Finite Group Databasebeta

← #34080855

Subgroups — #34080855

Order 19328.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14558994C211yesmaximal, characteristic, complemented
2C2×Q16×D151C211yesmaximal, characteristic, complemented
3Q8×C22⋊D151C211yesmaximal, characteristic
4#23752875C211yesmaximal, characteristic
5#23752590C211yesmaximal, characteristic, complemented
6#23752452C211yesmaximal, characteristic, complemented
7#23752451C211yesmaximal, characteristic, complemented
8#23752421C211yesmaximal, characteristic, complemented
9#23752420C211yesmaximal, characteristic, complemented
10#23752370C211yesmaximal, characteristic, complemented
11#23752369C211yesmaximal, characteristic, complemented
12#23752366C211yesmaximal, characteristic, complemented
13#23752304C211yesmaximal, characteristic, complemented
14(C22⋊D151)⋊C8C211yesmaximal, characteristic
15#451×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19C2×Dic604C2211yescharacteristic
20C2×Dic604C2211yescharacteristic
21C2×#14558994—24no—
22C2×#14558994C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24C2×#14558994C2211yescharacteristic
25C2×#14558994C2211yescharacteristic
26C2×#14558994C2211yescharacteristic
27Q16×D151—24no—
28C22×C151⋊C8C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic
30#18012738—21no—
31#18012737—21no—
32#18012737C2211yescharacteristic
33#18012737C2211yescharacteristic
34#18012719C2211yescharacteristic
35#18012718—21no—
36#18012718C2211yescharacteristic
37#18012717—21no—
38#18012716—21no—
39#18012715—21no—
40#18012715C2211yescharacteristic
41Q8×Dic151C2211yescharacteristic
42#18012704C2211yescharacteristic
43C4×C22⋊D151—21no—
44C4×C22⋊D151C2211yescharacteristic
45(C22⋊D151)⋊C4—21no—
46#18012672C2211yescharacteristic
47Dic151⋊C8C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
50#18012663C2211yescharacteristic
51#18012662C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic
53C8×Dic151C2211yescharacteristic
54C22×Q8×C151C2211yescharacteristic
55C2×Q16×C151C2211yescharacteristic
56C2×Q16×C151C2211yescharacteristic
57C22⋊Q8×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60C22⋊C8×C151C2211yescharacteristic
61C2×Dic302—21no—
62C2×Dic302—21no—
63C2×Dic302—22no—
64C2×Dic302—21no—
65C2×Dic302—41no—
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68C2×Dic302C2311yescharacteristic
69Q8×D151—22no—
70Q8×D151—22no—
71Q8×D151—41no—
72Q8×D151—41no—
73C2×C22⋊D151D411yescharacteristic
74C22×Dic151—21no—
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151C2311yescharacteristic
78Dic604—22no—
79Dic604—41no—
80#14558994—22no—
81#14558994—22no—
82#14558994—22no—
83#14558994—22no—
84#14558994D414yescomplemented
85C2×C151⋊C8—22no—
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C8×D151—22no—
89C4⋊Dic151—21no—
90C4⋊Dic151—21no—
91C4⋊Dic151C2311yescharacteristic
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99Dic151⋊C4D411yescharacteristic
100C22⋊Dic151—21no—
101C22⋊Dic151D411yescharacteristic
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4D411yescharacteristic
105C4×Dic151—21no—
106C4×Dic151—21no—
107C4×Dic151C2311yescharacteristic
108C2×Q8×C151—21no—
109C2×Q8×C151—22no—
110C2×Q8×C151—41no—
111C2×Q8×C151C2311yescharacteristic
112C2×Q8×C151C2311yescharacteristic
113C2×Q8×C151C2311yescharacteristic
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116Q16×C151—22no—
117Q16×C151—41no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C4⋊C4×C151—21no—
121C4⋊C4×C151C2311yescharacteristic
122C22⋊C4×C151—21no—
123C22×D151C2×D411yescharacteristic
124Dic302—21no—
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302—21no—
129Dic302—42no—
130Dic302—42no—
131Dic302—42no—
132Dic302C2×D412yes—
133C22⋊D151Q1614yescomplemented
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—42no—
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⋊C8C2×D412yes—
148C23×C151C2×D411yescharacteristic
149Q8×C151—21no—
150Q8×C151—21no—
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151—21no—
154Q8×C151—42no—
155Q8×C151C2×D412yes—
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—42no—
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2411yescharacteristic
165C8×C151—21no—
166C8×C151—21no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151C2×Q1612yescomplemented
170C22×C151C22×D411yescharacteristic
171C2×D151—21no—
172C2×D151—21no—
173C2×D151C2×Q1612yescomplemented
174C4×C151—21no—
175C4×C151—22no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151—41no—
179C4×C151C22×D411yescharacteristic
180C4×C151H(5,𝔽2)11yescharacteristic
181Dic151—21no—
182Dic151—22no—
183Dic151—21no—
