Finite Group Databasebeta

← C2×#22625460 #34017784

Subgroups — C2×#22625460 #34017784

Order 18688.

1182 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989607C211yesmaximal, characteristic
2C2×#17989607C211yesmaximal, characteristic
3#22625460C218yesmaximal, direct product factor
4C2×#17989446C214yesmaximal, complemented
5C22×#14556590C211yesmaximal, characteristic
6#17989607—22no—
7#17989607—22no—
8#17989607C2214yes—
9#17989607C2214yes—
10C2×#14556658C2212yes—
11C2×#14556658C2212yes—
12C2×C22⋊#10596833—21no—
13C2×C22⋊#10596833—21no—
14C2×#14556646—21no—
15C2×#14556646—21no—
16#17989446C22116yescomplemented
17C23×Dic146—21no—
18C2×#14556590—21no—
19C2×#14556590—21no—
20C2×#14556590—22no—
21C2×#14556590—22no—
22C2×#14556590C412yes—
23C2×#14556590C414yes—
24C2×#14556590C2212yes—
25C2×#14556590C2214yes—
26C22×C4⋊Dic73C411yescharacteristic
27C22×#11924007—21no—
28C22×C4×Dic73C2211yescharacteristic
29C22×C4⋊C4×C73C411yescharacteristic
30C22×#10596833—22no—
31C22×#10596833—22no—
32#14556658—22no—
33#14556658—22no—
34#14556658C2314yes—
35#14556658C2314yes—
36C22⋊#10596833—24no—
37C22⋊#10596833—24no—
38#14556646—24no—
39#14556646—24no—
40C22×Dic146—24no—
41C22×Dic146—22no—
42C22×Dic146—24no—
43C22×Dic146—22no—
44C22×Dic146—48no—
45C23×Dic73—21no—
46C23×Dic73D411yescharacteristic
47C23×Dic73D411yescharacteristic
48#14556590—24no—
49#14556590—24no—
50#14556590—24no—
51#14556590—24no—
52#14556590—24no—
53#14556590—22no—
54#14556590—22no—
55#14556590C2×C414yes—
56#14556590C2×C418yes—
57#14556590C2314yes—
58C2×C4⋊Dic73—22no—
59C2×C4⋊Dic73—21no—
60C2×C4⋊Dic73C2×C412yes—
61C2×C4⋊Dic73C2×C414yes—
62C2×#11924007—24no—
63C2×#11924007—22no—
64C2×#11924007—24no—
65C2×#11924007—22no—
66C2×C4×Dic73C2×C412yes—
67C2×C4×Dic73C2×C411yescharacteristic
68C2×C4×Dic73D411yescharacteristic
69C2×C4×Dic73D411yescharacteristic
70C2×C4×Dic73D412yes—
71C2×C4×Dic73D412yes—
72C2×C4×Dic73C2311yescharacteristic
73C2×C4×Dic73C2312yes—
74C23×C4×C73—21no—
75C23×C4×C73C2×C411yescharacteristic
76C2×C4⋊C4×C73—22no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73C2×C412yes—
79C2×C4⋊C4×C73C2×C414yes—
80C2×#10596833—24no—
81C2×#10596833—24no—
82C2×#10596833—44no—
83C2×#10596833—44no—
84C2×Dic146—28no—
85C2×Dic146—24no—
86C2×Dic146—24no—
87C2×Dic146—48no—
88C2×Dic146—416no—
89C2×Dic146—416no—
90C2×Dic146—48no—
91C22×Dic73—24no—
92C22×Dic73—24no—
93C22×Dic73—24no—
94C22×Dic73—22no—
95C22×Dic73—44no—
96C22×Dic73C22⋊C412yes—
97C22×Dic73C22⋊C411yescharacteristic
98C22×Dic73C22⋊C412yes—
99C22×Dic73C22⋊C411yescharacteristic
100C22×Dic73C2×D412yes—
101C22×Dic73C2×D412yes—
102C22×Dic73C2×D411yescharacteristic
103C22×Dic73C2×D411yescharacteristic
104C4⋊Dic73—24no—
105C4⋊Dic73—22no—
106C4⋊Dic73C22×C414yes—
107#11924007—28no—
108#11924007—24no—
109#11924007—24no—
110C4×Dic73C22⋊C412yes—
111C4×Dic73C22⋊C412yes—
112C4×Dic73C22⋊C412yes—
113C4×Dic73C22×C412yes—
114C4×Dic73C22×C411yescharacteristic
115C4×Dic73C2×D412yes—
116C4×Dic73C2×D412yes—
