Finite Group Databasebeta

← #34111851

Subgroups — #34111851

Order 20096.

484 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097792C211yesmaximal, characteristic, complemented
2C2×#19097791C211yesmaximal, characteristic, complemented
3#23757925C211yesmaximal, characteristic, complemented
4#23757922C211yesmaximal, characteristic, complemented
5#23757651C211yesmaximal, characteristic, complemented
6#23757513C211yesmaximal, characteristic, complemented
7#23757512C211yesmaximal, characteristic, complemented
8#23757477C211yesmaximal, characteristic, complemented
9#23757476C211yesmaximal, characteristic, complemented
10#23757437C211yesmaximal, characteristic, complemented
11#23757436C211yesmaximal, characteristic, complemented
12#23757434C211yesmaximal, characteristic, complemented
13#23757353C211yesmaximal, characteristic, complemented
14#23757336C211yesmaximal, characteristic, complemented
15#452×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578954C2211yescharacteristic
18C2×#14578953C2211yescharacteristic
19#19097792—24no—
20#19097791—24no—
21C2×Dic628C2211yescharacteristic
22C2×#14578944C2211yescharacteristic
23C2×#14578944C2211yescharacteristic
24C2×#14578943C2211yescharacteristic
25C2×#14578942C2211yescharacteristic
26C2×#14578941C2211yescharacteristic
27C2×#14578939C2211yescharacteristic
28C22×#11929434C2211yescharacteristic
29C2×C8×D157C2211yescharacteristic
30#19097769C2211yescharacteristic
31#19097769C2211yescharacteristic
32#19097756—21no—
33#19097754—21no—
34#19097753—21no—
35#19097752—21no—
36#19097751C2211yescharacteristic
37#19097750C2211yescharacteristic
38#19097747C2211yescharacteristic
39#19097744—21no—
40#19097743—21no—
41D4×Dic157C2211yescharacteristic
42#19097733C2211yescharacteristic
43C4×C22⋊D157C2211yescharacteristic
44C2×#14578933—21no—
45C4⋊C4×D157—21no—
46#19097704C2211yescharacteristic
47#19097700C2211yescharacteristic
48#19097696C2211yescharacteristic
49#19097695C2211yescharacteristic
50#19097694C2211yescharacteristic
51#19097693C2211yescharacteristic
52#19097683C2211yescharacteristic
53C8×Dic157C2211yescharacteristic
54C2×#41×C157C2211yescharacteristic
55C2×Q16×C157C2211yescharacteristic
56C2×SD16×C157C2211yescharacteristic
57C22⋊Q8×C157C2211yescharacteristic
58#103×C157C2211yescharacteristic
59#102×C157C2211yescharacteristic
60C22⋊C8×C157C2211yescharacteristic
61#14578955—22no—
62#14578955—41no—
63#14578954—22no—
64#14578954—41no—
65#14578953—22no—
66#14578953—41no—
67C2×Dic314C2311yescharacteristic
68C2×Dic314C2311yescharacteristic
69C2×D628—21no—
70C2×D628C2311yescharacteristic
71C2×C22⋊D157—21no—
72C2×C22⋊D157—21no—
73C2×C22⋊D157D411yescharacteristic
74C22×Dic157—21no—
75C22×Dic157—21no—
76C2×C4×D157—21no—
77C2×C4×D157—21no—
78C2×C4×D157—21no—
79C2×C4×D157C2311yescharacteristic
80Dic628—41no—
81#14578944—22no—
82#14578944—22no—
83#14578943—22no—
84#14578942—22no—
85#14578941—22no—
86#14578939D414yescomplemented
87C2×#11929434—22no—
88C2×#11929434C2311yescharacteristic
89C2×#11929434C2311yescharacteristic
90C8×D157—22no—
91C4⋊Dic157—21no—
92C4⋊Dic157C2311yescharacteristic
93#14578933—21no—
94#14578933—21no—
95#14578933—21no—
96#14578933—21no—
97#14578933—21no—
98#14578933—21no—
99#14578933D411yescharacteristic
100C22⋊Dic157—21no—
101C22⋊Dic157—21no—
102C22⋊Dic157D411yescharacteristic
103#14578931—21no—
