Finite Group Databasebeta

← #49161691

Subgroups — #49161691

Order 37504.

704 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D293C211yesmaximal, characteristic
2C2×#22627584C211yesmaximal, characteristic
3C2×#22627584C211yesmaximal, characteristic
4#34036026C211yesmaximal, characteristic, complemented
5#34036024C211yesmaximal, characteristic, complemented
6#34036004C211yesmaximal, characteristic, complemented
7#34036003C211yesmaximal, characteristic, complemented
8#34036000C211yesmaximal, characteristic, complemented
9#34035993C211yesmaximal, characteristic, complemented
10#34035987C211yesmaximal, characteristic, complemented
11#34035986C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic293C211yesmaximal, characteristic, complemented
13C2×#22627531C211yesmaximal, characteristic, complemented
14#95×D293C211yesmaximal, characteristic, complemented
15#385×C293C211yesmaximal, characteristic, complemented
16C22×C22⋊D293C2211yescharacteristic
17C23×Dic293C2211yescharacteristic
18C23×Dic293C2211yescharacteristic
19C22×C4×D293C2211yescharacteristic
20C22×C4×D293C2211yescharacteristic
21C22×C4×D293C2211yescharacteristic
22C4×C22⋊D293—24no—
23#22627584—24no—
24#22627584C418yescomplemented
25C2×C4⋊Dic293C2211yescharacteristic
26C2×C4⋊Dic293C2211yescharacteristic
27C2×#17989781C2211yescharacteristic
28C2×#17989781C2211yescharacteristic
29C2×#17989781C2211yescharacteristic
30C2×#17989781C2211yescharacteristic
31C2×#17989781C2211yescharacteristic
32C2×C22⋊Dic293C2211yescharacteristic
33C2×#17989779C2211yescharacteristic
34C2×#17989779C2211yescharacteristic
35C2×#17989779C2211yescharacteristic
36C2×C4×Dic293C2211yescharacteristic
37C2×C4×Dic293C2211yescharacteristic
38C2×C4×Dic293C2211yescharacteristic
39#22627531C2211yescharacteristic
40#22627531C2211yescharacteristic
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×C22⋊D293C2×C414yes—
56C2×C22⋊D293D414yes—
57C2×C22⋊D293Q814yes—
58C22×Dic293—22no—
59C22×Dic293—22no—
60C22×Dic293—41no—
61C22×Dic293—41no—
62C22×Dic293—41no—
63C22×Dic293C2×C414yescomplemented
64C22×Dic293C2311yescharacteristic
65C22×Dic293C2311yescharacteristic
66C22×Dic293C2311yescharacteristic
67C22×Dic293C2311yescharacteristic
68C22×Dic293C2311yescharacteristic
69C22×Dic293C2311yescharacteristic
70C22×Dic293C2311yescharacteristic
71C2×C4×D293—22no—
72C2×C4×D293—22no—
73C2×C4×D293—22no—
74C2×C4×D293—22no—
75C2×C4×D293—41no—
76C2×C4×D293—41no—
77C2×C4×D293—41no—
78C2×C4×D293—41no—
79C2×C4×D293C2×C414yescomplemented
80C4⋊Dic293—22no—
81C4⋊Dic293—41no—
82#17989781—22no—
83#17989781—22no—
84#17989781—41no—
85#17989781—41no—
86#17989781C2×C414yescomplemented
87C22⋊Dic293—22no—
88#17989779—22no—
89#17989779—22no—
90#17989779C2×C414yescomplemented
91C4×Dic293—22no—
92C4×Dic293—22no—
93C4×Dic293C2×C414yescomplemented
94C24×C293C2311yescharacteristic
95C22×C4×C293—22no—
96C22×C4×C293—22no—
97C22×C4×C293—41no—
98C22×C4×C293C2311yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C22×C4×C293C2311yescharacteristic
101C22×C4×C293C2311yescharacteristic
102C22×C4×C293C2311yescharacteristic
103C22×C4×C293C2311yescharacteristic
104C4⋊C4×C293—22no—
105C4⋊C4×C293—41no—
106C22⋊C4×C293—22no—
107C22⋊C4×C293C2×C414yescomplemented
108C22×D293—21no—
109C22×D293—21no—
110C22×D293—21no—
111C22×D293—21no—
112C22×D293C22×C412yes—
113C22×D293C2×D412yes—
114C22×D293C2×Q812yes—
115C22⋊D293C4⋊C4116yescomplemented
