Finite Group Databasebeta

← #49175322

Subgroups — #49175322

Order 37504.

496 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34037080C211yesmaximal, characteristic, complemented
2#34037079C211yesmaximal, characteristic
3#34037079C211yesmaximal, characteristic
4#34037079C211yesmaximal, characteristic
5#34037078C211yesmaximal, characteristic, complemented
6#34037078C211yesmaximal, characteristic, complemented
7#34037078C211yesmaximal, characteristic, complemented
8#34037076C211yesmaximal, characteristic
9C4⋊C4×#11924078C211yesmaximal, characteristic, complemented
10C4⋊C4×#11924078C211yesmaximal, characteristic, complemented
11C4×C4⋊#11924078C211yesmaximal, characteristic, complemented
12C22⋊C4×#11924078C211yesmaximal, characteristic
13C22⋊C4×#11924078C211yesmaximal, characteristic
14#34037065C211yesmaximal, characteristic, complemented
15#126×D293C211yesmaximal, characteristic
16C23×#11924078C2211yescharacteristic
17C2×C4⋊#11924078C2211yescharacteristic
18C2×C4⋊#11924078C2211yescharacteristic
19C2×C4⋊#11924078C2211yescharacteristic
20C2×C4⋊#11924078C2211yescharacteristic
21C2×C4⋊#11924078C2211yescharacteristic
22C2×C22⋊#11924078C2211yescharacteristic
23C2×C22⋊#11924078C2211yescharacteristic
24C2×C22⋊#11924078C2211yescharacteristic
25C2×C4×#11924078C2211yescharacteristic
26C2×C4×#11924078C2211yescharacteristic
27C2×C4×#11924078C2211yescharacteristic
28C2×C4×#11924078C2211yescharacteristic
29C2×C4×#11924078C2211yescharacteristic
30C2×C4×#11924078C2211yescharacteristic
31C2×C4×#11924078C2211yescharacteristic
32(C2×#11924078)⋊C4C2211yescharacteristic
33(C2×#11924078)⋊C4C2211yescharacteristic
34(C2×#11924078)⋊C4C2211yescharacteristic
35(C2×#11924078)⋊C4C2211yescharacteristic
36(C2×#11924078)⋊C4C2211yescharacteristic
37(C2×#11924078)⋊C4C2211yescharacteristic
38(C2×#11924078)⋊C4C2211yescharacteristic
39(C2×#11924078)⋊C4C2211yescharacteristic
40(C2×#11924078)⋊C4C2211yescharacteristic
41(C2×#11924078)⋊C4C2211yescharacteristic
42(C2×#11924078)⋊C4C2211yescharacteristic
43(C2×#11924078)⋊C4C2211yescharacteristic
44#22627619C411yescharacteristic, complemented
45#22627619C411yescharacteristic, complemented
46#22627619C411yescharacteristic, complemented
47#22627618C411yescharacteristic, complemented
48#22627617C411yescharacteristic, complemented
49#22627617C411yescharacteristic, complemented
50#22627617C411yescharacteristic, complemented
51C4⋊C4×D293C2211yescharacteristic
52C4⋊C4×D293C2211yescharacteristic
53C4⋊C4×D293C2211yescharacteristic
54C22⋊C4×D293C2211yescharacteristic
55C22⋊C4×D293C2211yescharacteristic
56C22⋊C4×D293C2211yescharacteristic
57C42×D293C2211yescharacteristic
58#126×C293C411yescharacteristic, complemented
59C22×#11924078—22no—
60C22×#11924078—22no—
61C22×#11924078—41no—
62C22×#11924078C2311yescharacteristic
63C22×#11924078C2311yescharacteristic
64C22×#11924078C2311yescharacteristic
65C22×#11924078C2311yescharacteristic
66C22×#11924078C2311yescharacteristic
67C22×#11924078C2311yescharacteristic
68C22×#11924078C2311yescharacteristic
69C22×#11924078C2311yescharacteristic
70C4⋊#11924078—22no—
71C4⋊#11924078—22no—
72C4⋊#11924078—22no—
73C4⋊#11924078—22no—
74C4⋊#11924078—41no—
75C22⋊#11924078—22no—
76C22⋊#11924078—22no—
77C22⋊#11924078—41no—
78C4×#11924078—22no—
79C4×#11924078—22no—
80C4×#11924078—22no—
