Finite Group Databasebeta

← #34071870

Subgroups — #34071870

Order 19328.

596 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×#18012712C211yesmaximal, characteristic
2#23752114C211yesmaximal, characteristic, complemented
3#23752112C211yesmaximal, characteristic, complemented
4#23752105C211yesmaximal, characteristic, complemented
5#23752101C211yesmaximal, characteristic, complemented
6#23752099C211yesmaximal, characteristic, complemented
7#23752096C211yesmaximal, characteristic, complemented
8#23752091C211yesmaximal, characteristic, complemented
9#23752091C211yesmaximal, characteristic, complemented
10#23752090C211yesmaximal, characteristic, complemented
11#23752088C211yesmaximal, characteristic, complemented
12#23752074C211yesmaximal, characteristic, complemented
13C4×(C2×D151)⋊C4C211yesmaximal, characteristic, complemented
14C4×(C2×D151)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic
17C22×C22⋊D151C2211yescharacteristic
18C22×C22⋊D151C2211yescharacteristic
19C22×C4×D151C2211yescharacteristic
20C22×C4×D151C2211yescharacteristic
21#18012712C418yescomplemented
22C2×C4⋊Dic151C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×C22⋊Dic151C2211yescharacteristic
26C2×C22⋊Dic151C2211yescharacteristic
27C2×(C2×D151)⋊C4C2211yescharacteristic
28C2×(C2×D151)⋊C4C2211yescharacteristic
29C2×(C2×D151)⋊C4C2211yescharacteristic
30C2×(C2×D151)⋊C4C2211yescharacteristic
31C2×(C2×D151)⋊C4C2211yescharacteristic
32C2×(C2×D151)⋊C4C2211yescharacteristic
33C2×(C2×D151)⋊C4C2211yescharacteristic
34C2×(C2×D151)⋊C4C2211yescharacteristic
35C2×C4×Dic151C2211yescharacteristic
36C2×C4×Dic151C2211yescharacteristic
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C23×C4×C151C2211yescharacteristic
46C2×C22⋊C4×C151C2211yescharacteristic
47C2×C22⋊C4×C151C2211yescharacteristic
48C2×C42×C151C2211yescharacteristic
49C2×C42×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52C23×D151C2311yescharacteristic
53C23×D151C2311yescharacteristic
54C2×D604—41no—
55C2×D604—41no—
56C2×D604C2×C414yescomplemented
57C2×C22⋊D151—41no—
58C2×C22⋊D151—41no—
59C2×C22⋊D151—41no—
60C2×C22⋊D151—41no—
61C2×C22⋊D151C2×C414yes—
62C2×C22⋊D151C2×C414yescomplemented
63C22×Dic151C2311yescharacteristic
64C22×Dic151C2311yescharacteristic
65C22×Dic151C2311yescharacteristic
66C22×Dic151C2311yescharacteristic
67C22×Dic151C2311yescharacteristic
68C22×Dic151C2311yescharacteristic
69C2×C4×D151—22no—
70C2×C4×D151—41no—
71C2×C4×D151—41no—
72C2×C4×D151—41no—
73C2×C4×D151—41no—
74C2×C4×D151C2×C414yescomplemented
75C4⋊Dic151—41no—
76Dic151⋊C4—41no—
77Dic151⋊C4C2×C414yescomplemented
78C22⋊Dic151—41no—
79C22⋊Dic151—41no—
80(C2×D151)⋊C4—22no—
81(C2×D151)⋊C4—22no—
82(C2×D151)⋊C4—22no—
83(C2×D151)⋊C4—41no—
84(C2×D151)⋊C4—41no—
85(C2×D151)⋊C4—41no—
86(C2×D151)⋊C4—41no—
87(C2×D151)⋊C4C2×C414yescomplemented
88C4×Dic151—41no—
89C4×Dic151—41no—
90C24×C151C2311yescharacteristic
91C22×C4×C151—22no—
92C22×C4×C151—41no—
93C22×C4×C151—41no—
94C22×C4×C151C2311yescharacteristic
95C22×C4×C151C2311yescharacteristic
96C22×C4×C151C2311yescharacteristic
97C22×C4×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C22⋊C4×C151—22no—
101C22⋊C4×C151C2×C414yescomplemented
102C42×C151—41no—
103C42×C151—41no—
104C22×D151—21no—
105C22×D151—21no—
106C22×D151—21no—
107C22×D151—21no—
