Finite Group Databasebeta

← #34079964

Subgroups — #34079964

Order 19328.

422 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
1#23752790C211yesmaximal, characteristic, complemented
2#23752776C211yesmaximal, characteristic, complemented
3#23752554C211yesmaximal, characteristic, complemented
4#23752537C211yesmaximal, characteristic, complemented
5#23752531C211yesmaximal, characteristic, complemented
6#23752526C211yesmaximal, characteristic, complemented
7#23752465C211yesmaximal, characteristic, complemented
8#23752458C211yesmaximal, characteristic, complemented
9#23752448C211yesmaximal, characteristic, complemented
10#23752441C211yesmaximal, characteristic, complemented
11#23752365C211yesmaximal, characteristic, complemented
12#23752359C211yesmaximal, characteristic, complemented
13#23752359C211yesmaximal, characteristic, complemented
14#23752348C211yesmaximal, characteristic, complemented
15#408×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic, complemented
17C22×D604C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21C2×D1208C2211yescharacteristic
22#18012735—21no—
23#18012728—21no—
24#18012718C2211yescharacteristic
25#18012718C2211yescharacteristic, complemented
26#18012715—21no—
27#18012713C2211yescharacteristic
28#18012713C2211yescharacteristic
29#18012713C2211yescharacteristic
30#18012713C2211yescharacteristic
31#18012713C2211yescharacteristic
32#18012713C2211yescharacteristic, complemented
33#18012711—21no—
34#18012711—21no—
35#18012710—21no—
36#18012707—21no—
37#18012707—21no—
38#18012698C2211yescharacteristic
39C2×C4⋊Dic151C2211yescharacteristic, complemented
40#18012673C2211yescharacteristic, complemented
41#18012673C2211yescharacteristic, complemented
42#18012671C2211yescharacteristic, complemented
43#18012671C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012664C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic, complemented
52C2×#41×C151C2211yescharacteristic
53C2×M16×C151C2211yescharacteristic, complemented
54C22×C8×C151C2211yescharacteristic, complemented
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—41no—
61#14559004—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604—41no—
65C2×D604—41no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C22×Dic151—21no—
77C2×C4×D151—21no—
78#14558993—41no—
79#14558993—41no—
80D1208—41no—
81D1208—41no—
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98C4×Dic151—21no—
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151D411yescharacteristic
102C2×D4×C151D411yescharacteristic
103C2×D4×C151D411yescharacteristic
104C2×D4×C151D411yescharacteristic
105C22×C4×C151C2311yescharacteristic
106C22×C4×C151C2311yescharacteristic
107C22×C4×C151C2311yescharacteristic
108M16×C151—41no—
109C2×C8×C151—41no—
110C2×C8×C151C2311yescharacteristic
111C2×C8×C151C2311yescharacteristic
112C2×C8×C151C2311yescharacteristic
113C2×C8×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—42no—
118C22×D151—81no—
119C22×D151—81no—
120Dic302—21no—
121Dic302—21no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—21no—
126D604—21no—
127D604—21no—
128D604—42no—
129C22⋊D151—42no—
130C22⋊D151—81no—
131C22⋊D151—81no—
132C22⋊D151—81no—
133C22⋊D151—81no—
134C22⋊D151—81no—
135C22⋊D151—81no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C2×Dic151—21no—
140C2×Dic151—21no—
141C2×Dic151—81no—
142C4×D151—42no—
143C23×C151C2×D411yescharacteristic
144C23×C151C2×D411yescharacteristic
145C23×C151C2×D411yescharacteristic
146Q8×C151—41no—
147D4×C151—41no—
148D4×C151—41no—
149D4×C151—41no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2×D411yescharacteristic
159C2×C4×C151C2411yescharacteristic
160C8×C151—21no—
161C8×C151—21no—
162C8×C151—21no—
163C8×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151C22×D411yescharacteristic
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—84no—
184C4×C151—21no—
185C4×C151—21no—
186C4×C151—21no—
187C4×C151H(5,𝔽2)11yescharacteristic
188C4×C151H(5,𝔽2)11yescharacteristic
189Dic151—41no—
190Dic151—41no—
191Dic151—41no—
192Dic151—41no—
193Dic151—41no—
194C2×C151—41no—
195C2×C151—41no—
196C2×C151—41no—
197C2×C151#53411yescharacteristic
198C2×C151#57611yescharacteristic
199C2×C151#57711yescharacteristic
200D151—81no—
201D151—81no—
202D151—81no—
203C151#319811yescharacteristic, complemented, Sylow
204#3198—1511nomaximal, Sylow
205#537—1511no—
206#535—1511no—
207#485—1511no—
208#482—1511no—
209#481—1511no—
210#480—1511no—
211#469—1511no—
212#468—1511no—
213#466—1511no—
214#465—1511no—
215#450—1511no—
216#449—1511no—
217#449—1511no—
218#447—1511no—
