Finite Group Databasebeta

← C2×#22608403 #33052607

Subgroups — C2×#22608403 #33052607

Order 18688.

990 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989144C211yesmaximal, characteristic
2C2×#17988640C211yesmaximal, characteristic
3#22608403C218yesmaximal, direct product factor
4C2×#17988317C214yesmaximal, complemented
5C2×#432×C73C211yesmaximal, characteristic
6#17989144—22no—
7#17989144—22no—
8#17989144C414yes—
9#17989144C2214yes—
10C2×#14556591C411yescharacteristic
11C2×#14556591C411yescharacteristic
12C2×#14556583—21no—
13C2×#14556570—21no—
14C2×#14556570C412yes—
15C2×C4×Dic146—21no—
16C2×C4×Dic146C2212yes—
17C2×#14556550—21no—
18#17988640—22no—
19#17988640C2214yes—
20C2×C4⋊#10596831—21no—
21C2×C22⋊#10596831—21no—
22C2×C4×#10596831C2212yes—
23#17988317C22116yescomplemented
24C22×C42×C73C2211yescharacteristic
25#432×C73—22no—
26#432×C73C2214yes—
27C2×C4⋊C8×C73C2212yes—
28C2×C22⋊C8×C73—21no—
29C2×#97×C73—21no—
30C22×Dic146—21no—
31C22×Dic146C2×C412yes—
32C22×#10596831—22no—
33#14556591—22no—
34#14556591—22no—
35#14556591C2×C414yes—
36#14556591C2×C414yes—
37#14556583—24no—
38#14556583—24no—
39#14556570—24no—
40#14556570—24no—
41#14556570—24no—
42#14556570C2×C418yes—
43C4×Dic146—24no—
44C4×Dic146—22no—
45C4×Dic146—22no—
46C4×Dic146—24no—
47C4×Dic146C2×C414yes—
48C4×Dic146C2314yes—
49#14556550—24no—
50#14556550—24no—
51C2×C4⋊Dic73—21no—
52C2×C4⋊Dic73—21no—
53C2×C4⋊Dic73—21no—
54C2×C4⋊Dic73C2×C412yes—
55C2×#11924007—22no—
56C2×#11924007—22no—
57C2×C22⋊Dic73—22no—
58C2×C4×Dic73—22no—
59C4⋊#10596831—24no—
60C22⋊#10596831—24no—
61C4×#10596831—22no—
62C4×#10596831C2314yes—
63C23×C4×C73C2×C411yescharacteristic
64C23×C4×C73D411yescharacteristic
65C23×C4×C73D411yescharacteristic
66C22×C8×C73—22no—
67C2×C42×C73C2×C411yescharacteristic
68C2×C42×C73C2×C412yes—
69C2×C42×C73D411yescharacteristic
70C2×C42×C73D412yes—
71C2×C42×C73D412yes—
72C2×C42×C73D411yescharacteristic
73C2×C42×C73C2312yes—
74C2×C42×C73C2311yescharacteristic
75C4⋊C8×C73—22no—
76C4⋊C8×C73C2314yes—
77C22⋊C8×C73—24no—
78#97×C73—24no—
79C2×Dic146—28no—
80C2×Dic146—22no—
81C2×Dic146—24no—
82C2×Dic146—44no—
83C2×Dic146C22×C414yes—
84C22×Dic73—22no—
85C22×Dic73—22no—
86C2×#10596831—24no—
87C2×#10596831—44no—
88C4⋊Dic73—24no—
89C4⋊Dic73—24no—
90C4⋊Dic73—24no—
91C4⋊Dic73—22no—
92C4⋊Dic73C22×C414yes—
93#11924007—28no—
94#11924007—24no—
95#11924007—24no—
96C22⋊Dic73—28no—
97C4×Dic73—24no—
98C4×Dic73—24no—
99C24×C73C22⋊C411yescharacteristic
100C22×C4×C73—24no—
101C22×C4×C73—24no—
102C22×C4×C73—42no—
103C22×C4×C73C22⋊C411yescharacteristic
104C22×C4×C73C22⋊C411yescharacteristic
105C22×C4×C73C22⋊C412yes—
106C22×C4×C73C22⋊C411yescharacteristic
107C22×C4×C73C22⋊C412yes—
108C22×C4×C73C22⋊C412yes—
109C22×C4×C73C22×C412yes—
110C22×C4×C73C22×C411yescharacteristic
111C22×C4×C73C2×D412yes—
112C22×C4×C73C2×D411yescharacteristic
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73C2×D412yes—
115C2×C8×C73—24no—
116C2×C8×C73—44no—
117C42×C73C22⋊C412yes—
118C42×C73C22⋊C412yes—
