C107#53411yescharacteristic
222C4×C107#57511yescharacteristic
223#33754C10711yesmaximal, characteristic, direct product factor, Sylow
224C2×C107—22no—
225C2×C107—22no—
226C2×C107—41no—
227C2×C107—161no—
228C2×C107—162no—
229C2×C107#318611yescharacteristic
230C2×C107C2×#50811yescharacteristic
231C2×C107C2×#50911yescharacteristic
232#3050C2×C10711yescharacteristic, complemented
233C2×#466C2×C10711yescharacteristic, complemented
234#2236C2×C10711yescharacteristic, complemented
235#2234C2×C10712yescomplemented
236#2233C2×C10711yescharacteristic, complemented
237#2217C2×C10712yescomplemented
238#2215C2×C10712yescomplemented
239#2187C2×C10711yescharacteristic, complemented
240#2186C2×C10712yescomplemented
241#2184C2×C10711yescharacteristic, complemented
242C2×C22⋊C16C2×C10711yescharacteristic, complemented
243C107#3375411yescharacteristic, direct product factor, Sylow
244C2×#135C22×C10711yescharacteristic, complemented
245C22×D8C22×C10711yescharacteristic
246C23×C8C22×C10711yescharacteristic
247#525—21no—
248C2×#121—21no—
249C2×SD32C22×C10712yescomplemented
250C2×D16C22×C10712yescomplemented
251C22×C16C22×C10712yescomplemented
252#467C22×C10711yescharacteristic
253#467C22×C10711yescharacteristic, complemented
254#466—21no—
255#466—21no—
256#466C22×C10711yescharacteristic
257#466C22×C10712yes—
258#466C22×C10712yes—
259#466C22×C10711yescharacteristic, complemented
260#465—21no—
261#465—21no—
262#427C22×C10711yescharacteristic, complemented
263C2×#107C22×C10711yescharacteristic
264#416—21no—
265C2×#102—21no—
266#367C22×C10712yescomplemented
267#366C22×C10712yescomplemented
268#358C22×C10712yescomplemented
269#357C22×C10712yescomplemented
270#357C22×C10712yescomplemented
271#357C22×C10712yescomplemented
272C22⋊C16C22×C10711yescharacteristic
273C22⋊C16C22×C10711yescharacteristic
274C22⋊C16C22×C10712yescomplemented
275C2×#41—21no—
276C22×D4—21no—
277C22×D4—41no—
278C23×C4D4×C10711yescharacteristic
279#135—42no—
280C2×Q16C23×C10711yescharacteristic
281C2×SD16—21no—
282C2×D8—21no—
283C2×D8—42no—
284C2×D8C23×C10712yes—
285C2×D8C23×C10711yescharacteristic
286C22×C8—42no—
287C22×C8D4×C10711yescharacteristic
288C22×C8D4×C10711yescharacteristic
289C22×C8D4×C10711yescharacteristic
290C22×C8C23×C10711yescharacteristic
291C22×C8C23×C10711yescharacteristic
292C22×C8C23×C10711yescharacteristic
293#123—41no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296#121—22no—
297#121—22no—
298#121—21no—
299#121—21no—
300#121—41no—
301#121—41no—
302#120—41no—
303C4×D4—41no—
304C4×D4—41no—
305#117—21no—
306C2×C4⋊C4—21no—
307C2×C22⋊C4—41no—
308SD32—42no—
309D16—42no—
310C2×C16—42no—
311C2×C16C23×C10712yes—
312C2×C16C23×C10712yes—
313#107—21no—
314#107C23×C10711yescharacteristic
315#107C23×C10711yescharacteristic
316#107C23×C10712yes—
317#106—21no—
318#103—21no—
319#103—21no—
320#102—22no—
321#102—22no—
322#102—21no—
323#102—21no—
324C24—41no—
325C24D8×C10711yescharacteristic
326#41—42no—
327#41—42no—
328C2×Q8—21no—
329C2×D4—22no—
330C2×D4—21no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—41no—
339C2×D4—84no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4D8×C10711yescharacteristic
345C22×C4D8×C10711yescharacteristic
346C22×C4D8×C10711yescharacteristic
347C22×C4C2×D4×C10711yescharacteristic
348C22×C4C2×D4×C10711yescharacteristic
349C22×C4C2×D4×C10711yescharacteristic
350Q16—22no—
351SD16—42no—
352D8—22no—
353D8—22no—