219#408D15111yescharacteristic, complemented
220C2×#41—1511no—
221C2×#41C2×D15111yescharacteristic
222C22×D4—1511no—
223C2×SD16—1511no—
224C2×SD16—1511no—
225C2×D8—1511no—
226C2×D8—1511no—
227C2×M16C2×D15111yescharacteristic, complemented
228C22×C8C2×D15111yescharacteristic, complemented
229#127—3021no—
230#124—3021no—
231C22⋊Q8—3021no—
232C22⋊Q8—1511no—
233C22⋊Q8—1511no—
234#121—3021no—
235#121—3021no—
236#121—3021no—
237#121—1511no—
238#121—1511no—
239#121—1511no—
240#121—1511no—
241#121—1511no—
242#121—1511no—
243#120—3021no—
244#120—3021no—
245#117—1511no—
246C2×C4⋊C4—1511no—
247#107—1511no—
248#107—1511no—
249#106—1511no—
250#106—1511no—
251#103—1511no—
252#103—1511no—
253#102—1511no—
254#102—1511no—
255#102—1511no—
256#102—1511no—
257#102—1511no—
258#102—1511no—
259C22⋊C8C2×D15111yescharacteristic
260C22⋊C8C2×D15111yescharacteristic
261C22⋊C8C2×D15111yescharacteristic, complemented
262C22⋊C8C2×D15111yescharacteristic, complemented
263C24—3021no—
264#41—41no—
265#41—41no—
266#41—6041no—
267#41—6041no—
268C2×Q8—1511no—
269C2×Q8D60411yescharacteristic
270C2×D4—3021no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—6041no—
279C2×D4—6041no—
280C2×D4—1511no—
281C2×D4—1511no—
282C2×D4—1511no—
283C2×D4D60411yescharacteristic
284C2×D4D60411yescharacteristic
285C2×D4D60411yescharacteristic
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4C22×D15111yescharacteristic
289C22×C4C22×D15111yescharacteristic
290C22×C4C22×D15111yescharacteristic
291SD16—6041no—
292SD16—6041no—
293D8—6041no—
294D8—6041no—
295M16—41no—
296C2×C8—41no—
297C2×C8C22×D15111yescharacteristic
298C2×C8C22×D15111yescharacteristic
299C2×C8C22×D15111yescharacteristic
300C2×C8C22×D15111yescharacteristic
301C4⋊C4—3021no—
302C4⋊C4—3021no—
303C4⋊C4—3021no—
304C4⋊C4—1511no—
305C4⋊C4—1511no—
306C4⋊C4—1511no—
307C4⋊C4—1511no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C22⋊C4—3021no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C42—3021no—
318C23—3021no—
319C23—3021no—
320C23—3021no—
321C23—6042no—
322C23—12081no—
323C23—12081no—
324C23C2×D60411yescharacteristic
325C23C2×D60411yescharacteristic
326C23C2×D60411yescharacteristic
327Q8—41no—
328Q8—3021no—
329Q8—3021no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—3021no—
334D4—3021no—
335D4—3021no—
336D4—3021no—
337D4—3021no—
338D4—3021no—
339D4—6042no—
340D4—6042no—
341D4—12081no—
342D4—12081no—
343D4—12081no—
344D4—12081no—
345D4—12081no—
346D4—12081no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—3021no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—6042no—
359C2×C4—12081no—
360C2×C4C2×D60411yescharacteristic
361C2×C4C2×D60411yescharacteristic
362C2×C4C2×D60411yescharacteristic
363C2×C4C23×D15111yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—6041no—
378C22—6041no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—6041no—
385C22—6041no—
386C22—12084no—
387C22C22×D60411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—6041no—
392C4—6041no—
393C4—6041no—
394C4—6041no—
395C4—6041no—
396C4#1801278411yescharacteristic
397C4#1801278411yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—12081no—
402C2—12081no—
403C2—12081no—
404C2#2375277411yescharacteristic
405C2#2375301711yescharacteristic
406C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#408×C151C2
socleC22×C151C22×D4
hypercenter#408D151
hypocenterC151#3198
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #23752790C2semidirect
2. #23752776C2semidirect
3. #23752554C2semidirect
4. #23752537C2semidirect
5. #23752531C2semidirect
6. #23752526C2semidirect
7. #23752465C2semidirect
8. #23752458C2semidirect
9. #23752448C2semidirect
10. #23752441C2semidirect
11. #23752365C2semidirect
12. #23752359C2semidirect
13. #23752359C2semidirect
14. #23752348C2semidirect
15. #408×C151C2semidirect
16. C2×#14559004C22semidirect
25. #18012718C22semidirect
32. #18012713C22semidirect
39. C2×C4⋊Dic151C22semidirect
40. #18012673C22semidirect
41. #18012673C22semidirect
42. #18012671C22semidirect
43. #18012671C22semidirect
44. #18012664C22semidirect
45. #18012664C22semidirect
50. #18012661C22semidirect
51. #18012661C22semidirect
53. C2×M16×C151C22semidirect
54. C22×C8×C151C22semidirect
57. C22⋊C8×C151C22semidirect
58. C22⋊C8×C151C22semidirect
203. C151#3198semidirect
219. #408D151semidirect
227. C2×M16C2×D151semidirect
228. C22×C8C2×D151semidirect
261. C22⋊C8C2×D151semidirect
262. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527902
#237527762
#237525542
#237525372
#237525312
#237525262
#237524652
#237524582
#237524482
#237524412
#237523652
#237523592
#237523482
#408×C1512
#3198151