Finite Group Databasebeta

← #34082726

Subgroups — #34082726

Order 19328.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752938C211yesmaximal, characteristic, complemented
2#23752931C213yesmaximal, complemented
3#23752902C213yesmaximal, complemented
4#23752896C213yesmaximal, complemented
5Q8×C22⋊D151C211yesmaximal, characteristic, complemented
6#23752869C211yesmaximal, characteristic, complemented
7#23752862C213yesmaximal, complemented
8#23752764C213yesmaximal, complemented
9#23752743C213yesmaximal, complemented
10#23752741C213yesmaximal, complemented
11#41×Dic151C211yesmaximal, characteristic, complemented
12C4×#14559003C213yesmaximal, complemented
13C2×Q8×Dic151C211yesmaximal, characteristic, complemented
14C4×Q8×D151C211yesmaximal, characteristic, complemented
15#548×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2213yes—
17C2×Q8×D151C2211yescharacteristic
18#18012738C2213yes—
19#18012737C2213yes—
20#18012732C2216yes—
21#18012732C2216yes—
22#18012731C2213yes—
23#18012730C2213yes—
24#18012729C2216yes—
25#18012726C2213yes—
26#18012721C2216yes—
27#18012720C2216yes—
28#18012718C2213yes—
29#18012718C2213yes—
30#18012716C2216yes—
31#18012715C2213yes—
32#18012710C2213yes—
33Q8×Dic151C2213yes—
34Q8×Dic151C2211yescharacteristic
35Q8×Dic151C2211yescharacteristic
36Q8×Dic151C2213yes—
37Q8×Dic151C2211yescharacteristic
38C4×Dic302C2213yes—
39C4×Dic302C2213yes—
40#18012704C2213yes—
41#18012704C2213yes—
42D4×Dic151C2213yes—
43D4×Dic151C2213yes—
44D4×Dic151C2213yes—
45C4×C22⋊D151C2213yes—
46C4×C22⋊D151C2213yes—
47(C22⋊D151)⋊C4C2213yes—
48(C22⋊D151)⋊C4C2211yescharacteristic
49#18012698C2213yes—
50#18012697C2213yes—
51#18012695C2216yes—
52#18012695C2213yes—
53#18012695C2213yes—
54C2×C4⋊Dic151C2213yes—
55C4⋊C4×D151C2213yes—
56C2×C4×Dic151C2213yes—
57C2×C4×Dic151C2213yes—
58C42×D151C2213yes—
59C2×#41×C151C2211yescharacteristic
60C22×Q8×C151C2211yescharacteristic
61#124×C151C2213yes—
62C22⋊Q8×C151C2213yes—
63#121×C151C2213yes—
64C4×Q8×C151C2211yescharacteristic
65C4×D4×C151C2213yes—
66#14559003—212no—
67C2×Dic302C2313yes—
68C2×Dic302C2313yes—
69Q8×D151—24no—
70C2×C22⋊D151C2313yes—
71C2×C22⋊D151C2311yescharacteristic
72C22×Dic151C2311yescharacteristic
73C22×Dic151C2313yes—
74C22×Dic151C2313yes—
75C22×Dic151C2313yes—
76C2×C4×D151C2311yescharacteristic
77C2×C4×D151C2313yes—
78C2×C4×D151C2313yes—
79C4⋊Dic151C2313yes—
80C4⋊Dic151C2313yes—
81C4⋊Dic151C2316yes—
82C4⋊Dic151C2313yes—
83C4⋊Dic151C2313yes—
84Dic151⋊C4C2316yes—
85Dic151⋊C4C2311yescharacteristic
86Dic151⋊C4C2313yes—
87Dic151⋊C4C2313yes—
88Dic151⋊C4C2313yes—
89Dic151⋊C4C2316yes—
90Dic151⋊C4C2316yes—
91C22⋊Dic151C2313yes—
92C22⋊Dic151C2313yes—
93C22⋊Dic151C2316yes—
94C22⋊Dic151C2316yes—
95(C2×D151)⋊C4C2311yescharacteristic
96(C2×D151)⋊C4C2313yes—
97C4×Dic151C2313yes—
98C4×Dic151C2313yes—
99C4×Dic151C2313yes—
100C4×Dic151C2311yescharacteristic
101C4×Dic151C2313yes—
102C4×Dic151C2313yes—
103C4×Dic151C2313yes—
104C4×Dic151C2313yes—
105C4×Dic151C2313yes—
106#41×C151—24no—
107C2×Q8×C151—24no—
108C2×Q8×C151C2313yes—
