Finite Group Databasebeta

← C2×#34036830 #49172309

Subgroups — C2×#34036830 #49172309

Order 37504.

1252 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036830C2116yesmaximal, direct product factor
2C2×#22627619C211yesmaximal, characteristic, complemented
3C2×#22627614C211yesmaximal, characteristic, complemented
4C2×#22627609C211yesmaximal, characteristic, complemented
5C2×#22627608C211yesmaximal, characteristic, complemented
6C2×#22627599C211yesmaximal, characteristic, complemented
7C2×#22627597C211yesmaximal, characteristic, complemented
8C2×#22627597C211yesmaximal, characteristic, complemented
9C2×#22627597C211yesmaximal, characteristic, complemented
10C2×C4×D1172C211yesmaximal, characteristic, complemented
11C2×#22627586C211yesmaximal, characteristic, complemented
12C2×#22627584C211yesmaximal, characteristic, complemented
13C2×#22627584C211yesmaximal, characteristic, complemented
14C2×#22627581C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×D293C211yesmaximal, characteristic, complemented
16C2×#126×C293C211yesmaximal, characteristic, complemented
17C22×D1172C2211yescharacteristic
18C22×D1172C2211yescharacteristic
19C22×D1172C2211yescharacteristic
20C22×C22⋊D293C2211yescharacteristic
21C22×C22⋊D293C2211yescharacteristic
22C22×C22⋊D293C2211yescharacteristic
23C23×Dic293C2211yescharacteristic
24C22×C4×D293C2211yescharacteristic
25C22×C4×D293C2211yescharacteristic
26C22×C4×D293C2211yescharacteristic
27C22×C4×D293C2211yescharacteristic
28C22×C4×D293C2211yescharacteristic
29#22627619C2218yescomplemented
30#22627614C2218yescomplemented
31#22627609C2218yescomplemented
32#22627608C2218yescomplemented
33#22627599C2218yescomplemented
34#22627597C2218yescomplemented
35#22627597C2218yescomplemented
36#22627597C2218yescomplemented
37C4×D1172C2218yescomplemented
38#22627586C2218yescomplemented
39#22627584C2218yescomplemented
40#22627584C2218yescomplemented
41#22627581C2218yescomplemented
42C2×C4⋊Dic293C2211yescharacteristic
43C2×C4⋊Dic293C2211yescharacteristic
44C2×#17989781C2211yescharacteristic
45C2×#17989781C2211yescharacteristic
46C2×#17989781C2211yescharacteristic
47C2×#17989781C2211yescharacteristic
48C2×#17989781C2211yescharacteristic
49C4⋊C4×D293C2218yescomplemented
50C2×#17989779C2211yescharacteristic
51C2×#17989779C2211yescharacteristic
52C2×#17989779C2211yescharacteristic
53C2×#17989779C2211yescharacteristic
54C2×#17989779C2211yescharacteristic
55C2×#17989779C2211yescharacteristic
56C2×#17989779C2211yescharacteristic
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
69C23×D293C2311yescharacteristic
70C2×D1172—24no—
71C2×D1172—24no—
72C2×D1172—42no—
73C2×D1172C2314yes—
74C2×D1172C2314yes—
75C2×D1172C2314yes—
76C2×C22⋊D293—24no—
77C2×C22⋊D293—24no—
78C2×C22⋊D293—42no—
79C2×C22⋊D293C2314yes—
80C2×C22⋊D293C2314yes—
81C2×C22⋊D293C2314yes—
82C22×Dic293—42no—
83C22×Dic293C2311yescharacteristic
84C22×Dic293C2311yescharacteristic
