Finite Group Databasebeta

← C2×#34036833 #49172313

Subgroups — C2×#34036833 #49172313

Order 37504.

1200 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036833C2116yesmaximal, direct product factor
2C2×#22627622C211yesmaximal, characteristic, complemented
3C2×#22627614C211yesmaximal, characteristic, complemented
4C2×#22627614C211yesmaximal, characteristic, complemented
5C2×#22627602C211yesmaximal, characteristic, complemented
6C2×#22627602C211yesmaximal, characteristic, complemented
7C2×#22627601C211yesmaximal, characteristic, complemented
8C2×#22627601C211yesmaximal, characteristic, complemented
9C2×#22627600C211yesmaximal, characteristic, complemented
10C2×#22627589C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊D293C211yesmaximal, characteristic
12C2×#22627584C211yesmaximal, characteristic
13C2×#22627584C211yesmaximal, characteristic
14C22×#17989781C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×D293C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C293C211yesmaximal, characteristic, complemented
17C22×Dic586C2211yescharacteristic
18C22×Dic586C2211yescharacteristic
19C22×C22⋊D293C2211yescharacteristic
20C23×Dic293C2211yescharacteristic
21C23×Dic293C2211yescharacteristic
22C22×C4×D293C2211yescharacteristic
23C22×C4×D293C2211yescharacteristic
24C22×C4×D293C2211yescharacteristic
25#22627622C2218yescomplemented
26#22627614C2218yescomplemented
27#22627614C2218yescomplemented
28#22627602C2218yescomplemented
29#22627602C2218yescomplemented
30#22627601C2218yescomplemented
31#22627601C2218yescomplemented
32#22627600C2218yescomplemented
33#22627589C2218yescomplemented
34C4×C22⋊D293C2218yes—
35#22627584C2218yes—
36#22627584C2218yes—
37C2×C4⋊Dic293C2211yescharacteristic
38C2×C4⋊Dic293C2211yescharacteristic
39C2×#17989781C2211yescharacteristic
40C2×#17989781C2211yescharacteristic
41C2×#17989781C2211yescharacteristic
42C2×#17989781C2211yescharacteristic
43C2×#17989781C2211yescharacteristic
44C2×#17989781C2211yescharacteristic
45C2×#17989781C2211yescharacteristic
46C2×#17989781C2211yescharacteristic
47C2×#17989781C2211yescharacteristic
48C2×#17989781C2211yescharacteristic
49C2×#17989781C2211yescharacteristic
50C2×#17989781C2218yescomplemented
51C4⋊C4×D293C2218yescomplemented
52C2×C22⋊Dic293C2211yescharacteristic
53C2×#17989779C2211yescharacteristic
54C2×#17989779C2211yescharacteristic
55C2×#17989779C2211yescharacteristic
56C2×C4×Dic293C2211yescharacteristic
57C2×C4×Dic293C2211yescharacteristic
58C2×C4×Dic293C2211yescharacteristic
59C22×Q8×C293C2211yescharacteristic
60C23×C4×C293C2211yescharacteristic
61C22⋊Q8×C293C2218yescomplemented
62C2×C4⋊C4×C293C2211yescharacteristic
63C2×C4⋊C4×C293C2211yescharacteristic
64C2×C4⋊C4×C293C2211yescharacteristic
65C2×C22⋊C4×C293C2211yescharacteristic
66C2×C22⋊C4×C293C2211yescharacteristic
67C23×D293C2311yescharacteristic
68C2×Dic586—24no—
