Finite Group Databasebeta

← #49170315

Subgroups — #49170315

Order 37504.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627652C211yesmaximal, characteristic, complemented
2C2×#22627646C211yesmaximal, characteristic, complemented
3#34036784C211yesmaximal, characteristic, complemented
4#34036775C211yesmaximal, characteristic, complemented
5#34036523C211yesmaximal, characteristic, complemented
6#34036387C211yesmaximal, characteristic, complemented
7#34036358C211yesmaximal, characteristic, complemented
8#34036345C211yesmaximal, characteristic, complemented
9#34036335C211yesmaximal, characteristic, complemented
10#34036293C211yesmaximal, characteristic, complemented
11#34036293C211yesmaximal, characteristic, complemented
12#34036282C211yesmaximal, characteristic, complemented
13#34036276C211yesmaximal, characteristic, complemented
14#34036242C211yesmaximal, characteristic, complemented
15#435×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C2×#17989802C2211yescharacteristic
18C2×#17989802C2211yescharacteristic, complemented
19C22×D1172C2211yescharacteristic
20#22627652—24no—
21#22627646—24no—
22C2×Dic1172C2211yescharacteristic, complemented
23C2×Dic1172C2211yescharacteristic, complemented
24C2×#17989791C2211yescharacteristic
25C2×#17989791C2211yescharacteristic
26C2×#17989791C2211yescharacteristic
27C2×#17989791C2211yescharacteristic
28C2×#17989791C2211yescharacteristic, complemented
29C2×D2344C2211yescharacteristic
30C2×D2344C2211yescharacteristic
31#22627624C2211yescharacteristic, complemented
32#22627612C2211yescharacteristic
33#22627609—21no—
34#22627606—21no—
35#22627606—21no—
36#22627603C2211yescharacteristic
37#22627603C2211yescharacteristic
38#22627603C2211yescharacteristic, complemented
39#22627598C2211yescharacteristic
40#22627597—21no—
41#22627595—21no—
42#22627592—21no—
43C4×D1172C2211yescharacteristic
44C4×D1172C2211yescharacteristic, complemented
45C4⋊C4×D293—21no—
46C22⋊C4×D293—21no—
47#22627556C2211yescharacteristic, complemented
48#22627549C2211yescharacteristic, complemented
49#22627549C2211yescharacteristic, complemented
50#22627549C2211yescharacteristic, complemented
51#22627546C2211yescharacteristic
52#22627546C2211yescharacteristic
53#22627546C2211yescharacteristic, complemented
54C2×M16×C293C2211yescharacteristic
55C22×C8×C293C2211yescharacteristic, complemented
56C4×D4×C293C2211yescharacteristic
57C4⋊C8×C293C2211yescharacteristic, complemented
58C22⋊C8×C293C2211yescharacteristic
59C22⋊C8×C293C2211yescharacteristic, complemented
60#97×C293C2211yescharacteristic, complemented
61C23×D293—21no—
62#17989802—22no—
63#17989802—22no—
64#17989802—22no—
65#17989802—41no—
66#17989802—41no—
67#17989802—41no—
68C2×Dic586C2311yescharacteristic
69C2×Dic586C2311yescharacteristic
70C2×Dic586C2311yescharacteristic
71C2×D1172—22no—
72C2×D1172—21no—
73C2×D1172—41no—
74C2×D1172C2311yescharacteristic
75C2×D1172C2311yescharacteristic
76C2×D1172C2311yescharacteristic
77C2×C22⋊D293—21no—
78C2×C22⋊D293—21no—
79C2×C22⋊D293—21no—
80C2×C22⋊D293—21no—
81C2×C4×D293—21no—
82C2×C4×D293—21no—
83C2×C4×D293—21no—
84C2×C4×D293—21no—
85C2×C4×D293—21no—
86Dic1172—22no—
87Dic1172—41no—
88#17989791—22no—
89#17989791—22no—
90#17989791—22no—
91#17989791—22no—
92#17989791—41no—
93D2344—22no—
94D2344D414yescomplemented
95C4⋊Dic293—21no—
96C4⋊Dic293—21no—
97C4⋊Dic293C2311yescharacteristic
98C4⋊Dic293C2311yescharacteristic
99#17989781—21no—
100#17989781—21no—
101#17989781—21no—
102C22⋊Dic293—21no—
103C22⋊Dic293—21no—
104C22⋊Dic293—21no—
105#17989779—21no—
106#17989779—21no—
107#17989779—21no—
108#17989779—21no—
109#17989779—21no—
110C2×D4×C293D411yescharacteristic
111C22×C4×C293C2311yescharacteristic
112C22×C4×C293C2311yescharacteristic
