Finite Group Databasebeta

← #49161869

Subgroups — #49161869

Order 37504.

548 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627602C211yesmaximal, characteristic
2#34036035C211yesmaximal, characteristic, complemented
3#34036033C211yesmaximal, characteristic, complemented
4#34036015C211yesmaximal, characteristic, complemented
5#34036013C211yesmaximal, characteristic, complemented
6#34036013C211yesmaximal, characteristic, complemented
7#34036010C211yesmaximal, characteristic, complemented
8#34036003C211yesmaximal, characteristic
9#34036000C211yesmaximal, characteristic
10#34035980C211yesmaximal, characteristic, complemented
11C4×#17989779C211yesmaximal, characteristic
12C4×#17989779C211yesmaximal, characteristic
13C4×#17989779C211yesmaximal, characteristic
14#95×D293C211yesmaximal, characteristic
15C4×C4⋊C4×C293C211yesmaximal, characteristic, complemented
16C22×Dic586C2211yescharacteristic
17C22×C4×D293C2211yescharacteristic
18C22×C4×D293C2211yescharacteristic
19C22×C4×D293C2211yescharacteristic
20#22627602C418yescomplemented
21C2×C4⋊Dic293C2211yescharacteristic
22C2×#17989781C2211yescharacteristic
23C2×#17989781C2211yescharacteristic
24C2×#17989781C2211yescharacteristic
25C2×#17989781C2211yescharacteristic
26C2×#17989779C2211yescharacteristic
27C2×#17989779C2211yescharacteristic
28C2×#17989779C2211yescharacteristic
29C2×#17989779C2211yescharacteristic
30C2×C4×Dic293C2211yescharacteristic
31C2×C4×Dic293C2211yescharacteristic
32C2×C4×Dic293C2211yescharacteristic
33#22627531C2211yescharacteristic
34#22627531C2211yescharacteristic
35#22627531C2211yescharacteristic
36#22627531C2211yescharacteristic
37#22627531C2211yescharacteristic
38#22627531C2211yescharacteristic
39#22627531C2211yescharacteristic
40#22627531C2211yescharacteristic
41#22627531C2211yescharacteristic
42#22627531C2211yescharacteristic
43#22627531C2211yescharacteristic
44#22627531C2211yescharacteristic
45C2×C4⋊C4×C293C2211yescharacteristic
46C2×C4⋊C4×C293C2211yescharacteristic
47C2×C42×C293C2211yescharacteristic
48C2×C42×C293C2211yescharacteristic
49C2×C42×C293C2211yescharacteristic
50#95×C293C2211yescharacteristic
51#95×C293C2211yescharacteristic
52C23×D293C2311yescharacteristic
53C2×Dic586—41no—
54C2×Dic586—41no—
55C2×Dic586C2×C414yescomplemented
56C22×Dic293C2311yescharacteristic
57C22×Dic293C2311yescharacteristic
58C22×Dic293C2311yescharacteristic
59C22×Dic293C2311yescharacteristic
60C22×Dic293C2311yescharacteristic
61C22×Dic293C2311yescharacteristic
62C22×Dic293C2311yescharacteristic
63C2×C4×D293—22no—
64C2×C4×D293—22no—
65C2×C4×D293—22no—
66C2×C4×D293—22no—
67C2×C4×D293—41no—
68C2×C4×D293—41no—
69C2×C4×D293—41no—
70C2×C4×D293—41no—
71C2×C4×D293C2×C414yes—
72C4⋊Dic293—41no—
73#17989781—22no—
74#17989781—41no—
75#17989781C2×C414yescomplemented
76#17989781C2×C414yescomplemented
77#17989779—22no—
78#17989779C2×C414yes—
79#17989779C2×C414yes—
80#17989779Q814yescomplemented
81C4×Dic293—22no—
82C4×Dic293—41no—
83C4×Dic293—41no—
84C22×C4×C293C2311yescharacteristic
85C22×C4×C293C2311yescharacteristic
