Finite Group Databasebeta

← C2×#22626062 #34022194

Subgroups — C2×#22626062 #34022194

Order 18688.

1598 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556654C214yesmaximal
2C2×#17989546C211yesmaximal, characteristic
3C2×#17989531C211yesmaximal, characteristic
4#22626062C218yesmaximal, direct product factor
5C2×C4⋊Q8×D73C211yesmaximal, characteristic
6C22×#11924036C2212yes—
7C22×C4⋊#64408C2212yes—
8C2×#14556654—216no—
9C2×#14556654C22116yes—
10#17989546—22no—
11#17989546C2214yes—
12C2×#14556646—22no—
13#17989531—22no—
14#17989531C2214yes—
15C2×(C2×#64408)⋊C4—22no—
16C22×Q8×D73C2212yes—
17C2×#14556591C411yescharacteristic, complemented
18C2×#14556590—22no—
19C2×#14556589C412yescomplemented
20C4⋊Q8×D73—22no—
21C4⋊Q8×D73—22no—
22C4⋊Q8×D73C414yescomplemented
23C4⋊Q8×D73C2214yes—
24C2×C4⋊C4×D73—22no—
25C2×C42×D73C2211yescharacteristic
26C2×C4⋊Q8×C73C411yescharacteristic, complemented
27C23×#64408—22no—
28C2×#11924036—22no—
29C2×#11924036—24no—
30C2×#11924036D418yes—
31C2×#11924036C2314yes—
32C22×#10596833—22no—
33C2×C4⋊#64408—28no—
34C2×C4⋊#64408—22no—
35C2×C4⋊#64408C2314yes—
36#14556654—232no—
37#14556646—28no—
38(C2×#64408)⋊C4—28no—
39C22×Dic146—22no—
40C22×Dic146C2×C412yes—
41C2×Q8×D73—22no—
42C2×Q8×D73—22no—
43C2×Q8×D73—28no—
44C2×Q8×D73—28no—
45C2×Q8×D73C2×C414yes—
46C2×Q8×D73C2314yes—
47C22×C4×D73—22no—
48C22×C4×D73D412yes—
49C22×C4×D73C2311yescharacteristic
50#14556591—22no—
51#14556591C2×C414yescomplemented
52#14556590—28no—
53#14556590—28no—
54#14556589—24no—
55#14556589C2×C418yescomplemented
56C2×C4⋊Dic73—22no—
57C2×#11924007—24no—
58C4⋊C4×D73—28no—
59C4⋊C4×D73—28no—
60C2×C4×Dic73C2×C411yescharacteristic
61C2×C4×Dic73D412yes—
62C42×D73C2×C412yes—
63C42×D73D412yes—
64C42×D73D412yes—
65C42×D73C2312yes—
66C22×Q8×C73C2×C412yes—
67C4⋊Q8×C73—22no—
68C4⋊Q8×C73C2×C414yescomplemented
69C2×C4⋊C4×C73—22no—
70C2×C42×C73C2×C411yescharacteristic
71C22×#64408—24no—
72C22×#64408—44no—
73C22×#64408—48no—
74#11924036—28no—
75#11924036—24no—
76#11924036C2×D418yes—
77C2×#10596833—28no—
78C2×#10596833—24no—
79C4⋊#64408—28no—
80C4⋊#64408—44no—
81C23×D73C2×D411yescharacteristic
82C2×Dic146—28no—
83C2×Dic146—22no—
84C2×Dic146—24no—
85C2×Dic146—24no—
86C2×Dic146—48no—
87C2×Dic146C22×C414yes—
88Q8×D73—216no—
89Q8×D73—28no—
90Q8×D73—28no—
91Q8×D73—48no—
92Q8×D73—44no—
93Q8×D73—44no—
94C22×Dic73—22no—
95C22×Dic73C22⋊C412yes—
96C22×Dic73C2×D411yescharacteristic
97C2×C4×D73—28no—
98C2×C4×D73—24no—
99C2×C4×D73—24no—
100C2×C4×D73—44no—
101C2×C4×D73—44no—
102C2×C4×D73C22⋊C414yes—
103C2×C4×D73C22×C411yescharacteristic
104C2×C4×D73C2×D414yes—
105C2×C4×D73C2×D414yes—
106C2×C4×D73C2×D411yescharacteristic
107C2×C4×D73C2×D411yescharacteristic
108C2×C4×D73#4114yes—
109C2×C4×D73C2411yescharacteristic
110C4⋊Dic73—28no—
111#11924007—216no—
112C4×Dic73C22⋊C414yes—
113C4×Dic73C22⋊C412yes—
114C4×Dic73C22×C412yes—
115C4×Dic73C2×D414yes—
116C2×Q8×C73—22no—
117C2×Q8×C73—28no—
118C2×Q8×C73C22×C414yes—
119C22×C4×C73—22no—
120C22×C4×C73C22⋊C412yes—
