Finite Group Databasebeta

← C107×#10385 #41036349

Subgroups — C107×#10385 #41036349

Order 27392.

396 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2667C211yesmaximal, characteristic
2C107×#1996C211yesmaximal, characteristic
3C107×#1511C211yesmaximal, characteristic
4C107×#1508C211yesmaximal, characteristic
5C107×#1305C211yesmaximal, characteristic
6C107×#1297C211yesmaximal, characteristic
7C107×#1284C211yesmaximal, characteristic
8C2×C22⋊Q8×C107C2211yescharacteristic
9#407×C107C2211yescharacteristic
10#407×C107C2211yescharacteristic
11#399×C107—21no—
12#398×C107—21no—
13#398×C107—21no—
14#396×C107—21no—
15#389×C107—21no—
16#387×C107—21no—
17#381×C107C2211yescharacteristic
18#380×C107C2211yescharacteristic
19C4×C22⋊C4×C107C2211yescharacteristic
20C4×C22⋊C4×C107C2211yescharacteristic
21#342×C107—21no—
22#342×C107—21no—
23#328×C107—21no—
24#328×C107—21no—
25#328×C107—21no—
26#328×C107—21no—
27C22×Q8×C107Q811yescharacteristic
28C23×C4×C107C2311yescharacteristic
29C2×M16×C107—21no—
30C2×M16×C107—21no—
31C22⋊Q8×C107—21no—
32C22⋊Q8×C107—21no—
33C22⋊Q8×C107—21no—
34C22⋊Q8×C107—21no—
35C2×C4⋊C4×C107—21no—
36C2×C4⋊C4×C107—21no—
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×C107Q811yescharacteristic
44C2×C22⋊C4×C107—21no—
45C2×C22⋊C4×C107—21no—
46C2×C22⋊C4×C107—21no—
47C2×C22⋊C4×C107—21no—
48C2×C22⋊C4×C107D411yescharacteristic
49C2×C22⋊C4×C107D411yescharacteristic
50C2×C42×C107—21no—
51C2×C42×C107—21no—
52C22⋊C8×C107—21no—
53C22⋊C8×C107—21no—
54C22⋊C8×C107—21no—
55C22⋊C8×C107—21no—
56#95×C107—21no—
57#95×C107—21no—
58#95×C107—21no—
59#95×C107—21no—
60#95×C107—21no—
61#95×C107D411yescharacteristic
62#95×C107D411yescharacteristic
63#95×C107D411yescharacteristic
64#95×C107D411yescharacteristic
65C24×C107C2×D411yescharacteristic
66C2×Q8×C107—21no—
67C2×Q8×C107—21no—
68C2×Q8×C107—81no—
69C22×C4×C107—21no—
70C22×C4×C107—21no—
71C22×C4×C107—21no—
72C22×C4×C107—21no—
73C22×C4×C107—21no—
74C22×C4×C107—21no—
75C22×C4×C107—21no—
76C22×C4×C107—21no—
77C22×C4×C107—41no—
78C22×C4×C107—81no—
79C22×C4×C107C2×D411yescharacteristic
80C22×C4×C107C2×D411yescharacteristic
81C22×C4×C107C2×Q811yescharacteristic
82C22×C4×C107#4111yescharacteristic
83C22×C4×C107#4111yescharacteristic
84C22×C4×C107#4111yescharacteristic
85M16×C107—81no—
86M16×C107—81no—
87C2×C8×C107—41no—
88C2×C8×C107—41no—
89C4⋊C4×C107—21no—
90C4⋊C4×C107—21no—
91C4⋊C4×C107—42no—
92C4⋊C4×C107—42no—
93C4⋊C4×C107—41no—
94C4⋊C4×C107—41no—
95C4⋊C4×C107—81no—
96C4⋊C4×C107—81no—
97C4⋊C4×C107—81no—
98C4⋊C4×C107—81no—
99C4⋊C4×C107—81no—
100C22⋊C4×C107—22no—
101C22⋊C4×C107—42no—
102C22⋊C4×C107—41no—
103C22⋊C4×C107—41no—
104C22⋊C4×C107—41no—
105C22⋊C4×C107—41no—
106C22⋊C4×C107—41no—
107C22⋊C4×C107—81no—
108C42×C107—81no—
109C42×C107—81no—
110C23×C107—21no—
111C23×C107—21no—
112C23×C107—41no—
113C23×C107—41no—
114C23×C107#12011yescharacteristic
115C23×C107C22⋊Q811yescharacteristic
116C23×C107#12411yescharacteristic
117Q8×C107—81no—
118Q8×C107—81no—
119C2×C4×C107—22no—
120C2×C4×C107—41no—
121C2×C4×C107—41no—
122C2×C4×C107—41no—
123C2×C4×C107—41no—
124C2×C4×C107—41no—
125C2×C4×C107—41no—
126C2×C4×C107—41no—
127C2×C4×C107—41no—
128C2×C4×C107—41no—
129C2×C4×C107—42no—
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—41no—
144C2×C4×C107—41no—
145C2×C4×C107—41no—
146C2×C4×C107—81no—
147C2×C4×C107—81no—
148C2×C4×C107—81no—
149C2×C4×C107—81no—
150C2×C4×C107C22⋊Q811yescharacteristic
151C2×C4×C107C22⋊Q811yescharacteristic
152C2×C4×C107#12411yescharacteristic
153C2×C4×C107#12411yescharacteristic
154C8×C107—81no—
155C8×C107—81no—
156C22×C107—21no—
157C22×C107—21no—
158C22×C107—21no—
159C22×C107—21no—
160C22×C107—21no—
161C22×C107—21no—
162C22×C107—21no—
163C22×C107—21no—
164C22×C107—81no—