119C42×C73C22⋊C412yes—
120C42×C73C22×C411yescharacteristic
121C42×C73C22×C412yes—
122C42×C73C2×D412yes—
123C42×C73C2×D411yescharacteristic
124C42×C73C2×D411yescharacteristic
125C42×C73C2×D412yes—
126C42×C73C2411yescharacteristic
127C23×C73—22no—
128C23×C73—22no—
129C23×C73—22no—
130C23×C73C2×C22⋊C412yes—
131C23×C73C2×C22⋊C411yescharacteristic
132C2×C4×C73—22no—
133C2×C4×C73—22no—
134C2×C4×C73—22no—
135C2×C4×C73—22no—
136C2×C4×C73—24no—
137C2×C4×C73—24no—
138C2×C4×C73—24no—
139C2×C4×C73—24no—
140C2×C4×C73—42no—
141C2×C4×C73—42no—
142C2×C4×C73C2×C22⋊C411yescharacteristic
143C2×C4×C73C2×C22⋊C412yes—
144C2×C4×C73C2×C22⋊C412yes—
145C2×C4×C73C2×C22⋊C412yes—
146C2×C4×C73C2×C22⋊C411yescharacteristic
147C2×C4×C73C2×C22⋊C411yescharacteristic
148C2×C4×C73#13114yes—
149C2×C4×C73#13714yes—
150C2×C4×C73C23×C411yescharacteristic
151C2×C4×C73C22×D411yescharacteristic
152C2×C4×C73C22×D411yescharacteristic
153C2×Dic73—24no—
154C2×Dic73—24no—
155C2×Dic73—44no—
156C2×Dic73—44no—
157Dic146—28no—
158Dic146—48no—
159Dic146—44no—
160C8×C73—44no—
161#10596831—44no—
162C22×C73—22no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—44no—
166C22×C73#40812yes—
167C22×C73#41912yes—
168C22×C73#42112yes—
169C22×C73C22×C22⋊C411yescharacteristic
170C4×C73—22no—
171C4×C73—22no—
172C4×C73—21no—
173C4×C73—22no—
174C4×C73—21no—
175C4×C73#40812yes—
176C4×C73#41912yes—
177C4×C73C2×#13112yes—
178C4×C73C2×#13712yes—
179Dic73—44no—
180Dic73—44no—
181C2×#1497—731nomaximal, Sylow
182C2×C73—42no—
183C2×C73#149714yescomplemented
184C2×C73C2×#40811yescharacteristic
185C2×C73C2×#41911yescharacteristic
186C2×C73C2×#42111yescharacteristic
187C2×#533—731no—
188C2×#432D7311yescharacteristic
189C2×#431—731no—
190#1497—738no—
191C2×Q8⋊C8—734no—
192C73C2×#149711yescharacteristic, complemented, Sylow
193#533—734no—
194#533—734no—
195#533—1462no—
196#533—1462no—
197C2×C4⋊Q8—731no—
198C2×C4⋊Q8—731no—
199C2×#125—1461no—
200C2×C22⋊Q8—732no—
201C2×C22⋊Q8—1461no—
202C2×C4×Q8—732no—
203C2×C4×Q8—1461no—
204C2×#117—1461no—
205C22×C42C2×D7311yescharacteristic
206#432—22no—
207#432C2×D7314yes—
208#431—734no—
209#431—1462no—
210C2×C4⋊C8—1461no—
211C2×C4⋊C8C2×D7312yes—
212C2×C22⋊C8—21no—
213C2×C22⋊C8—1461no—
214C2×#97—21no—
215C2×C4×C8—732no—
216Q8⋊C8—7316no—
217C22×Q8—732no—
218C22×Q8—1461no—
219C23×C4C4×D7311yescharacteristic
220C23×C4D29211yescharacteristic
221C23×C4C22⋊D7311yescharacteristic
222C22×C8—22no—
223C22×C8—1462no—
224C4⋊Q8—734no—
225C4⋊Q8—734no—
226C4⋊Q8—1462no—
227C4⋊Q8—1462no—
228#125—1464no—
229#125—1464no—
230C22⋊Q8—738no—
231C22⋊Q8—1464no—
232C22⋊Q8—1464no—
233C22⋊Q8—1464no—
234C4×Q8—734no—
235C4×Q8—734no—
236C4×Q8—1464no—
237C4×Q8—1462no—
238C4×Q8—1464no—
239C4×Q8—1462no—
240#117—1464no—
241#117—1464no—
242C2×C4⋊C4—732no—
243C2×C4⋊C4—1461no—
244C2×C4⋊C4—1461no—
245C2×C4⋊C4—1462no—
246C2×C4⋊C4—1461no—
247C2×C4⋊C4—1462no—
248C2×C22⋊C4—1462no—
249C2×C42—1462no—
250C2×C42C4×D7311yescharacteristic
251C2×C42C4×D7312yes—
252C2×C42D29211yescharacteristic
253C2×C42D29212yes—
