Finite Group Databasebeta

← C2×#34036745 #49172158

Subgroups — C2×#34036745 #49172158

Order 37504.

1132 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036745C2116yesmaximal, direct product factor
2C2×#22627623C211yesmaximal, characteristic, complemented
3C2×#22627619C211yesmaximal, characteristic, complemented
4C2×#22627612C211yesmaximal, characteristic, complemented
5C2×#22627610C211yesmaximal, characteristic, complemented
6C2×#22627610C211yesmaximal, characteristic, complemented
7C2×#22627609C211yesmaximal, characteristic, complemented
8C2×#22627608C211yesmaximal, characteristic, complemented
9C2×#22627604C211yesmaximal, characteristic, complemented
10C2×#22627602C211yesmaximal, characteristic, complemented
11C2×#22627601C211yesmaximal, characteristic, complemented
12C2×#22627597C211yesmaximal, characteristic
13C2×C4×Dic586C211yesmaximal, characteristic, complemented
14C2×#22627584C211yesmaximal, characteristic, complemented
15C2×#22627582C211yesmaximal, characteristic, complemented
16C2×#126×C293C211yesmaximal, characteristic, complemented
17C22×Dic586C2211yescharacteristic
18C22×Dic586C2211yescharacteristic
19C22×Dic586C2211yescharacteristic
20C22×D1172C2211yescharacteristic
21C22×C22⋊D293C2211yescharacteristic
22C22×C22⋊D293C2211yescharacteristic
23C23×Dic293C2211yescharacteristic
24C22×C4×D293C2211yescharacteristic
25C22×C4×D293C2211yescharacteristic
26#22627623C2218yescomplemented
27#22627619C2218yescomplemented
28#22627612C2218yescomplemented
29#22627610C2218yescomplemented
30#22627610C2218yescomplemented
31#22627609C2218yescomplemented
32#22627608C2218yescomplemented
33#22627604C2218yescomplemented
34#22627602C2218yescomplemented
35#22627601C2218yescomplemented
36#22627597C2218yes—
37C4×Dic586C2218yescomplemented
38#22627584C2218yescomplemented
39#22627582C2218yescomplemented
40C2×C4⋊Dic293C2211yescharacteristic
41C2×C4⋊Dic293C2211yescharacteristic
42C2×C4⋊Dic293C2211yescharacteristic
43C2×#17989781C2211yescharacteristic
44C2×#17989781C2211yescharacteristic
45C2×#17989781C2211yescharacteristic
46C2×#17989781C2211yescharacteristic
47C2×C22⋊Dic293C2211yescharacteristic
48C2×#17989779C2211yescharacteristic
49C2×#17989779C2211yescharacteristic
50C2×#17989779C2211yescharacteristic
51C2×#17989779C2211yescharacteristic
52C2×#17989779C2211yescharacteristic
53C2×#17989779C2211yescharacteristic
54C2×#17989779C2211yescharacteristic
55C2×#17989779C2211yescharacteristic
56C2×C4×Dic293C2211yescharacteristic
57C2×C4×Dic293C2211yescharacteristic
58C2×C4×Dic293C2211yescharacteristic
59#126×C293C2218yescomplemented
60C2×C4⋊C4×C293C2211yescharacteristic
61C2×C4⋊C4×C293C2211yescharacteristic
62C2×C4⋊C4×C293C2211yescharacteristic
63C2×C22⋊C4×C293C2211yescharacteristic
64C2×C22⋊C4×C293C2211yescharacteristic
65C2×C22⋊C4×C293C2211yescharacteristic
66C2×C42×C293C2211yescharacteristic
67C23×D293C2311yescharacteristic