86C22×C4×C293C2311yescharacteristic
87C22×C4×C293C2311yescharacteristic
88C22×C4×C293C2311yescharacteristic
89C22×C4×C293C2311yescharacteristic
90C22×C4×C293C2311yescharacteristic
91C4⋊C4×C293—22no—
92C4⋊C4×C293C2×C414yescomplemented
93C42×C293—22no—
94C42×C293—41no—
95C42×C293—41no—
96C22×D293—21no—
97C22×D293—21no—
98C22×D293—21no—
99C22×D293—21no—
100C22×D293C22×C412yes—
101C22×D293C2×Q812yes—
102C22×D293#4112yes—
103Dic586—44no—
104C2×Dic293—21no—
105C2×Dic293—21no—
106C2×Dic293—21no—
107C2×Dic293—21no—
108C2×Dic293—21no—
109C2×Dic293—21no—
110C2×Dic293—21no—
111C2×Dic293—21no—
112C2×Dic293—21no—
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×Dic293C22×C412yes—
122C2×Dic293C22×C412yes—
123C2×Dic293C22×C412yes—
124C2×Dic293C2×Q812yes—
125C4×D293—44no—
126C4×D293—44no—
127C4×D293—44no—
128C23×C293C2411yescharacteristic
129C2×C4×C293—21no—
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293C22×C412yes—
145C2×C4×C293C22×C412yes—
146C2×C4×C293C22×C412yes—
147C2×C4×C293C2×Q812yes—
148C2×C4×C293#4112yes—
149C2×C4×C293#4112yes—
150C22×C293C23×C411yescharacteristic
151C22×C293C22×Q811yescharacteristic
152C22×C293C2×#4111yescharacteristic
153C22×C293C2×#4111yescharacteristic
154C22×C293C2×#4111yescharacteristic
155C22×C293H(5,𝔽2)11yescharacteristic
156C22×C293H(5,𝔽2)11yescharacteristic
157C2×D293—22no—
158C2×D293—22no—
159C2×D293—22no—
160C2×D293—22no—
161C2×D293—22no—
162C2×D293—22no—
163C2×D293C4×Q814yes—
164C4×C293—22no—
165C4×C293—22no—
166C4×C293—22no—
167C4×C293—22no—
168C4×C293—22no—
169C4×C293—22no—
170C4×C293—41no—
171Dic293—22no—
172Dic293—22no—
173Dic293—22no—
174Dic293—22no—
175Dic293—41no—
176Dic293—41no—
177Dic293—41no—
178C2×C293C2×C4×Q811yescharacteristic
179C2×C293C4×#4111yescharacteristic
180C2×C293#51811yescharacteristic
181C2×C293#55111yescharacteristic
182C2×C293#55111yescharacteristic
183C2×C293#55411yescharacteristic
184C2×C293#55411yescharacteristic
185D293—24no—
186C293#236811yescharacteristic, complemented, Sylow
187#2368—2931nomaximal, Sylow
188C2×C22⋊Q8—2931no—
189#391—2931no—
190#391—2931no—
191#387—2931no—
192#387—2931no—
193#387—2931no—
194#387—2931no—
195#385—2931no—
196#385—2931no—
197C4×C4⋊C4—2931no—
198C4×C4⋊C4D29311yescharacteristic, complemented
199C4×C22⋊C4—2931no—
200C4×C22⋊C4—2931no—
201C4×C22⋊C4—2931no—
202C2×#95—2931no—
203C22×Q8—2931no—
204C23×C4—2931no—
205C23×C4—2931no—
206C23×C4—2931no—
207C22⋊Q8—2938no—
208C2×C4⋊C4—2931no—
209C2×C4⋊C4—2931no—
210C2×C4⋊C4—2931no—
211C2×C4⋊C4—2931no—
212C2×C4⋊C4—2931no—
213C2×C4⋊C4C2×D29311yescharacteristic
214C2×C4⋊C4C2×D29311yescharacteristic
215C2×C22⋊C4—2931no—
216C2×C22⋊C4—2931no—
217C2×C22⋊C4—2931no—
218C2×C22⋊C4—2931no—
219C2×C42—2931no—
220C2×C42—2931no—
221C2×C42—2931no—
222C2×C42C2×D29311yescharacteristic
223C2×C42C2×D29311yescharacteristic
224C2×C42C2×D29311yescharacteristic
225#95—2931no—
226#95—2931no—
227#95—2931no—
228#95—2931no—
229#95—2931no—
230#95—2931no—
231#95—2931no—
232#95—2931no—
233#95—2931no—
234#95—2931no—
235#95—2931no—
236#95—2931no—
237#95C2×D29311yescharacteristic
