Finite Group Databasebeta

← #49161853

Subgroups — #49161853

Order 37504.

632 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627610C211yesmaximal, characteristic
2C2×#22627589C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D293C211yesmaximal, characteristic
4#34036033C211yesmaximal, characteristic, complemented
5#34036029C211yesmaximal, characteristic
6#34036022C211yesmaximal, characteristic, complemented
7#34036021C211yesmaximal, characteristic, complemented
8#34036019C211yesmaximal, characteristic, complemented
9#34036017C211yesmaximal, characteristic, complemented
10#34036000C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic293C211yesmaximal, characteristic, complemented
12#34035980C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic293C211yesmaximal, characteristic, complemented
14#34035976C211yesmaximal, characteristic, complemented
15#385×C293C211yesmaximal, characteristic, complemented
16C22×Dic586C2211yescharacteristic
17C22×C22⋊D293C2211yescharacteristic
18C22×C4×D293C2211yescharacteristic
19#22627610C418yescomplemented
20#22627589—24no—
21C4×C22⋊D293—24no—
22C2×C4⋊Dic293C2211yescharacteristic
23C2×#17989781C2211yescharacteristic
24C2×#17989781C2211yescharacteristic
25C2×#17989781C2211yescharacteristic
26C2×C22⋊Dic293C2211yescharacteristic
27C2×C22⋊Dic293C2211yescharacteristic
28C2×C22⋊Dic293C2211yescharacteristic
29C2×#17989779C2211yescharacteristic
30C2×#17989779C2211yescharacteristic
31C2×#17989779C2211yescharacteristic
32C2×#17989779C2211yescharacteristic
33C2×#17989779C2211yescharacteristic
34C2×C4×Dic293C2211yescharacteristic
35C2×C4×Dic293C2211yescharacteristic
36C2×C4×Dic293C2211yescharacteristic
37C2×C4×Dic293C2211yescharacteristic
38C2×C4×Dic293C2211yescharacteristic
39C2×C4×Dic293C2211yescharacteristic
40C2×C4×Dic293C2211yescharacteristic
41#22627531C2211yescharacteristic
42#22627531C2211yescharacteristic
43#22627531C2211yescharacteristic
44#22627531C2211yescharacteristic
45#22627531C2211yescharacteristic
46#22627531C2211yescharacteristic
47C23×C4×C293C2211yescharacteristic
48C2×C4⋊C4×C293C2211yescharacteristic
49C2×C4⋊C4×C293C2211yescharacteristic
50C2×C22⋊C4×C293C2211yescharacteristic
51C2×C22⋊C4×C293C2211yescharacteristic
52#95×C293C2211yescharacteristic
53#95×C293C2211yescharacteristic
54C23×D293C2311yescharacteristic
55C2×Dic586—22no—
56C2×Dic586—22no—
57C2×Dic586C2×C414yescomplemented
58C2×C22⋊D293—22no—
59C2×C22⋊D293—22no—
60C2×C22⋊D293C2×C414yes—
61C22×Dic293C2311yescharacteristic
62C22×Dic293C2311yescharacteristic
63C22×Dic293C2311yescharacteristic
64C22×Dic293C2311yescharacteristic
65C22×Dic293C2311yescharacteristic
66C22×Dic293C2311yescharacteristic
67C22×Dic293C2311yescharacteristic
68C2×C4×D293—22no—
69C2×C4×D293—22no—
70C2×C4×D293—41no—
71C4⋊Dic293—22no—
72#17989781—22no—
73#17989781—22no—
74#17989781D414yes—
75C22⋊Dic293—22no—
76C22⋊Dic293—22no—
77C22⋊Dic293C2×C414yescomplemented
78#17989779—22no—
79#17989779—22no—
80#17989779—41no—
81#17989779C2×C414yescomplemented
82#17989779C2×C414yescomplemented
83C4×Dic293—22no—
84C4×Dic293—22no—
85C4×Dic293—22no—
86C4×Dic293—22no—
87C4×Dic293—41no—
88C4×Dic293—41no—
89C4×Dic293C2×C414yescomplemented
90C24×C293C2311yescharacteristic
91C22×C4×C293—22no—
92C22×C4×C293—22no—
93C22×C4×C293—41no—
94C22×C4×C293C2311yescharacteristic
95C22×C4×C293C2311yescharacteristic
96C22×C4×C293C2311yescharacteristic
97C22×C4×C293C2311yescharacteristic