69C2×Dic586—42no—
70C2×Dic586C2314yes—
71C2×Dic586C2314yes—
72C2×C22⋊D293Q818yescomplemented
73C2×C22⋊D293C2314yes—
74C22×Dic293—24no—
75C22×Dic293—42no—
76C22×Dic293C2314yes—
77C22×Dic293C2311yescharacteristic
78C22×Dic293C2311yescharacteristic
79C22×Dic293C2311yescharacteristic
80C22×Dic293C2311yescharacteristic
81C22×Dic293C2311yescharacteristic
82C22×Dic293C2314yes—
83C22×Dic293C2311yescharacteristic
84C22×Dic293C2311yescharacteristic
85C2×C4×D293—24no—
86C2×C4×D293—42no—
87C2×C4×D293—42no—
88C2×C4×D293C2314yes—
89C2×C4×D293C2314yes—
90C2×C4×D293C2314yes—
91C4⋊Dic293C2314yes—
92C4⋊Dic293C2314yes—
93#17989781C2314yes—
94#17989781C2314yes—
95#17989781C2314yes—
96#17989781C2314yes—
97#17989781C2314yes—
98#17989781C2314yes—
99#17989781C2314yes—
100#17989781C2314yes—
101#17989781C2314yes—
102#17989781C2314yes—
103#17989781C2314yes—
104C22⋊Dic293C2314yes—
105#17989779C2314yes—
106#17989779C2314yes—
107#17989779C2314yes—
108C4×Dic293C2314yes—
109C4×Dic293C2314yes—
110C4×Dic293C2314yes—
111C24×C293C2311yescharacteristic
112C2×Q8×C293—42no—
113C2×Q8×C293C2314yes—
114C22×C4×C293—42no—
115C22×C4×C293C2311yescharacteristic
116C22×C4×C293C2311yescharacteristic
117C22×C4×C293C2311yescharacteristic
118C22×C4×C293C2311yescharacteristic
119C22×C4×C293C2311yescharacteristic
120C22×C4×C293C2311yescharacteristic
121C22×C4×C293C2314yes—
122C4⋊C4×C293C2314yes—
123C4⋊C4×C293C2314yes—
124C4⋊C4×C293C2314yes—
125C22⋊C4×C293C2314yes—
126C22⋊C4×C293C2314yes—
127C22×D293—22no—
128C22×D293—22no—
129C22×D293C2×Q814yes—
130C22×D293C2412yes—
131Dic586—28no—
132Dic586—44no—
133C22⋊D293C2×Q8116yescomplemented
134C2×Dic293—22no—
135C2×Dic293—22no—
136C2×Dic293—22no—
137C2×Dic293—22no—
138C2×Dic293—22no—
139C2×Dic293—28no—
140C2×Dic293—44no—
141C2×Dic293C2×Q814yes—
142C2×Dic293#4114yes—
143C2×Dic293C2412yes—
144C2×Dic293C2412yes—
145C2×Dic293C2412yes—
146C2×Dic293C2412yes—
147C2×Dic293C2412yes—
148C2×Dic293C2412yes—
149C2×Dic293C2412yes—
150C4×D293—28no—
151C4×D293—44no—
152C4×D293—44no—
153C23×C293—22no—
154C23×C293—22no—
155C23×C293C2×Q814yes—
156C23×C293C2412yes—
157C23×C293C2411yescharacteristic
158Q8×C293—44no—
159C2×C4×C293—22no—
160C2×C4×C293—22no—
161C2×C4×C293—22no—
162C2×C4×C293—22no—
163C2×C4×C293—22no—
164C2×C4×C293—22no—
165C2×C4×C293—44no—
166C2×C4×C293C2412yes—
167C2×C4×C293C2412yes—
168C2×C4×C293C2412yes—
169C2×C4×C293C2412yes—
170C2×C4×C293C2412yes—
171C2×C4×C293C2412yes—
172C22×C293—28no—
173C22×C293—22no—
174C22×C293—22no—
175C22×C293C22×Q814yes—
176C22×C293C22×Q812yes—
177C22×C293C2×#4112yes—
178C22×C293H(5,𝔽2)12yes—
179C22×C293C2511yescharacteristic
180C2×D293—28no—
181C2×D293—22no—
182C2×D293—22no—
183C2×D293C22×Q814yes—
184C4×C293—22no—
185C4×C293—22no—
186C4×C293—22no—
187C4×C293—22no—
188C4×C293—22no—
189C4×C293—22no—
190Dic293—22no—
191Dic293—22no—
192Dic293—22no—
193Dic293—22no—
