Finite Group Databasebeta

← C2×#22622920 #33966894

Subgroups — C2×#22622920 #33966894

Order 18688.

1958 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989310C212yesmaximal, complemented
2#22622920C2116yesmaximal, direct product factor
3C2×#17988971C212yesmaximal
4C2×#17988967C211yesmaximal, characteristic, complemented
5C2×#17988810C214yesmaximal, complemented
6C2×#17988793C212yesmaximal, complemented
7C2×C4×Dic292C212yesmaximal, complemented
8C2×C4×D584C211yesmaximal, characteristic
9C2×C8×Q8×C73C211yesmaximal, characteristic, complemented
10C22×Dic292C2212yes—
11C22×Dic292C2212yes—
12C22×#11924017C2214yes—
13C22×D584C2211yescharacteristic
14#17989310—28no—
15#17989310C22116yescomplemented
16C2×#14556591C2212yes—
17C2×#14556586—24no—
18C2×#14556579C2214yes—
19C2×#14556567—22no—
20C2×C4×Dic146C2214yes—
21C2×C4×D292C2212yes—
22C2×#14556549—22no—
23#17988971C22116yes—
24#17988967C2218yescomplemented
25#17988810C22132yescomplemented
26#17988793C22116yescomplemented
27C4×Dic292C22116yescomplemented
28C4×D584C2218yes—
29C2×#14556525C2211yescharacteristic
30C2×#14556516C2214yes—
31C2×#14556513C2212yes—
32C2×C4×Q8×C73C2211yescharacteristic
33C8×Q8×C73C2218yescomplemented
34C2×C4⋊C8×C73C2211yescharacteristic
35C2×C4⋊C8×C73C2212yes—
36C2×C4×C8×C73C2211yescharacteristic
37C2×C4×C8×C73C2212yes—
38C22×Dic146C2314yes—
39C22×D292C2312yes—
40C22×C4×D73—22no—
41C2×Dic292—28no—
42C2×Dic292—44no—
43C2×Dic292C2318yes—
44C2×Dic292C2318yes—
45C2×#11924017—48no—
46C2×#11924017C23116yes—
47C2×D584—24no—
48C2×D584C2314yes—
49#14556591—24no—
50#14556591C2318yes—
51#14556586—232no—
52#14556579—28no—
53#14556579C23116yes—
54#14556567—216no—
55C4×Dic146—28no—
56C4×Dic146C23116yes—
57C4×D292—24no—
58C4×D292C2318yes—
59#14556549—216no—
60C2×C4⋊Dic73—22no—
61C2×C4⋊Dic73—22no—
62C2×C4⋊Dic73C2312yes—
63C2×#11924007—24no—
64C2×#11924005—24no—
65C2×#11924005—22no—
66C2×#11924005—24no—
67C2×C4×Dic73—24no—
68#14556525C2314yes—
69#14556516C23116yes—
70#14556513C2318yes—
71C22×Q8×C73D411yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2312yes—
74C22×C8×C73C2311yescharacteristic
75C4×Q8×C73D414yes—
76C4×Q8×C73C2314yes—
77C2×C4⋊C4×C73D411yescharacteristic
78C2×C4⋊C4×C73D412yes—
79C2×C42×C73C2311yescharacteristic
80C2×C42×C73C2312yes—
81C4⋊C8×C73C2314yes—
82C4⋊C8×C73C2318yes—
83C4×C8×C73C2314yes—
84C4×C8×C73C2318yes—
85C23×D73—22no—
86C2×Dic146—28no—
87C2×Dic146—28no—
88C2×Dic146—24no—
89C2×Dic146C2418yes—
90C2×D292—24no—
91C2×D292—24no—
92C2×D292—22no—
93C2×D292C2414yes—
94C22×Dic73—22no—
95C22×Dic73—24no—
96C2×C4×D73—28no—
97C2×C4×D73—48no—
98Dic292—216no—
99Dic292—48no—
100#11924017—416no—
101D584—28no—
102C4⋊Dic73—28no—
103C4⋊Dic73—28no—
104C4⋊Dic73—22no—
105C4⋊Dic73C2414yes—
106#11924007—216no—
107#11924005—216no—
108#11924005—28no—
109#11924005—216no—
110C4×Dic73—216no—
111C2×Q8×C73—24no—
112C2×Q8×C73C2×D414yes—
113C22×C4×C73C2×D412yes—
114C22×C4×C73C2×D411yescharacteristic
115C22×C4×C73C2×D412yes—
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73C2411yescharacteristic
118C2×C8×C73—24no—