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×Dic293—21no—
128C2×Dic293—21no—
129C2×Dic293—21no—
130C2×Dic293—21no—
131C2×Dic293—44no—
132C2×Dic293—44no—
133C2×Dic293C22×C412yes—
134C2×Dic293C22×C412yes—
135C2×Dic293C22×C412yes—
136C2×Dic293C2×D412yes—
137C2×Dic293C2×Q812yes—
138C2×Dic293#4112yes—
139C4×D293—44no—
140C4×D293—44no—
141C4×D293—44no—
142C23×C293—21no—
143C23×C293—21no—
144C23×C293—21no—
145C23×C293—21no—
146C23×C293C22×C412yes—
147C23×C293C2×D412yes—
148C23×C293C2×Q812yes—
149C23×C293C2411yescharacteristic
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—21no—
158C2×C4×C293—21no—
159C2×C4×C293—21no—
160C2×C4×C293—21no—
161C2×C4×C293—21no—
162C2×C4×C293—21no—
163C2×C4×C293—21no—
164C2×C4×C293—21no—
165C2×C4×C293—44no—
166C2×C4×C293C22×C412yes—
167C2×C4×C293C22×C412yes—
168C2×C4×C293#4112yes—
169C22×C293—22no—
170C22×C293—22no—
171C22×C293—22no—
172C22×C293—22no—
173C22×C293—22no—
174C22×C293—22no—
175C22×C293C2×C4⋊C414yes—
176C22×C293C23×C411yescharacteristic
177C22×C293C22×D411yescharacteristic
178C22×C293C22×Q811yescharacteristic
179C22×C293C2×#4111yescharacteristic
180C22×C293C2×#4111yescharacteristic
181C22×C293H(5,𝔽2)11yescharacteristic
182C22×C293H(5,𝔽2)11yescharacteristic
183C2×D293—22no—
184C2×D293—22no—
185C2×D293—22no—
186C2×D293—22no—
187C2×D293—22no—
188C2×D293—22no—
189C2×D293C2×C4⋊C414yes—
190C4×C293—22no—
191C4×C293—22no—
192C4×C293—22no—
193C4×C293—41no—
194C4×C293—41no—
195C4×C293—41no—
196Dic293—22no—
197Dic293—22no—
198Dic293—22no—
199Dic293—41no—
200Dic293—41no—
201Dic293—41no—
202Dic293C2×C4⋊C414yes—
203C2×C293—24no—
204C2×C293C22×C4⋊C411yescharacteristic
205C2×C293C4×#4111yescharacteristic
206C2×C293#51811yescharacteristic
207C2×C293#54611yescharacteristic
208C2×C293#54611yescharacteristic
209C2×C293#55411yescharacteristic
210C2×C293#55411yescharacteristic
211D293—24no—
212C293#234911yescharacteristic, complemented, Sylow
213#2349—2931nomaximal, Sylow
214C2×C4×D4—2931no—
215C2×C4×D4—2931no—
216C2×C4×D4—2931no—
217#389—2931no—
218#389—2931no—
219#385—2931no—
220#385—2931no—
221#385—2931no—
222#385D29311yescharacteristic, complemented
223#382—2931no—
224#380—2931no—
225#380—2931no—
226C4×C4⋊C4—2931no—
227C2×#95—2931no—
228C2×#95—2931no—
229C22×D4—2931no—
230C23×C4—2931no—
231C23×C4—2931no—
232C23×C4—2931no—
233C23×C4—2931no—
234C23×C4—2931no—
235C23×C4C2×D29311yescharacteristic
236C4×D4—2938no—
237C4×D4—5864no—
238C4×D4—5864no—
239C2×C4⋊C4—2931no—
240C2×C4⋊C4—2931no—
241C2×C4⋊C4—2931no—
242C2×C4⋊C4—2931no—
243C2×C4⋊C4—2931no—
244C2×C4⋊C4—2931no—
245C2×C4⋊C4—2931no—
246C2×C4⋊C4C2×D29311yescharacteristic
247C2×C4⋊C4C2×D29311yescharacteristic
248C2×C22⋊C4—2931no—
249C2×C22⋊C4—2931no—
250C2×C22⋊C4—2931no—
251C2×C22⋊C4—2931no—
252C2×C22⋊C4C2×D29311yescharacteristic
253C2×C22⋊C4C2×D29311yescharacteristic
254C2×C42—2931no—
255C2×C42—2931no—
256C2×C42—2931no—
257#95—2931no—
258#95—2931no—
259#95—2931no—
260#95—2931no—
261#95—2931no—
262#95—2931no—
263#95—2931no—
264#95—2931no—
265#95C2×D29311yescharacteristic
266#95C2×D29311yescharacteristic
267C24—2931no—
268C24C22×D29311yescharacteristic
269C2×D4—2934no—
270C2×D4—2934no—
271C2×D4—2934no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—2931no—
276C22×C4—2931no—
277C22×C4—2931no—
278C22×C4—2931no—
279C22×C4—2934no—
280C22×C4—2934no—
281C22×C4—2931no—
282C22×C4—2931no—
283C22×C4—2931no—
284C22×C4—5862no—
285C22×C4—5862no—