184Dic151—41no—
185Dic151—41no—
186Dic151—41no—
187Dic151C2×Q1612yescomplemented
188C2×C151—22no—
189C2×C151D4211yescharacteristic
190C2×C151C22×Q1611yescharacteristic
191C2×C151#57811yescharacteristic
192D151—22no—
193C151D4×Q1611yescharacteristic, complemented, Sylow
194D4×Q16—1511nomaximal, Sylow
195C22×Q16—1511no—
196C22×Q16—1511no—
197D4×Q8—1511no—
198D4×Q8—1511no—
199#494—1511no—
200#467—1511no—
201#467—1511no—
202#462—1511no—
203#462—1511no—
204#451—1511no—
205#451—1511no—
206#451—1511no—
207#451D15111yescharacteristic, complemented
208C4×Q16—1511no—
209C8×D4—1511no—
210C22×Q8—1511no—
211C22×Q8—1511no—
212C22×Q8—1511no—
213C22×Q8C2×D15111yescharacteristic
214C2×Q16—3024no—
215C2×Q16—3024no—
216C2×Q16—1511no—
217C2×Q16—1511no—
218C2×Q16—1511no—
219C2×Q16—1511no—
220C2×Q16—1511no—
221C2×Q16—1511no—
222C2×Q16—1511no—
223C2×Q16C2×D15111yescharacteristic
224C2×Q16C2×D15111yescharacteristic
225C22×C8—1511no—
226C22×C8—1511no—
227C4⋊Q8—3021no—
228C4⋊Q8—3021no—
229C4⋊Q8—1511no—
230C4⋊Q8—1511no—
231C22⋊Q8—3021no—
232C22⋊Q8—3021no—
233C22⋊Q8—3021no—
234C22⋊Q8—3021no—
235C22⋊Q8—1511no—
236C22⋊Q8—1511no—
237C22⋊Q8—1511no—
238C22⋊Q8C2×D15111yescharacteristic
239C4×Q8—1511no—
240C4×Q8—1511no—
241C4×D4—3021no—
242C4×D4—3021no—
243C4×D4—1511no—
244#107—1511no—
245C4⋊C8—1511no—
246#103—1511no—
247#103—1511no—
248#103—1511no—
249#103—1511no—
250#103C2×D15111yescharacteristic
251#103C2×D15111yescharacteristic
252C22⋊C8—1511no—
253C22⋊C8C2×D15111yescharacteristic
254C4×C8—1511no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—3021no—
259C2×Q8—3021no—
260C2×Q8—3022no—
261C2×Q8—3021no—
262C2×Q8—3022no—
263C2×Q8—3022no—
264C2×Q8—6041no—
265C2×Q8—6041no—
266C2×Q8—6041no—
267C2×Q8—1511no—
268C2×Q8—1511no—
269C2×Q8—1511no—
270C2×Q8C22×D15111yescharacteristic
271C2×Q8C22×D15111yescharacteristic
272C2×Q8C22×D15111yescharacteristic
273C2×D4—1511no—
274C22×C4—21no—
275C22×C4—3021no—
276C22×C4—3021no—
277C22×C4—3021no—
278C22×C4—1511no—
279C22×C4C22×D15111yescharacteristic
280Q16—22no—
281Q16—41no—
282Q16—3022no—
283Q16—3022no—
284Q16—3022no—
285Q16—3022no—
286Q16—3022no—
287Q16—6041no—
288Q16—1514no—
289C2×C8—3022no—
290C2×C8—3022no—
291C2×C8—1511no—
292C2×C8—1511no—
293C2×C8C22×D15111yescharacteristic
294C2×C8C22×D15111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—3021no—
297C4⋊C4—3021no—
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—3021no—
302C4⋊C4—3021no—
303C4⋊C4—3021no—
304C4⋊C4—3021no—
305C4⋊C4—1511no—
306C4⋊C4—1511no—
307C4⋊C4C22×D15111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—1511no—
313C22⋊C4—1511no—
314C42—3021no—
315C42—3021no—
316C42—1511no—
317C23—1511no—
318C23D4×D15111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—3021no—
326Q8—3021no—
327Q8—3021no—
328Q8—3021no—
329Q8—3021no—
330Q8—6042no—
331Q8—6042no—
332Q8—6042no—
333Q8—1512no—
334Q8D4×D15112yes—
335D4—1514no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—6042no—
350C2×C4—6042no—
351C2×C4—6042no—
352C2×C4—1511no—
353C2×C4—1511no—
354C2×C4—1511no—
355C2×C4D4×D15111yescharacteristic
356C2×C4C23×D15111yescharacteristic
357C8—21no—
358C8—21no—
359C8—3021no—
360C8—1512no—
361C22—21no—
362C22—21no—
363C22—3021no—
364C22—3021no—
365C22—1512no—
366C22Q16×D15112yescomplemented
367C22C2×D4×D15111yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—3021no—
374C4—3021no—
375C4—3022no—
376C4—6041no—
377C4—6041no—
378C4—6041no—
379C4—1512no—
380C4C2×D4×D15111yescharacteristic
381C4#1801278411yescharacteristic
382C2—22no—
383C2—3022no—
384C2#2375284411yescharacteristic
385C2C2×Q16×D15111yescharacteristic
386C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#451×C151C2
socleC22×C151C22×D4
prime radicalC2×C22⋊D151D4
hypercenter#451D151
hypocenterC151D4×Q16
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C22×#14558994C2semidirect
2. C2×Q16×D151C2semidirect
5. #23752590C2semidirect
6. #23752452C2semidirect
7. #23752451C2semidirect
8. #23752421C2semidirect
9. #23752420C2semidirect
10. #23752370C2semidirect
11. #23752369C2semidirect
12. #23752366C2semidirect
13. #23752304C2semidirect
15. #451×C151C2semidirect
84. #14558994D4semidirect
133. C22⋊D151Q16semidirect
169. C22×C151C2×Q16semidirect
173. C2×D151C2×Q16semidirect
187. Dic151C2×Q16semidirect
193. C151D4×Q16semidirect
207. #451D151semidirect
366. C22Q16×D151semidirect

Maximal subgroups

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

subgroupindex
C22×#145589942
C2×Q16×D1512
Q8×C22⋊D1512
#237528752
#237525902
#237524522
#237524512
#237524212
#237524202
#237523702
#237523692
#237523662
#237523042
(C22⋊D151)⋊C82
#451×C1512
D4×Q16151