81C4×#11924078—22no—
82C4×#11924078—41no—
83C4×#11924078—41no—
84C4×#11924078—41no—
85C23×D293C2311yescharacteristic
86C2×C4×D293C2311yescharacteristic
87C2×C4×D293C2311yescharacteristic
88C2×C4×D293C2311yescharacteristic
89C2×C4×D293C2311yescharacteristic
90C2×C4×D293C2311yescharacteristic
91C2×C4×D293C2311yescharacteristic
92C4⋊Dic293C2×C411yescharacteristic, complemented
93C4⋊Dic293C2×C411yescharacteristic, complemented
94C4⋊Dic293C2×C411yescharacteristic, complemented
95#17989781C2×C411yescharacteristic, complemented
96#17989781C2×C411yescharacteristic, complemented
97#17989781C2×C411yescharacteristic, complemented
98#17989781C2×C411yescharacteristic, complemented
99#17989781C2×C411yescharacteristic, complemented
100#17989781C2×C411yescharacteristic, complemented
101C22⋊Dic293C2×C411yescharacteristic
102C22⋊Dic293C2×C411yescharacteristic
103C22⋊Dic293C2×C411yescharacteristic
104#17989779C2×C411yescharacteristic
105#17989779C2×C411yescharacteristic
106#17989779C2×C411yescharacteristic
107#17989779C2×C411yescharacteristic
108#17989779C2×C411yescharacteristic
109#17989779C2×C411yescharacteristic
110C4×Dic293C2×C411yescharacteristic, complemented
111C4×Dic293C2×C411yescharacteristic, complemented
112C4×Dic293C2×C411yescharacteristic, complemented
113C4⋊C4×C293C2×C411yescharacteristic, complemented
114C4⋊C4×C293C2×C411yescharacteristic, complemented
115C4⋊C4×C293C2×C411yescharacteristic, complemented
116C22⋊C4×C293C2×C411yescharacteristic
117C22⋊C4×C293C2×C411yescharacteristic
118C22⋊C4×C293C2×C411yescharacteristic
119C42×C293C2×C411yescharacteristic, complemented
120C2×#11924078—21no—
121C2×#11924078—21no—
122C2×#11924078—21no—
123C2×#11924078—21no—
124C2×#11924078—21no—
125C2×#11924078—21no—
126C2×#11924078—21no—
127C2×#11924078—21no—
128C2×#11924078—21no—
129C2×#11924078—21no—
130C2×#11924078—21no—
131C2×#11924078—21no—
132C2×#11924078—21no—
133C2×#11924078—21no—
134C2×#11924078—21no—
135C2×#11924078—21no—
136C2×#11924078—21no—
137C2×#11924078—21no—
138C2×#11924078—21no—
139C2×#11924078—21no—
140C2×#11924078—44no—
141C2×#11924078#4112yes—
142C2×#11924078#4112yes—
143C2×#11924078#4112yes—
144C2×#11924078#4112yes—
145C22×D293—21no—
146C22×D293—21no—
147C22×D293—21no—
148C22×D293—21no—
149C22×D293—21no—
150C22×D293—21no—
151C22×D293C22×C411yescharacteristic
152C22×D293C2411yescharacteristic
153C2×Dic293C22×C411yescharacteristic
154C2×Dic293C22×C411yescharacteristic
155C2×Dic293C22×C411yescharacteristic
156C2×Dic293C22×C411yescharacteristic
157C2×Dic293C22×C411yescharacteristic
158C2×Dic293C22×C411yescharacteristic
159C4×D293—21no—
160C4×D293—21no—
161C4×D293—21no—
162C4×D293—21no—
163C4×D293—21no—
164C4×D293—21no—
165C4×D293—21no—
166C4×D293—21no—
167C4×D293—21no—
168C4×D293—21no—
169C4×D293—21no—
170C4×D293—21no—
171C23×C293C22×C411yescharacteristic
172C2×C4×C293C22×C411yescharacteristic
173C2×C4×C293C22×C411yescharacteristic
174C2×C4×C293C22×C411yescharacteristic
175C2×C4×C293C22×C411yescharacteristic
176C2×C4×C293C22×C411yescharacteristic
177C2×C4×C293C22×C411yescharacteristic
178C22×C293—21no—
179C22×C293—21no—
180C22×C293—21no—
181C22×C293C23×C411yescharacteristic
182C2×D293—21no—
183C2×D293—21no—
184C2×D293—21no—
185C2×D293—41no—
186C2×D293—41no—
187C2×D293—41no—
188C2×D293—41no—