68C23×D293C2311yescharacteristic
69C2×Dic586—24no—
70C2×Dic586—42no—
71C2×Dic586—42no—
72C2×Dic586C2314yes—
73C2×Dic586C2314yes—
74C2×Dic586C2314yes—
75C2×D1172—42no—
76C2×D1172C2314yes—
77C2×C22⋊D293—24no—
78C2×C22⋊D293—42no—
79C2×C22⋊D293C2314yes—
80C2×C22⋊D293C2314yes—
81C22×Dic293—42no—
82C22×Dic293C2311yescharacteristic
83C22×Dic293C2311yescharacteristic
84C22×Dic293C2311yescharacteristic
85C22×Dic293C2311yescharacteristic
86C22×Dic293C2311yescharacteristic
87C22×Dic293C2314yes—
88C22×Dic293C2311yescharacteristic
89C2×C4×D293—24no—
90C2×C4×D293—42no—
91C2×C4×D293C2314yes—
92C2×C4×D293C2314yes—
93C4⋊Dic293C2314yes—
94C4⋊Dic293C2314yes—
95C4⋊Dic293C2314yes—
96#17989781C2314yes—
97#17989781C2314yes—
98#17989781C2314yes—
99#17989781C2314yes—
100C22⋊Dic293C2314yes—
101#17989779C2314yes—
102#17989779C2314yes—
103#17989779C2314yes—
104#17989779C2314yes—
105#17989779C2314yes—
106#17989779C2314yes—
107#17989779C2314yes—
108#17989779C2314yes—
109C4×Dic293C2314yes—
110C4×Dic293C2314yes—
111C4×Dic293C2314yes—
112C24×C293C2311yescharacteristic
113C22×C4×C293C2311yescharacteristic
114C22×C4×C293C2311yescharacteristic
115C22×C4×C293C2311yescharacteristic
116C22×C4×C293C2311yescharacteristic
117C22×C4×C293C2311yescharacteristic
118C22×C4×C293C2311yescharacteristic
119C4⋊C4×C293C2314yes—
120C4⋊C4×C293C2314yes—
121C4⋊C4×C293C2314yes—
122C22⋊C4×C293C2314yes—
123C22⋊C4×C293C2314yes—
124C22⋊C4×C293C2314yes—
125C42×C293C2314yes—
126C22×D293—22no—
127C22×D293—22no—
128C22×D293—22no—
129C22×D293—22no—
130C22×D293—22no—
131C22×D293—22no—
132C22×D293C2412yes—
133C22×D293C2412yes—
134Dic586—28no—
135Dic586—44no—
136Dic586—44no—
137D1172—44no—
138C22⋊D293—28no—
139C22⋊D293—44no—
140C2×Dic293—22no—
141C2×Dic293—22no—
142C2×Dic293—22no—
143C2×Dic293—22no—
144C2×Dic293—22no—
145C2×Dic293—44no—
146C2×Dic293#4114yes—
147C2×Dic293C2412yes—
148C2×Dic293C2412yes—
149C2×Dic293C2412yes—
150C2×Dic293C2412yes—
151C2×Dic293C2412yes—
152C2×Dic293C2412yes—
153C4×D293—28no—
154C4×D293—44no—
155C23×C293—22no—
156C23×C293—22no—
157C23×C293—22no—
158C23×C293C2412yes—
159C23×C293C2411yescharacteristic
160C2×C4×C293—22no—
161C2×C4×C293—22no—
162C2×C4×C293—22no—
163C2×C4×C293—22no—
164C2×C4×C293—22no—
165C2×C4×C293—22no—
166C2×C4×C293C2412yes—
167C2×C4×C293C2412yes—
168C2×C4×C293C2412yes—
169C2×C4×C293C2412yes—
170C2×C4×C293C2412yes—
171C2×C4×C293C2412yes—
172C22×C293—22no—
173C22×C293—22no—
174C22×C293—22no—
175C22×C293—44no—
176C22×C293C2×#4112yes—
177C22×C293H(5,𝔽2)12yes—
178C22×C2932−1+412yes—
179C22×C293C2511yescharacteristic
180C2×D293—22no—
181C2×D293—22no—
182C2×D293—22no—
183C2×D293—22no—
184C2×D293—22no—
185C2×D293—22no—
186C2×D293—44no—
187C2×D293—44no—
188C4×C293—22no—
189C4×C293—22no—
190C4×C293—22no—
191C4×C293—22no—
192C4×C293—22no—
193C4×C293—22no—
194Dic293—22no—
195Dic293—22no—
196Dic293—22no—
197Dic293—22no—
198Dic293—22no—
