Finite Group Databasebeta

← #34080770

Subgroups — #34080770

Order 19328.

482 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012771C211yesmaximal, characteristic, complemented
2#23752881C211yesmaximal, characteristic
3Q8×C22⋊D151C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752458C211yesmaximal, characteristic, complemented
6#23752455C211yesmaximal, characteristic, complemented
7#23752420C211yesmaximal, characteristic, complemented
8#23752410C211yesmaximal, characteristic, complemented
9#23752374C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752351C211yesmaximal, characteristic, complemented
12#23752349C211yesmaximal, characteristic, complemented
13Q16×Dic151C211yesmaximal, characteristic, complemented
14#23752288C211yesmaximal, characteristic, complemented
15C2×#137×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18#18012771—24no—
19C2×#14558994C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23C2×#14558991C2211yescharacteristic
24C2×#14558987C2211yescharacteristic
25#18012737—21no—
26#18012737C2211yescharacteristic
27#18012735—21no—
28#18012735C2211yescharacteristic
29#18012718—21no—
30#18012718C2211yescharacteristic
31#18012715—21no—
32#18012715C2211yescharacteristic
33#18012713—21no—
34#18012713C2211yescharacteristic
35#18012710—21no—
36#18012710C2211yescharacteristic
37Q8×Dic151C2211yescharacteristic
38Q8×Dic151C2211yescharacteristic
39C4×C22⋊D151—21no—
40C4×C22⋊D151—21no—
41C4×C22⋊D151C2211yescharacteristic
42#18012673C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012663C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012660C2211yescharacteristic
50C22⋊(C151⋊C8)C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C8×Dic151C2211yescharacteristic
53C2×#41×C151C2211yescharacteristic
54C22×Q8×C151C2211yescharacteristic
55#137×C151—24no—
56C2×Q16×C151C2211yescharacteristic
57C2×Q16×C151C2211yescharacteristic
58C2×SD16×C151C2211yescharacteristic
59C2×SD16×C151C2211yescharacteristic
60C2×M16×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—41no—
63C2×Dic302—21no—
64C2×Dic302C2311yescharacteristic
65Q8×D151—22no—
66Q8×D151—41no—
67C2×D604—21no—
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151D411yescharacteristic
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151C2311yescharacteristic
77#14558994—22no—
78#14558993—22no—
79#14558992—41no—
80#14558991—22no—
81#14558991—41no—
82#14558987—22no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C4⋊Dic151—21no—
86C4⋊Dic151—21no—
87C4⋊Dic151C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93Dic151⋊C4D411yescharacteristic
94C22⋊Dic151—21no—
95C22⋊Dic151—21no—
96C22⋊Dic151D411yescharacteristic
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4D411yescharacteristic
100C4×Dic151—21no—
101C4×Dic151—21no—
102C4×Dic151C2311yescharacteristic
103#41×C151—22no—
104#41×C151—41no—
105C2×Q8×C151—21no—
106C2×Q8×C151—22no—
107C2×Q8×C151—41no—
108C2×Q8×C151C2311yescharacteristic
109C2×Q8×C151C2311yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151—21no—
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116Q16×C151—22no—
117Q16×C151D414yescomplemented
118SD16×C151—22no—
119SD16×C151—22no—
120M16×C151—22no—
121C2×C8×C151C2311yescharacteristic
122C2×C8×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127Dic302—42no—
128D604—21no—
129D604—21no—
130D604—42no—
131C22⋊D151—22no—
132C22⋊D151—42no—
133C22⋊D151—81no—
134C22⋊D151—81no—
135C22⋊D151—81no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C4×D151—21no—
143C4×D151—21no—
144C4×D151—42no—
145C4×D151—42no—
146C151⋊C8—21no—
147C151⋊C8—21no—
148C23×C151—21no—
149C23×C151C2×D411yescharacteristic
150Q8×C151—21no—
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151—21no—
154Q8×C151—42no—
155Q8×C151C2×D412yes—
156Q8×C151C2×D412yes—
157D4×C151—21no—
158D4×C151—21no—
159D4×C151—42no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—42no—
166C2×C4×C151—42no—
167C2×C4×C151C2×D411yescharacteristic
168C2×C4×C151C2411yescharacteristic
169C8×C151—21no—
170C8×C151C2×D412yes—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151—21no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151C22×D411yescharacteristic
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—21no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—41no—
184C4×C151—21no—
185C4×C151—22no—
186C4×C151—22no—
187C4×C151—41no—
188C4×C151C22×D411yescharacteristic
189C4×C151H(5,𝔽2)11yescharacteristic
190Dic151—21no—
191Dic151—21no—
192Dic151—41no—
193Dic151—41no—
194Dic151—41no—
195Dic151#13712yescomplemented
196C2×C151—41no—
197C2×C151—81no—
198C2×C151D4211yescharacteristic
199C2×C151C2×#13711yescharacteristic
