Finite Group Databasebeta

← C2×#22625461 #34017786

Subgroups — C2×#22625461 #34017786

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×#17989610C211yesmaximal, characteristic
2C2×#17989610C211yesmaximal, characteristic
3#22625461C218yesmaximal, direct product factor
4C2×#17989446C214yesmaximal, complemented
5C2×C4⋊Q8×D73C211yesmaximal, characteristic
6#17989610—22no—
7#17989610—22no—
8#17989610C2214yes—
9#17989610C2214yes—
10C2×#14556658C2212yes—
11C2×#14556658C2212yes—
12C2×#14556648—21no—
13C2×#14556648—21no—
14C2×#14556646—21no—
15C2×#14556646—21no—
16#17989446C22116yescomplemented
17C22×Q8×D73—21no—
18C2×#14556591C411yescharacteristic
19C2×#14556590—21no—
20C2×#14556590C2212yes—
21C2×#14556589—21no—
22C4⋊Q8×D73—22no—
23C4⋊Q8×D73—22no—
24C4⋊Q8×D73C414yes—
25C4⋊Q8×D73C2214yes—
26C2×C4⋊C4×D73—21no—
27C2×C4⋊C4×D73C412yes—
28C2×C42×D73C2211yescharacteristic
29C2×C4⋊Q8×C73C411yescharacteristic
30C22×#10596833—22no—
31C22×#10596833—22no—
32#14556658—22no—
33#14556658—22no—
34#14556658C2314yes—
35#14556658C2314yes—
36#14556648—24no—
37#14556648—24no—
38#14556646—24no—
39#14556646—24no—
40C22×Dic146—22no—
41C22×Dic146—21no—
42C2×Q8×D73—24no—
43C2×Q8×D73—24no—
44C2×Q8×D73—48no—
45C22×C4×D73—22no—
46C22×C4×D73C2×C411yescharacteristic
47C22×C4×D73D411yescharacteristic
48C22×C4×D73D411yescharacteristic
49#14556591—22no—
50#14556591C2×C414yes—
51#14556590—24no—
52#14556590—22no—
53#14556590—22no—
54#14556590—24no—
55#14556590C2×C414yes—
56#14556590C2314yes—
57#14556589—24no—
58#14556589—24no—
59C2×C4⋊Dic73—21no—
60C2×C4⋊Dic73C2×C412yes—
61C2×#11924007—22no—
62C2×#11924007—22no—
63C4⋊C4×D73—24no—
64C4⋊C4×D73—24no—
65C4⋊C4×D73—24no—
66C4⋊C4×D73C2×C418yes—
67C2×C4×Dic73D411yescharacteristic
68C2×C4×Dic73D411yescharacteristic
69C2×C4×Dic73C2311yescharacteristic
70C42×D73C2×C412yes—
71C42×D73D412yes—
72C42×D73D412yes—
73C42×D73C2312yes—
74C22×Q8×C73—21no—
75C4⋊Q8×C73—22no—
76C4⋊Q8×C73C2×C414yes—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73C2×C412yes—
79C2×C42×C73C2×C411yescharacteristic
80C2×#10596833—24no—
81C2×#10596833—24no—
82C2×#10596833—44no—
83C2×#10596833—44no—
84C23×D73C22⋊C411yescharacteristic
85C2×Dic146—24no—
86C2×Dic146—24no—
87C2×Dic146—24no—
88C2×Dic146—44no—
89C2×Dic146—48no—
90Q8×D73—416no—
91Q8×D73—416no—
92C22×Dic73—22no—
93C22×Dic73C22⋊C411yescharacteristic
94C22×Dic73C2×D411yescharacteristic
95C22×Dic73C2×D411yescharacteristic
96C2×C4×D73—24no—
97C2×C4×D73—24no—
98C2×C4×D73—24no—
99C2×C4×D73—28no—
100C2×C4×D73—48no—
101C2×C4×D73C22⋊C412yes—
102C2×C4×D73C22⋊C412yes—
103C2×C4×D73C22⋊C412yes—
104C2×C4×D73C22×C412yes—
105C2×C4×D73C2×D412yes—
106C2×C4×D73C2×D412yes—
107C4⋊Dic73—24no—
108C4⋊Dic73—22no—
109C4⋊Dic73C22×C414yes—
110#11924007—24no—
111#11924007—28no—
112#11924007—24no—
113C4×Dic73C22⋊C412yes—
114C4×Dic73C22⋊C412yes—