199Dic293C2×#4114yes—
200C2×C293—42no—
201C2×C293#54214yescomplemented
202C2×C293C22×#4111yescharacteristic
203C2×C293C2×H(5,𝔽2)11yescharacteristic
204C2×C293C2×2−1+411yescharacteristic
205D293—42no—
206D293—42no—
207C293C2×#54211yescharacteristic, complemented, Sylow
208C2×#542—2931nomaximal, Sylow
209#542—29316no—
210C2×C4⋊Q8—2931no—
211C2×#126—2931no—
212C2×#126D29311yescharacteristic, complemented
213C2×#124—2931no—
214C2×#124—2931no—
215C2×#124—2931no—
216C2×#123—2931no—
217C2×#123—2931no—
218C2×C22⋊Q8—2931no—
219C2×C22⋊Q8—2931no—
220C2×C22⋊Q8—2931no—
221C2×#121—2931no—
222C2×C4×Q8—2931no—
223C2×C4×D4—2931no—
224C2×#117—2931no—
225C22×Q8—2931no—
226C22×Q8—2931no—
227C22×Q8—2931no—
228C22×D4—2931no—
229C22×D4—2931no—
230C22×D4—2931no—
231C23×C4—2931no—
232C23×C4—2931no—
233C23×C4—2931no—
234C4⋊Q8—2938no—
235#126—2938no—
236#126C2×D29318yescomplemented
237#124—2938no—
238#124—2938no—
239#124—2938no—
240#123—2938no—
241#123—2938no—
242C22⋊Q8—2938no—
243C22⋊Q8—2938no—
244C22⋊Q8—2938no—
245#121—2938no—
246C4×Q8—2938no—
247C4×D4—2938no—
248#117—2938no—
249C2×C4⋊C4—2931no—
250C2×C4⋊C4—2931no—
251C2×C4⋊C4—2931no—
252C2×C4⋊C4—2931no—
253C2×C4⋊C4—2931no—
254C2×C4⋊C4—2931no—
255C2×C4⋊C4—2931no—
256C2×C4⋊C4C2×D29311yescharacteristic
257C2×C4⋊C4C2×D29311yescharacteristic
258C2×C4⋊C4C2×D29311yescharacteristic
259C2×C22⋊C4—2931no—
260C2×C22⋊C4—2931no—
261C2×C22⋊C4—2931no—
262C2×C22⋊C4—2931no—
263C2×C22⋊C4—2931no—
264C2×C22⋊C4—2931no—
265C2×C22⋊C4—2931no—
266C2×C22⋊C4—2931no—
267C2×C22⋊C4—2931no—
268C2×C22⋊C4C2×D29311yescharacteristic
269C2×C22⋊C4C2×D29311yescharacteristic
270C2×C22⋊C4C2×D29311yescharacteristic
271C2×C42—2931no—
272C2×C42—2931no—
273C2×C42—2931no—
274C2×C42C2×D29311yescharacteristic
275C24—2931no—
276C24—2931no—
277C24C22×D29311yescharacteristic
278C2×Q8—2934no—
279C2×Q8—2934no—
280C2×Q8—2934no—
281C2×Q8—5864no—
282C2×Q8—11722no—
283C2×Q8—11722no—
284C2×D4—2934no—
285C2×D4—2934no—
286C2×D4—2934no—
287C2×D4—5864no—
288C2×D4—11722no—
289C2×D4—11722no—
290C22×C4—2931no—
291C22×C4—2931no—
292C22×C4—2931no—
293C22×C4—2931no—
294C22×C4—2931no—
295C22×C4—2931no—
296C22×C4—2934no—
297C22×C4—2934no—
298C22×C4—2934no—
299C22×C4—5864no—
300C22×C4—11722no—
301C22×C4—11722no—
302C22×C4C22×D29311yescharacteristic
303C22×C4C22×D29311yescharacteristic
304C22×C4C22×D29311yescharacteristic
305C22×C4C22×D29311yescharacteristic
306C22×C4C22×D29311yescharacteristic
307C22×C4C22×D29311yescharacteristic
308C4⋊C4—2934no—
309C4⋊C4—2934no—
310C4⋊C4—2934no—
311C4⋊C4—2934no—
312C4⋊C4—2934no—
313C4⋊C4—2934no—
314C4⋊C4—2934no—
315C4⋊C4C22×D29314yes—
316C4⋊C4C22×D29314yes—
317C4⋊C4C22×D29314yes—
318C22⋊C4—2934no—
319C22⋊C4—2934no—
320C22⋊C4—2934no—
321C22⋊C4—2934no—
322C22⋊C4—2934no—
323C22⋊C4—2934no—
324C22⋊C4—2934no—
325C22⋊C4—2934no—
326C22⋊C4—2934no—
327C22⋊C4C22×D29314yes—
328C22⋊C4C22×D29314yes—
329C22⋊C4C22×D29314yes—