104#14578931—21no—
105#14578931—21no—
106#14578931D411yescharacteristic
107C4×Dic157C2311yescharacteristic
108#41×C157—22no—
109#41×C157—41no—
110C2×Q8×C157C2311yescharacteristic
111C2×Q8×C157C2311yescharacteristic
112C2×D4×C157—21no—
113C2×D4×C157C2311yescharacteristic
114C22×C4×C157—21no—
115C22×C4×C157C2311yescharacteristic
116Q16×C157—41no—
117SD16×C157—22no—
118C2×C8×C157C2311yescharacteristic
119C2×C8×C157C2311yescharacteristic
120C4⋊C4×C157—21no—
121C4⋊C4×C157C2311yescharacteristic
122C22⋊C4×C157—21no—
123C22×D157—21no—
124C22×D157C2×D411yescharacteristic
125Dic314—21no—
126Dic314—21no—
127Dic314—21no—
128Dic314—21no—
129D628—21no—
130D628—42no—
131D628C2×D412yes—
132C22⋊D157—22no—
133C22⋊D157—42no—
134C22⋊D157—42no—
135C2×Dic157—21no—
136C2×Dic157—21no—
137C2×Dic157—21no—
138C2×Dic157—42no—
139C2×Dic157—42no—
140C2×Dic157C2×D411yescharacteristic
141C2×Dic157C2×D411yescharacteristic
142C2×Dic157C2×D411yescharacteristic
143C4×D157—21no—
144C4×D157—21no—
145C4×D157—42no—
146C4×D157—42no—
147C4×D157—42no—
148#11929434—21no—
149#11929434C2×D412yes—
150C23×C157—21no—
151C23×C157C2×D411yescharacteristic
152Q8×C157—21no—
153Q8×C157—21no—
154Q8×C157—21no—
155Q8×C157—21no—
156D4×C157—21no—
157D4×C157—42no—
158D4×C157C2×D412yes—
159C2×C4×C157—21no—
160C2×C4×C157—21no—
161C2×C4×C157—21no—
162C2×C4×C157—21no—
163C2×C4×C157—21no—
164C2×C4×C157—42no—
165C2×C4×C157C2×D411yescharacteristic
166C2×C4×C157C2411yescharacteristic
167C8×C157—21no—
168C8×C157—21no—
169C22×C157—21no—
170C22×C157—22no—
171C22×C157—21no—
172C22×C157—21no—
173C22×C157—41no—
174C22×C157—41no—
175C22×C157C22×D411yescharacteristic
176C2×D157—21no—
177C2×D157—22no—
178C2×D157—21no—
179C2×D157—21no—
180C2×D157—41no—
181C2×D157—41no—
182C4×C157—21no—
183C4×C157—41no—
184C4×C157—41no—
185C4×C157—41no—
186C4×C157C22×D411yescharacteristic
187C4×C157H(5,𝔽2)11yescharacteristic
188Dic157—21no—
189Dic157—21no—
190Dic157—41no—
191Dic157—41no—
192Dic157—41no—
193Dic157#13512yescomplemented
194C2×C157—41no—
195C2×C157—42no—
196C2×C157D4211yescharacteristic
197C2×C157C2×#13511yescharacteristic
198C2×C157#57811yescharacteristic
199D157—41no—
200D157—42no—
201C157#328311yescharacteristic, complemented, Sylow
202#3283—1571nomaximal, Sylow
203C2×#135—1571no—
204C2×#135—1571no—
205#547—1571no—
206#547—1571no—
207#494—1571no—
208#467—1571no—
209#467—1571no—
210#461—1571no—
211#461—1571no—
212#452—1571no—
213#452—1571no—
214#452—1571no—
215#452D15711yescharacteristic, complemented
216C4×D8—1571no—
217C8×D4—1571no—
218C2×#41—1571no—
219C2×#41—1571no—
220C2×#41—1571no—
221C2×#41C2×D15711yescharacteristic
222#135—3144no—
223#135—3144no—
224C2×Q16—1571no—
225C2×Q16—1571no—
226C2×Q16—1571no—
227C2×Q16C2×D15711yescharacteristic
228C2×SD16—1571no—
229C2×SD16—1571no—
230C2×SD16—1571no—
231C2×SD16C2×D15711yescharacteristic
232C2×D8—1571no—
233C22×C8—1571no—
234C22×C8—1571no—
235C4⋊Q8—1571no—
236C4⋊Q8—1571no—
237#123—3141no—
238#123—3141no—
239#123—3141no—
240#123—3141no—
241C22⋊Q8—1571no—
242C22⋊Q8—1571no—
243C22⋊Q8—1571no—
244C22⋊Q8C2×D15711yescharacteristic
245#121—3141no—
246#121—3141no—
247C4×D4—1571no—
248C4×D4—1571no—
249C4×D4—1571no—
250C2×C4⋊C4—3141no—
251C2×C4⋊C4—3141no—
252#107—1571no—
253C4⋊C8—1571no—
254#103—1571no—
255#103—1571no—
256#103—1571no—
257#103C2×D15711yescharacteristic
258#102—1571no—