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—21no—
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151C22×C412yes—
117C22×D151C22×C412yes—
118D604—44no—
119C22⋊D151—44no—
120C22⋊D151—44no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151C22×C412yes—
138C2×Dic151C22×C412yes—
139C4×D151—44no—
140C4×D151—44no—
141C23×C151—21no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151C22×C412yes—
148C23×C151C2411yescharacteristic
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—44no—
164C2×C4×C151C22×C412yes—
165C2×C4×C151C22×C412yes—
166C2×C4×C151#4112yes—
167C2×C4×C151#4112yes—
168C22×C151—22no—
169C22×C151—22no—
170C22×C151—22no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151C23×C411yescharacteristic
176C22×C151C2×#4111yescharacteristic
177C22×C151C2×#4111yescharacteristic
178C22×C151H(5,𝔽2)11yescharacteristic
179C22×C151H(5,𝔽2)11yescharacteristic
180C22×C151H(5,𝔽2)11yescharacteristic
181C22×C151H(5,𝔽2)11yescharacteristic
182C2×D151—22no—
183C2×D151—22no—
184C2×D151—22no—
185C2×D151—22no—
186C2×D151—22no—
187C2×D151—22no—
188C2×D151—41no—
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C2×D151—41no—
196C4×C151—22no—
197C4×C151—22no—
198C4×C151—22no—
199C4×C151—22no—
200C4×C151—41no—
201C4×C151—41no—
202Dic151—22no—
203Dic151—22no—
204Dic151—41no—
205Dic151—41no—
206Dic151—41no—
207Dic151—41no—
208C2×C151—42no—
209C2×C151C4×#4111yescharacteristic
210C2×C151#51811yescharacteristic
211C2×C151#51811yescharacteristic
212C2×C151#53811yescharacteristic
213C2×C151#53811yescharacteristic
214C2×C151#54011yescharacteristic
215C2×C151#54011yescharacteristic
216D151—42no—
217D151—42no—
218C151#233311yescharacteristic, complemented, Sylow
219#2333—1511nomaximal, Sylow
220C2×#121—1511no—
221#390—1511no—
222#390—1511no—
223#388—1511no—
224#388—1511no—
225#387—1511no—
226#387—1511no—
227#386—1511no—
228#386—1511no—
229#386—1511no—
230#386—1511no—
231#381—1511no—
232C4×C22⋊C4—1511no—
233C4×C22⋊C4—1511no—
234C4×C22⋊C4D15111yescharacteristic, complemented
235C22×D4—1511no—
236C22×D4—1511no—
237C22×D4—1511no—
238C23×C4—1511no—
239C23×C4—1511no—
240C23×C4C2×D15111yescharacteristic
241#121—1518no—
242C2×C4⋊C4—1511no—
243C2×C4⋊C4—1511no—
244C2×C4⋊C4—1511no—
245C2×C22⋊C4—1511no—
246C2×C22⋊C4—1511no—
247C2×C22⋊C4—1511no—
248C2×C22⋊C4—1511no—
249C2×C22⋊C4—1511no—
250C2×C22⋊C4—1511no—
251C2×C22⋊C4—1511no—
252C2×C22⋊C4—1511no—
253C2×C22⋊C4—1511no—
254C2×C22⋊C4—1511no—
255C2×C22⋊C4C2×D15111yescharacteristic
256C2×C22⋊C4C2×D15111yescharacteristic
257C2×C42—1511no—
258C2×C42—1511no—
259C2×C42C2×D15111yescharacteristic
260C2×C42C2×D15111yescharacteristic
261#95—1511no—
262#95—1511no—
263#95—1511no—
264#95—1511no—
265#95—1511no—
266#95—1511no—
267#95—1511no—
268#95—1511no—
269#95C2×D15111yescharacteristic
270#95C2×D15111yescharacteristic
271C24—1511no—
272C24—1511no—
273C24C22×D15111yescharacteristic
274C2×D4—6041no—
275C2×D4—6041no—
276C2×D4—6041no—
277C2×D4—6041no—
278C2×D4—6041no—
279C2×D4—6041no—
280C2×D4—1514no—
281C2×D4—1514no—
282C2×D4—1514no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—3022no—
287C22×C4—6041no—
288C22×C4—6041no—
289C22×C4—6041no—
290C22×C4—6041no—
291C22×C4—1511no—
292C22×C4—1511no—
293C22×C4—1511no—
294C22×C4—1511no—
295C22×C4—1511no—
296C22×C4—1511no—
297C22×C4—1514no—
