Finite Group Databasebeta

← #49161720

Subgroups — #49161720

Order 37504.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627584C211yesmaximal, characteristic
2#34036022C211yesmaximal, characteristic, complemented
3#34036016C211yesmaximal, characteristic, complemented
4#34036010C211yesmaximal, characteristic, complemented
5#34036005C211yesmaximal, characteristic
6#34036005C211yesmaximal, characteristic
7#34035996C211yesmaximal, characteristic, complemented
8#34035990C211yesmaximal, characteristic, complemented
9#34035986C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic293C211yesmaximal, characteristic, complemented
11C4×#17989779C211yesmaximal, characteristic, complemented
12#34035976C211yesmaximal, characteristic, complemented
13#34035975C211yesmaximal, characteristic, complemented
14#95×D293C211yesmaximal, characteristic, complemented
15#388×C293C211yesmaximal, characteristic, complemented
16C22×C22⋊D293C2211yescharacteristic
17C23×Dic293C2211yescharacteristic
18C22×C4×D293C2211yescharacteristic
19C22×C4×D293C2211yescharacteristic
20C22×C4×D293C2211yescharacteristic
21#22627584C418yescomplemented
22C2×C4⋊Dic293C2211yescharacteristic
23C2×#17989781C2211yescharacteristic
24C2×C22⋊Dic293C2211yescharacteristic
25C2×C22⋊Dic293C2211yescharacteristic
26C2×#17989779C2211yescharacteristic
27C2×#17989779C2211yescharacteristic
28C2×#17989779C2211yescharacteristic
29C2×C4×Dic293C2211yescharacteristic
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×C22⋊C4×C293C2211yescharacteristic
47C2×C22⋊C4×C293C2211yescharacteristic
48C2×C22⋊C4×C293C2211yescharacteristic
49C2×C42×C293C2211yescharacteristic
50#95×C293C2211yescharacteristic
51#95×C293C2211yescharacteristic
52C23×D293C2311yescharacteristic
53C2×C22⋊D293—22no—
54C2×C22⋊D293—22no—
55C2×C22⋊D293C2×C414yes—
56C22×Dic293—41no—
57C22×Dic293—41no—
58C22×Dic293C2×C414yescomplemented
59C22×Dic293C2311yescharacteristic
60C22×Dic293C2311yescharacteristic
61C22×Dic293C2311yescharacteristic
62C22×Dic293C2311yescharacteristic
63C22×Dic293C2311yescharacteristic
64C22×Dic293C2311yescharacteristic
65C22×Dic293C2311yescharacteristic
66C2×C4×D293—22no—
67C2×C4×D293—22no—
68C2×C4×D293—22no—
69C2×C4×D293—22no—
70C2×C4×D293—41no—
71C2×C4×D293—41no—
72C2×C4×D293—41no—
73C2×C4×D293—41no—
74C2×C4×D293C2×C414yes—
75C4⋊Dic293—41no—
76#17989781C2×C414yescomplemented
77C22⋊Dic293—22no—
78C22⋊Dic293—41no—
79#17989779—22no—
80#17989779—22no—
81#17989779C2×C414yes—
82C4×Dic293—22no—
83C4×Dic293—41no—
84C4×Dic293—41no—
85C4×Dic293C2×C414yescomplemented
86C24×C293C2311yescharacteristic
87C22×C4×C293C2311yescharacteristic
88C22×C4×C293C2311yescharacteristic
89C22×C4×C293C2311yescharacteristic
90C22×C4×C293C2311yescharacteristic
91C22×C4×C293C2311yescharacteristic
92C22×C4×C293C2311yescharacteristic
93C4⋊C4×C293—41no—
94C22⋊C4×C293—22no—
95C22⋊C4×C293—41no—
96C22⋊C4×C293C2×C414yescomplemented
97C42×C293—22no—
98C22×D293—21no—
99C22×D293—21no—
100C22×D293—21no—
101C22×D293—21no—
102C22×D293C22×C412yes—
103C22×D293#4112yes—
104C22×D293#4112yes—
105C22⋊D293—28no—
