Finite Group Databasebeta

← Q8×#99×C103 #39927787

Subgroups — Q8×#99×C103 #39927787

Order 26368.

1354 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C103C211yesmaximal, characteristic
2Q8×C22⋊C4×C103C212yesmaximal, complemented
3C103×#1996C216yesmaximal, complemented
4C103×#1799C213yesmaximal
5C4×#99×C103C213yesmaximal
6C23×Q8×C103C411yescharacteristic, complemented
7C23×Q8×C103C2211yescharacteristic
8D4×Q8×C103—22no—
9D4×Q8×C103—26no—
10C2×C4⋊Q8×C103C413yescomplemented
11C2×C22⋊Q8×C103C413yescomplemented
12C2×C22⋊Q8×C103C2213yes—
13C2×C4×Q8×C103—22no—
14C2×C4×Q8×C103C411yescharacteristic, complemented
15C2×C4×D4×C103C2213yes—
16C2×#99×C103C2213yes—
17C2×#99×C103C2211yescharacteristic
18#391×C103—26no—
19#380×C103C2216yes—
20C4×C22⋊C4×C103C2216yes—
21#342×C103C2216yes—
22#342×C103C2216yes—
23C22×Q8×C103—23no—
24C22×Q8×C103—21no—
25C22×Q8×C103—44no—
26C22×Q8×C103—44no—
27C22×Q8×C103C2×C411yescharacteristic
28C22×Q8×C103C2×C413yes—
29C22×Q8×C103C2×C413yes—
30C22×Q8×C103D412yes—
31C22×Q8×C103D416yes—
32C22×D4×C103C2311yescharacteristic
33C23×C4×C103C2×C413yes—
34C23×C4×C103C2313yes—
35C4⋊Q8×C103—26no—
36C4⋊Q8×C103—26no—
37C22⋊Q8×C103—26no—
38C22⋊Q8×C103—26no—
39C22⋊Q8×C103—26no—
40C22⋊Q8×C103—26no—
41C4×Q8×C103—23no—
42C4×Q8×C103—21no—
43C4×Q8×C103—48no—
44C4×D4×C103—26no—
45C4×D4×C103—26no—
46C2×C4⋊C4×C103—26no—
47C2×C4⋊C4×C103C2×C413yes—
48C2×C4⋊C4×C103C2×C413yes—
49C2×C4⋊C4×C103C2×C416yes—
50C2×C22⋊C4×C103C2×C413yes—
51C2×C22⋊C4×C103C2316yes—
52C2×C22⋊C4×C103C2313yes—
53C2×C22⋊C4×C103C2312yes—
54C2×C42×C103—26no—
55C2×C42×C103C2×C413yes—
56#99×C103—26no—
57#99×C103Q814yesdirect product factor
58#95×C103—26no—
59#95×C103—26no—
60C24×C103C22×C411yescharacteristic
61C24×C103C2411yescharacteristic
62C2×Q8×C103—28no—
63C2×Q8×C103—24no—
64C2×Q8×C103—23no—
65C2×Q8×C103—23no—
66C2×Q8×C103—46no—
67C2×Q8×C103—412no—
68C2×Q8×C103—46no—
69C2×Q8×C103—412no—
70C2×Q8×C103—44no—
71C2×Q8×C103C22⋊C413yes—
72C2×Q8×C103C22⋊C416yes—
73C2×Q8×C103C22⋊C416yes—
74C2×Q8×C103C22⋊C411yescharacteristic
75C2×D4×C103—22no—
76C2×D4×C103—22no—
77C2×D4×C103C2×Q812yes—
78C2×D4×C103#4112yes—
79C22×C4×C103—22no—
80C22×C4×C103—23no—
81C22×C4×C103—23no—
82C22×C4×C103—26no—
83C22×C4×C103—46no—
84C22×C4×C103—46no—
85C22×C4×C103C22×C413yes—
86C22×C4×C103C22×C411yescharacteristic
87C22×C4×C103C22×C413yes—
88C22×C4×C103C22×C413yes—
89C22×C4×C103C22×C413yes—
90C22×C4×C103C2×D416yes—
91C22×C4×C103C2×D416yes—
92C4⋊C4×C103—26no—
93C4⋊C4×C103—23no—
94C4⋊C4×C103—23no—
95C4⋊C4×C103—212no—
96C4⋊C4×C103—412no—
97C22⋊C4×C103—26no—
98C22⋊C4×C103—22no—
99C22⋊C4×C103—26no—
100C22⋊C4×C103—26no—
101C22⋊C4×C103—26no—
102C22⋊C4×C103C2×Q814yescomplemented
103C42×C103—23no—
104C42×C103—23no—
105C42×C103—412no—
106C23×C103—21no—
107C23×C103—21no—
108C23×C103—41no—
109C23×C103—41no—
110C23×C103—41no—
111C23×C103—41no—
112C23×C103C4×Q812yescomplemented
113C23×C103C23×C411yescharacteristic
114C23×C103C22×D412yes—
115C23×C103C22×Q811yescharacteristic
116C23×C103C2×#4111yescharacteristic
117C23×C1032−1+412yes—
118Q8×C103—26no—
119Q8×C103—212no—
120Q8×C103—46no—
121Q8×C103—46no—