117C4×Dic73C2×D411yescharacteristic
118C4×Dic73C2×D411yescharacteristic
119C4×Dic73C2411yescharacteristic
120C24×C73C22⋊C411yescharacteristic
121C22×C4×C73—24no—
122C22×C4×C73—24no—
123C22×C4×C73—22no—
124C22×C4×C73—44no—
125C22×C4×C73C22⋊C412yes—
126C22×C4×C73C22⋊C411yescharacteristic
127C22×C4×C73C22×C412yes—
128C22×C4×C73C22×C411yescharacteristic
129C4⋊C4×C73—24no—
130C4⋊C4×C73—22no—
131C4⋊C4×C73C22×C414yes—
132C23×C73—22no—
133C23×C73—22no—
134C23×C73#10114yes—
135C23×C73C2×C22⋊C412yes—
136C23×C73C2×C22⋊C411yescharacteristic
137C2×C4×C73—24no—
138C2×C4×C73—22no—
139C2×C4×C73—24no—
140C2×C4×C73—22no—
141C2×C4×C73—24no—
142C2×C4×C73—48no—
143C2×C4×C73—44no—
144C2×C4×C73C2×C22⋊C412yes—
145C2×C4×C73C2×C22⋊C411yescharacteristic
146C2×C4×C73C23×C411yescharacteristic
147C2×Dic73—22no—
148C2×Dic73—22no—
149C2×Dic73—24no—
150C2×Dic73—24no—
151C2×Dic73—24no—
152C2×Dic73—24no—
153C2×Dic73—24no—
154C2×Dic73—48no—
155C2×Dic73—44no—
156C2×Dic73C2×C22⋊C412yes—
157C2×Dic73C2×C22⋊C412yes—
158C2×Dic73C2×C22⋊C411yescharacteristic
159C2×Dic73C2×C22⋊C411yescharacteristic
160C2×Dic73AGL(1,ℤ/8)14yes—
161C2×Dic73#13714yes—
162C2×Dic73C22×D411yescharacteristic
163C2×Dic73C22×D411yescharacteristic
164Dic146—416no—
165Dic146—48no—
166Dic146—48no—
167#10596833—44no—
168#10596833—44no—
169C22×C73—28no—
170C22×C73—22no—
171C22×C73—22no—
172C22×C73C2×#10114yes—
173C22×C73C2×#10112yes—
174C22×C73#41812yes—
175C22×C73#41912yes—
176C22×C73C22×C22⋊C411yescharacteristic
177C4×C73—21no—
178C4×C73—22no—
179C4×C73—21no—
180C4×C73—44no—
181Dic73—22no—
182Dic73—22no—
183Dic73—44no—
184Dic73#41812yes—
185Dic73#41912yes—
186Dic73C2×AGL(1,ℤ/8)12yes—
187Dic73C2×#13712yes—
188C2×#1556—731nomaximal, Sylow
189C2×C73—24no—
190C2×C73#155614yescomplemented
191C2×C73C22×#10111yescharacteristic
192C2×C73C2×#41811yescharacteristic
193C2×C73C2×#41911yescharacteristic
194C22×C4⋊Q8—731no—
195C2×#432—731no—
196C2×#432—731no—
197#1556—738no—
198C2×#332—734no—
199C73C2×#155611yescharacteristic, complemented, Sylow
200C23×Q8—1461no—
201C2×C4⋊Q8—732no—
202C2×C4⋊Q8—734no—
203C2×C4⋊Q8—732no—
204C2×C4⋊Q8—734no—
205C2×C4⋊Q8—1461no—
206C2×C4⋊Q8—1461no—
207C2×C4⋊Q8—1462no—
208C2×C4⋊Q8—1462no—
209C22×C4⋊C4—731no—
210C22×C4⋊C4—1461no—
211C22×C4⋊C4#6440811yescharacteristic
212C22×C42—731no—
213#432—734no—
214#432—734no—
215#432—1462no—
216#432—1462no—
217C2×C4⋊C8—732no—
218C2×C4⋊C8—732no—
219C2×C22⋊C8—1461no—
220C2×C22⋊C8—1461no—
221C2×#97—1461no—
222C2×#97—1461no—
223#332—7316no—
224C22×Q8—2928no—
225C22×Q8—1464no—
226C22×Q8—1464no—
227C22×Q8—1462no—
228C22×Q8—1462no—
229C23×C4—21no—
230C23×C4—731no—
231C23×C4—731no—
232C23×C4—1461no—
233C23×C4C2×#6440811yescharacteristic
234C22×C8—1462no—
235C22×C8—1462no—
236C4⋊Q8—734no—
237C4⋊Q8—734no—
238C4⋊Q8—738no—
239C4⋊Q8—1464no—
240C4⋊Q8—1464no—
241C4⋊Q8—1464no—
242C4⋊Q8—1464no—
243C4⋊Q8—1464no—
244C4⋊Q8—1462no—
245C4⋊Q8—1462no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—734no—
249C2×C4⋊C4—732no—
250C2×C4⋊C4—1464no—
