Finite Group Databasebeta

← #49161938

Subgroups — #49161938

Order 37504.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627597C211yesmaximal, characteristic
2#34036031C211yesmaximal, characteristic, complemented
3#34036029C211yesmaximal, characteristic, complemented
4#34036021C211yesmaximal, characteristic, complemented
5#34036016C211yesmaximal, characteristic, complemented
6#34036013C211yesmaximal, characteristic, complemented
7#34036007C211yesmaximal, characteristic, complemented
8#34036006C211yesmaximal, characteristic, complemented
9#34036006C211yesmaximal, characteristic, complemented
10#34036005C211yesmaximal, characteristic, complemented
11#34036004C211yesmaximal, characteristic, complemented
12#34036000C211yesmaximal, characteristic, complemented
13#34035991C211yesmaximal, characteristic, complemented
14#34035986C211yesmaximal, characteristic, complemented
15#388×C293C211yesmaximal, characteristic, complemented
16C22×D1172C2211yescharacteristic
17C22×C22⋊D293C2211yescharacteristic
18C22×C22⋊D293C2211yescharacteristic
19C23×Dic293C2211yescharacteristic
20C22×C4×D293C2211yescharacteristic
21C22×C4×D293C2211yescharacteristic
22#22627597C418yescomplemented
23C2×C4⋊Dic293C2211yescharacteristic
24C2×C4⋊Dic293C2211yescharacteristic
25C2×#17989781C2211yescharacteristic
26C2×#17989781C2211yescharacteristic
27C2×C22⋊Dic293C2211yescharacteristic
28C2×#17989779C2211yescharacteristic
29C2×#17989779C2211yescharacteristic
30C2×#17989779C2211yescharacteristic
31C2×#17989779C2211yescharacteristic
32C2×#17989779C2211yescharacteristic
33C2×#17989779C2211yescharacteristic
34C2×#17989779C2211yescharacteristic
35C2×#17989779C2211yescharacteristic
36C2×C4×Dic293C2211yescharacteristic
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
53C23×D293C2311yescharacteristic
54C2×D1172—41no—
55C2×D1172—41no—
56C2×D1172C2×C414yescomplemented
57C2×C22⋊D293—41no—
58C2×C22⋊D293—41no—
59C2×C22⋊D293—41no—
60C2×C22⋊D293—41no—
61C2×C22⋊D293C2×C414yes—
62C2×C22⋊D293C2×C414yescomplemented
63C22×Dic293—41no—
64C22×Dic293—41no—
65C22×Dic293—41no—
66C22×Dic293C2311yescharacteristic
67C22×Dic293C2311yescharacteristic
68C22×Dic293C2311yescharacteristic
69C22×Dic293C2311yescharacteristic
70C22×Dic293C2311yescharacteristic
71C22×Dic293C2311yescharacteristic
72C2×C4×D293—41no—
73C2×C4×D293—41no—
74C2×C4×D293—41no—
75C2×C4×D293—41no—
76C2×C4×D293—41no—
77C2×C4×D293C2×C414yescomplemented
78C4⋊Dic293—41no—
79C4⋊Dic293—41no—
80#17989781—41no—
81#17989781C2×C414yescomplemented
82C22⋊Dic293—41no—
83#17989779—41no—
84#17989779—41no—
85#17989779—41no—
86#17989779—41no—
87#17989779—41no—
88#17989779—41no—
89#17989779—41no—
90#17989779C2×C414yescomplemented
91C4×Dic293—41no—
92C24×C293C2311yescharacteristic
93C22×C4×C293C2311yescharacteristic
94C22×C4×C293C2311yescharacteristic
95C22×C4×C293C2311yescharacteristic
96C22×C4×C293C2311yescharacteristic
97C22×C4×C293C2311yescharacteristic
98C22×C4×C293C2311yescharacteristic
99C4⋊C4×C293—41no—
100C22⋊C4×C293—41no—
101C22⋊C4×C293—41no—
102C22⋊C4×C293C2×C414yescomplemented
103C42×C293—41no—
104C22×D293—21no—
105C22×D293—21no—
106C22×D293—21no—
107C22×D293—21no—
108C22×D293—21no—
109C22×D293—21no—
110C22×D293—21no—
111C22×D293—21no—
112C22×D293—21no—
113C22×D293—21no—
114C22×D293—21no—
115C22×D293—21no—
116C22×D293C22×C412yes—