115C4×Dic73C22×C411yescharacteristic
116C4×Dic73C2×D411yescharacteristic
117C4×Dic73C2×D411yescharacteristic
118C4×Dic73C2×D412yes—
119C4×Dic73C2×D412yes—
120C4×Dic73C2411yescharacteristic
121C2×Q8×C73—24no—
122C2×Q8×C73—44no—
123C22×C4×C73—22no—
124C22×C4×C73C22⋊C411yescharacteristic
125C22×C4×C73C22⋊C411yescharacteristic
126C22×C4×C73C22×C411yescharacteristic
127C4⋊C4×C73—24no—
128C4⋊C4×C73—22no—
129C4⋊C4×C73C22×C414yes—
130C42×C73C22⋊C412yes—
131C42×C73C22×C412yes—
132C23×C73C2×C22⋊C411yescharacteristic
133C22×D73—22no—
134C22×D73—22no—
135C22×D73#10114yes—
136C22×D73C2×C22⋊C412yes—
137Q8×C73—48no—
138C2×C4×C73—22no—
139C2×C4×C73—22no—
140C2×C4×C73—22no—
141C2×C4×C73—24no—
142C2×C4×C73—44no—
143C2×C4×C73C2×C22⋊C411yescharacteristic
144C2×C4×C73C2×C22⋊C412yes—
145C2×C4×C73C2×C22⋊C412yes—
146C2×C4×C73C23×C411yescharacteristic
147C2×Dic73—22no—
148C2×Dic73—24no—
149C2×Dic73—44no—
150C2×Dic73C2×C22⋊C412yes—
151C2×Dic73C2×C22⋊C411yescharacteristic
152C2×Dic73C2×C22⋊C411yescharacteristic
153C2×Dic73AGL(1,ℤ/8)14yes—
154C2×Dic73#13714yes—
155C2×Dic73C22×D411yescharacteristic
156C2×Dic73C22×D411yescharacteristic
157C4×D73—24no—
158C4×D73—24no—
159C4×D73—24no—
160C4×D73—24no—
161C4×D73—24no—
162C4×D73—24no—
163C4×D73—416no—
164Dic146—48no—
165Dic146—48no—
166Dic146—48no—
167#10596833—44no—
168#10596833—44no—
169C22×C73C2×#10112yes—
170C22×C73#41812yes—
171C22×C73#41912yes—
172C22×C73C22×C22⋊C411yescharacteristic
173C2×D73—28no—
174C2×D73—22no—
175C2×D73—22no—
176C2×D73C2×#10114yes—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—22no—
180C4×C73—22no—
181C4×C73—44no—
182Dic73—22no—
183Dic73—44no—
184Dic73#41812yes—
185Dic73#41912yes—
186Dic73C2×AGL(1,ℤ/8)12yes—
187Dic73C2×#13712yes—
188C2×#1556—731nomaximal, Sylow
189C2×C73#155614yescomplemented
190C2×C73C22×#10111yescharacteristic
191C2×C73C2×#41811yescharacteristic
192C2×C73C2×#41911yescharacteristic
193D73—24no—
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—734no—
202C2×C4⋊Q8—734no—
203C2×C4⋊Q8—732no—
204C2×C4⋊Q8—731no—
205C2×C4⋊Q8—1461no—
206C2×C4⋊Q8—1462no—
207C2×C4⋊Q8—1462no—
208C2×C4⋊Q8—1461no—
209C2×C4⋊Q8#6440811yescharacteristic
210C22×C4⋊C4—732no—
211C22×C4⋊C4—1461no—
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—21no—
225C22×Q8—2928no—
226C22×Q8—1462no—
227C22×Q8—1464no—
228C22×Q8—1464no—
229C22×Q8—1461no—
230C23×C4—731no—
231C23×C4—731no—
232C23×C4—731no—
233C23×C4—1462no—
234C22×C8—1462no—
235C22×C8—1462no—
236C4⋊Q8—22no—
237C4⋊Q8—734no—
238C4⋊Q8—734no—
239C4⋊Q8—734no—
240C4⋊Q8—1464no—
241C4⋊Q8—1464no—
242C4⋊Q8—1462no—
243C4⋊Q8—1462no—
244C4⋊Q8—1464no—
245C4⋊Q8—1464no—
246C4⋊Q8—1462no—
247C4⋊Q8C2×#6440814yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—732no—
250C2×C4⋊C4—738no—
251C2×C4⋊C4—1464no—
252C2×C4⋊C4—1464no—
253C2×C4⋊C4—1464no—
254C2×C4⋊C4—1462no—
