Finite Group Databasebeta

← C107×#13677 #41039641

Subgroups — C107×#13677 #41039641

Order 27392.

420 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3288C211yesmaximal, characteristic, complemented
2C107×#2202C211yesmaximal, characteristic, complemented
3C107×#2199C211yesmaximal, characteristic, complemented
4C107×#1655C211yesmaximal, characteristic, complemented
5C107×#1406C211yesmaximal, characteristic, complemented
6C107×#1404C211yesmaximal, characteristic, complemented
7C107×#1403C211yesmaximal, characteristic, complemented
8#577×C107—21no—
9#576×C107—21no—
10H(3,𝔽4)×C107C2211yescharacteristic, complemented
11#496×C107—21no—
12#496×C107C2211yescharacteristic
13#472×C107—21no—
14#471×C107—21no—
15B(4,𝔽2)×C107—21no—
16#455×C107C2211yescharacteristic
17#454×C107—21no—
18#454×C107C2211yescharacteristic
19#453×C107—21no—
20#444×C107—21no—
21#355×C107—21no—
22#355×C107C2211yescharacteristic, complemented
23#354×C107C2211yescharacteristic, complemented
24AΣL(1,𝔽16)×C107—21no—
25#329×C107—21no—
26#329×C107C2211yescharacteristic, complemented
272−1+4×C107D411yescharacteristic, complemented
28H(5,𝔽2)×C107—21no—
29H(5,𝔽2)×C107D411yescharacteristic
30#137×C107—21no—
31#137×C107—41no—
32AGL(1,ℤ/8)×C107—21no—
33AGL(1,ℤ/8)×C107—21no—
34AGL(1,ℤ/8)×C107—21no—
35AGL(1,ℤ/8)×C107—41no—
36AGL(1,ℤ/8)×C107—41no—
37AGL(1,ℤ/8)×C107—41no—
38AGL(1,ℤ/8)×C107—41no—
39#135×C107—21no—
40#135×C107—41no—
41#135×C107—41no—
42C2×SD16×C107—21no—
43C2×SD16×C107—41no—
44C2×SD16×C107—41no—
45C2×D8×C107—21no—
46C2×D8×C107—41no—
47C2×D8×C107—41no—
48#131×C107—21no—
49#131×C107—21no—
50#127×C107D411yescharacteristic, complemented
51#124×C107—21no—
52#124×C107—21no—
53#124×C107—41no—
54#124×C107C2311yescharacteristic
55#120×C107—21no—
56#120×C107—41no—
57#120×C107—41no—
58#108×C107—21no—
59#104×C107—21no—
60#104×C107—21no—
61#104×C107—41no—
62#101×C107—21no—
63#101×C107D411yescharacteristic, complemented
64#100×C107—21no—
65#100×C107D411yescharacteristic
66#99×C107—21no—
67#99×C107—41no—
68#97×C107—21no—
69#97×C107D411yescharacteristic, complemented
70C24×C107—21no—
71#41×C107—21no—
72#41×C107—21no—
73#41×C107—41no—
74#41×C107—41no—
75#41×C107—41no—
76#41×C107—41no—
77#41×C107—41no—
78C2×Q8×C107—21no—
79C2×Q8×C107—41no—
80C2×Q8×C107C2×D411yescharacteristic
81C2×D4×C107—21no—
82C2×D4×C107—21no—
83C2×D4×C107—21no—
84C2×D4×C107—41no—
85C2×D4×C107—41no—
86C2×D4×C107—41no—
87C2×D4×C107—41no—
88C2×D4×C107—41no—
89C2×D4×C107—41no—
90C2×D4×C107—81no—
91C2×D4×C107—81no—
92C2×D4×C107C2×D411yescharacteristic
93Q16×C107—21no—
94Q16×C107—41no—
95SD16×C107—21no—
96SD16×C107—21no—
97SD16×C107—41no—
98SD16×C107—41no—
99SD16×C107—41no—
100SD16×C107—41no—
101SD16×C107—41no—
102SD16×C107—41no—
103SD16×C107—82no—
104SD16×C107—81no—
105D8×C107—21no—
106D8×C107—41no—
107D8×C107—41no—
108D8×C107—41no—
109D8×C107—41no—
110D8×C107—41no—
111D8×C107—82no—
112D8×C107—81no—
113M16×C107—21no—
114M16×C107—21no—
115M16×C107—41no—
116M16×C107—41no—
117M16×C107—41no—
118C2×C8×C107—21no—
119C2×C8×C107—41no—
120C2×C8×C107—41no—
121C2×C8×C107—41no—