189C2×D293C2×#4111yescharacteristic
190C2×D293C2×#4111yescharacteristic
191C2×D293C2×#4111yescharacteristic
192C2×D293C2×#4111yescharacteristic
193C2×D293H(5,𝔽2)11yescharacteristic
194C2×D2932−1+411yescharacteristic
195#11924078—22no—
196#11924078—22no—
197#11924078—22no—
198#11924078—22no—
199#11924078—41no—
200#11924078—41no—
201#11924078—41no—
202#11924078—41no—
203C4×C293—21no—
204C4×C293—21no—
205C4×C293—21no—
206C4×C293—21no—
207C4×C293—21no—
208C4×C293—21no—
209Dic293—21no—
210Dic293—21no—
211Dic293—21no—
212Dic293—21no—
213Dic293—21no—
214Dic293—21no—
215C2×C293—41no—
216C2×C293C4×#4111yescharacteristic
217C2×C293C4×#4111yescharacteristic
218C2×C293#52011yescharacteristic
219D293—41no—
220D293#55111yescharacteristic
221D293#55211yescharacteristic
222D293#55311yescharacteristic
223D293#55611yescharacteristic
224C293#237311yescharacteristic, complemented, Sylow
225#2373—2931nomaximal, Sylow
226C2×#126—2931no—
227#389—2931no—
228#388—2931no—
229#388—2931no—
230#388—2931no—
231#387—2931no—
232#387—2931no—
233#387—2931no—
234#385—2931no—
235C4×C4⋊C4—2931no—
236C4×C4⋊C4—2931no—
237C4×C4⋊C4—2931no—
238C4×C22⋊C4—2931no—
239C4×C22⋊C4—2931no—
240#376—2931no—
241C23×C4—2931no—
242#126—2931no—
243#126—2931no—
244#126—2931no—
245#126—2931no—
246#126—2931no—
247#126—2931no—
248#126—2931no—
249#126#1192407811yescharacteristic, complemented
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⋊C4—2931no—
257C2×C4⋊C4—2931no—
258C2×C22⋊C4—2931no—
259C2×C22⋊C4—2931no—
260C2×C22⋊C4—2931no—
261C2×C22⋊C4—2931no—
262C2×C22⋊C4—2931no—
263C2×C22⋊C4—2931no—
264C2×C42—2931no—
265C2×C42—2931no—
266C2×C42—2931no—
267C2×C42—2931no—
268C2×C42—2931no—
269C2×C42—2931no—
270C2×C42—2931no—
271C2×C42—2931no—
272#95—2931no—
273#95—2931no—
274#95—2931no—
275#95—2931no—
276#95—2931no—
277#95—2931no—
278#95—2931no—
279#95—2931no—
280#95—2931no—
281#95—2931no—
282#95—2931no—
283#95—2931no—
284C24—2931no—
285C22×C4—2931no—
286C22×C4—2931no—
287C22×C4—2931no—
288C22×C4—2931no—
289C22×C4—2931no—
290C22×C4—2931no—
291C22×C4—2931no—
292C22×C4—2931no—
293C22×C4—2931no—
294C22×C4—2931no—
295C22×C4—2931no—
296C22×C4—2931no—
297C22×C4—2931no—
298C22×C4—2931no—
299C22×C4—5862no—
300C22×C4—5862no—
301C22×C4—11721no—
302C4⋊C4—2931no—
303C4⋊C4—2931no—
304C4⋊C4—2931no—
305C4⋊C4—2931no—
306C4⋊C4—2931no—
307C4⋊C4—2931no—
308C4⋊C4—2931no—
309C4⋊C4—2931no—
310C4⋊C4—2931no—
311C4⋊C4—5862no—
312C4⋊C4—5862no—
313C4⋊C4—5862no—
314C4⋊C4—5862no—
315C4⋊C4—11721no—
316C4⋊C4C2×#1192407811yescharacteristic, complemented
317C4⋊C4C2×#1192407811yescharacteristic, complemented
318C4⋊C4C2×#1192407811yescharacteristic, complemented
319C22⋊C4—2931no—
320C22⋊C4—2931no—
321C22⋊C4—2931no—
322C22⋊C4—2931no—
323C22⋊C4—2931no—
324C22⋊C4—2931no—
325C22⋊C4—2931no—
326C22⋊C4—2931no—
327C22⋊C4—2931no—
328C22⋊C4—5862no—
329C22⋊C4—5862no—
330C22⋊C4—11721no—
331C22⋊C4C2×#1192407811yescharacteristic
332C22⋊C4C2×#1192407811yescharacteristic
333C22⋊C4C2×#1192407811yescharacteristic
334C42—2931no—
335C42—2931no—
336C42—2931no—
337C42—5862no—
338C42—5862no—
339C42—5862no—
340C42—5862no—
341C42—11721no—
342C42—11721no—
343C42—11721no—
344C42C2×#1192407811yescharacteristic, complemented
345C23—2931no—
346C23—2931no—
347C23—5861no—
348C23—5861no—
349C23—5861no—
350C23—5861no—
351C23—5861no—
352C23—5861no—