98C22×C4×C293C2311yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C4⋊C4×C293—22no—
101C4⋊C4×C293—22no—
102C22⋊C4×C293—41no—
103C22⋊C4×C293C2×C414yescomplemented
104C22×D293—21no—
105C22×D293—21no—
106C22×D293—21no—
107C22×D293—21no—
108C22×D293—21no—
109C22×D293—21no—
110C22×D293C22×C412yes—
111Dic586—28no—
112C22⋊D293—28no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293—21no—
126C2×Dic293—21no—
127C2×Dic293C22×C412yes—
128C2×Dic293C22×C412yes—
129C2×Dic293C22×C412yes—
130C2×Dic293C2×D412yes—
131C2×Dic293C2×D412yes—
132C2×Dic293#4112yes—
133C2×Dic293#4112yes—
134C4×D293—44no—
135C23×C293—21no—
136C23×C293—21no—
137C23×C293—21no—
138C23×C293—21no—
139C23×C293—21no—
140C23×C293—21no—
141C23×C293C22×C412yes—
142C23×C293C2411yescharacteristic
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293—21no—
148C2×C4×C293—21no—
149C2×C4×C293—21no—
150C2×C4×C293—21no—
151C2×C4×C293—21no—
152C2×C4×C293—21no—
153C2×C4×C293—21no—
154C2×C4×C293—21no—
155C2×C4×C293—21no—
156C2×C4×C293—21no—
157C2×C4×C293—44no—
158C2×C4×C293C22×C412yes—
159C2×C4×C293C22×C412yes—
160C2×C4×C293C2×D412yes—
161C2×C4×C293#4112yes—
162C22×C293—22no—
163C22×C293—22no—
164C22×C293—22no—
165C22×C293—41no—
166C22×C293—41no—
167C22×C293—41no—
168C22×C293—41no—
169C22×C293C23×C411yescharacteristic
170C22×C293C22×D411yescharacteristic
171C22×C293C2×#4111yescharacteristic
172C22×C293C2×#4111yescharacteristic
173C22×C293C2×#4111yescharacteristic
174C22×C293H(5,𝔽2)11yescharacteristic
175C22×C2932−1+411yescharacteristic
176C2×D293—22no—
177C2×D293—22no—
178C2×D293—22no—
179C2×D293—41no—
180C2×D293—41no—
181C2×D293—41no—
182C2×D293—41no—
183C4×C293—22no—
184C4×C293—22no—
185C4×C293—22no—
186C4×C293—22no—
187C4×C293—41no—
188C4×C293—41no—
189Dic293—22no—
190Dic293—22no—
191Dic293—22no—
192Dic293—22no—
193Dic293—41no—
194Dic293—41no—
195Dic293C4×D414yes—
196C2×C293—42no—
197C2×C293C2×C4×D411yescharacteristic
198C2×C293C4×#4111yescharacteristic
199C2×C293#52011yescharacteristic
200C2×C293#54611yescharacteristic
201C2×C293#54811yescharacteristic
202C2×C293#55611yescharacteristic
203C2×C293#55911yescharacteristic
204D293—42no—
205C293#236711yescharacteristic, complemented, Sylow
206#2367—2931nomaximal, Sylow
207C2×#124—2931no—
208C2×C4×Q8—2931no—
209C2×C4×D4—2931no—
210#391—2931no—
211#390—2931no—
212#388—2931no—
213#388—2931no—
214#388—2931no—
215#388—2931no—
216#385—2931no—
217#385D29311yescharacteristic, complemented
218C4×C4⋊C4—2931no—
219C4×C4⋊C4—2931no—
220C4×C22⋊C4—2931no—
221C4×C22⋊C4—2931no—
222C22×Q8—2931no—
223C22×D4—2931no—
224C23×C4—2931no—
225C23×C4C2×D29311yescharacteristic
226#124—2938no—
227C4×Q8—5864no—
228C4×D4—5864no—
229C2×C4⋊C4—2931no—
230C2×C4⋊C4—2931no—
231C2×C4⋊C4—2931no—
232C2×C4⋊C4—2931no—
233C2×C4⋊C4C2×D29311yescharacteristic
234C2×C4⋊C4C2×D29311yescharacteristic
235C2×C22⋊C4—2931no—
236C2×C22⋊C4—2931no—
237C2×C22⋊C4—2931no—
238C2×C22⋊C4—2931no—
239C2×C22⋊C4—2931no—
240C2×C22⋊C4—2931no—
241C2×C22⋊C4—2931no—
242C2×C22⋊C4—2931no—
243C2×C22⋊C4C2×D29311yescharacteristic
244C2×C22⋊C4C2×D29311yescharacteristic
245C2×C42—2931no—
246C2×C42—2931no—
247C2×C42—2931no—
248C2×C42—2931no—
249C2×C42—2931no—
250C2×C42—2931no—
251C2×C42—2931no—
252#95—2931no—
253#95—2931no—
254#95—2931no—
255#95—2931no—
256#95—2931no—
257#95—2931no—
258#95C2×D29311yescharacteristic
259#95C2×D29311yescharacteristic
260C24—2931no—
261C24C22×D29311yescharacteristic
262C2×Q8—2934no—
263C2×Q8—5862no—
264C2×Q8—5862no—
265C2×D4—2934no—
266C2×D4—5862no—
