Finite Group Databasebeta

← C2×#22609496 #33068645

Subgroups — C2×#22609496 #33068645

Order 18688.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988794C211yesmaximal, characteristic, complemented
2C2×#17988784C211yesmaximal, characteristic
3C2×#17988717C211yesmaximal, characteristic, complemented
4#22609496C218yesmaximal, direct product factor
5C2×#17988338C211yesmaximal, characteristic, complemented
6C2×#17988333C211yesmaximal, characteristic, complemented
7C2×#17988331C211yesmaximal, characteristic
8C2×#486×C73C211yesmaximal, characteristic
9C22×#11924018—21no—
10C22×#11924016—21no—
11C2×C4×Dic146C2211yescharacteristic
12#17988794—22no—
13#17988794C2214yescomplemented
14#17988784—22no—
15#17988784C2214yes—
16#17988717—22no—
17#17988717C2214yescomplemented
18C2×C4⋊#10596831C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×#14556520—21no—
22C2×#14556515—21no—
23C2×#14556512—21no—
24C2×#14556501—21no—
25#17988338C2214yescomplemented
26#17988333C2214yescomplemented
27#17988331C2214yes—
28C2×C4⋊Q8×C73C2211yescharacteristic
29C2×#127×C73C2211yescharacteristic
30#486×C73—22no—
31#486×C73C2214yes—
32C2×#102×C73—21no—
33C2×#102×C73—21no—
34C2×C4×C8×C73C2211yescharacteristic
35C22×Dic146D411yescharacteristic
36C2×#11924018—24no—
37C2×#11924018—44no—
38C2×#11924016—24no—
39C2×#11924016—44no—
40C22×#10596831—21no—
41C22×#10596831—21no—
42C22×#10596831—21no—
43C4×Dic146—21no—
44C4×Dic146—21no—
45C4×Dic146D412yes—
46C4×Dic146C2312yes—
47C2×C4⋊Dic73D411yescharacteristic
48C2×#11924007—21no—
49C2×C4×Dic73—21no—
50C4⋊#10596831—21no—
51C4⋊#10596831—21no—
52C4⋊#10596831—21no—
53C4⋊#10596831C2312yes—
54C4⋊#10596831C2312yes—
55C4⋊#10596831C2312yes—
56#14556520—24no—
57#14556515—24no—
58#14556512—24no—
59#14556501—24no—
60C22×Q8×C73—21no—
61C22×D4×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×C8×C73D411yescharacteristic
65C22×C8×C73D411yescharacteristic
66C4⋊Q8×C73—21no—
67C4⋊Q8×C73—21no—
68C4⋊Q8×C73—21no—
69C4⋊Q8×C73C2312yes—
70#127×C73—21no—
71#127×C73—21no—
72#127×C73—21no—
73#127×C73C2312yes—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C42×C73C2311yescharacteristic
77#102×C73—24no—
78#102×C73—24no—
79C4×C8×C73D412yes—
80C4×C8×C73C2312yes—
81C2×Dic146—22no—
82C2×Dic146—22no—
83C2×Dic146—21no—
84C2×Dic146C2×D412yes—
85C22×Dic73—21no—
86C22×Dic73—21no—
87#11924018—48no—
88#11924016—48no—
89C2×#10596831—22no—
90C2×#10596831—22no—
91C2×#10596831—22no—
92C2×#10596831—42no—
93C2×#10596831—42no—
94C2×#10596831—42no—
95C4⋊Dic73—21no—
96C4⋊Dic73C2×D412yes—
97#11924007—22no—
98#11924007—22no—
99C4×Dic73—22no—
100C4×Dic73—22no—
101C24×C73—41no—
102C2×Q8×C73—22no—
103C2×Q8×C73—41no—
104C2×Q8×C73—42no—
105C2×Q8×C73—42no—
106C2×D4×C73—22no—
107C2×D4×C73—22no—
108C2×D4×C73—22no—
109C2×D4×C73—41no—
110C2×D4×C73—41no—
111C2×D4×C73—41no—
112C2×D4×C73—42no—
113C2×D4×C73—42no—
114C2×D4×C73—42no—
115C2×D4×C73—42no—
116C2×D4×C73—82no—
117C22×C4×C73—41no—
118C22×C4×C73C2×D411yescharacteristic
119C22×C4×C73C2×D411yescharacteristic
120C22×C4×C73#4111yescharacteristic
121C2×C8×C73—22no—
122C2×C8×C73—22no—
123C2×C8×C73C2×D412yes—
124C2×C8×C73C2×D412yes—
125C4⋊C4×C73—22no—
