Finite Group Databasebeta

← #34111685

Subgroups — #34111685

Order 20096.

478 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
2#23757934C211yesmaximal, characteristic, complemented
3#23757922C211yesmaximal, characteristic, complemented
4#23757666C211yesmaximal, characteristic, complemented
5#23757519C211yesmaximal, characteristic, complemented
6#23757511C211yesmaximal, characteristic, complemented
7#23757490C211yesmaximal, characteristic, complemented
8#23757481C211yesmaximal, characteristic, complemented
9#23757434C211yesmaximal, characteristic, complemented
10#23757432C211yesmaximal, characteristic, complemented
11#23757429C211yesmaximal, characteristic, complemented
12#23757418C211yesmaximal, characteristic, complemented
13#23757374C211yesmaximal, characteristic, complemented
14#23757342C211yesmaximal, characteristic, complemented
15C2×#137×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578953C2211yescharacteristic
18#19097792—24no—
19C2×#14578944C2211yescharacteristic
20C2×#14578944C2211yescharacteristic
21C2×#14578943C2211yescharacteristic
22C2×#14578941C2211yescharacteristic
23C2×#14578939C2211yescharacteristic
24C2×C8×D157C2211yescharacteristic
25#19097769C2211yescharacteristic
26#19097760—21no—
27#19097760C2211yescharacteristic
28#19097754—21no—
29#19097752—21no—
30#19097750C2211yescharacteristic
31#19097747—21no—
32#19097747C2211yescharacteristic
33#19097747C2211yescharacteristic
34#19097745—21no—
35#19097745C2211yescharacteristic
36#19097743—21no—
37Q8×Dic157C2211yescharacteristic
38D4×Dic157C2211yescharacteristic
39C4×C22⋊D157—21no—
40C4×C22⋊D157C2211yescharacteristic
41C2×#14578933—21no—
42#19097705C2211yescharacteristic
43#19097700C2211yescharacteristic
44#19097696C2211yescharacteristic
45#19097695C2211yescharacteristic
46#19097695C2211yescharacteristic
47#19097695C2211yescharacteristic
48#19097693C2211yescharacteristic
49#19097692C2211yescharacteristic
50C22⋊#11929434C2211yescharacteristic
51#19097683C2211yescharacteristic
52#19097681C2211yescharacteristic
53C2×#41×C157C2211yescharacteristic
54C22×Q8×C157C2211yescharacteristic
55#137×C157—24no—
56C2×Q16×C157C2211yescharacteristic
57C2×Q16×C157C2211yescharacteristic
58C2×SD16×C157C2211yescharacteristic
59C2×SD16×C157C2211yescharacteristic
60C2×M16×C157C2211yescharacteristic
61#14578955—22no—
62#14578955—41no—
63#14578953—22no—
64#14578953—41no—
65C2×Dic314C2311yescharacteristic
66C2×D628—21no—
67C2×D628C2311yescharacteristic
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C2×C22⋊D157D411yescharacteristic
71C22×Dic157—21no—
72C22×Dic157—21no—
73C2×C4×D157—21no—
74C2×C4×D157C2311yescharacteristic
75#14578944—22no—
76#14578944—41no—
77#14578943—22no—
78#14578941—41no—
79#14578939—22no—
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C8×D157—22no—
83C4⋊Dic157—21no—
84C4⋊Dic157C2311yescharacteristic
85C4⋊Dic157C2311yescharacteristic
86#14578933—21no—
87#14578933—21no—
88#14578933—21no—
89#14578933—21no—
90#14578933—21no—
91#14578933D411yescharacteristic
92C22⋊Dic157—21no—
93C22⋊Dic157—21no—
94C22⋊Dic157D411yescharacteristic
95#14578931—21no—
96#14578931—21no—
97#14578931—21no—
98#14578931—21no—
99#14578931—21no—
100#14578931D411yescharacteristic