353C23C22×#1192407811yescharacteristic
354C2×C4—2932no—
355C2×C4—2932no—
356C2×C4—2932no—
357C2×C4—2932no—
358C2×C4—2931no—
359C2×C4—2931no—
360C2×C4—2931no—
361C2×C4—2931no—
362C2×C4—2931no—
363C2×C4—2931no—
364C2×C4—5861no—
365C2×C4—5861no—
366C2×C4—5861no—
367C2×C4—5861no—
368C2×C4—5861no—
369C2×C4—5861no—
370C2×C4—5861no—
371C2×C4—5861no—
372C2×C4—5861no—
373C2×C4—5861no—
374C2×C4—5861no—
375C2×C4—5861no—
376C2×C4—5861no—
377C2×C4—5861no—
378C2×C4—5861no—
379C2×C4—5861no—
380C2×C4—5861no—
381C2×C4—5861no—
382C2×C4—5861no—
383C2×C4—5861no—
384C2×C4—5861no—
385C2×C4—5861no—
386C2×C4—5861no—
387C2×C4—5861no—
388C2×C4—5861no—
389C2×C4—5861no—
390C2×C4—5861no—
391C2×C4—5861no—
392C2×C4—5861no—
393C2×C4—5861no—
394C2×C4—5861no—
395C2×C4—5861no—
396C2×C4—11724no—
397C2×C4C22×#1192407811yescharacteristic
398C2×C4C22×#1192407811yescharacteristic
399C2×C4C22×#1192407811yescharacteristic
400C2×C4C22×#1192407811yescharacteristic
401C2×C4C22×#1192407811yescharacteristic
402C2×C4C22×#1192407811yescharacteristic
403C22—21no—
404C22—21no—
405C22—21no—
406C22—2931no—
407C22—2931no—
408C22—2931no—
409C22—2931no—
410C22—2931no—
411C22—2931no—
412C22—5861no—
413C22—5861no—
414C22—5861no—
415C22—11721no—
416C22—11721no—
417C22—11721no—
418C22—11721no—
419C22C23×#1192407811yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—5862no—
427C4—5862no—
428C4—5862no—
429C4—5862no—
430C4—5861no—
431C4—5861no—
432C4—5861no—
433C4—5861no—
434C4—5861no—
435C4—5861no—
436C4—11721no—
437C4—11721no—
438C4—11721no—
439C4—11721no—
440C2—41no—
441C2—2931no—
442C2—2931no—
443C2—2931no—
444C2—2931no—
445C2—11721no—
446C2#41×#1192407811yescharacteristic
447C2#41×#1192407811yescharacteristic
448C2#3403719811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#11924078
commutator, socleC22×C293C23×C4
Fitting#126×C293C4
prime radicalC23×D293C23
cosocleC22×D293C24
hypercenter#126#11924078
hypocenterC293#2373
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #34037080C2semidirect
5. #34037078C2semidirect
6. #34037078C2semidirect
7. #34037078C2semidirect
9. C4⋊C4×#11924078C2semidirect
10. C4⋊C4×#11924078C2semidirect
11. C4×C4⋊#11924078C2semidirect
14. #34037065C2semidirect
44. #22627619C4semidirect
45. #22627619C4semidirect
46. #22627619C4semidirect
47. #22627618C4semidirect
48. #22627617C4semidirect
49. #22627617C4semidirect
50. #22627617C4semidirect
58. #126×C293C4semidirect
92. C4⋊Dic293C2×C4semidirect
93. C4⋊Dic293C2×C4semidirect
94. C4⋊Dic293C2×C4semidirect
95. #17989781C2×C4semidirect
96. #17989781C2×C4semidirect
97. #17989781C2×C4semidirect
98. #17989781C2×C4semidirect
99. #17989781C2×C4semidirect
100. #17989781C2×C4semidirect
110. C4×Dic293C2×C4semidirect
111. C4×Dic293C2×C4semidirect
112. C4×Dic293C2×C4semidirect
113. C4⋊C4×C293C2×C4semidirect
114. C4⋊C4×C293C2×C4semidirect
115. C4⋊C4×C293C2×C4semidirect
119. C42×C293C2×C4semidirect
224. C293#2373semidirect
249. #126#11924078semidirect
316. C4⋊C4C2×#11924078semidirect
317. C4⋊C4C2×#11924078semidirect
318. C4⋊C4C2×#11924078semidirect
344. C42C2×#11924078semidirect

Maximal subgroups

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

subgroupindex
#340370802
#340370792
#340370782
#340370762
C4⋊C4×#119240782
C4×C4⋊#119240782
C22⋊C4×#119240782
#340370652
#126×D2932
#2373293