117C22×D293C22×C412yes—
118D1172—44no—
119C22⋊D293—44no—
120C22⋊D293—44no—
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—21no—
132C2×Dic293—21no—
133C2×Dic293—21no—
134C2×Dic293—21no—
135C2×Dic293—21no—
136C2×Dic293—21no—
137C2×Dic293—44no—
138C2×Dic293C22×C412yes—
139C2×Dic293C22×C412yes—
140C4×D293—44no—
141C4×D293—44no—
142C23×C293—21no—
143C23×C293—21no—
144C23×C293—21no—
145C23×C293—21no—
146C23×C293—21no—
147C23×C293—21no—
148C23×C293C22×C412yes—
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—21no—
166C2×C4×C293C22×C412yes—
167C2×C4×C293C22×C412yes—
168C22×C293—22no—
169C22×C293—22no—
170C22×C293—22no—
171C22×C293—41no—
172C22×C293—41no—
173C22×C293—41no—
174C22×C293—41no—
175C22×C293C23×C411yescharacteristic
176C22×C293H(5,𝔽2)11yescharacteristic
177C22×C293H(5,𝔽2)11yescharacteristic
178C22×C293H(5,𝔽2)11yescharacteristic
179C22×C293H(5,𝔽2)11yescharacteristic
180C22×C293H(5,𝔽2)11yescharacteristic
181C22×C2932−1+411yescharacteristic
182C2×D293—22no—
183C2×D293—22no—
184C2×D293—22no—
185C2×D293—22no—
186C2×D293—22no—
187C2×D293—22no—
188C2×D293—41no—
189C2×D293—41no—
190C2×D293—41no—
191C2×D293—41no—
192C2×D293—41no—
193C2×D293—41no—
194C2×D293—41no—
195C2×D293—41no—
196C4×C293—22no—
197C4×C293—22no—
198C4×C293—41no—
199C4×C293—41no—
200C4×C293—41no—
201C4×C293—41no—
202Dic293—22no—
203Dic293—22no—
204Dic293—41no—
205Dic293—41no—
206Dic293—41no—
207Dic293—41no—
208C2×C293—42no—
209C2×C293#51811yescharacteristic
210C2×C293#51811yescharacteristic
211C2×C293#52011yescharacteristic
212C2×C293#56011yescharacteristic
213C2×C293#56011yescharacteristic
214C2×C293#56211yescharacteristic
215C2×C293#56211yescharacteristic
216D293—42no—
217D293—42no—
218C293#237711yescharacteristic, complemented, Sylow
219#2377—2931nomaximal, Sylow
220C2×#121—2931no—
221#390—2931no—
222#390—2931no—
223#388—2931no—
224#388D29311yescharacteristic, complemented
225#387—2931no—
226#387—2931no—
227#386—2931no—
228#386—2931no—
229#386—2931no—
230#386—2931no—
231#385—2931no—
232#385—2931no—
233#381—2931no—
234#380—2931no—
235C22×D4—2931no—
236C22×D4—2931no—
237C22×D4—2931no—
238C23×C4—2931no—
239C23×C4—2931no—
240C23×C4—2931no—
241#121—2938no—
242C2×C4⋊C4—2931no—
243C2×C4⋊C4—2931no—
244C2×C4⋊C4—2931no—
245C2×C4⋊C4—2931no—
246C2×C4⋊C4C2×D29311yescharacteristic
247C2×C22⋊C4—2931no—
248C2×C22⋊C4—2931no—
249C2×C22⋊C4—2931no—
250C2×C22⋊C4—2931no—
251C2×C22⋊C4—2931no—
252C2×C22⋊C4—2931no—
253C2×C22⋊C4—2931no—
254C2×C22⋊C4—2931no—
255C2×C22⋊C4—2931no—
256C2×C22⋊C4C2×D29311yescharacteristic
257C2×C22⋊C4C2×D29311yescharacteristic
258C2×C22⋊C4C2×D29311yescharacteristic
259C2×C42—2931no—
260C2×C42C2×D29311yescharacteristic
261#95—2931no—
262#95—2931no—
263#95—2931no—
264#95—2931no—
265#95—2931no—
266#95—2931no—
267#95—2931no—
268#95—2931no—
269#95C2×D29311yescharacteristic
270#95C2×D29311yescharacteristic
271C24—2931no—
272C24—2931no—
273C24C22×D29311yescharacteristic
274C2×D4—2934no—
275C2×D4—2934no—
276C2×D4—2934no—
277C2×D4—11721no—
278C2×D4—11721no—
279C2×D4—11721no—
280C2×D4—11721no—
281C2×D4—11721no—
282C2×D4—11721no—
283C22×C4—2931no—
284C22×C4—2931no—
285C22×C4—2934no—
286C22×C4—2931no—
287C22×C4—2931no—
288C22×C4—2931no—
289C22×C4—2931no—
290C22×C4—11721no—
291C22×C4—11721no—
292C22×C4—11721no—
293C22×C4—11721no—
294C22×C4—11721no—
295C22×C4—11721no—
