Finite Group Databasebeta

← C107×#7761 #41033725

Subgroups — C107×#7761 #41033725

Order 27392.

436 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2806C211yesmaximal, characteristic
2C107×#2058C211yesmaximal, characteristic
3C107×#2024C211yesmaximal, characteristic
4C107×#2016C211yesmaximal, characteristic
5C107×#1272C211yesmaximal, characteristic
6C107×#1272C211yesmaximal, characteristic
7C107×#1271C211yesmaximal, characteristic
8C22×Q16×C107—21no—
9C2×C4⋊Q8×C107C2211yescharacteristic
10C2×#106×C107—21no—
11C2×#103×C107—21no—
12C2×#103×C107—21no—
13#398×C107—21no—
14#398×C107—21no—
15#395×C107—21no—
16#391×C107—21no—
17#391×C107C2211yescharacteristic
18#391×C107C2211yescharacteristic
19#389×C107—21no—
20#389×C107C2211yescharacteristic
21#387×C107—21no—
22#340×C107—21no—
23#340×C107—21no—
24#336×C107C2211yescharacteristic
25#336×C107C2211yescharacteristic
26#336×C107C2211yescharacteristic
27C22×Q8×C107—21no—
28C22×Q8×C107D411yescharacteristic
29C22×Q8×C107D411yescharacteristic
30C2×Q16×C107—42no—
31C2×Q16×C107—42no—
32C2×Q16×C107—42no—
33C22×C8×C107—21no—
34C22×C8×C107—21no—
35C22×C8×C107—21no—
36C4⋊Q8×C107—42no—
37C2×C4⋊C4×C107—21no—
38C2×C4⋊C4×C107—21no—
39C2×C4⋊C4×C107—21no—
40C2×C4⋊C4×C107—21no—
41C2×C4⋊C4×C107—21no—
42C2×C4⋊C4×C107—21no—
43C2×C4⋊C4×C107—21no—
44C2×C4⋊C4×C107D411yescharacteristic
45C2×C4⋊C4×C107D411yescharacteristic
46C2×C4⋊C4×C107D411yescharacteristic
47C2×C4⋊C4×C107D411yescharacteristic
48C2×C42×C107—21no—
49C2×C42×C107C2311yescharacteristic
50#106×C107—42no—
51#103×C107—42no—
52#103×C107—42no—
53#95×C107—21no—
54#95×C107—21no—
55#95×C107—21no—
56#95×C107—21no—
57#95×C107—21no—
58#95×C107—21no—
59#95×C107—21no—
60#95×C107—21no—
61C2×Q8×C107—21no—
62C2×Q8×C107—22no—
63C2×Q8×C107—21no—
64C2×Q8×C107—21no—
65C2×Q8×C107—41no—
66C2×Q8×C107—41no—
67C2×Q8×C107—41no—
68C2×Q8×C107—41no—
69C2×Q8×C107—41no—
70C2×Q8×C107—41no—
71C2×Q8×C107—41no—
72C2×Q8×C107—41no—
73C2×Q8×C107—41no—
74C2×Q8×C107SD1612yes—
75C22×C4×C107—21no—
76C22×C4×C107—21no—
77C22×C4×C107—21no—
78C22×C4×C107—21no—
79C22×C4×C107—21no—
80C22×C4×C107—21no—
81C22×C4×C107—41no—
82C22×C4×C107C2×D411yescharacteristic
83C22×C4×C107C2×D411yescharacteristic
84C22×C4×C107C2×D411yescharacteristic
85Q16×C107—48no—
86C2×C8×C107—22no—
87C2×C8×C107—22no—
88C2×C8×C107—41no—
89C2×C8×C107—41no—
90C2×C8×C107—41no—
91C2×C8×C107—41no—
92C2×C8×C107—41no—
93C2×C8×C107—41no—
94C2×C8×C107—41no—
95C4⋊C4×C107—21no—
96C4⋊C4×C107—22no—
97C4⋊C4×C107—22no—
98C4⋊C4×C107—41no—
99C4⋊C4×C107—41no—
100C4⋊C4×C107—41no—
101C4⋊C4×C107—41no—
102C4⋊C4×C107—41no—
103C4⋊C4×C107—41no—
104C4⋊C4×C107—41no—
105C4⋊C4×C107—81no—
106C4⋊C4×C107—81no—
107C4⋊C4×C107—81no—
108C4⋊C4×C107—81no—
109C4⋊C4×C107Q1612yescomplemented
110C42×C107—41no—
111C42×C107—81no—
112C23×C107#12011yescharacteristic
113Q8×C107—42no—
114Q8×C107—42no—
115Q8×C107—42no—
116Q8×C107—42no—
117Q8×C107—81no—
118Q8×C107—81no—
119Q8×C107—81no—
120Q8×C107—81no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—22no—
128C2×C4×C107—22no—
129C2×C4×C107—41no—
130C2×C4×C107—41no—
131C2×C4×C107—41no—
132C2×C4×C107—41no—
133C2×C4×C107—41no—
134C2×C4×C107—41no—
135C2×C4×C107—41no—
136C2×C4×C107—41no—
137C2×C4×C107—41no—
138C2×C4×C107—41no—
139C2×C4×C107—41no—
140C2×C4×C107—41no—
141C2×C4×C107—41no—
142C2×C4×C107—41no—
143C2×C4×C107—42no—
144C2×C4×C107—41no—
145C2×C4×C107—41no—
146C2×C4×C107—81no—
147C2×C4×C107—81no—
148C2×C4×C107C2×SD1611yescharacteristic
149C2×C4×C107C2×Q1611yescharacteristic
150C2×C4×C107#13511yescharacteristic
151C2×C4×C107#13711yescharacteristic
152C2×C4×C107#13711yescharacteristic
153C2×C4×C107#13711yescharacteristic
154C8×C107—42no—
155C8×C107—42no—
156C8×C107—81no—
157C22×C107#44811yescharacteristic
158C22×C107#45111yescharacteristic