126C4⋊C4×C73—22no—
127C4⋊C4×C73—41no—
128C4⋊C4×C73—41no—
129C42×C73C2×D411yescharacteristic
130C42×C73C2×D411yescharacteristic
131C42×C73#4111yescharacteristic
132C42×C73C2411yescharacteristic
133C23×C73—42no—
134C23×C73—82no—
135C23×C73—82no—
136C23×C73—82no—
137C23×C73#12111yescharacteristic
138Q8×C73—42no—
139Q8×C73—42no—
140Q8×C73—82no—
141D4×C73—42no—
142D4×C73—42no—
143D4×C73—42no—
144D4×C73—42no—
145D4×C73—82no—
146D4×C73—82no—
147D4×C73—82no—
148D4×C73—82no—
149C2×C4×C73—22no—
150C2×C4×C73—42no—
151C2×C4×C73—82no—
152C2×C4×C73#12111yescharacteristic
153C2×C4×C73#12111yescharacteristic
154C2×C4×C73#12111yescharacteristic
155C2×C4×C73#13512yes—
156C2×C4×C73AGL(1,ℤ/8)12yes—
157C2×C4×C73AGL(1,ℤ/8)12yes—
158C2×C4×C73#13712yes—
159C2×C4×C73C22×D411yescharacteristic
160C2×C4×C73C22×D411yescharacteristic
161C2×C4×C73C2×#4111yescharacteristic
162C2×Dic73—22no—
163C2×Dic73—22no—
164C2×Dic73—42no—
165C2×Dic73—42no—
166Dic146—22no—
167Dic146—22no—
168Dic146—42no—
169C8×C73—22no—
170C8×C73—22no—
171#10596831—42no—
172#10596831—42no—
173#10596831—42no—
174C22×C73—82no—
175C22×C73—82no—
176C22×C73—82no—
177C22×C73—164no—
178C22×C73#46412yes—
179C22×C73#46912yes—
180C22×C73#47112yes—
181C22×C73C2×#12111yescharacteristic
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—82no—
185C4×C73#46412yes—
186C4×C73#46912yes—
187C4×C73C2×#13511yescharacteristic
188C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
189C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
190C4×C73C2×#13711yescharacteristic
191Dic73—42no—
192Dic73—42no—
193C2×#1702—731nomaximal, Sylow
194C2×C73—162no—
195C2×C73#170214yescomplemented
196C2×C73C2×#46411yescharacteristic
197C2×C73C2×#46911yescharacteristic
198C2×C73C2×#47111yescharacteristic
199C2×#486D7311yescharacteristic
200C2×#462—731no—
201C2×#460—731no—
202C2×#446—731no—
203#1702—738no—
204C2×#334—731no—
205C2×#332—731no—
206C2×#331—731no—
207C73C2×#170211yescharacteristic, complemented, Sylow
208C22×Q16—1461no—
209C22×SD16—1461no—
210C2×C4⋊Q8C2×D7311yescharacteristic
211C2×#127C2×D7311yescharacteristic
212C2×C4×Q8—731no—
213#486—22no—
214#486C2×D7314yes—
215#462—734no—
216#462—1462no—
217#460—734no—
218#460—1462no—
219#446—734no—
220#446—1462no—
221C2×C4⋊C8—731no—
222C2×C4⋊C8—731no—
223C2×C4⋊C8—731no—
224C2×C4⋊C8—1461no—
225C2×#103—1461no—
226C2×#102—21no—
227C2×#102—21no—
228C2×#102—1461no—
229C2×#97—1461no—
230C2×C4×C8C2×D7311yescharacteristic
231#334—734no—
232#332—734no—
233#331—734no—
234C22×Q8—21no—
235C22×Q8—731no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4—21no—
239C2×Q16—2924no—
240C2×Q16—1464no—
241C2×SD16—2924no—
242C2×SD16—1464no—
243C22×C8—1461no—
244C22×C8—1461no—
245C22×C8—1461no—
246C22×C8C22⋊D7311yescharacteristic
247C22×C8C22⋊D7311yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8C22×D7312yes—
252#127—21no—
253#127—21no—
254#127—21no—
255#127C22×D7312yes—
256C4×Q8—732no—
257C4×Q8—732no—
258C4×Q8—1461no—
259C4×Q8—1461no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—731no—
263C2×C4⋊C4—1461no—
264C2×C42—1461no—
265C2×C42C22×D7311yescharacteristic
266C4⋊C8—732no—
267C4⋊C8—732no—
268C4⋊C8—732no—