109C2×Q8×C151C2311yescharacteristic
110C2×D4×C151C2313yes—
111C2×D4×C151C2313yes—
112C22×C4×C151C2313yes—
113C22×C4×C151C2313yes—
114C4⋊C4×C151C2313yes—
115C4⋊C4×C151C2313yes—
116C22⋊C4×C151C2311yescharacteristic
117C22⋊C4×C151C2313yes—
118C22⋊C4×C151C2316yes—
119C42×C151C2313yes—
120C22×D151C2411yescharacteristic
121Dic302—26no—
122Dic302—26no—
123C22⋊D151—26no—
124C22⋊D151#4114yescomplemented
125C2×Dic151—26no—
126C2×Dic151—26no—
127C2×Dic151—22no—
128C2×Dic151—26no—
129C2×Dic151C2411yescharacteristic
130C2×Dic151C2413yes—
131C2×Dic151C2413yes—
132C2×Dic151C2413yes—
133C2×Dic151C2413yes—
134C2×Dic151C2411yescharacteristic
135C2×Dic151C2411yescharacteristic
136C4×D151—26no—
137C4×D151—26no—
138C4×D151—22no—
139C23×C151C2413yes—
140C23×C151C2411yescharacteristic
141Q8×C151—26no—
142Q8×C151#4114yescomplemented
143D4×C151—26no—
144D4×C151—26no—
145C2×C4×C151—26no—
146C2×C4×C151—26no—
147C2×C4×C151C2413yes—
148C2×C4×C151C2411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C2×C4×C151C2413yes—
151C2×C4×C151C2413yes—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—23no—
155C22×C151—23no—
156C22×C151—23no—
157C22×C151C2×#4112yes—
158C22×C151C2511yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151C2×#4112yes—
162C4×C151—21no—
163C4×C151—23no—
164C4×C151—23no—
165C4×C151—21no—
166C4×C151C2×#4116yes—
167Dic151—23no—
168Dic151—23no—
169Dic151—23no—
170Dic151—21no—
171Dic151—23no—
172Dic151C2×#4112yes—
173Dic1512−1+412yes—
174C2×C151—22no—
175C2×C151—43no—
176C2×C151C22×#4111yescharacteristic
177C2×C151C22×#4111yescharacteristic
178C2×C151C2×2−1+411yescharacteristic
179D151—22no—
180C151#348211yescharacteristic, complemented, Sylow
181#3482—1511nomaximal, Sylow
182#557—1511no—
183#556—1513no—
184#552—1513no—
185#552—1513no—
186D4×Q8—1511no—
187#548—1511no—
188#548D15111yescharacteristic, complemented
189#547—1513no—
190#533—1513no—
191#529—1513no—
192#529—1513no—
193C4×#41—1511no—
194C4×#41—1513no—
195C2×C4×Q8—1511no—
196C2×C4×Q8—1511no—
197C2×#41—1513no—
198C2×#41C2×D15111yescharacteristic
199C22×Q8—1511no—
200C22×Q8C2×D15111yescharacteristic
201C4⋊Q8—1513no—
202C4⋊Q8—1513no—
203#126—1516no—
204#126—1516no—
205#125—1513no—
206#125—1516no—
207#125—1513no—
208#124—1513no—
209#124C2×D15113yes—
210#123—1516no—
211#123—1516no—
212C22⋊Q8—1513no—
213C22⋊Q8—1513no—
214C22⋊Q8—1513no—
215C22⋊Q8—1516no—
216C22⋊Q8C2×D15113yes—
217#121—1513no—
218#121C2×D15113yes—
219C4×Q8—1511no—
220C4×Q8—1513no—
221C4×Q8—1511no—
222C4×Q8—1513no—
223C4×Q8—1511no—
224C4×Q8—1513no—
225C4×Q8—1513no—
226C4×Q8—1513no—
227C4×Q8—1513no—
228C4×Q8C2×D15111yescharacteristic
229C4×D4—1513no—
230C4×D4—1513no—
231C4×D4—1513no—
232C4×D4—1513no—
233C4×D4—1513no—
234C4×D4—1511no—
235C4×D4—1513no—
236C4×D4C2×D15113yes—
237#117—1513no—
238#117—1513no—
239#117—1513no—
240#117—1513no—
241#117—1516no—
242C2×C4⋊C4—1513no—
243C2×C4⋊C4—1513no—
244C2×C42—1513no—
245C2×C42—1513no—
246C2×C42—1513no—
247#41—24no—
248#41—30212no—
249C2×Q8—24no—
250C2×Q8—3024no—
251C2×Q8—1513no—
252C2×Q8—1513no—
