Finite Group Databasebeta

← #34080834

Subgroups — #34080834

Order 19328.

494 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012760C211yesmaximal, characteristic, complemented
2#23752881C211yesmaximal, characteristic, complemented
3#23752861C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752441C211yesmaximal, characteristic, complemented
6#23752438C211yesmaximal, characteristic, complemented
7#23752420C211yesmaximal, characteristic, complemented
8#23752405C211yesmaximal, characteristic, complemented
9#23752374C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752357C211yesmaximal, characteristic, complemented
12#23752354C211yesmaximal, characteristic, complemented
13SD16×Dic151C211yesmaximal, characteristic, complemented
14C8×C22⋊D151C211yesmaximal, characteristic, complemented
15C2×#135×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18#18012760—24no—
19C2×#14558994C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24C2×C8×D151C2211yescharacteristic
25#18012737C2211yescharacteristic
26#18012735—21no—
27#18012735C2211yescharacteristic
28#18012722—21no—
29#18012720—21no—
30#18012718C2211yescharacteristic
31#18012715C2211yescharacteristic
32#18012713—21no—
33#18012713C2211yescharacteristic
34#18012711—21no—
35#18012710—21no—
36#18012710C2211yescharacteristic
37Q8×Dic151C2211yescharacteristic
38D4×Dic151C2211yescharacteristic
39C4×C22⋊D151—21no—
40C4×C22⋊D151C2211yescharacteristic
41C2×Dic151⋊C4—21no—
42#18012671C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic
50C22⋊(C151⋊C8)C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C8×Dic151C2211yescharacteristic
53C2×#41×C151C2211yescharacteristic
54C2×#41×C151C2211yescharacteristic
55#135×C151—24no—
56C2×Q16×C151C2211yescharacteristic
57C2×SD16×C151C2211yescharacteristic
58C2×SD16×C151C2211yescharacteristic
59C2×D8×C151C2211yescharacteristic
60C22×C8×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—41no—
63#14559003—22no—
64#14559003—41no—
65C2×Dic302C2311yescharacteristic
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151D411yescharacteristic
74C22×Dic151—21no—
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151C2311yescharacteristic
78#14558994—22no—
79#14558993—22no—
80#14558992—41no—
81#14558991—41no—
82#14558989—22no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C8×D151—22no—
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⋊Dic151—21no—
97C22⋊Dic151D411yescharacteristic
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4D411yescharacteristic
101C4×Dic151—21no—
102C4×Dic151C2311yescharacteristic
103#41×C151—22no—
104#41×C151—22no—
105#41×C151—41no—
106#41×C151—41no—
107C2×Q8×C151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116Q16×C151—22no—
117SD16×C151—22no—
118SD16×C151D414yescomplemented
119D8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151C2311yescharacteristic
122C2×C8×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127D604—21no—
128D604—21no—
129D604—42no—
130C22⋊D151—22no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C22⋊D151—81no—
134C22⋊D151—81no—
135C22⋊D151—81no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C2×Dic151—42no—
140C2×Dic151—42no—
141C2×Dic151C2×D411yescharacteristic
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C4×D151—21no—
145C4×D151—21no—
146C4×D151—42no—
147C151⋊C8—21no—
148C151⋊C8—21no—
149C23×C151—21no—
150C23×C151—21no—
151C23×C151C2×D411yescharacteristic
152Q8×C151—21no—
153Q8×C151—21no—
154Q8×C151—21no—
155Q8×C151C2×D412yes—
156D4×C151—21no—
157D4×C151—21no—
158D4×C151—21no—
159D4×C151—42no—
160D4×C151—42no—
161D4×C151C2×D412yes—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151C2×D411yescharacteristic
169C2×C4×C151C2411yescharacteristic
170C8×C151—21no—
171C8×C151C2×D412yes—
172C22×C151—21no—
173C22×C151—22no—
174C22×C151—21no—
175C22×C151—21no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151C22×D411yescharacteristic
182C2×D151—21no—
183C2×D151—21no—
184C2×D151—21no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C4×C151—21no—
189C4×C151—22no—
190C4×C151—41no—
191C4×C151C22×D411yescharacteristic
192C4×C151H(5,𝔽2)11yescharacteristic
193Dic151—21no—
194Dic151—21no—
195Dic151—41no—
196Dic151—41no—
197Dic151—41no—
198Dic151#13512yescomplemented
199C2×C151—41no—
200C2×C151—42no—
201C2×C151—81no—
202C2×C151D4211yescharacteristic
203C2×C151C2×#13511yescharacteristic
204C2×C151#57711yescharacteristic
205D151—41no—
206D151—81no—
207C151#328411yescharacteristic, complemented, Sylow