296C22×C4—11721no—
297C22×C4—11721no—
298C22×C4C22×D29311yescharacteristic
299C22×C4C22×D29311yescharacteristic
300C22×C4C22×D29311yescharacteristic
301C22×C4C22×D29311yescharacteristic
302C22×C4C22×D29311yescharacteristic
303C22×C4C22×D29311yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—2934no—
306C4⋊C4—11721no—
307C4⋊C4—11721no—
308C4⋊C4—11721no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—2934no—
312C22⋊C4—11721no—
313C22⋊C4—11721no—
314C22⋊C4—11721no—
315C22⋊C4—11721no—
316C22⋊C4—11721no—
317C22⋊C4—11721no—
318C22⋊C4—11721no—
319C22⋊C4—11721no—
320C22⋊C4C4×D29314yescomplemented
321C42—41no—
322C42—11721no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—2932no—
330C23—2932no—
331C23—5861no—
332C23—5861no—
333C23—5861no—
334C23—5861no—
335C23—5861no—
336C23—5861no—
337C23—5861no—
338C23—5861no—
339C23—5861no—
340C23—5861no—
341C23—5861no—
342C23—5861no—
343C23C2×C4×D29312yes—
344C23C23×D29311yescharacteristic
345D4—11724no—
346D4—11724no—
347D4—11724no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—2932no—
365C2×C4—2932no—
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—5861no—
375C2×C4—5861no—
376C2×C4—5861no—
377C2×C4—5861no—
378C2×C4—5861no—
379C2×C4—5861no—
380C2×C4—5861no—
381C2×C4—5861no—
382C2×C4—11724no—
383C2×C4—11724no—
384C2×C4—11724no—
385C2×C4C2×C4×D29312yes—
386C2×C4C2×C4×D29312yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—5862no—
395C22—5862no—
396C22—5862no—
397C22—5862no—
398C22—5862no—
399C22—5862no—
400C22—11721no—
401C22—11721no—
402C22—11721no—
403C22—11721no—
404C22—11721no—
405C22—11721no—
406C22—11721no—
407C22—11721no—
408C22C22×C4×D29311yescharacteristic
409C22#2262766911yescharacteristic
410C22#2262766911yescharacteristic
411C22#2262767011yescharacteristic
412C22#2262767011yescharacteristic
413C22#2262767011yescharacteristic
414C22#2262767111yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—5862no—
422C4—5862no—
423C4—11721no—
424C4—11721no—
425C4—11721no—
426C4—11721no—
427C2—42no—
428C2—11722no—
429C2—11722no—
430C2#3403660111yescharacteristic
431C2#3403660111yescharacteristic
432C2#3403660911yescharacteristic
433C2#3403686711yescharacteristic
434C2#3403687011yescharacteristic
435C2#3403687311yescharacteristic
436C2#3403687611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#388×C293C2
socle, cosocleC23×C293C24
prime radicalC2×#22627597C2
hypercenter#388D293
hypocenterC293#2377
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #34036031C2semidirect
3. #34036029C2semidirect
4. #34036021C2semidirect
5. #34036016C2semidirect
6. #34036013C2semidirect
7. #34036007C2semidirect
8. #34036006C2semidirect
9. #34036006C2semidirect
10. #34036005C2semidirect
11. #34036004C2semidirect
12. #34036000C2semidirect
13. #34035991C2semidirect
14. #34035986C2semidirect
15. #388×C293C2semidirect
22. #22627597C4semidirect
56. C2×D1172C2×C4semidirect
62. C2×C22⋊D293C2×C4semidirect
77. C2×C4×D293C2×C4semidirect
81. #17989781C2×C4semidirect
90. #17989779C2×C4semidirect
102. C22⋊C4×C293C2×C4semidirect
218. C293#2377semidirect
224. #388D293semidirect
320. C22⋊C4C4×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226275972
#340360312
#340360292
#340360212
#340360162
#340360132
#340360072
#340360062
#340360052
#340360042
#340360002
#340359912
#340359862
#388×C2932
#2377293