330C42—2934no—
331C42—2934no—
332C42—2934no—
333C42C22×D29314yes—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—2932no—
338C23—2932no—
339C23—5862no—
340C23—5862no—
341C23—5862no—
342C23—5862no—
343C23—5862no—
344C23—5862no—
345C23C23×D29312yes—
346C23C23×D29311yescharacteristic
347Q8—5868no—
348Q8—11724no—
349Q8—11724no—
350D4—5868no—
351D4—11724no—
352D4—11724no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—2934no—
360C2×C4—2932no—
361C2×C4—2932no—
362C2×C4—2932no—
363C2×C4—2932no—
364C2×C4—2932no—
365C2×C4—2932no—
366C2×C4—5868no—
367C2×C4—5862no—
368C2×C4—5862no—
369C2×C4—5862no—
370C2×C4—5862no—
371C2×C4—5862no—
372C2×C4—11724no—
373C2×C4—11724no—
374C2×C4C23×D29312yes—
375C2×C4C23×D29312yes—
376C2×C4C23×D29312yes—
377C2×C4C23×D29312yes—
378C2×C4C23×D29312yes—
379C2×C4C23×D29312yes—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—44no—
384C22—5862no—
385C22—5862no—
386C22—5862no—
387C22—5862no—
388C22—5862no—
389C22—5862no—
390C22—11724no—
391C22—11724no—
392C22#41×D29312yes—
393C22#2262767012yes—
394C22#2262767112yes—
395C22C24×D29311yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—2934no—
403C4—5862no—
404C4—5862no—
405C4—5862no—
406C4—5862no—
407C4—5862no—
408C2—42no—
409C2—11722no—
410C2—11722no—
411C2#3403674514yesdirect product factor
412C2C2×#41×D29311yescharacteristic
413C2C2×#2262767011yescharacteristic
414C2C2×#2262767111yescharacteristic
subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×#126×C293C2
socleC23×C293C24
prime radicalC2×#22627597C2
hypercenterC2×#126D293
hypocenterC293C2×#542
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #34036745C2direct (N × H)
2. C2×#22627623C2semidirect
3. C2×#22627619C2semidirect
4. C2×#22627612C2semidirect
5. C2×#22627610C2semidirect
6. C2×#22627610C2semidirect
7. C2×#22627609C2semidirect
8. C2×#22627608C2semidirect
9. C2×#22627604C2semidirect
10. C2×#22627602C2semidirect
11. C2×#22627601C2semidirect
13. C2×C4×Dic586C2semidirect
14. C2×#22627584C2semidirect
15. C2×#22627582C2semidirect
16. C2×#126×C293C2semidirect
26. #22627623C22semidirect
27. #22627619C22semidirect
28. #22627612C22semidirect
29. #22627610C22semidirect
30. #22627610C22semidirect
31. #22627609C22semidirect
32. #22627608C22semidirect
33. #22627604C22semidirect
34. #22627602C22semidirect
35. #22627601C22semidirect
37. C4×Dic586C22semidirect
38. #22627584C22semidirect
39. #22627582C22semidirect
59. #126×C293C22semidirect
201. C2×C293#542semidirect
207. C293C2×#542semidirect
212. C2×#126D293semidirect
236. #126C2×D293semidirect
411. C2#34036745direct (N × H)

Maximal subgroups

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

subgroupindex
#340367452
C2×#226276232
C2×#226276192
C2×#226276122
C2×#226276102
C2×#226276092
C2×#226276082
C2×#226276042
C2×#226276022
C2×#226276012
C2×#226275972
C2×C4×Dic5862
C2×#226275842
C2×#226275822
C2×#126×C2932
C2×#542293