Finite Group Databasebeta

← #49161724

Subgroups — #49161724

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×#22627586C211yesmaximal, characteristic
2#34036021C211yesmaximal, characteristic, complemented
3#34036019C211yesmaximal, characteristic, complemented
4#34036015C211yesmaximal, characteristic, complemented
5#34036007C211yesmaximal, characteristic
6#34036007C211yesmaximal, characteristic
7#34035996C211yesmaximal, characteristic, complemented
8#34035991C211yesmaximal, characteristic, complemented
9#34035986C211yesmaximal, characteristic, complemented
10C4×#17989779C211yesmaximal, characteristic, complemented
11C4×#17989779C211yesmaximal, characteristic, complemented
12#34035976C211yesmaximal, characteristic, complemented
13#34035974C211yesmaximal, characteristic, complemented
14#95×D293C211yesmaximal, characteristic, complemented
15#387×C293C211yesmaximal, characteristic, complemented
16C22×D1172C2211yescharacteristic
17C22×C4×D293C2211yescharacteristic
18C22×C4×D293C2211yescharacteristic
19C22×C4×D293C2211yescharacteristic
20C22×C4×D293C2211yescharacteristic
21#22627586C418yescomplemented
22C2×C4⋊Dic293C2211yescharacteristic
23C2×#17989779C2211yescharacteristic
24C2×#17989779C2211yescharacteristic
25C2×#17989779C2211yescharacteristic
26C2×#17989779C2211yescharacteristic
27C2×#17989779C2211yescharacteristic
28C2×#17989779C2211yescharacteristic
29C2×#17989779C2211yescharacteristic
30C2×#17989779C2211yescharacteristic
31C2×C4×Dic293C2211yescharacteristic
32C2×C4×Dic293C2211yescharacteristic
33C2×C4×Dic293C2211yescharacteristic
34C2×C4×Dic293C2211yescharacteristic
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
48#95×C293C2211yescharacteristic
49#95×C293C2211yescharacteristic
50#95×C293C2211yescharacteristic
51#95×C293C2211yescharacteristic
52C23×D293C2311yescharacteristic
53C23×D293C2311yescharacteristic
54C2×D1172—22no—
55C2×D1172—22no—
56C2×D1172C2×C414yes—
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×D293—41no—
72C2×C4×D293—41no—
73C2×C4×D293C2×C414yes—
74C2×C4×D293C2×C414yescomplemented
75C4⋊Dic293—41no—
76#17989779—22no—
77#17989779—22no—
78#17989779—22no—
79#17989779—22no—
80#17989779—41no—
81#17989779—41no—
82#17989779C2×C414yes—
83#17989779C2×C414yescomplemented
84C4×Dic293—22no—
85C4×Dic293—22no—
86C4×Dic293—41no—
87C4×Dic293C2×C414yescomplemented
88C22×C4×C293C2311yescharacteristic
89C22×C4×C293C2311yescharacteristic
90C22×C4×C293C2311yescharacteristic
91C22×C4×C293C2311yescharacteristic
92C22×C4×C293C2311yescharacteristic
93C22×C4×C293C2311yescharacteristic
94C22×C4×C293C2311yescharacteristic
95C4⋊C4×C293—41no—
96C4⋊C4×C293C2×C414yescomplemented
97C42×C293—41no—
98C22×D293—21no—
99C22×D293—21no—
100C22×D293—21no—
101C22×D293—21no—
102C22×D293—21no—
103C22×D293—21no—
104C22×D293—21no—
105C22×D293—21no—
106C22×D293—21no—
107C22×D293—21no—
108C22×D293C22×C412yes—
109C22×D293C22×C412yes—
110C22×D293#4112yes—
111C22×D293#4112yes—
112D1172—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×Dic293—21no—
128C2×Dic293C22×C412yes—
129C2×Dic293C22×C412yes—
130C2×Dic293#4112yes—
131C4×D293—44no—
132C4×D293—44no—
133C4×D293—44no—
134C4×D293—44no—
135C23×C293C2411yescharacteristic
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×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×C293C22×C412yes—
154C2×C4×C293C22×C412yes—
155C2×C4×C293C22×C412yes—
156C2×C4×C293#4112yes—
157C22×C293C23×C411yescharacteristic
158C22×C293C2×#4111yescharacteristic
159C22×C293C2×#4111yescharacteristic
160C22×C293C2×#4111yescharacteristic
161C22×C293C2×#4111yescharacteristic
162C22×C293H(5,𝔽2)11yescharacteristic
163C22×C293H(5,𝔽2)11yescharacteristic
164C2×D293—22no—
165C2×D293—22no—
166C2×D293—22no—
167C2×D293—22no—
168C2×D293—22no—
169C2×D293—22no—
170C2×D293—22no—
171C2×D293—22no—
172C2×D293—22no—
173C2×D293—41no—
174C2×D293—41no—
175C2×D293—41no—
176C2×D293—41no—
177C2×D293#11714yes—
178C4×C293—22no—
179C4×C293—22no—
180C4×C293—22no—
181C4×C293—22no—
182C4×C293—41no—
183C4×C293—41no—
184C4×C293—41no—
185Dic293—22no—
186Dic293—22no—
187Dic293—22no—
188Dic293—41no—
189Dic293—41no—
190Dic293—41no—