200C2×C151#57711yescharacteristic
201D151—41no—
202D151—81no—
203C151#327811yescharacteristic, complemented, Sylow
204#3278—1511nomaximal, Sylow
205C2×#137—1511no—
206C2×#137D15111yescharacteristic, complemented
207#550—1511no—
208D4×Q8—1511no—
209#492—1511no—
210#468—1511no—
211#468—1511no—
212#462—1511no—
213#460—1511no—
214#452—1511no—
215#452—1511no—
216#448—1511no—
217#448—1511no—
218C4×Q16—1511no—
219#436—1511no—
220C2×#41—1511no—
221C2×#41C2×D15111yescharacteristic
222C22×Q8—1511no—
223C22×Q8C2×D15111yescharacteristic
224#137—24no—
225#137—3024no—
226C2×Q16—1511no—
227C2×Q16C2×D15111yescharacteristic
228C2×Q16C2×D15111yescharacteristic
229C2×SD16—1511no—
230C2×SD16—1511no—
231C2×SD16—1511no—
232C2×SD16—1511no—
233C2×SD16C2×D15111yescharacteristic
234C2×SD16C2×D15111yescharacteristic
235C2×M16—1511no—
236C2×M16C2×D15111yescharacteristic
237C4⋊Q8—3021no—
238C4⋊Q8—1511no—
239#127—3021no—
240#127—1511no—
241C22⋊Q8—3021no—
242C22⋊Q8—3021no—
243C22⋊Q8—1511no—
244C22⋊Q8—1511no—
245#121—3021no—
246#121—3021no—
247#121—1511no—
248#121—1511no—
249C4×Q8—1511no—
250C4×Q8—1511no—
251C4×D4—3021no—
252C4×D4—3021no—
253C4×D4—1511no—
254#107—1511no—
255C4⋊C8—1511no—
256#103—1511no—
257#103—1511no—
258#103—1511no—
259#103—1511no—
260#102—1511no—
261#102—1511no—
262C22⋊C8—1511no—
263C22⋊C8—1511no—
264C4×C8—1511no—
265#41—22no—
266#41—41no—
267#41—3022no—
268#41—6041no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—3021no—
273C2×Q8—3022no—
274C2×Q8—6041no—
275C2×Q8—1511no—
276C2×Q8C22×D15111yescharacteristic
277C2×Q8C22×D15111yescharacteristic
278C2×Q8C22×D15111yescharacteristic
279C2×D4—21no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—3021no—
283C2×D4—3021no—
284C2×D4—3021no—
285C2×D4—1511no—
286C2×D4—1511no—
287C2×D4C22×D15111yescharacteristic
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—3021no—
291C22×C4—3021no—
292C22×C4—1511no—
293C22×C4C22×D15111yescharacteristic
294Q16—22no—
295Q16—3022no—
296Q16C22⋊D15114yescomplemented
297SD16—22no—
298SD16—22no—
299SD16—3022no—
300SD16—3022no—
301SD16—6041no—
302SD16—6041no—
303M16—22no—
304M16—3022no—
305C2×C8—1511no—
306C2×C8—1511no—
307C2×C8C22×D15111yescharacteristic
308C2×C8C22×D15111yescharacteristic
309C4⋊C4—3021no—
310C4⋊C4—3021no—
311C4⋊C4—3021no—
312C4⋊C4—3021no—
313C4⋊C4—3021no—
314C4⋊C4—3021no—
315C4⋊C4—1511no—
316C4⋊C4—1511no—
317C4⋊C4—1511no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—1511no—
323C22⋊C4—1511no—
324C42—3021no—
325C42—3021no—
326C42—1511no—
327C23—21no—
328C23—3021no—
329C23—1511no—
330C23D4×D15111yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—21no—
335Q8—42no—
336Q8—3021no—
337Q8—3021no—
338Q8—6042no—
339Q8C2×C22⋊D15112yes—
340Q8C2×C22⋊D15112yes—
341D4—21no—
342D4—21no—
343D4—42no—
344D4—3022no—
345D4—3021no—
346D4—3021no—
347D4—6042no—
348D4—6042no—
349D4—12081no—
350D4—12081no—
351D4—12081no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—3021no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—3021no—
363C2×C4—3021no—
364C2×C4—6042no—
365C2×C4—6042no—
366C2×C4—1511no—
367C2×C4—1511no—
368C2×C4—1511no—
369C2×C4D4×D15111yescharacteristic
370C2×C4C23×D15111yescharacteristic
371C8—21no—
372C8—3021no—
373C8—3021no—
374C8C2×C22⋊D15112yes—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—3021no—
382C22—3021no—
383C22—3021no—
384C22—6041no—
385C22—6041no—
386C22—6041no—
387C22C2×D4×D15111yescharacteristic
388C4—21no—
389C4—22no—
390C4—22no—
391C4—41no—
392C4—3021no—
393C4—3021no—
394C4—6041no—
395C4—6041no—
396C4—6041no—
397C4—1512no—
398C4C22×C22⋊D15111yescharacteristic
399C4#1801278411yescharacteristic
400C2—41no—
401C2—81no—
402C2—6041no—
403C2—12081no—
404C2D4×C22⋊D15111yescharacteristic
405C2#137×D15111yescharacteristic
406C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#137×C151C2
socleC22×C151C22×D4
prime radical#23752881C2
hypercenterC2×#137D151
hypocenterC151#3278
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#18012771C2semidirect
3. Q8×C22⋊D151C2semidirect
4. #23752583C2semidirect
5. #23752458C2semidirect
6. #23752455C2semidirect
7. #23752420C2semidirect
8. #23752410C2semidirect
9. #23752374C2semidirect
10. #23752373C2semidirect
11. #23752351C2semidirect
12. #23752349C2semidirect
13. Q16×Dic151C2semidirect
14. #23752288C2semidirect
15. C2×#137×C151C2semidirect
117. Q16×C151D4semidirect
195. Dic151#137semidirect
203. C151#3278semidirect
206. C2×#137D151semidirect
296. Q16C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
#237528812
Q8×C22⋊D1512
#237525832
#237524582
#237524552
#237524202
#237524102
#237523742
#237523732
#237523512
#237523492
Q16×Dic1512
#237522882
C2×#137×C1512
#3278151