194Dic293—22no—
195Dic293C22×Q814yes—
196Dic293C2×#4114yes—
197C2×C293—24no—
198C2×C293#55414yescomplemented
199C2×C293C23×Q811yescharacteristic
200C2×C293C22×#4111yescharacteristic
201C2×C293C2×H(5,𝔽2)11yescharacteristic
202D293—24no—
203C293C2×#55411yescharacteristic, complemented, Sylow
204C2×#554—2931nomaximal, Sylow
205#554—29316no—
206C2×C4⋊Q8—2931no—
207C2×#125—2931no—
208C2×#125—2931no—
209C2×C22⋊Q8—2931no—
210C2×C22⋊Q8—2931no—
211C2×C22⋊Q8—2931no—
212C2×C22⋊Q8—2931no—
213C2×C22⋊Q8—2931no—
214C2×C22⋊Q8D29311yescharacteristic, complemented
215C2×C4×Q8—2931no—
216C2×C4×D4—2931no—
217C2×C4×D4—2931no—
218C2×C4×D4—2931no—
219C22×C4⋊C4—2931no—
220C22×C4⋊C4—2931no—
221C22×Q8—2931no—
222C22×Q8—2931no—
223C22×Q8C2×D29311yescharacteristic
224C22×D4—2931no—
225C23×C4—2931no—
226C23×C4—2931no—
227C23×C4—2931no—
228C23×C4—2931no—
229C23×C4—2931no—
230C23×C4C2×D29311yescharacteristic
231C4⋊Q8—2938no—
232#125—2938no—
233#125—2938no—
234C22⋊Q8—2938no—
235C22⋊Q8—2938no—
236C22⋊Q8—2938no—
237C22⋊Q8—2938no—
238C22⋊Q8—2938no—
239C22⋊Q8C2×D29318yescomplemented
240C4×Q8—2938no—
241C4×D4—2938no—
242C4×D4—2938no—
243C4×D4—2938no—
244C2×C4⋊C4—2931no—
245C2×C4⋊C4—2931no—
246C2×C4⋊C4—2931no—
247C2×C4⋊C4—2931no—
248C2×C4⋊C4—2931no—
249C2×C4⋊C4—2931no—
250C2×C4⋊C4—2938no—
251C2×C4⋊C4—2931no—
252C2×C4⋊C4—2931no—
253C2×C4⋊C4—2931no—
254C2×C4⋊C4—2931no—
255C2×C4⋊C4—2931no—
256C2×C4⋊C4—2931no—
257C2×C4⋊C4—2931no—
258C2×C4⋊C4—2938no—
259C2×C4⋊C4C2×D29311yescharacteristic
260C2×C4⋊C4C2×D29311yescharacteristic
261C2×C4⋊C4C2×D29311yescharacteristic
262C2×C22⋊C4—2931no—
263C2×C22⋊C4—2931no—
264C2×C22⋊C4—2931no—
265C2×C22⋊C4—2931no—
266C2×C22⋊C4C2×D29311yescharacteristic
267C2×C22⋊C4C2×D29311yescharacteristic
268C2×C42—2931no—
269C2×C42—2931no—
270C2×C42—2931no—
271C24—2931no—
272C24C22×D29311yescharacteristic
273C2×Q8—42no—
274C2×Q8—2934no—
275C2×Q8—2934no—
276C2×Q8—5864no—
277C2×Q8—11722no—
278C2×Q8C22×D29314yes—
279C2×D4—2938no—
280C2×D4—2934no—
281C22×C4—42no—
282C22×C4—2931no—
283C22×C4—2931no—
284C22×C4—2934no—
285C22×C4—2931no—
286C22×C4—2931no—
287C22×C4—2931no—
288C22×C4—2931no—
289C22×C4—2931no—
290C22×C4—2934no—
291C22×C4—2934no—
292C22×C4—2934no—
293C22×C4—2934no—
294C22×C4—5864no—
295C22×C4—5864no—
296C22×C4—11722no—
297C22×C4—11722no—
298C22×C4—11722no—
299C22×C4C22×D29311yescharacteristic
300C22×C4C22×D29311yescharacteristic
301C22×C4C22×D29311yescharacteristic
302C22×C4C22×D29311yescharacteristic
303C22×C4C22×D29311yescharacteristic
304C22×C4C22×D29311yescharacteristic
305C22×C4C22×D29314yes—
306C4⋊C4—2934no—
307C4⋊C4—2934no—
308C4⋊C4—2934no—
309C4⋊C4—2934no—
310C4⋊C4—2934no—
311C4⋊C4—2934no—
312C4⋊C4—2934no—
313C4⋊C4—2934no—
314C4⋊C4—2934no—
315C4⋊C4—2934no—
316C4⋊C4—2934no—
317C4⋊C4—2934no—
318C4⋊C4—2934no—
319C4⋊C4C22×D29314yes—
320C4⋊C4C22×D29314yes—
321C4⋊C4C22×D29314yes—
322C22⋊C4—2934no—