259#102C2×D15711yescharacteristic
260C22⋊C8—1571no—
261C22⋊C8C2×D15711yescharacteristic
262C4×C8—1571no—
263#41—22no—
264#41—41no—
265#41—3142no—
266#41—3142no—
267#41—3142no—
268#41—6281no—
269#41—6281no—
270#41—6281no—
271C2×Q8—1571no—
272C2×Q8—1571no—
273C2×Q8C22×D15711yescharacteristic
274C2×Q8C22×D15711yescharacteristic
275C2×D4—21no—
276C2×D4—3141no—
277C2×D4—3141no—
278C2×D4—3141no—
279C2×D4—1571no—
280C2×D4—1571no—
281C2×D4C22×D15711yescharacteristic
282C22×C4—21no—
283C22×C4—3141no—
284C22×C4—3141no—
285C22×C4—3141no—
286C22×C4—3141no—
287C22×C4—3141no—
288C22×C4—1571no—
289C22×C4C22×D15711yescharacteristic
290Q16—41no—
291Q16—3142no—
292Q16—3142no—
293Q16—6281no—
294SD16—22no—
295SD16—3142no—
296SD16—3142no—
297SD16—3142no—
298D8—1574no—
299C2×C8—3142no—
300C2×C8—3142no—
301C2×C8—1571no—
302C2×C8—1571no—
303C2×C8C22×D15711yescharacteristic
304C2×C8C22×D15711yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—3141no—
307C4⋊C4—3141no—
308C4⋊C4—3141no—
309C4⋊C4—3141no—
310C4⋊C4—3141no—
311C4⋊C4—3141no—
312C4⋊C4—3141no—
313C4⋊C4—1571no—
314C4⋊C4—1571no—
315C4⋊C4C22×D15711yescharacteristic
316C22⋊C4—21no—
317C22⋊C4—3141no—
318C22⋊C4—3141no—
319C22⋊C4—3141no—
320C22⋊C4—3141no—
321C22⋊C4—3141no—
322C22⋊C4—1571no—
323C22⋊C4—1571no—
324C42—1571no—
325C23—21no—
326C23—3141no—
327C23—1571no—
328C23D4×D15711yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—3141no—
334Q8—3141no—
335Q8—3141no—
336Q8—3141no—
337D4—21no—
338D4—42no—
339D4—3142no—
340D4—3141no—
341D4—6282no—
342D4—6282no—
343D4—6282no—
344D4—1572no—
345D4D4×D15712yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—3141no—
353C2×C4—3141no—
354C2×C4—3141no—
355C2×C4—3141no—
356C2×C4—3141no—
357C2×C4—6282no—
358C2×C4—6282no—
359C2×C4—6282no—
360C2×C4—6282no—
361C2×C4—6282no—
362C2×C4—1571no—
363C2×C4—1571no—
364C2×C4—1571no—
365C2×C4D4×D15711yescharacteristic
366C2×C4C23×D15711yescharacteristic
367C8—21no—
368C8—21no—
369C8—3141no—
370C8—1572no—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—3141no—
378C22—3141no—
379C22—3142no—
380C22—3141no—
381C22—6281no—
382C22—6281no—
383C22C2×D4×D15711yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—3141no—
389C4—3141no—
390C4—6281no—
391C4—6281no—
392C4—6281no—
393C4—1572no—
394C4C2×D4×D15711yescharacteristic
395C4#1909781611yescharacteristic
396C2—41no—
397C2—42no—
398C2—6281no—
399C2—6282no—
400C2#2375790511yescharacteristic
401C2#135×D15711yescharacteristic
402C2#2375808911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#452×C157C2
socleC22×C157C22×D4
hypercenter#452D157
hypocenterC157#3283
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#19097792C2semidirect
2. C2×#19097791C2semidirect
3. #23757925C2semidirect
4. #23757922C2semidirect
5. #23757651C2semidirect
6. #23757513C2semidirect
7. #23757512C2semidirect
8. #23757477C2semidirect
9. #23757476C2semidirect
10. #23757437C2semidirect
11. #23757436C2semidirect
12. #23757434C2semidirect
13. #23757353C2semidirect
14. #23757336C2semidirect
15. #452×C157C2semidirect
86. #14578939D4semidirect
193. Dic157#135semidirect
201. C157#3283semidirect
215. #452D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977922
C2×#190977912
#237579252
#237579222
#237576512
#237575132
#237575122
#237574772
#237574762
#237574372
#237574362
#237574342
#237573532
#237573362
#452×C1572
#3283157