253C2×Q8C22×D15113yes—
254C2×Q8C22×D15111yescharacteristic
255C2×D4—1513no—
256C2×D4—1511no—
257C2×D4C22×D15113yes—
258C2×D4C22×D15113yes—
259C22×C4—1511no—
260C22×C4—1513no—
261C22×C4—1513no—
262C22×C4—1513no—
263C22×C4—1511no—
264C22×C4—1513no—
265C22×C4—1513no—
266C22×C4C22×D15113yes—
267C22×C4C22×D15113yes—
268C4⋊C4—1516no—
269C4⋊C4—1511no—
270C4⋊C4—1513no—
271C4⋊C4—1513no—
272C4⋊C4—1513no—
273C4⋊C4—1516no—
274C4⋊C4—1516no—
275C4⋊C4—1513no—
276C4⋊C4—1513no—
277C4⋊C4—1516no—
278C4⋊C4—1513no—
279C4⋊C4—1513no—
280C4⋊C4C22×D15113yes—
281C4⋊C4C22×D15113yes—
282C22⋊C4—1513no—
283C22⋊C4—1516no—
284C22⋊C4—1513no—
285C22⋊C4—1516no—
286C22⋊C4—1511no—
287C22⋊C4—1513no—
288C22⋊C4C22×D15111yescharacteristic
289C22⋊C4C22×D15113yes—
290C22⋊C4C22×D15116yes—
291C42—1513no—
292C42—1511no—
293C42—1513no—
294C42—1513no—
295C42—1513no—
296C42—1513no—
297C42—1513no—
298C42—1513no—
299C42—1513no—
300C42C22×D15113yes—
301C23—1511no—
302C23C23×D15113yes—
303C23C23×D15111yescharacteristic
304Q8—26no—
305Q8—3026no—
306Q8—3026no—
307Q8#1455900314yescomplemented
308D4—26no—
309D4—26no—
310D4—3026no—
311D4—1514no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—3026no—
315C2×C4—3022no—
316C2×C4—3026no—
317C2×C4—3026no—
318C2×C4—3022no—
319C2×C4—3026no—
320C2×C4—3026no—
321C2×C4—1511no—
322C2×C4—1513no—
323C2×C4—1513no—
324C2×C4—1513no—
325C2×C4—1513no—
326C2×C4—1511no—
327C2×C4—1511no—
328C2×C4C23×D15111yescharacteristic
329C2×C4C23×D15111yescharacteristic
330C2×C4C23×D15113yes—
331C2×C4C23×D15113yes—
332C2×C4C23×D15113yes—
333C22—21no—
334C22—21no—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—3021no—
339C22—3021no—
340C22—1512no—
341C22#41×D15112yes—
342C22C24×D15111yescharacteristic
343C4—23no—
344C4—21no—
345C4—23no—
346C4—21no—
347C4—3023no—
348C4—3023no—
349C4—3023no—
350C4—3021no—
351C4—3023no—
352C4—1512no—
353C4—1512no—
354C4C2×#1455900316yes—
355C2—22no—
356C2—43no—
357C2—3022no—
358C2C2×#41×D15111yescharacteristic
359C2C22×#1455900311yescharacteristic
360C22−1+4×D15111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D151
commutator, socle, cosocleC22×C151C25
Fitting#548×C151C2
hypercenter#548D151
hypocenterC151#3482
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #23752938C2semidirect
2. #23752931C2semidirect
3. #23752902C2semidirect
4. #23752896C2semidirect
5. Q8×C22⋊D151C2semidirect
6. #23752869C2semidirect
7. #23752862C2semidirect
8. #23752764C2semidirect
9. #23752743C2semidirect
10. #23752741C2semidirect
11. #41×Dic151C2semidirect
12. C4×#14559003C2semidirect
13. C2×Q8×Dic151C2semidirect
14. C4×Q8×D151C2semidirect
15. #548×C151C2semidirect
124. C22⋊D151#41semidirect
142. Q8×C151#41semidirect
180. C151#3482semidirect
188. #548D151semidirect
307. Q8#14559003semidirect

Maximal subgroups

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

subgroupindex
#237529382
#237529312
#237529022
#237528962
Q8×C22⋊D1512
#237528692
#237528622
#237527642
#237527432
#237527412
#41×Dic1512
C4×#145590032
C2×Q8×Dic1512
C4×Q8×D1512
#548×C1512
#3482151