323C22⋊C4—2934no—
324C22⋊C4—2934no—
325C22⋊C4—2934no—
326C22⋊C4C22×D29314yes—
327C22⋊C4C22×D29314yes—
328C42—2934no—
329C42—2934no—
330C42—2934no—
331C23—22no—
332C23—22no—
333C23—2934no—
334C23—2932no—
335C23—5862no—
336C23—5862no—
337C23Q8×D29314yes—
338C23C23×D29312yes—
339C23C23×D29311yescharacteristic
340Q8—44no—
341Q8—5868no—
342Q8—11724no—
343D4—29316no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—44no—
351C2×C4—2934no—
352C2×C4—2934no—
353C2×C4—2932no—
354C2×C4—2932no—
355C2×C4—2932no—
356C2×C4—2932no—
357C2×C4—2932no—
358C2×C4—2932no—
359C2×C4—2932no—
360C2×C4—5868no—
361C2×C4—5868no—
362C2×C4—5862no—
363C2×C4—5862no—
364C2×C4—5862no—
365C2×C4—5862no—
366C2×C4—5862no—
367C2×C4—11724no—
368C2×C4—11724no—
369C2×C4—11724no—
370C2×C4C23×D29312yes—
371C2×C4C23×D29312yes—
372C2×C4C23×D29312yes—
373C2×C4C23×D29312yes—
374C2×C4C23×D29312yes—
375C2×C4C23×D29312yes—
376C22—28no—
377C22—22no—
378C22—22no—
379C22—2934no—
380C22—5868no—
381C22—5862no—
382C22—5862no—
383C22C2×Q8×D29314yes—
384C22C2×Q8×D29312yes—
385C22#41×D29312yes—
386C22#2262766912yes—
387C22C24×D29311yescharacteristic
388C4—22no—
389C4—22no—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—2934no—
395C4—2934no—
396C4—5862no—
397C4—5862no—
398C4—5862no—
399C4—5862no—
400C4—5862no—
401C2—24no—
402C2—5864no—
403C2#3403683314yesdirect product factor
404C2C22×Q8×D29311yescharacteristic
405C2C2×#41×D29311yescharacteristic
406C2C2×#2262766911yescharacteristic
subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×C22⋊Q8×C293C2
socleC23×C293C24
prime radicalC22×C22⋊D293C22
hypercenterC2×C22⋊Q8D293
hypocenterC293C2×#554
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #34036833C2direct (N × H)
2. C2×#22627622C2semidirect
3. C2×#22627614C2semidirect
4. C2×#22627614C2semidirect
5. C2×#22627602C2semidirect
6. C2×#22627602C2semidirect
7. C2×#22627601C2semidirect
8. C2×#22627601C2semidirect
9. C2×#22627600C2semidirect
10. C2×#22627589C2semidirect
14. C22×#17989781C2semidirect
15. C2×C4⋊C4×D293C2semidirect
16. C2×C22⋊Q8×C293C2semidirect
25. #22627622C22semidirect
26. #22627614C22semidirect
27. #22627614C22semidirect
28. #22627602C22semidirect
29. #22627602C22semidirect
30. #22627601C22semidirect
31. #22627601C22semidirect
32. #22627600C22semidirect
33. #22627589C22semidirect
50. C2×#17989781C22semidirect
51. C4⋊C4×D293C22semidirect
61. C22⋊Q8×C293C22semidirect
72. C2×C22⋊D293Q8semidirect
133. C22⋊D293C2×Q8semidirect
198. C2×C293#554semidirect
203. C293C2×#554semidirect
214. C2×C22⋊Q8D293semidirect
239. C22⋊Q8C2×D293semidirect
403. C2#34036833direct (N × H)

Maximal subgroups

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

subgroupindex
#340368332
C2×#226276222
C2×#226276142
C2×#226276022
C2×#226276012
C2×#226276002
C2×#226275892
C2×C4×C22⋊D2932
C2×#226275842
C22×#179897812
C2×C4⋊C4×D2932
C2×C22⋊Q8×C2932
C2×#554293