85C22×Dic293C2311yescharacteristic
86C22×Dic293C2311yescharacteristic
87C22×Dic293C2314yes—
88C22×Dic293C2311yescharacteristic
89C2×C4×D293—24no—
90C2×C4×D293—24no—
91C2×C4×D293—42no—
92C2×C4×D293—42no—
93C2×C4×D293—42no—
94C2×C4×D293C2314yes—
95C2×C4×D293C2314yes—
96C2×C4×D293C2314yes—
97C2×C4×D293C2314yes—
98C2×C4×D293C2314yes—
99C4⋊Dic293C2314yes—
100C4⋊Dic293C2314yes—
101#17989781C2314yes—
102#17989781C2314yes—
103#17989781C2314yes—
104#17989781C2314yes—
105#17989781C2314yes—
106#17989779C2314yes—
107#17989779C2314yes—
108#17989779C2314yes—
109#17989779C2314yes—
110#17989779C2314yes—
111#17989779C2314yes—
112#17989779C2314yes—
113C4×Dic293C2314yes—
114C4×Dic293C2314yes—
115C24×C293C2311yescharacteristic
116C22×C4×C293C2311yescharacteristic
117C22×C4×C293C2311yescharacteristic
118C22×C4×C293C2311yescharacteristic
119C22×C4×C293C2311yescharacteristic
120C22×C4×C293C2311yescharacteristic
121C22×C4×C293C2311yescharacteristic
122C4⋊C4×C293C2314yes—
123C4⋊C4×C293C2314yes—
124C4⋊C4×C293C2314yes—
125C22⋊C4×C293C2314yes—
126C22⋊C4×C293C2314yes—
127C22⋊C4×C293C2314yes—
128C42×C293C2314yes—
129C22×D293—22no—
130C22×D293—22no—
131C22×D293—22no—
132C22×D293—22no—
133C22×D293—22no—
134C22×D293—22no—
135C22×D293—22no—
136C22×D293—22no—
137C22×D293#4114yes—
138C22×D293C2412yes—
139C22×D293C2412yes—
140C22×D293C2412yes—
141D1172—28no—
142D1172—28no—
143D1172—44no—
144C22⋊D293—28no—
145C22⋊D293—28no—
146C22⋊D293—44no—
147C2×Dic293—22no—
148C2×Dic293—22no—
149C2×Dic293—22no—
150C2×Dic293—22no—
151C2×Dic293—44no—
152C2×Dic293#4114yes—
153C2×Dic293C2412yes—
154C2×Dic293C2412yes—
155C2×Dic293C2412yes—
156C2×Dic293C2412yes—
157C2×Dic293C2412yes—
158C4×D293—28no—
159C4×D293—28no—
160C4×D293—44no—
161C4×D293—44no—
162C4×D293—44no—
163C23×C293—22no—
164C23×C293—22no—
165C23×C293—22no—
166C23×C293C2412yes—
167C23×C293C2411yescharacteristic
168C2×C4×C293—22no—
169C2×C4×C293—22no—
170C2×C4×C293—22no—
171C2×C4×C293—22no—
172C2×C4×C293—22no—
173C2×C4×C293—22no—
174C2×C4×C293C2412yes—
175C2×C4×C293C2412yes—
176C2×C4×C293C2412yes—
177C2×C4×C293C2412yes—
178C2×C4×C293C2412yes—
179C2×C4×C293C2412yes—
180C22×C293—22no—
181C22×C293—22no—
182C22×C293—22no—
183C22×C293—44no—
184C22×C293C2×#4112yes—
185C22×C293C2×#4112yes—
186C22×C293H(5,𝔽2)12yes—
187C22×C293C2511yescharacteristic
188C2×D293—28no—
189C2×D293—22no—
190C2×D293—22no—
191C2×D293—22no—
192C2×D293—22no—
193C2×D293—22no—
194C2×D293—22no—
195C2×D293—22no—
196C2×D293—22no—
197C2×D293—44no—
198C2×D293—44no—
199C2×D293C2×#4114yes—
200C4×C293—22no—
201C4×C293—22no—
202C4×C293—22no—
203C4×C293—22no—
204C4×C293—22no—
205C4×C293—22no—
206Dic293—22no—
207Dic293—22no—
208Dic293—22no—
209Dic293—22no—
210Dic293C2×#4114yes—
211C2×C293—42no—
212C2×C293#55314yescomplemented
213C2×C293C22×#4111yescharacteristic
214C2×C293C22×#4111yescharacteristic
215C2×C293C2×H(5,𝔽2)11yescharacteristic
216D293—24no—
217D293—42no—