254C2×C42C22⋊D7312yes—
255C2×C42C22⋊D7311yescharacteristic
256C2×C42C22×D7312yes—
257C2×C42C22×D7311yescharacteristic
258C4⋊C8—22no—
259C4⋊C8—1464no—
260C4⋊C8C22×D7314yes—
261C22⋊C8—24no—
262C22⋊C8—1464no—
263#97—24no—
264C4×C8—734no—
265C4×C8—1462no—
266C24#1192400511yescharacteristic
267C2×Q8—2924no—
268C2×Q8—734no—
269C2×Q8—1468no—
270C2×Q8—1464no—
271C2×Q8—1462no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—42no—
275C22×C4—1462no—
276C22×C4—1462no—
277C22×C4#1192400511yescharacteristic
278C22×C4#1192400512yes—
279C22×C4#1192400511yescharacteristic
280C22×C4#1192400511yescharacteristic
281C22×C4#1192400512yes—
282C22×C4#1192400512yes—
283C22×C4C2×C4×D7312yes—
284C22×C4C2×C4×D7311yescharacteristic
285C22×C4C2×C22⋊D7312yes—
286C22×C4C2×C22⋊D7311yescharacteristic
287C22×C4C2×D29211yescharacteristic
288C22×C4C2×D29212yes—
289C2×C8—24no—
290C2×C8—44no—
291C2×C8—2924no—
292C2×C8—1464no—
293C4⋊C4—734no—
294C4⋊C4—1464no—
295C4⋊C4—1468no—
296C4⋊C4—1462no—
297C4⋊C4—1464no—
298C4⋊C4—1464no—
299C4⋊C4—1464no—
300C4⋊C4—1464no—
301C22⋊C4—1468no—
302C42—1464no—
303C42—1464no—
304C42#1192400512yes—
305C42#1192400512yes—
306C42#1192400512yes—
307C42C2×C4×D7311yescharacteristic
308C42C2×C4×D7312yes—
309C42C2×C22⋊D7312yes—
310C42C2×C22⋊D7311yescharacteristic
311C42C2×D29211yescharacteristic
312C42C2×D29212yes—
313C42C23×D7311yescharacteristic
314C23—22no—
315C23—22no—
316C23—22no—
317C23C2×#1192400512yes—
318C23C2×#1192400511yescharacteristic
319Q8—2928no—
320Q8—2924no—
321Q8—1468no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—2924no—
333C2×C4—2924no—
334C2×C4—1464no—
335C2×C4—1464no—
336C2×C4C2×#1192400511yescharacteristic
337C2×C4C2×#1192400512yes—
338C2×C4C2×#1192400512yes—
339C2×C4C2×#1192400512yes—
340C2×C4C2×#1192400511yescharacteristic
341C2×C4C2×#1192400511yescharacteristic
342C2×C4#1455659914yes—
343C2×C4#1455662114yes—
344C2×C4C22×C4×D7311yescharacteristic
345C2×C4C22×C22⋊D7311yescharacteristic
346C2×C4C22×D29211yescharacteristic
347C8—44no—
348C8—2924no—
349C22—22no—
350C22—22no—
351C22—22no—
352C22—44no—
353C22#1798855512yes—
354C22#1798859512yes—
355C22#1798860312yes—
356C22C22×#1192400511yescharacteristic
357C4—22no—
358C4—22no—
359C4—21no—
360C4—22no—
361C4—21no—
362C4—2924no—
363C4—2924no—
364C4#1798855512yes—
365C4#1798859512yes—
366C4C2×#1455659912yes—
367C4C2×#1455662112yes—
368C2—42no—
369C2#2260840314yesdirect product factor
370C2C2×#1798855511yescharacteristic
371C2C2×#1798859511yescharacteristic
372C2C2×#1798860311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC2×#432×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC42×C73C24
hypercenterC2×#432D73
hypocenterC73C2×#1497
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. #22608403C2direct (N × H)
4. C2×#17988317C2semidirect
23. #17988317C22semidirect
183. C2×C73#1497semidirect
192. C73C2×#1497semidirect
369. C2#22608403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891442
C2×#179886402
#226084032
C2×#179883172
C2×#432×C732
C2×#149773