269C4⋊C8—1464no—
270C4⋊C8—1461no—
271C4⋊C8—1461no—
272C4⋊C8—1461no—
273#103—1464no—
274#102—24no—
275#102—24no—
276#102—1464no—
277#97—1464no—
278C4×C8C22⋊D7312yes—
279C4×C8C22×D7312yes—
280C24—41no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—732no—
286C2×Q8—1462no—
287C2×Q8—1462no—
288C2×Q8—1461no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—82no—
300C22×C4—41no—
301C22×C4—1461no—
302C22×C4—1461no—
303C22×C4D4×D7311yescharacteristic
304C22×C4C2×C22⋊D7311yescharacteristic
305C22×C4#1192402711yescharacteristic
306Q16—2928no—
307SD16—2928no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—2922no—
311C2×C8—2922no—
312C2×C8—2922no—
313C2×C8—1462no—
314C2×C8—1462no—
315C2×C8—1462no—
316C2×C8C2×C22⋊D7312yes—
317C2×C8C2×C22⋊D7312yes—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—732no—
323C4⋊C4—1462no—
324C4⋊C4—1461no—
325C4⋊C4—1462no—
326C42—1462no—
327C42—1462no—
328C42D4×D7311yescharacteristic
329C42C2×C22⋊D7311yescharacteristic
330C42#1192402711yescharacteristic
331C42C23×D7311yescharacteristic
332C23—42no—
333C23—82no—
334C23—82no—
335C23—82no—
336C23#1455656211yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—2922no—
341Q8—1462no—
342Q8—1462no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—82no—
348D4—82no—
349D4—82no—
350D4—82no—
351C2×C4—22no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—2922no—
355C2×C4—2922no—
356C2×C4—1462no—
357C2×C4—1462no—
358C2×C4#1455656211yescharacteristic
359C2×C4#1455656211yescharacteristic
360C2×C4#1455656211yescharacteristic
361C2×C4#1455661112yes—
362C2×C4#1455661512yes—
363C2×C4#1455661512yes—
364C2×C4#1455662112yes—
365C2×C4C2×D4×D7311yescharacteristic
366C2×C4C22×C22⋊D7311yescharacteristic
367C2×C4C2×#1192402711yescharacteristic
368C8—22no—
369C8—22no—
370C8—2922no—
371C8—2922no—
372C8—2922no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—164no—
377C22#1798880612yes—
378C22#1798883712yes—
379C22#1798884712yes—
380C22C2×#1455656211yescharacteristic
381C4—21no—
382C4—21no—
383C4—82no—
384C4—2922no—
385C4—2922no—
386C4#1798880612yes—
387C4#1798883712yes—
388C4C2×#1455661111yescharacteristic
389C4C2×#1455661511yescharacteristic
390C4C2×#1455661511yescharacteristic
391C4C2×#1455662111yescharacteristic
392C2—162no—
393C2#2260949614yesdirect product factor
394C2C2×#1798880611yescharacteristic
395C2C2×#1798883711yescharacteristic
396C2C2×#1798884711yescharacteristic
subgroupG/H
centerC23#14556562
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC2×#486×C73C2
socleC23×C73#121
prime radicalC2×#127×C73C22
hypercenterC2×#486D73
hypocenterC73C2×#1702
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#17988794C2semidirect
3. C2×#17988717C2semidirect
4. #22609496C2direct (N × H)
5. C2×#17988338C2semidirect
6. C2×#17988333C2semidirect
13. #17988794C22semidirect
17. #17988717C22semidirect
25. #17988338C22semidirect
26. #17988333C22semidirect
195. C2×C73#1702semidirect
207. C73C2×#1702semidirect
393. C2#22609496direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179887942
C2×#179887842
C2×#179887172
#226094962
C2×#179883382
C2×#179883332
C2×#179883312
C2×#486×C732
C2×#170273