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×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—44no—
124C2×Dic293C22×C412yes—
125C2×Dic293C22×C412yes—
126C2×Dic293C22×C412yes—
127C2×Dic293#4112yes—
128C4×D293—44no—
129C4×D293—44no—
130C4×D293—44no—
131C23×C293—21no—
132C23×C293—21no—
133C23×C293—21no—
134C23×C293—21no—
135C23×C293—21no—
136C23×C293—21no—
137C23×C293C22×C412yes—
138C23×C293C2411yescharacteristic
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
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×C293C22×C412yes—
155C2×C4×C293C22×C412yes—
156C2×C4×C293#4112yes—
157C22×C293—22no—
158C22×C293—22no—
159C22×C293—22no—
160C22×C293—41no—
161C22×C293—41no—
162C22×C293—41no—
163C22×C293—41no—
164C22×C293C23×C411yescharacteristic
165C22×C293C2×#4111yescharacteristic
166C22×C293C2×#4111yescharacteristic
167C22×C293C2×#4111yescharacteristic
168C22×C293C2×#4111yescharacteristic
169C22×C293H(5,𝔽2)11yescharacteristic
170C22×C293H(5,𝔽2)11yescharacteristic
171C2×D293—22no—
172C2×D293—22no—
173C2×D293—22no—
174C2×D293—22no—
175C2×D293—22no—
176C2×D293—22no—
177C2×D293#11714yes—
178C4×C293—22no—
179C4×C293—22no—
180C4×C293—22no—
181C4×C293—41no—
182C4×C293—41no—
183C4×C293—41no—
184Dic293—22no—
185Dic293—22no—
186Dic293—22no—
187Dic293—22no—
188Dic293—41no—
189Dic293—41no—
190Dic293—41no—
191C2×C293—42no—
192C2×C293C2×#11711yescharacteristic
193C2×C293C4×#4111yescharacteristic
194C2×C293#51811yescharacteristic
195C2×C293#55111yescharacteristic
196C2×C293#55111yescharacteristic
197C2×C293#55311yescharacteristic
198C2×C293#55311yescharacteristic
199D293—24no—
200C293#235311yescharacteristic, complemented, Sylow
201#2353—2931nomaximal, Sylow
202C2×C4×D4—2931no—
203#388—2931no—
204#388D29311yescharacteristic, complemented
205#387—2931no—
206#387—2931no—
207#386—2931no—
208#386—2931no—
209#383—2931no—
210#381—2931no—
211#380—2931no—
212C4×C22⋊C4—2931no—
213C4×C22⋊C4—2931no—
214C4×C22⋊C4—2931no—
215#376—2931no—
216C2×#95—2931no—
217C22×D4—2931no—
218C23×C4—2931no—
219C23×C4—2931no—
220C23×C4—2931no—
221C23×C4—2931no—
222C4×D4—2938no—
223C2×C4⋊C4—2931no—
224C2×C4⋊C4—2931no—
225C2×C4⋊C4C2×D29311yescharacteristic
226C2×C22⋊C4—2931no—
227C2×C22⋊C4—2931no—
228C2×C22⋊C4—2931no—
229C2×C22⋊C4—2931no—
230C2×C22⋊C4—2931no—
231C2×C22⋊C4C2×D29311yescharacteristic
232C2×C22⋊C4C2×D29311yescharacteristic
233C2×C22⋊C4C2×D29311yescharacteristic
234C2×C42—2931no—
235C2×C42—2931no—
236C2×C42—2931no—
237C2×C42—2931no—
238C2×C42C2×D29311yescharacteristic
239#95—2931no—
240#95—2931no—
241#95—2931no—
242#95—2931no—
243#95—2931no—
244#95—2931no—
245#95—2931no—
246#95—2931no—
247#95—2931no—
248#95—2931no—
249#95—2931no—
250#95—2931no—
251#95C2×D29311yescharacteristic
252#95C2×D29311yescharacteristic
253C24—2931no—
254C24C22×D29311yescharacteristic
255C2×D4—2934no—
256C2×D4—5862no—
257C2×D4—5862no—
258C22×C4—2931no—
259C22×C4—2931no—
260C22×C4—2931no—
261C22×C4—2931no—
262C22×C4—2934no—
263C22×C4—2934no—
264C22×C4—2931no—
265C22×C4—2931no—
266C22×C4—2931no—
267C22×C4—5862no—
268C22×C4—5862no—
269C22×C4—5862no—
270C22×C4—5862no—
271C22×C4—11721no—
272C22×C4—11721no—
273C22×C4—11721no—