122Q8×C103—46no—
123Q8×C103#9914yesdirect product factor
124D4×C103—24no—
125D4×C103—24no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—212no—
129C2×C4×C103—26no—
130C2×C4×C103—23no—
131C2×C4×C103—23no—
132C2×C4×C103—24no—
133C2×C4×C103—43no—
134C2×C4×C103—46no—
135C2×C4×C103—46no—
136C2×C4×C103—42no—
137C2×C4×C103—42no—
138C2×C4×C103—46no—
139C2×C4×C103—43no—
140C2×C4×C103—43no—
141C2×C4×C103—46no—
142C2×C4×C103—46no—
143C2×C4×C103—46no—
144C2×C4×C103C2×C22⋊C413yes—
145C2×C4×C103C2×C22⋊C416yes—
146C2×C4×C103C2×C22⋊C413yes—
147C2×C4×C103C4×Q812yescomplemented
148C22×C103—22no—
149C22×C103—21no—
150C22×C103—22no—
151C22×C103—21no—
152C22×C103—22no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103—42no—
156C22×C103—42no—
157C22×C103—42no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103C22×C22⋊C411yescharacteristic
161C22×C103C2×C4×Q811yescharacteristic
162C22×C103#51911yescharacteristic
163C22×C103#54812yes—
164C22×C103D4×Q812yes—
165C4×C103—22no—
166C4×C103—23no—
167C4×C103—26no—
168C4×C103—44no—
169C4×C103—43no—
170C4×C103—43no—
171C4×C103—86no—
172C4×C103C2×#9916yes—
173Q8×#99C10311yesmaximal, characteristic, direct product factor, Sylow
174C2×C103—22no—
175C2×C103—22no—
176C2×C103—21no—
177C2×C103—21no—
178C2×C103—42no—
179C2×C103Q8×C22⋊C411yescharacteristic
180C2×C103C22×#9911yescharacteristic
181C2×C103#288411yescharacteristic
182C2×D4×Q8C2×C10311yescharacteristic
183Q8×C22⋊C4C2×C10312yescomplemented
184#1996C2×C10316yescomplemented
185#1799C2×C10313yes—
186C4×#99C2×C10313yes—
187C103Q8×#9911yescharacteristic, direct product factor, Sylow
188C23×Q8C4×C10311yescharacteristic, complemented
189C23×Q8C22×C10311yescharacteristic
190D4×Q8—22no—
191D4×Q8—26no—
192C2×C4⋊Q8C4×C10313yescomplemented
193C2×C22⋊Q8C4×C10313yescomplemented
194C2×C22⋊Q8C22×C10313yes—
195C2×C4×Q8—22no—
196C2×C4×Q8C4×C10311yescharacteristic, complemented
197C2×C4×D4C22×C10313yes—
198C2×#99C22×C10313yes—
199C2×#99C22×C10311yescharacteristic
200#391—26no—
201#380C22×C10316yes—
202C4×C22⋊C4C22×C10316yes—
203#342C22×C10316yes—
204#342C22×C10316yes—
205C22×Q8—23no—
206C22×Q8—21no—
207C22×Q8—44no—
208C22×Q8—44no—
209C22×Q8C2×C4×C10311yescharacteristic
210C22×Q8C2×C4×C10313yes—
211C22×Q8C2×C4×C10313yes—
212C22×Q8D4×C10312yes—
213C22×Q8D4×C10316yes—
214C22×D4C23×C10311yescharacteristic
215C23×C4C2×C4×C10313yes—
216C23×C4C23×C10313yes—
217C4⋊Q8—26no—
218C4⋊Q8—26no—
219C22⋊Q8—26no—
220C22⋊Q8—26no—
221C22⋊Q8—26no—
222C22⋊Q8—26no—
223C4×Q8—23no—
224C4×Q8—21no—
225C4×Q8—48no—
226C4×D4—26no—
227C4×D4—26no—
228C2×C4⋊C4—26no—
229C2×C4⋊C4C2×C4×C10313yes—
230C2×C4⋊C4C2×C4×C10313yes—
231C2×C4⋊C4C2×C4×C10316yes—
232C2×C22⋊C4C2×C4×C10313yes—
233C2×C22⋊C4C23×C10316yes—
234C2×C22⋊C4C23×C10313yes—
235C2×C22⋊C4C23×C10312yes—
236C2×C42—26no—
237C2×C42C2×C4×C10313yes—
238#99—26no—
239#99Q8×C10314yesdirect product factor
240#95—26no—
241#95—26no—
242C24C22×C4×C10311yescharacteristic
243C24C24×C10311yescharacteristic
244C2×Q8—28no—
245C2×Q8—24no—
246C2×Q8—23no—
247C2×Q8—23no—
248C2×Q8—46no—
249C2×Q8—412no—
250C2×Q8—46no—
251C2×Q8—412no—
252C2×Q8—44no—