159C22×C107#45211yescharacteristic
160C22×C107#45311yescharacteristic
161C22×C107#45511yescharacteristic
162C22×C107#45611yescharacteristic
163C22×C107B(4,𝔽2)11yescharacteristic
164C4×C107—21no—
165C4×C107—21no—
166C4×C107—21no—
167C4×C107—21no—
168C4×C107—21no—
169C4×C107—21no—
170C4×C107—42no—
171C4×C107—42no—
172C4×C107—82no—
173C4×C107—81no—
174C4×C107—81no—
175C4×C107—81no—
176C4×C107—81no—
177#7761C10711yesmaximal, characteristic, direct product factor, Sylow
178C2×C107#159611yescharacteristic
179C2×C107#160511yescharacteristic
180C2×C107#160611yescharacteristic
181C2×C107#163211yescharacteristic
182C2×C107#164511yescharacteristic
183C2×C107#165311yescharacteristic
184C2×C107#166111yescharacteristic
185#2806C2×C10711yescharacteristic
186#2058C2×C10711yescharacteristic
187#2024C2×C10711yescharacteristic
188#2016C2×C10711yescharacteristic
189#1272C2×C10711yescharacteristic
190#1272C2×C10711yescharacteristic
191#1271C2×C10711yescharacteristic
192C107#776111yescharacteristic, direct product factor, Sylow
193C22×Q16—21no—
194C2×C4⋊Q8C22×C10711yescharacteristic
195C2×#106—21no—
196C2×#103—21no—
197C2×#103—21no—
198#398—21no—
199#398—21no—
200#395—21no—
201#391—21no—
202#391C22×C10711yescharacteristic
203#391C22×C10711yescharacteristic
204#389—21no—
205#389C22×C10711yescharacteristic
206#387—21no—
207#340—21no—
208#340—21no—
209#336C22×C10711yescharacteristic
210#336C22×C10711yescharacteristic
211#336C22×C10711yescharacteristic
212C22×Q8—21no—
213C22×Q8D4×C10711yescharacteristic
214C22×Q8D4×C10711yescharacteristic
215C2×Q16—42no—
216C2×Q16—42no—
217C2×Q16—42no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C4⋊Q8—42no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C10711yescharacteristic
230C2×C4⋊C4D4×C10711yescharacteristic
231C2×C4⋊C4D4×C10711yescharacteristic
232C2×C4⋊C4D4×C10711yescharacteristic
233C2×C42—21no—
234C2×C42C23×C10711yescharacteristic
235#106—42no—
236#103—42no—
237#103—42no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8SD16×C10712yes—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4C2×D4×C10711yescharacteristic
268C22×C4C2×D4×C10711yescharacteristic
269C22×C4C2×D4×C10711yescharacteristic
270Q16—48no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—81no—
293C4⋊C4—81no—
294C4⋊C4Q16×C10712yescomplemented
295C42—41no—
296C42—81no—
297C23#120×C10711yescharacteristic
298Q8—42no—
299Q8—42no—
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304Q8—81no—
305Q8—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4C2×SD16×C10711yescharacteristic
334C2×C4C2×Q16×C10711yescharacteristic
335C2×C4#135×C10711yescharacteristic
336C2×C4#137×C10711yescharacteristic
337C2×C4#137×C10711yescharacteristic
338C2×C4#137×C10711yescharacteristic
339C8—42no—
340C8—42no—
341C8—81no—
342C22#448×C10711yescharacteristic
343C22#451×C10711yescharacteristic
344C22#452×C10711yescharacteristic
345C22#453×C10711yescharacteristic
346C22#455×C10711yescharacteristic
347C22#456×C10711yescharacteristic
348C22B(4,𝔽2)×C10711yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—42no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—82no—
362C2C107×#159611yescharacteristic
363C2C107×#160511yescharacteristic
364C2C107×#160611yescharacteristic
365C2C107×#163211yescharacteristic
366C2C107×#164511yescharacteristic
367C2C107×#165311yescharacteristic
368C2C107×#166111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C107#120
commutator, Frattini, cosocleC2×C42C23×C107
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
109. C4⋊C4×C107Q16semidirect
177. #7761C107direct (N × H)
192. C107#7761direct (N × H)
294. C4⋊C4Q16×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#28062
C107×#20582
C107×#20242
C107×#20162
C107×#12722
C107×#12712
#7761107