Finite Group Databasebeta

← #34078767

Subgroups — #34078767

Order 19328.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012760C211yesmaximal, characteristic, complemented
2C2×#18012745C211yesmaximal, characteristic, complemented
3#23752792C211yesmaximal, characteristic, complemented
4#23752791C211yesmaximal, characteristic, complemented
5#23752469C211yesmaximal, characteristic, complemented
6#23752468C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752463C211yesmaximal, characteristic, complemented
9#23752442C211yesmaximal, characteristic, complemented
10#23752441C211yesmaximal, characteristic, complemented
11#23752438C211yesmaximal, characteristic, complemented
12#106×D151C211yesmaximal, characteristic, complemented
13#23752212C211yesmaximal, characteristic, complemented
14#23752210C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14559003C2211yescharacteristic
19#18012760—24no—
20C2×#14558994C2211yescharacteristic
21C2×#14558993C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23#18012745—24no—
24C2×#14558988C2211yescharacteristic
25C2×#14558987C2211yescharacteristic
26C2×#14558987C2211yescharacteristic
27C2×C8×D151C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012719C2211yescharacteristic
30#18012718C2211yescharacteristic
31#18012717—21no—
32#18012716—21no—
33#18012715C2211yescharacteristic
34#18012714—21no—
35#18012714C2211yescharacteristic
36#18012713C2211yescharacteristic
37#18012712—21no—
38#18012712—21no—
39#18012712—21no—
40#18012711—21no—
41#18012710—21no—
42#18012710C2211yescharacteristic
43C4⋊C4×D151C2211yescharacteristic
44C4⋊C4×D151C2211yescharacteristic
45#18012671C2211yescharacteristic
46#18012670C2211yescharacteristic
47#18012670C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012663C2211yescharacteristic
50#18012662C2211yescharacteristic
51#18012661C2211yescharacteristic
52#18012660C2211yescharacteristic
53#18012659C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22×C8×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#106×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—22no—
63#14559004—22no—
64#14559004—22no—
65#14559003—22no—
66#14559003—22no—
67C2×Dic302D411yescharacteristic
68C2×Dic302C2311yescharacteristic
69C2×D604—21no—
70C2×D604—21no—
71C2×D604D411yescharacteristic
72C2×D604C2311yescharacteristic
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151D411yescharacteristic
77C2×C22⋊D151D411yescharacteristic
78C22×Dic151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151—21no—
82C2×C4×D151C2311yescharacteristic
83C2×C4×D151C2311yescharacteristic
84#14558994—22no—
85#14558993—22no—
86#14558989—22no—
87#14558988—22no—
88#14558987—22no—
89#14558987—22no—
90C2×C151⋊C8C2311yescharacteristic
91C2×C151⋊C8C2311yescharacteristic
92C8×D151—22no—
93C8×D151D414yescomplemented
94C4⋊Dic151—21no—
95C4⋊Dic151C2311yescharacteristic
96C4⋊Dic151C2311yescharacteristic
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99Dic151⋊C4—21no—
100Dic151⋊C4—21no—
101C22⋊Dic151—21no—
102C22⋊Dic151—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107C2×Q8×C151C2311yescharacteristic
108C2×D4×C151—21no—
109C2×D4×C151C2311yescharacteristic
110C22×C4×C151C2311yescharacteristic
111SD16×C151—22no—
112C2×C8×C151—22no—
113C2×C8×C151C2311yescharacteristic
114C2×C8×C151C2311yescharacteristic
115C4⋊C4×C151—21no—
116C4⋊C4×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22×D151—21no—
121C22×D151C2×D411yescharacteristic
122C22×D151C2×D411yescharacteristic
123Dic302—22no—
124Dic302—21no—
125Dic302—21no—
126D604—22no—
127D604—21no—
128D604—21no—
129D604—42no—
130D604—81no—
131C22⋊D151—22no—
132C22⋊D151—22no—
133C22⋊D151—42no—
134C22⋊D151—81no—
135C22⋊D151—81no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C2×Dic151—42no—
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C4×D151—21no—
143C4×D151—21no—
144C4×D151—42no—
145C4×D151—81no—
146C4×D151—81no—
147C4×D151C2×D412yes—
148C4×D151#4112yes—
149C151⋊C8—21no—
150C151⋊C8C2×D412yes—
151C23×C151—21no—
152C23×C151C2×D411yescharacteristic
153Q8×C151—21no—
154Q8×C151—21no—
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—81no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2411yescharacteristic
165C8×C151—21no—
166C8×C151C2×D412yes—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151C22×D411yescharacteristic
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151#12112yes—
183C4×C151—21no—
184C4×C151—41no—
185C4×C151—41no—
186C4×C151—41no—
187C4×C151C22×D411yescharacteristic
188C4×C151C2×#4111yescharacteristic
189Dic151—21no—