253C2×Q8C22⋊C4×C10313yes—
254C2×Q8C22⋊C4×C10316yes—
255C2×Q8C22⋊C4×C10316yes—
256C2×Q8C22⋊C4×C10311yescharacteristic
257C2×D4—22no—
258C2×D4—22no—
259C2×D4C2×Q8×C10312yes—
260C2×D4#41×C10312yes—
261C22×C4—22no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—26no—
265C22×C4—46no—
266C22×C4—46no—
267C22×C4C22×C4×C10313yes—
268C22×C4C22×C4×C10311yescharacteristic
269C22×C4C22×C4×C10313yes—
270C22×C4C22×C4×C10313yes—
271C22×C4C22×C4×C10313yes—
272C22×C4C2×D4×C10316yes—
273C22×C4C2×D4×C10316yes—
274C4⋊C4—26no—
275C4⋊C4—23no—
276C4⋊C4—23no—
277C4⋊C4—212no—
278C4⋊C4—412no—
279C22⋊C4—26no—
280C22⋊C4—22no—
281C22⋊C4—26no—
282C22⋊C4—26no—
283C22⋊C4—26no—
284C22⋊C4C2×Q8×C10314yescomplemented
285C42—23no—
286C42—23no—
287C42—412no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23C4×Q8×C10312yescomplemented
295C23C23×C4×C10311yescharacteristic
296C23C22×D4×C10312yes—
297C23C22×Q8×C10311yescharacteristic
298C23C2×#41×C10311yescharacteristic
299C232−1+4×C10312yes—
300Q8—26no—
301Q8—212no—
302Q8—46no—
303Q8—46no—
304Q8—46no—
305Q8#99×C10314yesdirect product factor
306D4—24no—
307D4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—212no—
311C2×C4—26no—
312C2×C4—23no—
313C2×C4—23no—
314C2×C4—24no—
315C2×C4—43no—
316C2×C4—46no—
317C2×C4—46no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—46no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—46no—
324C2×C4—46no—
325C2×C4—46no—
326C2×C4C2×C22⋊C4×C10313yes—
327C2×C4C2×C22⋊C4×C10316yes—
328C2×C4C2×C22⋊C4×C10313yes—
329C2×C4C4×Q8×C10312yescomplemented
330C22—22no—
331C22—21no—
332C22—22no—
333C22—21no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22C22×C22⋊C4×C10311yescharacteristic
343C22C2×C4×Q8×C10311yescharacteristic
344C22#519×C10311yescharacteristic
345C22#548×C10312yes—
346C22D4×Q8×C10312yes—
347C4—22no—
348C4—23no—
349C4—26no—
350C4—44no—
351C4—43no—
352C4—43no—
353C4—86no—
354C4C2×#99×C10316yes—
355C2—22no—
356C2—22no—
357C2—21no—
358C2—21no—
359C2—42no—
360C2Q8×C22⋊C4×C10311yescharacteristic
361C2C22×#99×C10311yescharacteristic
362C2C103×#288411yescharacteristic
subgroupG/H
center, socleC22×C103C22×C22⋊C4
commutatorC23C23×C4×C103
Frattini, cosocleC24C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×Q8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊C4×C103C2semidirect
3. C103×#1996C2semidirect
6. C23×Q8×C103C4semidirect
10. C2×C4⋊Q8×C103C4semidirect
11. C2×C22⋊Q8×C103C4semidirect
14. C2×C4×Q8×C103C4semidirect
57. #99×C103Q8direct (N × H)
102. C22⋊C4×C103C2×Q8semidirect
112. C23×C103C4×Q8semidirect
123. Q8×C103#99direct (N × H)
147. C2×C4×C103C4×Q8semidirect
173. Q8×#99C103direct (N × H)
183. Q8×C22⋊C4C2×C103semidirect
184. #1996C2×C103semidirect
187. C103Q8×#99direct (N × H)
188. C23×Q8C4×C103semidirect
192. C2×C4⋊Q8C4×C103semidirect
193. C2×C22⋊Q8C4×C103semidirect
196. C2×C4×Q8C4×C103semidirect
239. #99Q8×C103direct (N × H)
284. C22⋊C4C2×Q8×C103semidirect
294. C23C4×Q8×C103semidirect
305. Q8#99×C103direct (N × H)
329. C2×C4C4×Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1032
Q8×C22⋊C4×C1032
C103×#19962
C103×#17992
C4×#99×C1032
Q8×#99103