267C2×D4—5862no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—2931no—
272C22×C4—2931no—
273C22×C4—2931no—
274C22×C4—2931no—
275C22×C4—2931no—
276C22×C4—2931no—
277C22×C4—2931no—
278C22×C4—5862no—
279C22×C4—5862no—
280C22×C4—11721no—
281C22×C4C22×D29311yescharacteristic
282C22×C4C22×D29311yescharacteristic
283C22×C4C22×D29311yescharacteristic
284C22×C4C22×D29311yescharacteristic
285C22×C4C22×D29311yescharacteristic
286C22×C4C22×D29311yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—2934no—
290C4⋊C4—5862no—
291C4⋊C4—5862no—
292C4⋊C4—5862no—
293C22⋊C4—41no—
294C22⋊C4—2934no—
295C22⋊C4—2934no—
296C22⋊C4—2934no—
297C22⋊C4—5862no—
298C22⋊C4—5862no—
299C22⋊C4—5862no—
300C22⋊C4—5862no—
301C22⋊C4—11721no—
302C22⋊C4C4×D29314yescomplemented
303C42—2934no—
304C42—5862no—
305C42—5862no—
306C42—5862no—
307C42—5862no—
308C42—11721no—
309C42—11721no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—2932no—
317C23—5861no—
318C23—5861no—
319C23—5861no—
320C23—5861no—
321C23—5861no—
322C23—5861no—
323C23C2×C4×D29312yes—
324C23C23×D29311yescharacteristic
325Q8—5868no—
326D4—5868no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—44no—
342C2×C4—2932no—
343C2×C4—2932no—
344C2×C4—2932no—
345C2×C4—2932no—
346C2×C4—2932no—
347C2×C4—2932no—
348C2×C4—2932no—
349C2×C4—5861no—
350C2×C4—5861no—
351C2×C4—5861no—
352C2×C4—5861no—
353C2×C4—5861no—
354C2×C4—5861no—
355C2×C4—5861no—
356C2×C4—5861no—
357C2×C4—5861no—
358C2×C4—5861no—
359C2×C4—5861no—
360C2×C4—5861no—
361C2×C4—5861no—
362C2×C4—5861no—
363C2×C4—11724no—
364C2×C4C2×C4×D29312yes—
365C2×C4C2×C4×D29312yes—
366C2×C4D4×D29312yes—
367C2×C4#1798980112yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—5862no—
376C22—5862no—
377C22—5862no—
378C22—11721no—
379C22—11721no—
380C22—11721no—
381C22—11721no—
382C22C22×C4×D29311yescharacteristic
383C22C2×D4×D29311yescharacteristic
384C22#41×D29311yescharacteristic
385C22#41×D29311yescharacteristic
386C22C2×#1798980111yescharacteristic
387C22#2262766911yescharacteristic
388C22#2262767211yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—2934no—
396C4—5862no—
397C4—5862no—
398C4—5862no—
399C4—5862no—
400C4—11721no—
401C4—11721no—
402C2—42no—
403C2—11722no—
404C2C4×D4×D29311yescharacteristic
405C2C4×#1798980111yescharacteristic
406C2#3403661011yescharacteristic
407C2#3403676611yescharacteristic
408C2#3403678911yescharacteristic
409C2#3403685011yescharacteristic
410C2#3403686311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#385×C293C2
socle, cosocleC23×C293C24
prime radicalC22×C22⋊D293C22
hypercenter#385D293
hypocenterC293#2367
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#22627589C2semidirect
4. #34036033C2semidirect
6. #34036022C2semidirect
7. #34036021C2semidirect
8. #34036019C2semidirect
9. #34036017C2semidirect
10. #34036000C2semidirect
11. C4⋊C4×Dic293C2semidirect
12. #34035980C2semidirect
13. C4×C22⋊Dic293C2semidirect
14. #34035976C2semidirect
15. #385×C293C2semidirect
19. #22627610C4semidirect
57. C2×Dic586C2×C4semidirect
77. C22⋊Dic293C2×C4semidirect
81. #17989779C2×C4semidirect
82. #17989779C2×C4semidirect
89. C4×Dic293C2×C4semidirect
103. C22⋊C4×C293C2×C4semidirect
205. C293#2367semidirect
217. #385D293semidirect
302. C22⋊C4C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276102
C2×#226275892
C2×C4×C22⋊D2932
#340360332
#340360292
#340360222
#340360212
#340360192
#340360172
#340360002
C4⋊C4×Dic2932
#340359802
C4×C22⋊Dic2932
#340359762
#385×C2932
#2367293