113M16×C293—22no—
114C2×C8×C293—22no—
115C2×C8×C293C2311yescharacteristic
116C2×C8×C293C2311yescharacteristic
117C2×C8×C293C2311yescharacteristic
118C2×C8×C293C2311yescharacteristic
119C4⋊C4×C293D411yescharacteristic
120C22⋊C4×C293D411yescharacteristic
121C22⋊C4×C293D411yescharacteristic
122C42×C293C2311yescharacteristic
123C22×D293—21no—
124C22×D293—21no—
125C22×D293—21no—
126C22×D293—42no—
127C22×D293—42no—
128C22×D293—81no—
129Dic586—21no—
130Dic586—21no—
131Dic586—21no—
132Dic586—21no—
133Dic586—21no—
134Dic586—21no—
135D1172—21no—
136D1172—21no—
137D1172—21no—
138D1172—21no—
139D1172—42no—
140D1172C2×D412yes—
141D1172C2×D412yes—
142C22⋊D293—42no—
143C22⋊D293—42no—
144C22⋊D293—42no—
145C22⋊D293—81no—
146C2×Dic293—21no—
147C2×Dic293—21no—
148C2×Dic293—21no—
149C2×Dic293—21no—
150C2×Dic293—21no—
151C4×D293—42no—
152C4×D293—42no—
153C4×D293—42no—
154C4×D293—42no—
155C4×D293—81no—
156C23×C293C2×D411yescharacteristic
157C23×C293C2×D411yescharacteristic
158D4×C293—41no—
159C2×C4×C293—21no—
160C2×C4×C293—21no—
161C2×C4×C293—21no—
162C2×C4×C293—21no—
163C2×C4×C293C2×D411yescharacteristic
164C2×C4×C293C2×D411yescharacteristic
165C2×C4×C293C2×D411yescharacteristic
166C2×C4×C293C2×D411yescharacteristic
167C2×C4×C293C2411yescharacteristic
168C8×C293—21no—
169C8×C293—21no—
170C8×C293—21no—
171C8×C293C2×D412yes—
172C22×C293—21no—
173C22×C293—21no—
174C22×C293—21no—
175C22×C293—21no—
176C22×C293—21no—
177C22×C293—21no—
178C22×C293C22×D411yescharacteristic
179C2×D293—22no—
180C2×D293—22no—
181C2×D293—41no—
182C2×D293—41no—
183C2×D293—41no—
184C2×D293—41no—
185C2×D293—41no—
186C2×D293—41no—
187C2×D293—41no—
188C2×D293—84no—
189C4×C293—21no—
190C4×C293—21no—
191C4×C293—21no—
192C4×C293—21no—
193C4×C293C22×D411yescharacteristic
194C4×C293H(5,𝔽2)11yescharacteristic
195Dic293—41no—
196Dic293—41no—
197Dic293—41no—
198Dic293—41no—
199Dic293—41no—
200C2×C293—41no—
201C2×C293—41no—
202C2×C293D4211yescharacteristic
203C2×C293#57511yescharacteristic
204C2×C293#57711yescharacteristic
205D293—42no—
206D293—42no—
207D293—81no—
208C293#326711yescharacteristic, complemented, Sylow
209#3267—2931nomaximal, Sylow
210C2×AGL(1,ℤ/8)—2931no—
211C2×#135—2931no—
212#547—2931no—
213#546—2931no—
214#497—2931no—
215#470—2931no—
216#465—2931no—
217#463—2931no—
218#461—2931no—
219#452—2931no—
220#452—2931no—
221#450—2931no—
222#449—2931no—
223#442—2931no—
224#435D29311yescharacteristic, complemented
225C2×#41—2931no—
226C2×#41—2931no—
227C2×#41—2931no—
228C22×D4—2931no—
229AGL(1,ℤ/8)—5864no—
230#135—5864no—
231C2×Q16—2931no—
232C2×Q16—2931no—
233C2×SD16—2931no—
234C2×SD16—2931no—
235C2×SD16—2931no—
236C2×SD16—2931no—
237C2×SD16—2931no—
238C2×D8—2931no—
239C2×D8—2931no—
240C2×M16C2×D29311yescharacteristic
241C22×C8C2×D29311yescharacteristic, complemented
242C4⋊Q8—2931no—
243#124—2931no—
244#123—5861no—
245#123—5861no—
246#123—5861no—
247C22⋊Q8—2931no—
248C22⋊Q8—2931no—
249C22⋊Q8—2931no—
250#121—2931no—
251#121—5861no—
252#121—5861no—
253#120—5861no—
254C4×D4—2931no—
255C4×D4—2931no—
256C4×D4C2×D29311yescharacteristic
257C2×C4⋊C4—5861no—
258C2×C22⋊C4—5861no—
259#106—2931no—
260C4⋊C8C2×D29311yescharacteristic, complemented
261#103—2931no—
262#103—2931no—
263#103—2931no—
264#102—2931no—
265#102—2931no—
266#102—2931no—
267C22⋊C8C2×D29311yescharacteristic
268C22⋊C8C2×D29311yescharacteristic, complemented
269#97C2×D29311yescharacteristic, complemented
270C24—5861no—
271#41—5862no—
272#41—5862no—
273#41—5862no—
274#41—11721no—
275#41—11721no—
276#41—11721no—
277C2×Q8—2931no—
278C2×Q8—2931no—
279C2×Q8—2931no—
280C2×D4—2931no—
281C2×D4—2931no—
282C2×D4—2931no—
283C2×D4—5862no—
284C2×D4—5861no—
285C2×D4—5861no—
286C2×D4—5861no—
287C2×D4—5861no—
288C2×D4—5861no—
289C2×D4—11721no—