165C22×C107—81no—
166C22×C107#39311yescharacteristic
167C22×C107#45511yescharacteristic
168C22×C107#45611yescharacteristic
169C4×C107—21no—
170C4×C107—21no—
171C4×C107—21no—
172C4×C107—21no—
173C4×C107—42no—
174C4×C107—81no—
175C4×C107—81no—
176C4×C107—81no—
177C4×C107—81no—
178C4×C107—81no—
179C4×C107—82no—
180C4×C107—81no—
181C4×C107—81no—
182#10385C10711yesmaximal, characteristic, direct product factor, Sylow
183C2×C107—21no—
184C2×C107—21no—
185C2×C107—41no—
186C2×C107—41no—
187C2×C107#202811yescharacteristic
188C2×C107#203111yescharacteristic
189C2×C107#203211yescharacteristic
190#2667C2×C10711yescharacteristic
191#1996C2×C10711yescharacteristic
192#1511C2×C10711yescharacteristic
193#1508C2×C10711yescharacteristic
194#1305C2×C10711yescharacteristic
195#1297C2×C10711yescharacteristic
196#1284C2×C10711yescharacteristic
197C107#1038511yescharacteristic, direct product factor, Sylow
198C2×C22⋊Q8C22×C10711yescharacteristic
199#407C22×C10711yescharacteristic
200#407C22×C10711yescharacteristic
201#399—21no—
202#398—21no—
203#398—21no—
204#396—21no—
205#389—21no—
206#387—21no—
207#381C22×C10711yescharacteristic
208#380C22×C10711yescharacteristic
209C4×C22⋊C4C22×C10711yescharacteristic
210C4×C22⋊C4C22×C10711yescharacteristic
211#342—21no—
212#342—21no—
213#328—21no—
214#328—21no—
215#328—21no—
216#328—21no—
217C22×Q8Q8×C10711yescharacteristic
218C23×C4C23×C10711yescharacteristic
219C2×M16—21no—
220C2×M16—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4Q8×C10711yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4D4×C10711yescharacteristic
239C2×C22⋊C4D4×C10711yescharacteristic
240C2×C42—21no—
241C2×C42—21no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95D4×C10711yescharacteristic
252#95D4×C10711yescharacteristic
253#95D4×C10711yescharacteristic
254#95D4×C10711yescharacteristic
255C24C2×D4×C10711yescharacteristic
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—81no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—81no—
269C22×C4C2×D4×C10711yescharacteristic
270C22×C4C2×D4×C10711yescharacteristic
271C22×C4C2×Q8×C10711yescharacteristic
272C22×C4#41×C10711yescharacteristic
273C22×C4#41×C10711yescharacteristic
274C22×C4#41×C10711yescharacteristic
275M16—81no—
276M16—81no—
277C2×C8—41no—
278C2×C8—41no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C22⋊C4—22no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—81no—
298C42—81no—
299C42—81no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23#120×C10711yescharacteristic
305C23C22⋊Q8×C10711yescharacteristic
306C23#124×C10711yescharacteristic
307Q8—81no—
308Q8—81no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
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—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4C22⋊Q8×C10711yescharacteristic
341C2×C4C22⋊Q8×C10711yescharacteristic
342C2×C4#124×C10711yescharacteristic
343C2×C4#124×C10711yescharacteristic
344C8—81no—
345C8—81no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22#393×C10711yescharacteristic
357C22#455×C10711yescharacteristic
358C22#456×C10711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—42no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—82no—
370C4—81no—
371C4—81no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2C107×#202811yescharacteristic
377C2C107×#203111yescharacteristic
378C2C107×#203211yescharacteristic
subgroupG/H
center, socleC22×C107#393
commutator, Frattini, cosocleC23×C4C23×C107
prime radicalC24×C107C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
182. #10385C107direct (N × H)
197. C107#10385direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#26672
C107×#19962
C107×#15112
C107×#15082
C107×#13052
C107×#12972
C107×#12842
#10385107