298C22×C4C22×D15111yescharacteristic
299C22×C4C22×D15111yescharacteristic
300C22×C4C22×D15111yescharacteristic
301C22×C4C22×D15111yescharacteristic
302C22×C4C22×D15111yescharacteristic
303C22×C4C22×D15111yescharacteristic
304C4⋊C4—6041no—
305C4⋊C4—6041no—
306C4⋊C4—1514no—
307C22⋊C4—22no—
308C22⋊C4—3022no—
309C22⋊C4—3022no—
310C22⋊C4—3022no—
311C22⋊C4—6041no—
312C22⋊C4—6041no—
313C22⋊C4—6041no—
314C22⋊C4—6041no—
315C22⋊C4—6041no—
316C22⋊C4—6041no—
317C22⋊C4—1514no—
318C22⋊C4C4×D15114yescomplemented
319C42—41no—
320C42—41no—
321C42—6041no—
322C42—6041no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—3021no—
330C23—3021no—
331C23—3021no—
332C23—3021no—
333C23—3021no—
334C23—3021no—
335C23—3021no—
336C23—3021no—
337C23—3021no—
338C23—3021no—
339C23—3021no—
340C23—3021no—
341C23—1512no—
342C23—1512no—
343C23C2×C4×D15112yes—
344C23C23×D15111yescharacteristic
345D4—6044no—
346D4—6044no—
347D4—6044no—
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—44no—
363C2×C4—3021no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—3021no—
369C2×C4—3021no—
370C2×C4—3021no—
371C2×C4—3021no—
372C2×C4—3021no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—3021no—
379C2×C4—6044no—
380C2×C4—6044no—
381C2×C4—1512no—
382C2×C4—1512no—
383C2×C4C2×C4×D15112yes—
384C2×C4C2×C4×D15112yes—
385C2×C4#1455900412yes—
386C2×C4#1455900412yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—3022no—
395C22—3022no—
396C22—3022no—
397C22—3022no—
398C22—3022no—
399C22—3022no—
400C22—6041no—
401C22—6041no—
402C22—6041no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22C22×C4×D15111yescharacteristic
409C22C2×#1455900411yescharacteristic
410C22C2×#1455900411yescharacteristic
411C22#1801278411yescharacteristic
412C22#1801278411yescharacteristic
413C22#1801278511yescharacteristic
414C22#1801278511yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—3022no—
422C4—3022no—
423C4—6041no—
424C4—6041no—
425C4—6041no—
426C4—6041no—
427C2—42no—
428C2—6042no—
429C2—6042no—
430C2C4×#1455900411yescharacteristic
431C2#2375268411yescharacteristic
432C2#2375268411yescharacteristic
433C2#2375279511yescharacteristic
434C2#2375280011yescharacteristic
435C2#2375281311yescharacteristic
436C2#2375281711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
FittingC4×C22⋊C4×C151C2
socle, cosocleC23×C151C24
prime radicalC2×#18012712C2
hypercenterC4×C22⋊C4D151
hypocenterC151#2333
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #23752114C2semidirect
3. #23752112C2semidirect
4. #23752105C2semidirect
5. #23752101C2semidirect
6. #23752099C2semidirect
7. #23752096C2semidirect
8. #23752091C2semidirect
9. #23752091C2semidirect
10. #23752090C2semidirect
11. #23752088C2semidirect
12. #23752074C2semidirect
13. C4×(C2×D151)⋊C4C2semidirect
14. C4×(C2×D151)⋊C4C2semidirect
15. C4×C22⋊C4×C151C2semidirect
21. #18012712C4semidirect
56. C2×D604C2×C4semidirect
62. C2×C22⋊D151C2×C4semidirect
74. C2×C4×D151C2×C4semidirect
77. Dic151⋊C4C2×C4semidirect
87. (C2×D151)⋊C4C2×C4semidirect
101. C22⋊C4×C151C2×C4semidirect
218. C151#2333semidirect
234. C4×C22⋊C4D151semidirect
318. C22⋊C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127122
#237521142
#237521122
#237521052
#237521012
#237520992
#237520962
#237520912
#237520902
#237520882
#237520742
C4×(C2×D151)⋊C42
C4×C22⋊C4×C1512
#2333151