101C4×Dic157—21no—
102C4×Dic157C2311yescharacteristic
103#41×C157—22no—
104#41×C157—41no—
105C2×Q8×C157—21no—
106C2×Q8×C157—22no—
107C2×Q8×C157—41no—
108C2×Q8×C157C2311yescharacteristic
109C2×Q8×C157C2311yescharacteristic
110C2×Q8×C157C2311yescharacteristic
111C2×D4×C157—21no—
112C2×D4×C157C2311yescharacteristic
113C22×C4×C157—21no—
114C22×C4×C157—21no—
115C22×C4×C157C2311yescharacteristic
116Q16×C157—22no—
117Q16×C157—22no—
118SD16×C157—22no—
119SD16×C157D414yescomplemented
120M16×C157—22no—
121C2×C8×C157C2311yescharacteristic
122C2×C8×C157C2311yescharacteristic
123C22×D157—21no—
124C22×D157C2×D411yescharacteristic
125Dic314—21no—
126Dic314—21no—
127D628—21no—
128D628—21no—
129D628—42no—
130C22⋊D157—41no—
131C22⋊D157—42no—
132C22⋊D157—42no—
133C2×Dic157—21no—
134C2×Dic157—21no—
135C2×Dic157—21no—
136C2×Dic157—42no—
137C2×Dic157—42no—
138C2×Dic157C2×D411yescharacteristic
139C2×Dic157C2×D411yescharacteristic
140C2×Dic157C2×D411yescharacteristic
141C4×D157—21no—
142C4×D157—21no—
143C4×D157—42no—
144#11929434—21no—
145#11929434—21no—
146C23×C157—21no—
147C23×C157C2×D411yescharacteristic
148Q8×C157—21no—
149Q8×C157—21no—
150Q8×C157—21no—
151Q8×C157—21no—
152Q8×C157—21no—
153Q8×C157—42no—
154Q8×C157C2×D412yes—
155D4×C157—21no—
156D4×C157—42no—
157D4×C157C2×D412yes—
158C2×C4×C157—21no—
159C2×C4×C157—21no—
160C2×C4×C157—21no—
161C2×C4×C157—21no—
162C2×C4×C157—21no—
163C2×C4×C157—42no—
164C2×C4×C157—42no—
165C2×C4×C157C2×D411yescharacteristic
166C2×C4×C157C2411yescharacteristic
167C8×C157—21no—
168C8×C157C2×D412yes—
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—21no—
178C2×D157—21no—
179C2×D157—41no—
180C2×D157—41no—
181C2×D157—41no—
182C4×C157—21no—
183C4×C157—22no—
184C4×C157—41no—
185C4×C157—41no—
186C4×C157C22×D411yescharacteristic
187C4×C157H(5,𝔽2)11yescharacteristic
188Dic157—21no—
189Dic157—21no—
190Dic157—21no—
191Dic157—41no—
192Dic157—41no—
193Dic157—41no—
194C2×C157—41no—
195C2×C157—42no—
196C2×C157D4211yescharacteristic
197C2×C157#57511yescharacteristic
198C2×C157#57811yescharacteristic
199D157—41no—
200D157—81no—
201C157#326911yescharacteristic, complemented, Sylow
202#3269—1571nomaximal, Sylow
203C2×#137D15711yescharacteristic, complemented
204C2×#135—1571no—
205#548—1571no—
206#547—1571no—
207#497—1571no—
208#468—1571no—
209#467—1571no—
210#463—1571no—
211#462—1571no—
212#452—1571no—
213#452—1571no—
214#451—1571no—
215#449—1571no—
216#440—1571no—
217#435—1571no—
218C2×#41—1571no—
219C2×#41—1571no—
220C2×#41C2×D15711yescharacteristic
221C22×Q8C2×D15711yescharacteristic
222#137—24no—
223#135—3144no—
224C2×Q16—1571no—
225C2×Q16—1571no—
226C2×Q16C2×D15711yescharacteristic
227C2×Q16C2×D15711yescharacteristic
228C2×SD16—1571no—
229C2×SD16—1571no—
230C2×SD16C2×D15711yescharacteristic
231C2×SD16C2×D15711yescharacteristic
232C2×D8—1571no—
233C2×M16C2×D15711yescharacteristic
234C22×C8—1571no—
235C4⋊Q8—1571no—
236#124—3141no—
237#124—1571no—
238#123—3141no—
239#123—3141no—
240C22⋊Q8—3141no—
241C22⋊Q8—1571no—
242C22⋊Q8—1571no—
243C22⋊Q8—1571no—
244#121—3141no—
245#121—3141no—
246#121—1571no—
247C4×Q8—1571no—
248C4×D4—3141no—
249C4×D4—1571no—
250C4×D4—1571no—
251C2×C4⋊C4—3141no—
252#107—1571no—
253C4⋊C8—1571no—
254#103—1571no—