274C22×C4—11721no—
275C22×C4—11721no—
276C22×C4—11721no—
277C22×C4C22×D29311yescharacteristic
278C22×C4C22×D29311yescharacteristic
279C22×C4C22×D29311yescharacteristic
280C22×C4C22×D29311yescharacteristic
281C22×C4C22×D29311yescharacteristic
282C22×C4C22×D29311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—2934no—
285C4⋊C4—11721no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—2934no—
289C22⋊C4—5862no—
290C22⋊C4—5862no—
291C22⋊C4—5862no—
292C22⋊C4—11721no—
293C22⋊C4C4×D29314yescomplemented
294C42—22no—
295C42—2934no—
296C42—5862no—
297C42—11721no—
298C42—11721no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—2932no—
306C23—2932no—
307C23—2932no—
308C23—5861no—
309C23—5861no—
310C23—5861no—
311C23—5861no—
312C23C2×C4×D29312yes—
313C23C23×D29311yescharacteristic
314D4—5868no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2932no—
331C2×C4—2932no—
332C2×C4—2932no—
333C2×C4—2932no—
334C2×C4—5861no—
335C2×C4—5861no—
336C2×C4—5861no—
337C2×C4—5861no—
338C2×C4—5861no—
339C2×C4—5861no—
340C2×C4—5861no—
341C2×C4—5861no—
342C2×C4—5861no—
343C2×C4—5861no—
344C2×C4—5861no—
345C2×C4—5861no—
346C2×C4—5861no—
347C2×C4—5861no—
348C2×C4—5861no—
349C2×C4—5861no—
350C2×C4—5861no—
351C2×C4—11724no—
352C2×C4—11724no—
353C2×C4—11724no—
354C2×C4—11724no—
355C2×C4C2×C4×D29312yes—
356C2×C4C2×C4×D29312yes—
357C2×C4#1798980112yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—2934no—
366C22—5862no—
367C22—5862no—
368C22—5862no—
369C22—5862no—
370C22—5862no—
371C22—5862no—
372C22C22×C4×D29311yescharacteristic
373C22#41×D29311yescharacteristic
374C22#41×D29311yescharacteristic
375C22#41×D29311yescharacteristic
376C22C2×#1798980111yescharacteristic
377C22#2262766911yescharacteristic
378C22#2262767011yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—5862no—
386C4—5862no—
387C4—5862no—
388C4—5862no—
389C4—11721no—
390C4—11721no—
391C4—11721no—
392C2—42no—
393C2—5864no—
394C2#117×D29311yescharacteristic
395C2C4×#1798980111yescharacteristic
396C2#3403660111yescharacteristic
397C2#3403680211yescharacteristic
398C2#3403680911yescharacteristic
399C2#3403682611yescharacteristic
400C2#3403683011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#388×C293C2
socle, cosocleC23×C293C24
prime radicalC22×C22⋊D293C22
hypercenter#388D293
hypocenterC293#2353
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #34036022C2semidirect
3. #34036016C2semidirect
4. #34036010C2semidirect
7. #34035996C2semidirect
8. #34035990C2semidirect
9. #34035986C2semidirect
10. C22⋊C4×Dic293C2semidirect
11. C4×#17989779C2semidirect
12. #34035976C2semidirect
13. #34035975C2semidirect
14. #95×D293C2semidirect
15. #388×C293C2semidirect
21. #22627584C4semidirect
58. C22×Dic293C2×C4semidirect
76. #17989781C2×C4semidirect
85. C4×Dic293C2×C4semidirect
96. C22⋊C4×C293C2×C4semidirect
200. C293#2353semidirect
204. #388D293semidirect
293. C22⋊C4C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226275842
#340360222
#340360162
#340360102
#340360052
#340359962
#340359902
#340359862
C22⋊C4×Dic2932
C4×#179897792
#340359762
#340359752
#95×D2932
#388×C2932
#2353293