255C2×C4⋊C4—1462no—
256C2×C4⋊C4—1461no—
257C2×C4⋊C4C2×#6440812yes—
258C2×C42—731no—
259C2×C42—731no—
260C2×C42—731no—
261C2×C42—732no—
262C2×C42—732no—
263C2×C42—732no—
264C2×C42—732no—
265C2×C42C2×#6440811yescharacteristic
266C4⋊C8—734no—
267C4⋊C8—734no—
268C4⋊C8—1462no—
269C4⋊C8—1462no—
270C22⋊C8—1464no—
271C22⋊C8—1464no—
272#97—1464no—
273#97—1464no—
274C24—731no—
275C2×Q8—24no—
276C2×Q8—44no—
277C2×Q8—2924no—
278C2×Q8—2928no—
279C2×Q8—29216no—
280C2×Q8—29216no—
281C2×Q8—1464no—
282C2×Q8—1464no—
283C2×Q8—1464no—
284C22×C4—22no—
285C22×C4—2928no—
286C22×C4—731no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—732no—
290C22×C4—732no—
291C22×C4—732no—
292C22×C4—732no—
293C22×C4—732no—
294C22×C4—732no—
295C22×C4—1468no—
296C22×C4—1464no—
297C22×C4—1464no—
298C22×C4—1464no—
299C22×C4—1462no—
300C22×C4C22⋊#6440811yescharacteristic
301C22×C4C22⋊#6440811yescharacteristic
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—1468no—
311C4⋊C4—1464no—
312C4⋊C4—1464no—
313C4⋊C4—1462no—
314C4⋊C4—1464no—
315C4⋊C4C22×#6440814yes—
316C42—731no—
317C42—731no—
318C42—732no—
319C42—732no—
320C42—732no—
321C42—732no—
322C42—731no—
323C42—731no—
324C42C22⋊#6440812yes—
325C42C22×#6440812yes—
326C23—732no—
327C23—734no—
328C23—1462no—
329C23—1462no—
330C23C2×C22⋊#6440811yescharacteristic
331Q8—48no—
332Q8—2928no—
333Q8—2928no—
334Q8—2928no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—44no—
340C2×C4—29216no—
341C2×C4—2924no—
342C2×C4—731no—
343C2×C4—731no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—734no—
347C2×C4—734no—
348C2×C4—732no—
349C2×C4—1464no—
350C2×C4—1464no—
351C2×C4—1464no—
352C2×C4—1464no—
353C2×C4—1464no—
354C2×C4—1464no—
355C2×C4—1464no—
356C2×C4—1462no—
357C2×C4C2×C22⋊#6440811yescharacteristic
358C2×C4C2×C22⋊#6440812yes—
359C2×C4C2×C22⋊#6440812yes—
360C2×C4C23×#6440811yescharacteristic
361C8—2924no—
362C8—2924no—
363C22—734no—
364C22—1468no—
365C22—1462no—
366C22—1462no—
367C22D73⋊#10112yes—
368C22#1798957912yes—
369C22#1798958012yes—
370C22C22×C22⋊#6440811yescharacteristic
371C4—21no—
372C4—21no—
373C4—22no—
374C4—22no—
375C4—44no—
376C4—2924no—
377C4—732no—
378C4—732no—
379C4—732no—
380C4—732no—
381C4—1462no—
382C2—1464no—
383C2#2262546114yesdirect product factor
384C2C2×D73⋊#10111yescharacteristic
385C2C2×#1798957911yescharacteristic
386C2C2×#1798958011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC2×C4⋊Q8×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC4×Dic73C24
hypercenterC2×C4⋊Q8#64408
hypocenterC73C2×#1556
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #22625461C2direct (N × H)
4. C2×#17989446C2semidirect
16. #17989446C22semidirect
189. C2×C73#1556semidirect
199. C73C2×#1556semidirect
383. C2#22625461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896102
#226254612
C2×#179894462
C2×C4⋊Q8×D732
C2×#155673