119C2×C8×C73—22no—
120C2×C8×C73#4114yes—
121C2×C8×C73C2412yes—
122C2×C8×C73C2414yes—
123C2×C8×C73C2412yes—
124C4⋊C4×C73C2×D414yes—
125C4⋊C4×C73C2×D418yes—
126C42×C73C2×D412yes—
127C42×C73C2×D414yes—
128C42×C73C2412yes—
129C42×C73C2414yes—
130C23×C73C22×D411yescharacteristic
131C22×D73—24no—
132C22×D73—44no—
133C22×D73—44no—
134C22×D73—44no—
135Q8×C73—28no—
136C2×C4×C73—24no—
137C2×C4×C73—24no—
138C2×C4×C73—22no—
139C2×C4×C73#13514yes—
140C2×C4×C73C22×D414yes—
141C2×C4×C73C22×D412yes—
142C2×C4×C73C22×D414yes—
143C2×C4×C73C22×D411yescharacteristic
144C2×C4×C73C22×D412yes—
145C2×C4×C73C2×#4112yes—
146C2×C4×C73H(5,𝔽2)12yes—
147C2×C4×C73C2511yescharacteristic
148C2×Dic73—24no—
149C2×Dic73—28no—
150C2×Dic73—48no—
151C2×Dic73—44no—
152D292—24no—
153D292—24no—
154D292—44no—
155C4×D73—416no—
156Dic146—28no—
157Dic146—28no—
158Dic146—48no—
159C8×C73—24no—
160C8×C73—22no—
161C8×C73C2×#4114yes—
162C22×C73#55012yes—
163C22×C73C2×#13512yes—
164C22×C73#57812yes—
165C22×C73C23×D411yescharacteristic
166C2×D73—44no—
167C2×D73—44no—
168C2×D73—44no—
169C2×D73—88no—
170C4×C73—24no—
171C4×C73—24no—
172C4×C73—22no—
173C4×C73#55012yes—
174C4×C73C2×#13514yes—
175C4×C73C22×#4111yescharacteristic
176C4×C73C2×H(5,𝔽2)11yescharacteristic
177Dic73—48no—
178Dic73—44no—
179C2×#3393—731nomaximal, Sylow
180C2×C73#339314yescomplemented
181C2×C73C2×#55011yescharacteristic
182C2×C73C22×#13511yescharacteristic
183C2×C73C2×#57811yescharacteristic
184D73—84no—
185C2×#556—732no—
186#3393—7316no—
187C2×#495—732no—
188C2×#494—731no—
189C2×#464—734no—
190C2×#461—732no—
191C2×C8×Q8D7311yescharacteristic, complemented
192C2×C4×Q16—732no—
193C2×C4×D8—731no—
194C73C2×#339311yescharacteristic, complemented, Sylow
195C22×Q16—732no—
196C22×Q16—732no—
197C22×SD16—734no—
198C22×D8—731no—
199#556—7316no—
200#556—1468no—
201C2×C4⋊Q8—732no—
202C2×#126—1464no—
203C2×#124—734no—
204C2×C22⋊Q8—1462no—
205C2×C4×Q8—734no—
206C2×C4×Q8C2×D7311yescharacteristic
207C2×C4×D4—732no—
208C2×#117—1462no—
209#495—7316no—
210#494—738no—
211#464—7332no—
212#461—7316no—
213C8×Q8C2×D7318yescomplemented
214C4×Q16—7316no—
215C4×D8—738no—
216C2×#107—731no—
217C2×C4⋊C8C2×D7311yescharacteristic
218C2×C4⋊C8C2×D7312yes—
219C2×#103—734no—
220C2×#102—732no—
221C2×C4×C8C2×D7311yescharacteristic
222C2×C4×C8C2×D7312yes—
223C22×Q8—734no—
224C22×Q8D29211yescharacteristic
225C22×D4—732no—
226C23×C4—1462no—
227C2×Q16—2924no—
228C2×Q16—738no—
229C2×Q16—738no—
230C2×Q16—1468no—
231C2×SD16—2928no—
232C2×SD16—7316no—
233C2×D8—734no—
234C2×D8—1464no—
235C22×C8C22×D7312yes—
236C22×C8C22×D7311yescharacteristic
237C22×C8C22×D7311yescharacteristic
238C4⋊Q8—738no—
239C4⋊Q8—1464no—
240#126—14632no—
241#124—7316no—
242#124—1468no—
243C22⋊Q8—14616no—
244C4×Q8—7316no—
245C4×Q8—1468no—
246C4×Q8D29214yes—
247C4×Q8C22×D7314yes—
248C4×D4—738no—
249C4×D4—1464no—
250#117—14616no—
251C2×C4⋊C4—732no—
252C2×C4⋊C4—1462no—
253C2×C4⋊C4—1464no—
254C2×C4⋊C4—1462no—
255C2×C4⋊C4D29211yescharacteristic
256C2×C4⋊C4D29212yes—
257C2×C22⋊C4—1464no—
258C2×C22⋊C4—1462no—
259C2×C22⋊C4—1464no—
260C2×C42—1464no—