255#103—1571no—
256#103—1571no—
257#103—1571no—
258#102—1571no—
259#102—1571no—
260C22⋊C8—1571no—
261C22⋊C8—1571no—
262#97—1571no—
263#41—22no—
264#41—41no—
265#41—3142no—
266#41—3142no—
267#41—6281no—
268#41—6281no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—1571no—
273C2×Q8C22×D15711yescharacteristic
274C2×Q8C22×D15711yescharacteristic
275C2×Q8C22×D15711yescharacteristic
276C2×D4—21no—
277C2×D4—3141no—
278C2×D4—3141no—
279C2×D4—3141no—
280C2×D4—1571no—
281C2×D4—1571no—
282C2×D4C22×D15711yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—3141no—
286C22×C4—3141no—
287C22×C4—3141no—
288C22×C4—1571no—
289C22×C4C22×D15711yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—3142no—
293Q16—6281no—
294SD16—22no—
295SD16—3142no—
296SD16—6281no—
297SD16C22⋊D15714yescomplemented
298D8—3142no—
299M16—22no—
300C2×C8—3142no—
301C2×C8—1571no—
302C2×C8—1571no—
303C2×C8C22×D15711yescharacteristic
304C2×C8C22×D15711yescharacteristic
305C4⋊C4—3141no—
306C4⋊C4—3141no—
307C4⋊C4—3141no—
308C4⋊C4—3141no—
309C4⋊C4—3141no—
310C4⋊C4—3141no—
311C4⋊C4—1571no—
312C4⋊C4—1571no—
313C4⋊C4—1571no—
314C22⋊C4—3141no—
315C22⋊C4—3141no—
316C22⋊C4—3141no—
317C22⋊C4—3141no—
318C22⋊C4—3141no—
319C22⋊C4—3141no—
320C22⋊C4—3141no—
321C22⋊C4—1571no—
322C22⋊C4—1571no—
323C42—3141no—
324C42—1571no—
325C23—21no—
326C23—3141no—
327C23—1571no—
328C23D4×D15711yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—3141no—
336Q8—3141no—
337Q8C2×C22⋊D15712yes—
338D4—21no—
339D4—42no—
340D4—3141no—
341D4—3141no—
342D4—6282no—
343D4—6281no—
344D4—6282no—
345D4—6282no—
346D4C2×C22⋊D15712yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—3141no—
355C2×C4—3141no—
356C2×C4—3141no—
357C2×C4—3141no—
358C2×C4—3141no—
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—3141no—
369C8—3141no—
370C8C2×C22⋊D15712yes—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—3141no—
378C22—3141no—
379C22—3141no—
380C22—6281no—
381C22—6281no—
382C22—6281no—
383C22C2×D4×D15711yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—3141no—
389C4—3141no—
390C4—3141no—
391C4—6281no—
392C4—6281no—
393C4—6281no—
394C4C22×C22⋊D15711yescharacteristic
395C4#1909781611yescharacteristic
396C2—41no—
397C2—42no—
398C2—6281no—
399C2—12561no—
400C2D4×C22⋊D15711yescharacteristic
401C2#2375807211yescharacteristic
402C2#2375808911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#137×C157C2
socleC22×C157C22×D4
hypercenterC2×#137D157
hypocenterC157#3269
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#19097792C2semidirect
2. #23757934C2semidirect
3. #23757922C2semidirect
4. #23757666C2semidirect
5. #23757519C2semidirect
6. #23757511C2semidirect
7. #23757490C2semidirect
8. #23757481C2semidirect
9. #23757434C2semidirect
10. #23757432C2semidirect
11. #23757429C2semidirect
12. #23757418C2semidirect
13. #23757374C2semidirect
14. #23757342C2semidirect
15. C2×#137×C157C2semidirect
119. SD16×C157D4semidirect
201. C157#3269semidirect
203. C2×#137D157semidirect
297. SD16C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977922
#237579342
#237579222
#237576662
#237575192
#237575112
#237574902
#237574812
#237574342
#237574322
#237574292
#237574182
#237573742
#237573422
C2×#137×C1572
#3269157