251C2×C4⋊C4—1464no—
252C2×C4⋊C4—1462no—
253C2×C4⋊C4—1462no—
254C2×C4⋊C4—1462no—
255C2×C4⋊C4—1461no—
256C2×C4⋊C4C2×#6440814yes—
257C2×C4⋊C4C2×#6440812yes—
258C2×C42—731no—
259C2×C42—731no—
260C2×C42—732no—
261C2×C42—732no—
262C2×C42—732no—
263C2×C42—731no—
264C2×C42—731no—
265C2×C42—732no—
266C4⋊C8—734no—
267C4⋊C8—734no—
268C4⋊C8—1462no—
269C4⋊C8—1462no—
270C22⋊C8—1464no—
271C22⋊C8—1464no—
272#97—1464no—
273#97—1464no—
274C24C22⋊#6440811yescharacteristic
275C2×Q8—2928no—
276C2×Q8—29216no—
277C2×Q8—29216no—
278C2×Q8—2928no—
279C2×Q8—1464no—
280C2×Q8—1464no—
281C2×Q8—1468no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—44no—
286C22×C4—2924no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—732no—
290C22×C4—732no—
291C22×C4—732no—
292C22×C4—732no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—1464no—
296C22×C4—1462no—
297C22×C4—1464no—
298C22×C4—1464no—
299C22×C4C22⋊#6440812yes—
300C22×C4C22⋊#6440811yescharacteristic
301C22×C4C22×#6440812yes—
302C22×C4C22×#6440811yescharacteristic
303C2×C8—2924no—
304C2×C8—2924no—
305C2×C8—1464no—
306C2×C8—1464no—
307C4⋊C4—24no—
308C4⋊C4—22no—
309C4⋊C4—734no—
310C4⋊C4—1464no—
311C4⋊C4—1464no—
312C4⋊C4—1468no—
313C4⋊C4—1464no—
314C4⋊C4—1462no—
315C4⋊C4C22×#6440814yes—
316C42—731no—
317C42—732no—
318C42—731no—
319C42—732no—
320C42—732no—
321C42—732no—
322C42—732no—
323C42—732no—
324C42—731no—
325C42—731no—
326C23—22no—
327C23—22no—
328C23#1455665214yes—
329C23C2×C22⋊#6440812yes—
330C23C2×C22⋊#6440811yescharacteristic
331Q8—2928no—
332Q8—2928no—
333Q8—29216no—
334C2×C4—24no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—48no—
340C2×C4—44no—
341C2×C4—2928no—
342C2×C4—2924no—
343C2×C4—731no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—731no—
347C2×C4—734no—
348C2×C4—734no—
349C2×C4—732no—
350C2×C4—732no—
351C2×C4—1464no—
352C2×C4—1464no—
353C2×C4—1464no—
354C2×C4—1464no—
355C2×C4—1464no—
356C2×C4—1462no—
357C2×C4—1462no—
358C2×C4C2×C22⋊#6440812yes—
359C2×C4C2×C22⋊#6440811yescharacteristic
360C2×C4C23×#6440811yescharacteristic
361C8—2924no—
362C8—2924no—
363C22—28no—
364C22—22no—
365C22—22no—
366C22C2×#1455665214yes—
367C22C2×#1455665212yes—
368C22#1798957912yes—
369C22#1798958012yes—
370C22C22×C22⋊#6440811yescharacteristic
371C4—21no—
372C4—21no—
373C4—22no—
374C4—44no—
375C4—2924no—
376C4—732no—
377C4—732no—
378C4—732no—
379C4—732no—
380C4—1462no—
381C4—1462no—
382C2—24no—
383C2#2262546014yesdirect product factor
384C2C22×#1455665211yescharacteristic
385C2C2×#1798957911yescharacteristic
386C2C2×#1798958011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC4×Dic73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73C2×#1556
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22625460C2direct (N × H)
4. C2×#17989446C2semidirect
16. #17989446C22semidirect
190. C2×C73#1556semidirect
199. C73C2×#1556semidirect
383. C2#22625460direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896072
#226254602
C2×#179894462
C22×#145565902
C2×#155673