261C2×C42C22×D7311yescharacteristic
262C2×C42C22×D7312yes—
263#107—734no—
264C4⋊C8C22×D7314yes—
265C4⋊C8C22×D7318yes—
266#103—7316no—
267#102—738no—
268C4×C8C22×D7314yes—
269C4×C8C22×D7318yes—
270C24—1462no—
271C2×Q8—24no—
272C2×Q8—738no—
273C2×Q8—1468no—
274C2×Q8—1468no—
275C2×Q8—1464no—
276C2×Q8C2×D29214yes—
277C2×D4—734no—
278C2×D4—1462no—
279C2×D4—1464no—
280C2×D4—1464no—
281C22×C4—2928no—
282C22×C4—1462no—
283C22×C4—1464no—
284C22×C4—1468no—
285C22×C4C2×D29212yes—
286C22×C4C2×D29211yescharacteristic
287C22×C4C2×D29212yes—
288C22×C4C2×D29211yescharacteristic
289C22×C4C23×D7311yescharacteristic
290Q16—2928no—
291Q16—14616no—
292SD16—29216no—
293D8—1468no—
294C2×C8—24no—
295C2×C8—22no—
296C2×C8#1192402914yes—
297C2×C8C23×D7312yes—
298C2×C8C23×D7314yes—
299C2×C8C23×D7312yes—
300C4⋊C4—734no—
301C4⋊C4—14616no—
302C4⋊C4—1462no—
303C4⋊C4—1468no—
304C4⋊C4—1468no—
305C4⋊C4C2×D29214yes—
306C4⋊C4C2×D29218yes—
307C22⋊C4—14616no—
308C22⋊C4—1468no—
309C22⋊C4—14616no—
310C42—14616no—
311C42C2×D29212yes—
312C42C2×D29214yes—
313C42C23×D7312yes—
314C42C23×D7314yes—
315C23—2924no—
316C23—2924no—
317C23—2924no—
318C23—1464no—
319C23C22×D29211yescharacteristic
320Q8—28no—
321Q8—2928no—
322Q8—1468no—
323Q8—1468no—
324D4—2924no—
325D4—1464no—
326D4—1464no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—2928no—
331C2×C4—2924no—
332C2×C4—29216no—
333C2×C4—1464no—
334C2×C4—1468no—
335C2×C4#1455661314yes—
336C2×C4C22×D29214yes—
337C2×C4C22×D29212yes—
338C2×C4C22×D29214yes—
339C2×C4C22×D29211yescharacteristic
340C2×C4C22×D29212yes—
341C2×C4C2×#1192402912yes—
342C2×C4#1455663712yes—
343C2×C4C24×D7311yescharacteristic
344C8—24no—
345C8—22no—
346C8C2×#1192402914yes—
347C22—2924no—
348C22—2924no—
349C22—2924no—
350C22—5848no—
351C22#1798925912yes—
352C22C2×#1455661312yes—
353C22#1798940412yes—
354C22C23×D29211yescharacteristic
355C4—24no—
356C4—24no—
357C4—22no—
358C4—2924no—
359C4—2928no—
360C4#1798925912yes—
361C4C2×#1455661314yes—
362C4C22×#1192402911yescharacteristic
363C4C2×#1455663711yescharacteristic
364C2—5844no—
365C2#2262292014yesdirect product factor
366C2C2×#1798925911yescharacteristic
367C2C22×#1455661311yescharacteristic
368C2C2×#1798940411yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C8×Q8×C73C2
socleC23×C73C22×D4
prime radicalC22×D584C22
hypercenterC2×C8×Q8D73
hypocenterC73C2×#3393
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#17989310C2semidirect
2. #22622920C2direct (N × H)
4. C2×#17988967C2semidirect
5. C2×#17988810C2semidirect
6. C2×#17988793C2semidirect
7. C2×C4×Dic292C2semidirect
9. C2×C8×Q8×C73C2semidirect
15. #17989310C22semidirect
24. #17988967C22semidirect
25. #17988810C22semidirect
26. #17988793C22semidirect
27. C4×Dic292C22semidirect
33. C8×Q8×C73C22semidirect
180. C2×C73#3393semidirect
191. C2×C8×Q8D73semidirect
194. C73C2×#3393semidirect
213. C8×Q8C2×D73semidirect
365. C2#22622920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893102
#226229202
C2×#179889712
C2×#179889672
C2×#179888102
C2×#179887932
C2×C4×Dic2922
C2×C4×D5842
C2×C8×Q8×C732
C2×#339373