191C2×C293C2×#11711yescharacteristic
192C2×C293C4×#4111yescharacteristic
193C2×C293#51811yescharacteristic
194C2×C293#55111yescharacteristic
195C2×C293#55111yescharacteristic
196C2×C293#55311yescharacteristic
197C2×C293#55311yescharacteristic
198D293—24no—
199D293—42no—
200C293#235311yescharacteristic, complemented, Sylow
201#2353—2931nomaximal, Sylow
202C2×C4×D4—2931no—
203#388—2931no—
204#388—2931no—
205#387—2931no—
206#387D29311yescharacteristic, complemented
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⋊C4C2×D29311yescharacteristic
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⋊C4—2931no—
232C2×C22⋊C4—2931no—
233C2×C22⋊C4—2931no—
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#95C2×D29311yescharacteristic
250#95C2×D29311yescharacteristic
251#95C2×D29311yescharacteristic
252#95C2×D29311yescharacteristic
253C24—2931no—
254C24—2931no—
255C2×D4—2934no—
256C2×D4—5862no—
257C2×D4—5862no—
258C22×C4—2931no—
259C22×C4—2931no—
260C22×C4—2931no—
261C22×C4—2934no—
262C22×C4—2934no—
263C22×C4—2931no—
264C22×C4—2931no—
265C22×C4—2931no—
266C22×C4—5862no—
267C22×C4—5862no—
268C22×C4—5862no—
269C22×C4—5862no—
270C22×C4—11721no—
271C22×C4—11721no—
272C22×C4—11721no—
273C22×C4—11721no—
274C22×C4—11721no—
275C22×C4—11721no—
276C22×C4C22×D29311yescharacteristic
277C22×C4C22×D29311yescharacteristic
278C22×C4C22×D29311yescharacteristic
279C22×C4C22×D29311yescharacteristic
280C22×C4C22×D29311yescharacteristic
281C22×C4C22×D29311yescharacteristic
282C22×C4C22×D29311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—11721no—
285C4⋊C4C4×D29314yescomplemented
286C22⋊C4—2934no—
287C22⋊C4—2934no—
288C22⋊C4—5862no—
289C22⋊C4—5862no—
290C22⋊C4—5862no—
291C22⋊C4—5862no—
292C22⋊C4—11721no—
293C22⋊C4—11721no—
294C42—41no—
295C42—2934no—
296C42—5862no—
297C42—5862no—
298C42—11721no—
299C23—2932no—
300C23—2932no—
301C23—2932no—
302C23—2932no—
303C23—5861no—
304C23—5861no—
305C23—5861no—
306C23—5861no—
307C23—5861no—
308C23—5861no—
309C23—5861no—
310C23—5861no—
311C23—5861no—
312C23—5861no—
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—21no—
331C2×C4—21no—
332C2×C4—2932no—
333C2×C4—2932no—
334C2×C4—2932no—
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—11724no—
351C2×C4—11724no—
352C2×C4—11724no—
353C2×C4—11724no—
354C2×C4C2×C4×D29312yes—
355C2×C4C2×C4×D29312yes—
356C2×C4C2×C4×D29312yes—
357C2×C4#1798980312yes—
358C22—2934no—
359C22—5862no—
360C22—5862no—
361C22—5862no—
362C22—5862no—
363C22—5862no—
364C22—5862no—
365C22—5862no—
366C22—5862no—
367C22—5862no—
368C22—11721no—
369C22—11721no—
370C22—11721no—
371C22—11721no—
372C22C22×C4×D29311yescharacteristic
373C22#41×D29311yescharacteristic
374C22#41×D29311yescharacteristic
375C22#41×D29311yescharacteristic
376C22C2×#1798980311yescharacteristic
377C22#2262766911yescharacteristic
378C22#2262767011yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—5862no—
387C4—5862no—
388C4—5862no—
389C4—11721no—
390C4—11721no—
391C4—11721no—
392C2—5864no—
393C2—11722no—
394C2#117×D29311yescharacteristic
395C2C4×#1798980311yescharacteristic
396C2#3403660111yescharacteristic
397C2#3403680411yescharacteristic
398C2#3403680611yescharacteristic
399C2#3403682411yescharacteristic
400C2#3403683211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#387×C293C2
socle, cosocleC23×C293C24
prime radicalC22×D1172C22
hypercenter#387D293
hypocenterC293#2353
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #34036021C2semidirect
3. #34036019C2semidirect
4. #34036015C2semidirect
7. #34035996C2semidirect
8. #34035991C2semidirect
9. #34035986C2semidirect
10. C4×#17989779C2semidirect
11. C4×#17989779C2semidirect
12. #34035976C2semidirect
13. #34035974C2semidirect
14. #95×D293C2semidirect
15. #387×C293C2semidirect
21. #22627586C4semidirect
74. C2×C4×D293C2×C4semidirect
83. #17989779C2×C4semidirect
87. C4×Dic293C2×C4semidirect
96. C4⋊C4×C293C2×C4semidirect
200. C293#2353semidirect
206. #387D293semidirect
285. C4⋊C4C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226275862
#340360212
#340360192
#340360152
#340360072
#340359962
#340359912
#340359862
C4×#179897792
#340359762
#340359742
#95×D2932
#387×C2932
#2353293