238#95C2×D29311yescharacteristic
239C24—2931no—
240C2×Q8—2934no—
241C2×Q8—11721no—
242C2×Q8—11721no—
243C22×C4—2931no—
244C22×C4—2931no—
245C22×C4—2931no—
246C22×C4—2931no—
247C22×C4—2934no—
248C22×C4—2931no—
249C22×C4—2931no—
250C22×C4—2931no—
251C22×C4—5862no—
252C22×C4—5862no—
253C22×C4—5862no—
254C22×C4—5862no—
255C22×C4—11721no—
256C22×C4—11721no—
257C22×C4—11721no—
258C22×C4—11721no—
259C22×C4C22×D29311yescharacteristic
260C22×C4C22×D29311yescharacteristic
261C22×C4C22×D29311yescharacteristic
262C22×C4C22×D29311yescharacteristic
263C22×C4C22×D29311yescharacteristic
264C22×C4C22×D29311yescharacteristic
265C22×C4C22×D29311yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—2934no—
268C4⋊C4—2934no—
269C4⋊C4—5862no—
270C4⋊C4—11721no—
271C4⋊C4—11721no—
272C4⋊C4C4×D29314yescomplemented
273C22⋊C4—2934no—
274C22⋊C4—2934no—
275C22⋊C4—2934no—
276C22⋊C4—5862no—
277C42—22no—
278C42—41no—
279C42—41no—
280C42—5862no—
281C42—11721no—
282C42—11721no—
283C23—2932no—
284C23—2932no—
285C23—2932no—
286C23—5861no—
287C23—5861no—
288C23—5861no—
289C23—5861no—
290C23C23×D29311yescharacteristic
291Q8—11724no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—2932no—
308C2×C4—2932no—
309C2×C4—2932no—
310C2×C4—2932no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—11724no—
329C2×C4—11724no—
330C2×C4—11724no—
331C2×C4C2×C4×D29312yes—
332C2×C4C2×C4×D29312yes—
333C2×C4C2×C4×D29312yes—
334C2×C4Q8×D29312yes—
335C2×C4#1798980212yes—
336C2×C4#1798980212yes—
337C22—2934no—
338C22—5862no—
339C22—5862no—
340C22—5862no—
341C22—5862no—
342C22—5862no—
343C22—5862no—
344C22C22×C4×D29311yescharacteristic
345C22C2×Q8×D29311yescharacteristic
346C22#41×D29311yescharacteristic
347C22C2×#1798980211yescharacteristic
348C22C2×#1798980211yescharacteristic
349C22#2262766911yescharacteristic
350C22#2262767011yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—5862no—
359C4—5862no—
360C4—5862no—
361C4—5862no—
362C4—11721no—
363C4—11721no—
364C4—11721no—
365C2—5864no—
366C2C4×Q8×D29311yescharacteristic
367C2C4×#1798980211yescharacteristic
368C2#3403660111yescharacteristic
369C2#3403680311yescharacteristic
370C2#3403680811yescharacteristic
371C2#3403683411yescharacteristic
372C2#3403683911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
FittingC4×C4⋊C4×C293C2
socle, cosocleC23×C293C24
prime radicalC23×D293C23
hypercenterC4×C4⋊C4D293
hypocenterC293#2368
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #34036035C2semidirect
3. #34036033C2semidirect
4. #34036015C2semidirect
5. #34036013C2semidirect
6. #34036013C2semidirect
7. #34036010C2semidirect
10. #34035980C2semidirect
15. C4×C4⋊C4×C293C2semidirect
20. #22627602C4semidirect
55. C2×Dic586C2×C4semidirect
75. #17989781C2×C4semidirect
76. #17989781C2×C4semidirect
80. #17989779Q8semidirect
92. C4⋊C4×C293C2×C4semidirect
186. C293#2368semidirect
198. C4×C4⋊C4D293semidirect
272. C4⋊C4C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276022
#340360352
#340360332
#340360152
#340360132
#340360102
#340360032
#340360002
#340359802
C4×#179897792
#95×D2932
C4×C4⋊C4×C2932
#2368293