122C22⋊C4×C107—21no—
123C22⋊C4×C107—41no—
124C22⋊C4×C107—41no—
125C22⋊C4×C107—41no—
126C22⋊C4×C107—41no—
127C22⋊C4×C107—41no—
128C22⋊C4×C107—81no—
129C42×C107—21no—
130C42×C107C2×D411yescharacteristic
131C23×C107—21no—
132C23×C107—41no—
133C23×C107—41no—
134C23×C107—41no—
135C23×C107—81no—
136C23×C107—81no—
137C23×C107—161no—
138Q8×C107—21no—
139Q8×C107—21no—
140Q8×C107—41no—
141Q8×C107—41no—
142Q8×C107—81no—
143D4×C107—21no—
144D4×C107—21no—
145D4×C107—41no—
146D4×C107—41no—
147D4×C107—41no—
148D4×C107—41no—
149D4×C107—41no—
150D4×C107—41no—
151D4×C107—81no—
152D4×C107—81no—
153D4×C107—81no—
154D4×C107—81no—
155D4×C107—81no—
156D4×C107—81no—
157D4×C107—81no—
158D4×C107—161no—
159D4×C107—162no—
160C2×C4×C107—21no—
161C2×C4×C107—21no—
162C2×C4×C107—41no—
163C2×C4×C107—41no—
164C2×C4×C107—41no—
165C2×C4×C107—41no—
166C2×C4×C107—81no—
167C2×C4×C107—81no—
168C2×C4×C107—81no—
169C2×C4×C107#12011yescharacteristic
170C8×C107—21no—
171C8×C107—21no—
172C8×C107—41no—
173C8×C107—41no—
174C8×C107—42no—
175C8×C107—81no—
176C22×C107—41no—
177C22×C107—41no—
178C22×C107—41no—
179C22×C107—81no—
180C22×C107—81no—
181C22×C107—81no—
182C22×C107—82no—
183C22×C107—81no—
184C22×C107—81no—
185C22×C107—161no—
186C22×C107—161no—
187C22×C107—161no—
188C22×C107—321no—
189C22×C107B(4,𝔽2)11yescharacteristic
190C4×C107—21no—
191C4×C107—41no—
192C4×C107—41no—
193C4×C107—41no—
194C4×C107—41no—
195C4×C107—81no—
196C4×C107—161no—
197#13677C10711yesmaximal, characteristic, direct product factor, Sylow
198C2×C107—21no—
199C2×C107—81no—
200C2×C107—81no—
201C2×C107—81no—
202C2×C107—161no—
203C2×C107—161no—
204C2×C107#219611yescharacteristic
205#3288C2×C10711yescharacteristic, complemented
206#2202C2×C10711yescharacteristic, complemented
207#2199C2×C10711yescharacteristic, complemented
208#1655C2×C10711yescharacteristic, complemented
209#1406C2×C10711yescharacteristic, complemented
210#1404C2×C10711yescharacteristic, complemented
211#1403C2×C10711yescharacteristic, complemented
212C107#1367711yescharacteristic, direct product factor, Sylow
213#577—21no—
214#576—21no—
215H(3,𝔽4)C22×C10711yescharacteristic, complemented
216#496—21no—
217#496C22×C10711yescharacteristic
218#472—21no—
219#471—21no—
220B(4,𝔽2)—21no—
221#455C22×C10711yescharacteristic
222#454—21no—
223#454C22×C10711yescharacteristic
224#453—21no—
225#444—21no—
226#355—21no—
227#355C22×C10711yescharacteristic, complemented
228#354C22×C10711yescharacteristic, complemented
229AΣL(1,𝔽16)—21no—
230#329—21no—
231#329C22×C10711yescharacteristic, complemented
2322−1+4D4×C10711yescharacteristic, complemented
233H(5,𝔽2)—21no—
234H(5,𝔽2)D4×C10711yescharacteristic
235#137—21no—
236#137—41no—
237AGL(1,ℤ/8)—21no—
238AGL(1,ℤ/8)—21no—
239AGL(1,ℤ/8)—21no—
240AGL(1,ℤ/8)—41no—
241AGL(1,ℤ/8)—41no—
242AGL(1,ℤ/8)—41no—
243AGL(1,ℤ/8)—41no—
244#135—21no—
245#135—41no—
246#135—41no—
247C2×SD16—21no—
248C2×SD16—41no—
249C2×SD16—41no—
250C2×D8—21no—
251C2×D8—41no—
252C2×D8—41no—
253#131—21no—
254#131—21no—
255#127D4×C10711yescharacteristic, complemented
256#124—21no—
257#124—21no—
258#124—41no—