190Dic151—41no—
191Dic151—41no—
192Dic151—41no—
193Dic151#12112yes—
194C2×C151—41no—
195C2×C151—81no—
196C2×C151C2×#12111yescharacteristic
197C2×C151#57711yescharacteristic
198C2×C151#57711yescharacteristic
199D151—22no—
200D151—41no—
201D151—81no—
202C151#306011yescharacteristic, complemented, Sylow
203#3060—1511nomaximal, Sylow
204C2×#135—1511no—
205C2×#131—1511no—
206#537—1511no—
207#537—1511no—
208#470—1511no—
209#470—1511no—
210#469—1511no—
211#469—1511no—
212#465—1511no—
213#465—1511no—
214#465—1511no—
215#465D15111yescharacteristic, complemented
216C2×#106—1511no—
217#417—1511no—
218#417—1511no—
219C2×#41—1511no—
220C2×#41—1511no—
221C2×#41—1511no—
222#135—3024no—
223C2×Q16—1511no—
224C2×SD16—1511no—
225C2×SD16C2×D15111yescharacteristic
226C2×D8—1511no—
227#131—3024no—
228C2×M16—1511no—
229C2×M16—1511no—
230C2×M16—1511no—
231C22×C8—1511no—
232C22×C8—1511no—
233C22×C8C2×D15111yescharacteristic
234C22⋊Q8—3021no—
235C22⋊Q8—3021no—
236C22⋊Q8—1511no—
237C22⋊Q8—1511no—
238C22⋊Q8—1511no—
239C22⋊Q8C2×D15111yescharacteristic
240#121—3021no—
241#121—3021no—
242#121—3021no—
243#121—3021no—
244#121—3021no—
245#121—3021no—
246#121—1511no—
247#121—1511no—
248#121—1511no—
249#121C2×D15111yescharacteristic
250C2×C4⋊C4—1511no—
251C2×C4⋊C4—1511no—
252#106—1511no—
253#106—1511no—
254#106—1511no—
255#106C2×D15111yescharacteristic
256#103—1511no—
257#103—1511no—
258#103—1511no—
259#103C2×D15111yescharacteristic
260#102—1511no—
261#102—1511no—
262#102—1511no—
263#102C2×D15111yescharacteristic
264#41—3022no—
265#41—3022no—
266#41—3022no—
267#41—3022no—
268#41—3022no—
269#41—3022no—
270C2×Q8—1511no—
271C2×Q8—1511no—
272C2×Q8C22×D15111yescharacteristic
273C2×D4—21no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—1511no—
280C2×D4—1511no—
281C2×D4—1511no—
282C2×D4—1511no—
283C2×D4C22×D15111yescharacteristic
284C22×C4—3021no—
285C22×C4—3021no—
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—1511no—
289C22×C4—1511no—
290C22×C4C22×D15111yescharacteristic
291Q16—3022no—
292SD16—22no—
293SD16—3022no—
294D8—3022no—
295M16—3022no—
296M16—3022no—
297M16—3022no—
298C2×C8—22no—
299C2×C8—3022no—
300C2×C8—1511no—
301C2×C8—1511no—
302C2×C8—1514no—
303C2×C8C22×D15111yescharacteristic
304C2×C8C22×D15111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—3021no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—3021no—
310C4⋊C4—3021no—
311C4⋊C4—1511no—
312C4⋊C4—1511no—
313C4⋊C4C22×D15111yescharacteristic
314C4⋊C4C22×D15111yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C23—21no—
324C23—3021no—
325C23—1511no—
326C23—1511no—
327C23D4×D15111yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—3022no—
331Q8—3021no—
332Q8—3021no—
333D4—21no—
334D4—21no—
335D4—81no—
336D4—3022no—
337D4—3022no—
338D4—3022no—
339D4—3021no—
340D4—3021no—
341D4—6042no—
342D4—6042no—
343D4—12081no—
344D4—12081no—
345D4—12081no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—3021no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—6042no—
357C2×C4—6042no—
358C2×C4—1511no—
359C2×C4—1511no—
360C2×C4—1512no—
361C2×C4—1512no—
362C2×C4—12081no—
363C2×C4—12081no—
364C2×C4D4×D15111yescharacteristic
365C2×C4C23×D15111yescharacteristic
366C8—21no—
367C8—3021no—
368C8—1512no—
369C8D4×D15112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3021no—
377C22—3021no—
378C22—3021no—
379C22—3021no—
380C22—3021no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—1512no—
385C22C2×D4×D15111yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—3021no—
391C4—6041no—
392C4—6041no—
393C4—6041no—
394C4—1512no—
395C4C2×D4×D15111yescharacteristic
396C4#41×D15111yescharacteristic
397C2—41no—
398C2—81no—
399C2—3022no—
400C2—6041no—
401C2—12081no—
402C2#121×D15111yescharacteristic
403C2#2375301811yescharacteristic
404C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
hypercenter#465D151
hypocenterC151#3060
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. C2×#18012745C2semidirect
3. #23752792C2semidirect
4. #23752791C2semidirect
5. #23752469C2semidirect
6. #23752468C2semidirect
7. #23752464C2semidirect
8. #23752463C2semidirect
9. #23752442C2semidirect
10. #23752441C2semidirect
11. #23752438C2semidirect
12. #106×D151C2semidirect
13. #23752212C2semidirect
14. #23752210C2semidirect
15. #465×C151C2semidirect
93. C8×D151D4semidirect
202. C151#3060semidirect
215. #465D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
C2×#180127452
#237527922
#237527912
#237524692
#237524682
#237524642
#237524632
#237524422
#237524412
#237524382
#106×D1512
#237522122
#237522102
#465×C1512
#3060151