218D293—42no—
219C293C2×#55311yescharacteristic, complemented, Sylow
220C2×#553—2931nomaximal, Sylow
221#553—29316no—
222C2×#126—2931no—
223C2×#126D29311yescharacteristic, complemented
224C2×#125—2931no—
225C2×#123—2931no—
226C2×#123—2931no—
227C2×#121—2931no—
228C2×#121—2931no—
229C2×#121—2931no—
230C2×#121—2931no—
231C2×C4×D4—2931no—
232C2×C4×D4—2931no—
233C2×C4×D4—2931no—
234C2×C4×D4—2931no—
235C2×#117—2931no—
236C22×C4⋊C4—2931no—
237C22×D4—2931no—
238C22×D4—2931no—
239C22×D4—2931no—
240C22×D4—2931no—
241C22×D4—2931no—
242C22×D4—2931no—
243C23×C4—2931no—
244C23×C4—2931no—
245C23×C4—2931no—
246C23×C4—2931no—
247C23×C4—2931no—
248C23×C4—2931no—
249#126—2938no—
250#126C2×D29318yescomplemented
251#125—2938no—
252#123—2938no—
253#123—2938no—
254#121—2938no—
255#121—2938no—
256#121—2938no—
257#121—2938no—
258C4×D4—2938no—
259C4×D4—2938no—
260C4×D4—2938no—
261C4×D4—2938no—
262#117—2938no—
263C2×C4⋊C4—2931no—
264C2×C4⋊C4—2931no—
265C2×C4⋊C4—2931no—
266C2×C4⋊C4—2931no—
267C2×C4⋊C4—2931no—
268C2×C4⋊C4—2931no—
269C2×C4⋊C4—2931no—
270C2×C4⋊C4—2938no—
271C2×C4⋊C4C2×D29311yescharacteristic
272C2×C4⋊C4C2×D29311yescharacteristic
273C2×C4⋊C4C2×D29311yescharacteristic
274C2×C22⋊C4—2931no—
275C2×C22⋊C4—2931no—
276C2×C22⋊C4—2931no—
277C2×C22⋊C4—2931no—
278C2×C22⋊C4—2931no—
279C2×C22⋊C4—2931no—
280C2×C22⋊C4—2931no—
281C2×C22⋊C4C2×D29311yescharacteristic
282C2×C22⋊C4C2×D29311yescharacteristic
283C2×C22⋊C4C2×D29311yescharacteristic
284C2×C42—2931no—
285C2×C42—2931no—
286C2×C42C2×D29311yescharacteristic
287C24—2931no—
288C24—2931no—
289C24—2931no—
290C24C22×D29311yescharacteristic
291C2×D4—2934no—
292C2×D4—2934no—
293C2×D4—2934no—
294C2×D4—2934no—
295C2×D4—2934no—
296C2×D4—2934no—
297C2×D4—5864no—
298C2×D4—5864no—
299C2×D4—5864no—
300C2×D4—5864no—
301C2×D4—11722no—
302C2×D4—11722no—
303C22×C4—2931no—
304C22×C4—2931no—
305C22×C4—2931no—
306C22×C4—2931no—
307C22×C4—2931no—
308C22×C4—2934no—
309C22×C4—2934no—
310C22×C4—2934no—
311C22×C4—2934no—
312C22×C4—2934no—
313C22×C4—2934no—
314C22×C4—5864no—
315C22×C4—5864no—
316C22×C4—11722no—
317C22×C4—11722no—
318C22×C4—11722no—
319C22×C4—11722no—
320C22×C4C22×D29311yescharacteristic
321C22×C4C22×D29311yescharacteristic
322C22×C4C22×D29311yescharacteristic
323C22×C4C22×D29311yescharacteristic
324C22×C4C22×D29311yescharacteristic
325C22×C4C22×D29311yescharacteristic
326C4⋊C4—2934no—
327C4⋊C4—2934no—
328C4⋊C4—2934no—
329C4⋊C4—2934no—
330C4⋊C4—2934no—
331C4⋊C4—2934no—
332C4⋊C4—2934no—
333C4⋊C4C22×D29314yes—
334C4⋊C4C22×D29314yes—
335C4⋊C4C22×D29314yes—
336C22⋊C4—2934no—
337C22⋊C4—2934no—
338C22⋊C4—2934no—
339C22⋊C4—2934no—
340C22⋊C4—2934no—
341C22⋊C4—2934no—
342C22⋊C4—2934no—
343C22⋊C4C22×D29314yes—
344C22⋊C4C22×D29314yes—
345C22⋊C4C22×D29314yes—
346C42—2934no—
347C42—2934no—
348C42C22×D29314yes—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—2934no—
353C23—2932no—
354C23—2932no—
355C23—2932no—
356C23—5862no—