121C22×C4×C73C22×C411yescharacteristic
122C4⋊C4×C73—28no—
123C42×C73C22⋊C412yes—
124C42×C73C22×C412yes—
125C23×C73C2×C22⋊C411yescharacteristic
126C22×D73C2×C22⋊C411yescharacteristic
127C22×D73#12412yes—
128C22×D73#12712yes—
129C22×D73#13718yes—
130C22×D73C22×D411yescharacteristic
131C2×#64408—44no—
132C2×#64408—48no—
133C2×#64408—88no—
134Q8×C73—28no—
135Q8×C73—44no—
136C2×C4×C73—24no—
137C2×C4×C73—24no—
138C2×C4×C73—44no—
139C2×C4×C73C2×C22⋊C414yes—
140C2×C4×C73C2×C22⋊C411yescharacteristic
141C2×C4×C73C4×D414yes—
142C2×C4×C73C23×C411yescharacteristic
143C2×Dic73—24no—
144C2×Dic73—24no—
145C2×Dic73—44no—
146C2×Dic73C2×C22⋊C414yes—
147C2×Dic73C2×C22⋊C411yescharacteristic
148C2×Dic73#12114yes—
149C2×Dic73C22×D411yescharacteristic
150C4×D73—28no—
151C4×D73—28no—
152C4×D73—44no—
153C4×D73—44no—
154C4×D73—48no—
155C4×D73C4×D414yes—
156C4×D73#12114yes—
157C4×D73#12412yes—
158C4×D73#12712yes—
159C4×D73C22×D412yes—
160C4×D73C2×#4112yes—
161Dic146—28no—
162Dic146—44no—
163Dic146—48no—
164Dic146—48no—
165#10596833—28no—
166C22×C73#39012yes—
167C22×C73#41914yes—
168C22×C73C22×C22⋊C411yescharacteristic
169C2×D73#39012yes—
170C2×D73#41914yes—
171C2×D73#49118yes—
172C2×D73#49718yes—
173C2×D73C2×#12411yescharacteristic
174C2×D73C2×#12711yescharacteristic
175C2×D73C2×#13714yes—
176#64408—84no—
177C4×C73—24no—
178C4×C73—44no—
179C4×C73#39012yes—
180C4×C73C2×C4×D412yes—
181Dic73—24no—
182Dic73—44no—
183Dic73#39012yes—
184Dic73C2×#12112yes—
185C2×#1960—731nomaximal, Sylow
186C2×C73#196014yescomplemented
187C2×C73C2×#39011yescharacteristic
188C2×C73C2×#41912yes—
189D73#196014yescomplemented
190D73C2×#49112yes—
191D73C2×#49712yes—
192C22×C4⋊Q8—731no—
193C22×#103—734no—
194C22×#97—731no—
195C2×#382—731no—
196#1960—738no—
197C73C2×#196011yescharacteristic, complemented, Sylow
198C23×Q8—732no—
199C23×C8—732no—
200C2×C4⋊Q8—732no—
201C2×C4⋊Q8—734no—
202C2×C4⋊Q8—734no—
203C2×C4⋊Q8—731no—
204C2×C4⋊Q8—1462no—
205C2×C4⋊Q8—1462no—
206C2×C4⋊Q8—1462no—
207C2×C4⋊Q8#6440811yescharacteristic, complemented
208C22×C4⋊C4—732no—
209C22×C4⋊C4—1462no—
210C22×C42—731no—
211C2×#103—7316no—
212C2×#103—14616no—
213C2×#97—734no—
214C2×#97—1462no—
215C2×#97—1462no—
216#382—734no—
217#382—1462no—
218C2×#95—1462no—
219C22×Q8—734no—
220C22×Q8—734no—
221C22×Q8—732no—
222C22×Q8—1462no—
223C22×Q8—1468no—
224C22×Q8—1468no—
225C22×Q8—1462no—
226C22×Q8—1462no—
227C22×Q8C2×#6440812yes—
228C23×C4—731no—
229C23×C4—732no—
230C23×C4—1462no—
231C23×C4—1462no—
232C22×C8—738no—
233C22×C8—734no—
234C22×C8—1462no—
235C22×C8—1464no—
236C22×C8—1462no—
237C4⋊Q8—22no—
238C4⋊Q8—738no—
239C4⋊Q8—734no—
240C4⋊Q8—1468no—
241C4⋊Q8—1468no—
242C4⋊Q8—1464no—
243C4⋊Q8—1462no—
244C4⋊Q8C2×#6440814yescomplemented
245C2×C4⋊C4—22no—
246C2×C4⋊C4—734no—
247C2×C4⋊C4—1468no—
248C2×C4⋊C4—1468no—
249C2×C4⋊C4—1462no—
250C2×C4⋊C4—1468no—
251C2×C4⋊C4—1464no—
252C2×C4⋊C4—1462no—
253C2×C42—732no—
254C2×C42—731no—
255C2×C42—732no—
256C2×C42—732no—
257C2×C42—732no—
258C2×C42—732no—
259C2×C42C2×#6440811yescharacteristic