259#124C23×C10711yescharacteristic
260#120—21no—
261#120—41no—
262#120—41no—
263#108—21no—
264#104—21no—
265#104—21no—
266#104—41no—
267#101—21no—
268#101D4×C10711yescharacteristic, complemented
269#100—21no—
270#100D4×C10711yescharacteristic
271#99—21no—
272#99—41no—
273#97—21no—
274#97D4×C10711yescharacteristic, complemented
275C24—21no—
276#41—21no—
277#41—21no—
278#41—41no—
279#41—41no—
280#41—41no—
281#41—41no—
282#41—41no—
283C2×Q8—21no—
284C2×Q8—41no—
285C2×Q8C2×D4×C10711yescharacteristic
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4C2×D4×C10711yescharacteristic
298Q16—21no—
299Q16—41no—
300SD16—21no—
301SD16—21no—
302SD16—41no—
303SD16—41no—
304SD16—41no—
305SD16—41no—
306SD16—41no—
307SD16—41no—
308SD16—82no—
309SD16—81no—
310D8—21no—
311D8—41no—
312D8—41no—
313D8—41no—
314D8—41no—
315D8—41no—
316D8—82no—
317D8—81no—
318M16—21no—
319M16—21no—
320M16—41no—
321M16—41no—
322M16—41no—
323C2×C8—21no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—81no—
334C42—21no—
335C42C2×D4×C10711yescharacteristic
336C23—21no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—81no—
341C23—81no—
342C23—161no—
343Q8—21no—
344Q8—21no—
345Q8—41no—
346Q8—41no—
347Q8—81no—
348D4—21no—
349D4—21no—
350D4—41no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—161no—
364D4—162no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4#120×C10711yescharacteristic
375C8—21no—
376C8—21no—
377C8—41no—
378C8—41no—
379C8—42no—
380C8—81no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—82no—
388C22—81no—
389C22—81no—
390C22—161no—
391C22—161no—
392C22—161no—
393C22—321no—
394C22B(4,𝔽2)×C10711yescharacteristic
395C4—21no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—81no—
401C4—161no—
402C2—21no—
403C2—81no—
404C2—81no—
405C2—81no—
406C2—161no—
407C2—161no—
408C2C107×#219611yescharacteristic
subgroupG/H
center, socleC2×C107#2196
commutator, Frattini, cosocle#124C23×C107
LCSG ▷ #124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C22×C107 ◁ C2×C4×C107 ◁ #124×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3288C2semidirect
2. C107×#2202C2semidirect
3. C107×#2199C2semidirect
4. C107×#1655C2semidirect
5. C107×#1406C2semidirect
6. C107×#1404C2semidirect
7. C107×#1403C2semidirect
10. H(3,𝔽4)×C107C22semidirect
22. #355×C107C22semidirect
23. #354×C107C22semidirect
26. #329×C107C22semidirect
27. 2−1+4×C107D4semidirect
50. #127×C107D4semidirect
63. #101×C107D4semidirect
69. #97×C107D4semidirect
197. #13677C107direct (N × H)
205. #3288C2×C107semidirect
206. #2202C2×C107semidirect
207. #2199C2×C107semidirect
208. #1655C2×C107semidirect
209. #1406C2×C107semidirect
210. #1404C2×C107semidirect
211. #1403C2×C107semidirect
212. C107#13677direct (N × H)
215. H(3,𝔽4)C22×C107semidirect
227. #355C22×C107semidirect
228. #354C22×C107semidirect
231. #329C22×C107semidirect
232. 2−1+4D4×C107semidirect
255. #127D4×C107semidirect
268. #101D4×C107semidirect
274. #97D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#32882
C107×#22022
C107×#21992
C107×#16552
C107×#14062
C107×#14042
C107×#14032
#13677107