357C23—5862no—
358C23—5862no—
359C23—5862no—
360C23—5862no—
361C23—5862no—
362C23—5862no—
363C23—5862no—
364C23C23×D29312yes—
365C23C23×D29311yescharacteristic
366D4—5868no—
367D4—5868no—
368D4—5868no—
369D4—5868no—
370D4—11724no—
371D4—11724no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—2934no—
379C2×C4—2932no—
380C2×C4—2932no—
381C2×C4—2932no—
382C2×C4—2932no—
383C2×C4—2932no—
384C2×C4—5868no—
385C2×C4—5868no—
386C2×C4—5862no—
387C2×C4—5862no—
388C2×C4—5862no—
389C2×C4—5862no—
390C2×C4—11724no—
391C2×C4—11724no—
392C2×C4—11724no—
393C2×C4—11724no—
394C2×C4C23×D29312yes—
395C2×C4C23×D29312yes—
396C2×C4C23×D29312yes—
397C2×C4C23×D29312yes—
398C2×C4C23×D29312yes—
399C2×C4C23×D29312yes—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—44no—
404C22—2934no—
405C22—5868no—
406C22—5862no—
407C22—5862no—
408C22—5862no—
409C22—5862no—
410C22—5862no—
411C22—5862no—
412C22—5862no—
413C22—5862no—
414C22—11724no—
415C22—11724no—
416C22#41×D29312yes—
417C22#41×D29312yes—
418C22#2262767012yes—
419C22C24×D29311yescharacteristic
420C4—22no—
421C4—22no—
422C4—22no—
423C4—22no—
424C4—22no—
425C4—22no—
426C4—2934no—
427C4—5862no—
428C4—5862no—
429C4—5862no—
430C4—5862no—
431C2—42no—
432C2—5864no—
433C2—11722no—
434C2—11722no—
435C2#3403683014yesdirect product factor
436C2C2×#41×D29311yescharacteristic
437C2C2×#41×D29311yescharacteristic
438C2C2×#2262767011yescharacteristic
subgroupG/H
centerC23C23×D293
commutator, cosocleC22×C293C25
FrattiniC22C24×D293
FittingC2×#126×C293C2
socleC23×C293C24
hypercenterC2×#126D293
hypocenterC293C2×#553
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #34036830C2direct (N × H)
2. C2×#22627619C2semidirect
3. C2×#22627614C2semidirect
4. C2×#22627609C2semidirect
5. C2×#22627608C2semidirect
6. C2×#22627599C2semidirect
7. C2×#22627597C2semidirect
8. C2×#22627597C2semidirect
9. C2×#22627597C2semidirect
10. C2×C4×D1172C2semidirect
11. C2×#22627586C2semidirect
12. C2×#22627584C2semidirect
13. C2×#22627584C2semidirect
14. C2×#22627581C2semidirect
15. C2×C4⋊C4×D293C2semidirect
16. C2×#126×C293C2semidirect
29. #22627619C22semidirect
30. #22627614C22semidirect
31. #22627609C22semidirect
32. #22627608C22semidirect
33. #22627599C22semidirect
34. #22627597C22semidirect
35. #22627597C22semidirect
36. #22627597C22semidirect
37. C4×D1172C22semidirect
38. #22627586C22semidirect
39. #22627584C22semidirect
40. #22627584C22semidirect
41. #22627581C22semidirect
49. C4⋊C4×D293C22semidirect
59. #126×C293C22semidirect
212. C2×C293#553semidirect
219. C293C2×#553semidirect
223. C2×#126D293semidirect
250. #126C2×D293semidirect
435. C2#34036830direct (N × H)

Maximal subgroups

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

subgroupindex
#340368302
C2×#226276192
C2×#226276142
C2×#226276092
C2×#226276082
C2×#226275992
C2×#226275972
C2×C4×D11722
C2×#226275862
C2×#226275842
C2×#226275812
C2×C4⋊C4×D2932
C2×#126×C2932
C2×#553293