Finite Group Databasebeta

← #34080773

Subgroups — #34080773

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×#18012772C211yesmaximal, characteristic, complemented
2C2×#18012768C211yesmaximal, characteristic, complemented
3#23752880C211yesmaximal, characteristic
4#23752875C211yesmaximal, characteristic, complemented
5#23752583C211yesmaximal, characteristic, complemented
6#23752459C211yesmaximal, characteristic, complemented
7#23752421C211yesmaximal, characteristic, complemented
8#23752411C211yesmaximal, characteristic, complemented
9#23752375C211yesmaximal, characteristic, complemented
10#23752372C211yesmaximal, characteristic, complemented
11#23752352C211yesmaximal, characteristic, complemented
12#23752350C211yesmaximal, characteristic, complemented
13#23752306C211yesmaximal, characteristic, complemented
14#23752288C211yesmaximal, characteristic, complemented
15#468×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C22×Dic302C2211yescharacteristic
19C2×Q8×D151C2211yescharacteristic
20#18012772—24no—
21#18012768—24no—
22C2×Dic604C2211yescharacteristic
23C2×Dic604C2211yescharacteristic
24C2×#14558994C2211yescharacteristic
25C2×#14558993C2211yescharacteristic
26C2×#14558993C2211yescharacteristic
27C2×#14558992C2211yescharacteristic
28C2×#14558992C2211yescharacteristic
29C2×#14558991C2211yescharacteristic
30C2×#14558987C2211yescharacteristic
31#18012738—21no—
32#18012737C2211yescharacteristic
33#18012735—21no—
34#18012735C2211yescharacteristic
35#18012719C2211yescharacteristic
36#18012717—21no—
37#18012716—21no—
38#18012714C2211yescharacteristic
39#18012712—21no—
40#18012711—21no—
41#18012704C2211yescharacteristic
42#18012704C2211yescharacteristic
43C4×C22⋊D151C2211yescharacteristic
44(C22⋊D151)⋊C4—21no—
45(C22⋊D151)⋊C4—21no—
46Dic151⋊C8C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012662C2211yescharacteristic
49#18012662C2211yescharacteristic
50#18012659C2211yescharacteristic
51C22⋊(C151⋊C8)C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic
53C8×Dic151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C2×M16×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#107×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559004—22no—
62#14559004—41no—
63#14559003—22no—
64#14559003—41no—
65C2×Dic302—21no—
66C2×Dic302—22no—
67C2×Dic302—21no—
68C2×Dic302—41no—
69C2×Dic302C2311yescharacteristic
70C2×Dic302C2311yescharacteristic
71C2×Dic302C2311yescharacteristic
72Q8×D151—22no—
73Q8×D151—41no—
74C2×D604—21no—
75C2×D604C2311yescharacteristic
76C2×C22⋊D151—21no—
77C2×C22⋊D151—21no—
78C2×C22⋊D151—21no—
79C2×C22⋊D151—21no—
80C2×C22⋊D151D411yescharacteristic
81C22×Dic151—21no—
82C22×Dic151—21no—
83C2×C4×D151—21no—
84C2×C4×D151—21no—
85C2×C4×D151C2311yescharacteristic
86Dic604—22no—
87Dic604D414yescomplemented
88#14558994—22no—
89#14558993—22no—
90#14558993—22no—
91#14558992—22no—
92#14558992—41no—
93#14558991—41no—
94#14558987—22no—
95C2×C151⋊C8C2311yescharacteristic
96C2×C151⋊C8C2311yescharacteristic
97C4⋊Dic151—21no—
98Dic151⋊C4—21no—
99Dic151⋊C4—21no—
100Dic151⋊C4—21no—
101Dic151⋊C4—21no—
102Dic151⋊C4D411yescharacteristic
103C22⋊Dic151D411yescharacteristic
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4D411yescharacteristic
107C4×Dic151—21no—
108C4×Dic151—21no—
109C4×Dic151C2311yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151—21no—
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151C2311yescharacteristic
114SD16×C151—22no—
115M16×C151—22no—
116C2×C8×C151C2311yescharacteristic
117C2×C8×C151C2311yescharacteristic
118C4⋊C4×C151—21no—
119C4⋊C4×C151C2311yescharacteristic
120C4⋊C4×C151C2311yescharacteristic
121C22⋊C4×C151—21no—
122C22⋊C4×C151—21no—
123C22×D151—21no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302—21no—
129Dic302—42no—
130Dic302—42no—
131Dic302C2×D412yes—
132Dic302C2×D412yes—
133D604—21no—
134D604—21no—
135D604—81no—
136C22⋊D151—22no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C22⋊D151—42no—
140C22⋊D151—81no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—42no—
145C2×Dic151—42no—