354D8—22no—
355D8—42no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8C2×D4×C10711yescharacteristic
363C2×C8C2×D4×C10711yescharacteristic
364C2×C8C2×D4×C10711yescharacteristic
365C2×C8C24×C10711yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—42no—
376C22⋊C4—42no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C42—41no—
380C16—22no—
381C16—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—41no—
386C23—42no—
387C23—82no—
388C23—82no—
389C23—82no—
390C23C2×D8×C10711yescharacteristic
391C23C2×D8×C10711yescharacteristic
392C23C2×D8×C10711yescharacteristic
393Q8—41no—
394Q8—41no—
395D4—42no—
396D4—41no—
397D4—42no—
398D4—41no—
399D4—82no—
400D4—84no—
401D4—82no—
402D4—82no—
403D4—84no—
404D4—82no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4C2×D8×C10711yescharacteristic
421C2×C4C2×D8×C10711yescharacteristic
422C2×C4C2×D8×C10711yescharacteristic
423C2×C4C22×D4×C10711yescharacteristic
424C8—21no—
425C8—21no—
426C8—21no—
427C8H(5,𝔽2)×C10712yes—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—44no—
436C22—81no—
437C22—82no—
438C22—82no—
439C22—81no—
440C22—81no—
441C22—82no—
442C22—164no—
443C22#508×C10712yes—
444C22#509×C10712yes—
445C22C22×D8×C10711yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—81no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4#534×C10711yescharacteristic
454C4#575×C10711yescharacteristic
455C2—22no—
456C2—22no—
457C2—41no—
458C2—162no—
459C2—161no—
460C2C107×#318611yescharacteristic
461C2C2×#508×C10711yescharacteristic
462C2C2×#509×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C22×D8
commutator, Frattini, cosocleC2×C8C24×C107
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ C23×C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3050C2semidirect
2. C2×#466×C107C2semidirect
3. C107×#2236C2semidirect
4. C107×#2234C2semidirect
5. C107×#2233C2semidirect
6. C107×#2217C2semidirect
7. C107×#2215C2semidirect
8. C107×#2187C2semidirect
9. C107×#2186C2semidirect
10. C107×#2184C2semidirect
11. C2×C22⋊C16×C107C2semidirect
12. C2×#135×C107C22semidirect
17. C2×SD32×C107C22semidirect
18. C2×D16×C107C22semidirect
19. C22×C16×C107C22semidirect
21. #467×C107C22semidirect
27. #466×C107C22semidirect
30. #427×C107C22semidirect
34. #367×C107C22semidirect
35. #366×C107C22semidirect
36. #358×C107C22semidirect
37. #357×C107C22semidirect
38. #357×C107C22semidirect
39. #357×C107C22semidirect
42. C22⋊C16×C107C22semidirect
223. #33754C107direct (N × H)
232. #3050C2×C107semidirect
233. C2×#466C2×C107semidirect
234. #2236C2×C107semidirect
235. #2234C2×C107semidirect
236. #2233C2×C107semidirect
237. #2217C2×C107semidirect
238. #2215C2×C107semidirect
239. #2187C2×C107semidirect
240. #2186C2×C107semidirect
241. #2184C2×C107semidirect
242. C2×C22⋊C16C2×C107semidirect
243. C107#33754direct (N × H)
244. C2×#135C22×C107semidirect
249. C2×SD32C22×C107semidirect
250. C2×D16C22×C107semidirect
251. C22×C16C22×C107semidirect
253. #467C22×C107semidirect
259. #466C22×C107semidirect
262. #427C22×C107semidirect
266. #367C22×C107semidirect
267. #366C22×C107semidirect
268. #358C22×C107semidirect
269. #357C22×C107semidirect
270. #357C22×C107semidirect
271. #357C22×C107semidirect
274. C22⋊C16C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30502
C2×#466×C1072
C107×#22362
C107×#22342
C107×#22332
C107×#22172
C107×#22152
C107×#21872
C107×#21862
C107×#21842
C2×C22⋊C16×C1072
#33754107