208#3284—1511nomaximal, Sylow
209C2×#135—1511no—
210C2×#135D15111yescharacteristic, complemented
211#550—1511no—
212#547—1511no—
213#492—1511no—
214#465—1511no—
215#465—1511no—
216#462—1511no—
217#459—1511no—
218#452—1511no—
219#452—1511no—
220#449—1511no—
221#449—1511no—
222C4×SD16—1511no—
223C8×D4—1511no—
224C2×#41—1511no—
225C2×#41—1511no—
226C2×#41C2×D15111yescharacteristic
227C2×#41C2×D15111yescharacteristic
228#135—24no—
229#135—3024no—
230C2×Q16—1511no—
231C2×Q16C2×D15111yescharacteristic
232C2×SD16—1511no—
233C2×SD16—1511no—
234C2×SD16—1511no—
235C2×SD16C2×D15111yescharacteristic
236C2×SD16C2×D15111yescharacteristic
237C2×D8—1511no—
238C2×D8C2×D15111yescharacteristic
239C22×C8—1511no—
240C22×C8C2×D15111yescharacteristic
241C4⋊Q8—1511no—
242#127—3021no—
243#127—1511no—
244#123—3021no—
245#123—3021no—
246C22⋊Q8—1511no—
247C22⋊Q8—1511no—
248#121—3021no—
249#121—3021no—
250#121—3021no—
251#121—1511no—
252#121—1511no—
253C4×Q8—1511no—
254C4×D4—3021no—
255C4×D4—1511no—
256C4×D4—1511no—
257C2×C4⋊C4—3021no—
258#106—1511no—
259C4⋊C8—1511no—
260#103—1511no—
261#103—1511no—
262#103—1511no—
263#102—1511no—
264#102—1511no—
265#102—1511no—
266C22⋊C8—1511no—
267C22⋊C8—1511no—
268C4×C8—1511no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—3022no—
274#41—3022no—
275#41—6041no—
276#41—6041no—
277C2×Q8—1511no—
278C2×Q8C22×D15111yescharacteristic
279C2×Q8C22×D15111yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—3021no—
283C2×D4—3021no—
284C2×D4—3021no—
285C2×D4—3021no—
286C2×D4—3021no—
287C2×D4—3021no—
288C2×D4—1511no—
289C2×D4—1511no—
290C2×D4C22×D15111yescharacteristic
291C2×D4C22×D15111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—3021no—
295C22×C4—3021no—
296C22×C4—3021no—
297C22×C4—1511no—
298C22×C4C22×D15111yescharacteristic
299Q16—22no—
300Q16—3022no—
301SD16—22no—
302SD16—3022no—
303SD16—6041no—
304SD16—6041no—
305SD16C22⋊D15114yescomplemented
306D8—22no—
307D8—3022no—
308C2×C8—22no—
309C2×C8—3022no—
310C2×C8—1511no—
311C2×C8—1511no—
312C2×C8C22×D15111yescharacteristic
313C2×C8C22×D15111yescharacteristic
314C4⋊C4—3021no—
315C4⋊C4—3021no—
316C4⋊C4—3021no—
317C4⋊C4—3021no—
318C4⋊C4—3021no—
319C4⋊C4—1511no—
320C4⋊C4—1511no—
321C4⋊C4—1511no—
322C22⋊C4—3021no—
323C22⋊C4—3021no—
324C22⋊C4—3021no—
325C22⋊C4—3021no—
326C22⋊C4—3021no—
327C22⋊C4—1511no—
328C22⋊C4—1511no—
329C42—3021no—
330C42—1511no—
331C23—21no—
332C23—21no—
333C23—3021no—
334C23—1511no—
335C23D4×D15111yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—3021no—
340Q8—3021no—
341Q8C2×C22⋊D15112yes—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—42no—
347D4—3022no—
348D4—3021no—
349D4—3021no—
350D4—6042no—
351D4—6042no—
352D4—6042no—
353D4—12081no—
354D4—12081no—
355D4—12081no—
356D4C2×C22⋊D15112yes—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—3021no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—6042no—
369C2×C4—6042no—
370C2×C4—6042no—
371C2×C4—1511no—
372C2×C4—1511no—
373C2×C4—1511no—
374C2×C4D4×D15111yescharacteristic
375C2×C4C23×D15111yescharacteristic
376C8—21no—
377C8—3021no—
378C8—3021no—
379C8C2×C22⋊D15112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—3021no—
390C22—3021no—
391C22—3021no—
392C22—6041no—
393C22—6041no—
394C22—6041no—
395C22C2×D4×D15111yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—3021no—
400C4—3021no—
401C4—6041no—
402C4—6041no—
403C4—6041no—
404C4—1512no—
405C4C22×C22⋊D15111yescharacteristic
406C4#1801278411yescharacteristic
407C2—41no—
408C2—42no—
409C2—81no—
410C2—6041no—
411C2—12081no—
412C2D4×C22⋊D15111yescharacteristic
413C2#135×D15111yescharacteristic
414C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#135×C151C2
socleC22×C151C22×D4
hypercenterC2×#135D151
hypocenterC151#3284
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. #23752881C2semidirect
3. #23752861C2semidirect
4. #23752583C2semidirect
5. #23752441C2semidirect
6. #23752438C2semidirect
7. #23752420C2semidirect
8. #23752405C2semidirect
9. #23752374C2semidirect
10. #23752373C2semidirect
11. #23752357C2semidirect
12. #23752354C2semidirect
13. SD16×Dic151C2semidirect
14. C8×C22⋊D151C2semidirect
15. C2×#135×C151C2semidirect
118. SD16×C151D4semidirect
198. Dic151#135semidirect
207. C151#3284semidirect
210. C2×#135D151semidirect
305. SD16C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
#237528812
#237528612
#237525832
#237524412
#237524382
#237524202
#237524052
#237523742
#237523732
#237523572
#237523542
SD16×Dic1512
C8×C22⋊D1512
C2×#135×C1512
#3284151