286C22×C4—5862no—
287C22×C4—5862no—
288C22×C4—5862no—
289C22×C4—5862no—
290C22×C4—11721no—
291C22×C4—11721no—
292C22×C4—11721no—
293C22×C4—11721no—
294C22×C4—11721no—
295C22×C4—11721no—
296C22×C4—11721no—
297C22×C4C22×D29311yescharacteristic
298C22×C4C22×D29311yescharacteristic
299C22×C4C22×D29311yescharacteristic
300C22×C4C22×D29311yescharacteristic
301C22×C4C22×D29311yescharacteristic
302C22×C4C22×D29311yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—2934no—
306C4⋊C4—5862no—
307C4⋊C4—5862no—
308C4⋊C4—5862no—
309C4⋊C4—11721no—
310C4⋊C4—11721no—
311C4⋊C4—11721no—
312C22⋊C4—22no—
313C22⋊C4—2934no—
314C22⋊C4—5862no—
315C22⋊C4—5862no—
316C22⋊C4—5862no—
317C22⋊C4C4×D29314yescomplemented
318C42—2934no—
319C42—5862no—
320C42—5862no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—2932no—
326C23—2932no—
327C23—2932no—
328C23—5861no—
329C23—5861no—
330C23—5861no—
331C23—5861no—
332C23C2×C4×D29312yes—
333C23D4×D29312yes—
334C23Q8×D29312yes—
335C23C23×D29311yescharacteristic
336D4—29316no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—44no—
353C2×C4—2932no—
354C2×C4—2932no—
355C2×C4—2932no—
356C2×C4—2932no—
357C2×C4—2932no—
358C2×C4—2932no—
359C2×C4—5861no—
360C2×C4—5861no—
361C2×C4—5861no—
362C2×C4—5861no—
363C2×C4—5861no—
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—11724no—
375C2×C4—11724no—
376C2×C4—11724no—
377C2×C4—11724no—
378C2×C4—11724no—
379C2×C4C2×C4×D29312yes—
380C2×C4C2×C4×D29312yes—
381C2×C4#1798980112yes—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—2934no—
389C22—5862no—
390C22—5862no—
391C22—5862no—
392C22—5862no—
393C22—5862no—
394C22—5862no—
395C22C4⋊C4×D29314yes—
396C22C22×C4×D29311yescharacteristic
397C22C2×D4×D29311yescharacteristic
398C22C2×Q8×D29311yescharacteristic
399C22#41×D29311yescharacteristic
400C22C2×#1798980111yescharacteristic
401C22#2262766911yescharacteristic
402C22#2262767011yescharacteristic
403C4—22no—
404C4—22no—
405C4—22no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—2934no—
410C4—5862no—
411C4—5862no—
412C4—5862no—
413C4—11721no—
414C4—11721no—
415C4—11721no—
416C2—24no—
417C2—5864no—
418C2C2×C4⋊C4×D29311yescharacteristic
419C2C4×#1798980111yescharacteristic
420C2#3403660111yescharacteristic
421C2#3403676611yescharacteristic
422C2#3403677111yescharacteristic
423C2#3403683311yescharacteristic
424C2#3403683711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#385×C293C2
socle, cosocleC23×C293C24
prime radicalC22×C22⋊D293C22
hypercenter#385D293
hypocenterC293#2349
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. #34036026C2semidirect
5. #34036024C2semidirect
6. #34036004C2semidirect
7. #34036003C2semidirect
8. #34036000C2semidirect
9. #34035993C2semidirect
10. #34035987C2semidirect
11. #34035986C2semidirect
12. C4⋊C4×Dic293C2semidirect
13. C2×#22627531C2semidirect
14. #95×D293C2semidirect
15. #385×C293C2semidirect
24. #22627584C4semidirect
63. C22×Dic293C2×C4semidirect
79. C2×C4×D293C2×C4semidirect
86. #17989781C2×C4semidirect
90. #17989779C2×C4semidirect
93. C4×Dic293C2×C4semidirect
107. C22⋊C4×C293C2×C4semidirect
115. C22⋊D293C4⋊C4semidirect
212. C293#2349semidirect
222. #385D293semidirect
317. C22⋊C4C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D2932
C2×#226275842
#340360262
#340360242
#340360042
#340360032
#340360002
#340359932
#340359872
#340359862
C4⋊C4×Dic2932
C2×#226275312
#95×D2932
#385×C2932
#2349293