290C2×D4D117211yescharacteristic
291C22×C4—5861no—
292C22×C4—5861no—
293C22×C4—5861no—
294C22×C4—5861no—
295C22×C4—5861no—
296C22×C4C22×D29311yescharacteristic
297C22×C4C22×D29311yescharacteristic
298Q16—5862no—
299Q16—11721no—
300SD16—5862no—
301SD16—5862no—
302SD16—5862no—
303SD16—5862no—
304SD16—11721no—
305D8—2934no—
306D8—5862no—
307M16—22no—
308C2×C8—22no—
309C2×C8C22×D29311yescharacteristic
310C2×C8C22×D29311yescharacteristic
311C2×C8C22×D29311yescharacteristic
312C2×C8C22×D29311yescharacteristic
313C4⋊C4—2931no—
314C4⋊C4—2931no—
315C4⋊C4—5861no—
316C4⋊C4—5861no—
317C4⋊C4—5861no—
318C4⋊C4—5861no—
319C4⋊C4—5861no—
320C4⋊C4D117211yescharacteristic
321C22⋊C4—5861no—
322C22⋊C4—5861no—
323C22⋊C4—5861no—
324C22⋊C4—5861no—
325C22⋊C4—5861no—
326C22⋊C4—5861no—
327C22⋊C4—5861no—
328C22⋊C4—5861no—
329C22⋊C4D117211yescharacteristic
330C22⋊C4D117211yescharacteristic
331C42C22×D29311yescharacteristic
332C23—23441no—
333C23—5861no—
334C23—5861no—
335C23—5861no—
336C23—11722no—
337C23—11722no—
338C23C2×D117211yescharacteristic
339C23C2×D117211yescharacteristic
340Q8—5861no—
341Q8—5861no—
342Q8—5861no—
343Q8—5861no—
344Q8—5861no—
345Q8—5861no—
346D4—41no—
347D4—2932no—
348D4—2932no—
349D4—23441no—
350D4—5861no—
351D4—5861no—
352D4—5861no—
353D4—5861no—
354D4—11722no—
355D4—11722no—
356D4—11722no—
357D4—11722no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—23441no—
363C2×C4—5861no—
364C2×C4—5861no—
365C2×C4—5861no—
366C2×C4—5861no—
367C2×C4—5861no—
368C2×C4—11722no—
369C2×C4—11722no—
370C2×C4—11722no—
371C2×C4—11722no—
372C2×C4C2×D117211yescharacteristic
373C2×C4C2×D117211yescharacteristic
374C2×C4C2×D117211yescharacteristic
375C2×C4C2×D117211yescharacteristic
376C2×C4C23×D29311yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D29312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—23444no—
388C22—5862no—
389C22—5862no—
390C22—11721no—
391C22—11721no—
392C22—11721no—
393C22—11721no—
394C22—11721no—
395C22—11721no—
396C22—11721no—
397C22C22×D117211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—11721no—
403C4—11721no—
404C4—11721no—
405C4—11721no—
406C4—11721no—
407C4C2×D4×D29311yescharacteristic
408C4#2262767011yescharacteristic
409C2—41no—
410C2—41no—
411C2—23441no—
412C2—11722no—
413C2—11722no—
414C2D4×D117211yescharacteristic
415C2#3403692911yescharacteristic
416C2#3403694111yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#435×C293C2
socleC22×C293C22×D4
hypercenter#435D293
hypocenterC293#3267
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#22627652C2semidirect
2. C2×#22627646C2semidirect
3. #34036784C2semidirect
4. #34036775C2semidirect
5. #34036523C2semidirect
6. #34036387C2semidirect
7. #34036358C2semidirect
8. #34036345C2semidirect
9. #34036335C2semidirect
10. #34036293C2semidirect
11. #34036293C2semidirect
12. #34036282C2semidirect
13. #34036276C2semidirect
14. #34036242C2semidirect
15. #435×C293C2semidirect
18. C2×#17989802C22semidirect
22. C2×Dic1172C22semidirect
23. C2×Dic1172C22semidirect
28. C2×#17989791C22semidirect
31. #22627624C22semidirect
38. #22627603C22semidirect
44. C4×D1172C22semidirect
47. #22627556C22semidirect
48. #22627549C22semidirect
49. #22627549C22semidirect
50. #22627549C22semidirect
53. #22627546C22semidirect
55. C22×C8×C293C22semidirect
57. C4⋊C8×C293C22semidirect
59. C22⋊C8×C293C22semidirect
60. #97×C293C22semidirect
94. D2344D4semidirect
208. C293#3267semidirect
224. #435D293semidirect
241. C22×C8C2×D293semidirect
260. C4⋊C8C2×D293semidirect
268. C22⋊C8C2×D293semidirect
269. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276522
C2×#226276462
#340367842
#340367752
#340365232
#340363872
#340363582
#340363452
#340363352
#340362932
#340362822
#340362762
#340362422
#435×C2932
#3267293