146C2×Dic151C2×D411yescharacteristic
147C2×Dic151C2×D411yescharacteristic
148C2×Dic151C2×D411yescharacteristic
149C4×D151—21no—
150C4×D151—21no—
151C4×D151—42no—
152C4×D151—42no—
153C151⋊C8—21no—
154C151⋊C8—21no—
155C23×C151—21no—
156C23×C151C2×D411yescharacteristic
157Q8×C151—21no—
158Q8×C151—21no—
159D4×C151—21no—
160D4×C151—21no—
161D4×C151—81no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
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—41no—
186C4×C151—41no—
187C4×C151—41no—
188C4×C151C22×D411yescharacteristic
189C4×C151H(5,𝔽2)11yescharacteristic
190Dic151—21no—
191Dic151—22no—
192Dic151—22no—
193Dic151—21no—
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×#137—1511no—
207#550—1511no—
208D4×Q8—1511no—
209#492—1511no—
210#468—1511no—
211#468D15111yescharacteristic, complemented
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×#41—1511no—
222C22×Q8—1511no—
223C22×Q8—1511no—
224#137—3024no—
225#137—3024no—
226C2×Q16—1511no—
227C2×Q16—1511no—
228C2×Q16—1511no—
229C2×SD16—1511no—
230C2×SD16—1511no—
231C2×SD16—1511no—
232C2×SD16—1511no—
233C2×SD16—1511no—
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⋊Q8C2×D15111yescharacteristic
245#121—3021no—
246#121—3021no—
247#121—1511no—
248#121C2×D15111yescharacteristic
249C4×Q8—1511no—
250C4×Q8—1511no—
251C4×D4—3021no—
252C4×D4—3021no—
253C4×D4—1511no—
254#107C2×D15111yescharacteristic
255C4⋊C8—1511no—
256#103—1511no—
257#103—1511no—
258#103—1511no—
259#103C2×D15111yescharacteristic
260#102—1511no—
261#102C2×D15111yescharacteristic
262C22⋊C8—1511no—
263C22⋊C8—1511no—
264C4×C8—1511no—
265#41—3022no—
266#41—3022no—
267#41—6041no—
268#41—6041no—
269C2×Q8—3021no—
270C2×Q8—3022no—
271C2×Q8—3021no—
272C2×Q8—3022no—
273C2×Q8—6041no—
274C2×Q8—6041no—
275C2×Q8—1511no—
276C2×Q8—1511no—
277C2×Q8—1511no—
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—3021no—
289C22×C4—3021no—
290C22×C4—3021no—
291C22×C4—3021no—
292C22×C4—1511no—
293C22×C4C22×D15111yescharacteristic
294Q16—3022no—
295Q16—3022no—
296Q16—1514no—
297SD16—22no—
298SD16—3022no—
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—21no—
310C4⋊C4—3021no—
311C4⋊C4—3021no—
312C4⋊C4—3021no—
313C4⋊C4—3021no—
314C4⋊C4—3021no—
315C4⋊C4—1511no—
316C4⋊C4C22×D15111yescharacteristic
317C4⋊C4C22×D15111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
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—3021no—
334Q8—3021no—
335Q8—3021no—
336Q8—3021no—
337Q8—6042no—
338Q8—6042no—
339Q8—1512no—
340Q8—1512no—
341D4—21no—
342D4—21no—
343D4—81no—
344D4—3022no—
345D4—3021no—
346D4—3021no—
347D4—6042no—
348D4—6042no—
349D4—6042no—
350D4—12081no—
351D4—12081no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—3021no—
360C2×C4—3021no—
361C2×C4—3021no—
362C2×C4—6042no—
363C2×C4—6042no—
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—
374C8D4×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—41no—
390C4—41no—
391C4—41no—
392C4—3021no—
393C4—3021no—
394C4—3022no—
395C4—3022no—
396C4—6041no—
397C4—1512no—
398C4C2×D4×D15111yescharacteristic
399C4#1801278511yescharacteristic
400C2—41no—
401C2—81no—
402C2—6041no—
403C2—12081no—
404C2#2375284611yescharacteristic
405C2#137×D15111yescharacteristic
406C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#468×C151C2
socleC22×C151C22×D4
prime radical#23752880C2
hypercenter#468D151
hypocenterC151#3278
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#18012772C2semidirect
2. C2×#18012768C2semidirect
4. #23752875C2semidirect
5. #23752583C2semidirect
6. #23752459C2semidirect
7. #23752421C2semidirect
8. #23752411C2semidirect
9. #23752375C2semidirect
10. #23752372C2semidirect
11. #23752352C2semidirect
12. #23752350C2semidirect
13. #23752306C2semidirect
14. #23752288C2semidirect
15. #468×C151C2semidirect
87. Dic604D4semidirect
195. Dic151#137semidirect
203. C151#3278semidirect
211. #468D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127722
C2×#180127682
#237528802
#237528752
#237525832
#237524592
#237524212
#237524112
#237523752
#237523722
#237523522
#237523502
#237523062
#237522882
#468×C1512
#3278151