260#103—14632no—
261#97—1468no—
262#95—1468no—
263C24—731no—
264C2×Q8—22no—
265C2×Q8—28no—
266C2×Q8—2928no—
267C2×Q8—2924no—
268C2×Q8—2928no—
269C2×Q8—2924no—
270C2×Q8—734no—
271C2×Q8—1464no—
272C2×Q8—1464no—
273C2×Q8—1468no—
274C2×Q8—1468no—
275C2×Q8—14616no—
276C2×Q8—1468no—
277C2×Q8—1462no—
278C2×Q8C22×#6440814yes—
279C22×C4—22no—
280C22×C4—2924no—
281C22×C4—2924no—
282C22×C4—2924no—
283C22×C4—2928no—
284C22×C4—731no—
285C22×C4—731no—
286C22×C4—731no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—734no—
290C22×C4—734no—
291C22×C4—732no—
292C22×C4—734no—
293C22×C4—734no—
294C22×C4—1464no—
295C22×C4—1464no—
296C22×C4—1468no—
297C22×C4—1464no—
298C22×C4—1462no—
299C22×C4C22⋊#6440812yes—
300C22×C4C22×#6440811yescharacteristic
301C2×C8—738no—
302C2×C8—1464no—
303C2×C8—1468no—
304C2×C8—1464no—
305C2×C8—1468no—
306C4⋊C4—28no—
307C4⋊C4—2924no—
308C4⋊C4—14616no—
309C4⋊C4—1468no—
310C4⋊C4—1468no—
311C42—732no—
312C42—734no—
313C42—732no—
314C42—734no—
315C42C22⋊#6440812yes—
316C42C22×#6440812yes—
317C23—731no—
318C23—731no—
319C23—732no—
320C23—732no—
321C23—738no—
322C23C2×C22⋊#6440811yescharacteristic
323Q8—28no—
324Q8—44no—
325Q8—2928no—
326Q8—2928no—
327Q8—2924no—
328Q8—1468no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—44no—
332C2×C4—2924no—
333C2×C4—2924no—
334C2×C4—2928no—
335C2×C4—2924no—
336C2×C4—2924no—
337C2×C4—2928no—
338C2×C4—5848no—
339C2×C4—731no—
340C2×C4—731no—
341C2×C4—734no—
342C2×C4—732no—
343C2×C4—732no—
344C2×C4—734no—
345C2×C4—732no—
346C2×C4—734no—
347C2×C4—732no—
348C2×C4—734no—
349C2×C4—1468no—
350C2×C4—1468no—
351C2×C4—1464no—
352C2×C4—1464no—
353C2×C4C2×C22⋊#6440814yes—
354C2×C4C2×C22⋊#6440811yescharacteristic
355C2×C4D4×#6440814yes—
356C2×C4C23×#6440811yescharacteristic
357C8—1468no—
358C22—738no—
359C22—738no—
360C22—731no—
361C22—731no—
362C22—732no—
363C22—734no—
364C22—734no—
365C22#1798953912yes—
366C22#1798958014yes—
367C22C22×C22⋊#6440811yescharacteristic
368C4—24no—
369C4—44no—
370C4—2924no—
371C4—5844no—
372C4—732no—
373C4—732no—
374C4—1464no—
375C4#1798953912yes—
376C4C2×D4×#6440812yes—
377C2—732no—
378C2—732no—
379C2—734no—
380C2#2262606214yesdirect product factor
381C2C2×#1798953911yescharacteristic
382C2C2×#1798958012yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC2×C4⋊Q8×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C2×D4
cosocleC2×C4×D73C24
hypercenterC2×C4⋊Q8#64408
hypocenterC73C2×#1960
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #22626062C2direct (N × H)
17. C2×#14556591C4semidirect
19. C2×#14556589C4semidirect
22. C4⋊Q8×D73C4semidirect
26. C2×C4⋊Q8×C73C4semidirect
51. #14556591C2×C4semidirect
55. #14556589C2×C4semidirect
68. C4⋊Q8×C73C2×C4semidirect
186. C2×C73#1960semidirect
189. D73#1960semidirect
197. C73C2×#1960semidirect
207. C2×C4⋊Q8#64408semidirect
244. C4⋊Q8C2×#64408semidirect
380. C2#22626062direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566542
C2×#179895462
C2×#179895312
#226260622
C2×C4⋊Q8×D732
C2×#196073