Finite Group Databasebeta

← #34102857

Subgroups — #34102857

Order 20096.

740 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097767C211yesmaximal, characteristic
2C2×C4×C22⋊D157C211yesmaximal, characteristic, complemented
3C2×#19097731C211yesmaximal, characteristic, complemented
4#23757173C211yesmaximal, characteristic, complemented
5#23757173C211yesmaximal, characteristic, complemented
6#23757153C211yesmaximal, characteristic, complemented
7#23757152C211yesmaximal, characteristic, complemented
8#23757151C211yesmaximal, characteristic, complemented
9#23757151C211yesmaximal, characteristic, complemented
10#23757150C211yesmaximal, characteristic, complemented
11#23757149C211yesmaximal, characteristic, complemented
12#23757149C211yesmaximal, characteristic, complemented
13#23757137C211yesmaximal, characteristic, complemented
14#23757118C211yesmaximal, characteristic, complemented
15#386×C157C211yesmaximal, characteristic, complemented
16C22×D628C2211yescharacteristic
17C22×C22⋊D157C2211yescharacteristic
18C22×C22⋊D157C2211yescharacteristic
19C22×C22⋊D157C2211yescharacteristic
20C22×C22⋊D157C2211yescharacteristic
21C23×Dic157C2211yescharacteristic
22C22×C4×D157C2211yescharacteristic
23C22×C4×D157C2211yescharacteristic
24#19097767C418yescomplemented
25C4×C22⋊D157—24no—
26#19097731—24no—
27C2×#14578933C2211yescharacteristic
28C2×#14578933C2211yescharacteristic
29C2×C22⋊Dic157C2211yescharacteristic
30C2×C22⋊Dic157C2211yescharacteristic
31C2×C22⋊Dic157C2211yescharacteristic
32C2×#14578931C2211yescharacteristic
33C2×#14578931C2211yescharacteristic
34C2×#14578931C2211yescharacteristic
35C2×#14578931C2211yescharacteristic
36C2×#14578931C2211yescharacteristic
37C2×#14578931C2211yescharacteristic
38C2×C4×Dic157C2211yescharacteristic
39C2×C4×Dic157C2211yescharacteristic
40C2×C4×Dic157C2211yescharacteristic
41#19097678C2211yescharacteristic
42#19097678C2211yescharacteristic
43#19097678C2211yescharacteristic
44#19097678C2211yescharacteristic
45#19097678C2211yescharacteristic
46#19097678C2211yescharacteristic
47C22×D4×C157C2211yescharacteristic
48C23×C4×C157C2211yescharacteristic
49C2×C22⋊C4×C157C2211yescharacteristic
50C2×C22⋊C4×C157C2211yescharacteristic
51C2×C22⋊C4×C157C2211yescharacteristic
52#95×C157C2211yescharacteristic
53#95×C157C2211yescharacteristic
54C23×D157C2311yescharacteristic
55C23×D157C2311yescharacteristic
56C2×D628—41no—
57C2×D628—41no—
58C2×D628C2×C414yescomplemented
59C2×C22⋊D157—22no—
60C2×C22⋊D157—22no—
61C2×C22⋊D157—22no—
62C2×C22⋊D157—22no—
63C2×C22⋊D157—41no—
64C2×C22⋊D157—41no—
65C2×C22⋊D157—41no—
66C2×C22⋊D157—41no—
67C2×C22⋊D157C2×C414yescomplemented
68C2×C22⋊D157C2×C414yescomplemented
69C2×C22⋊D157C2×C414yescomplemented
70C2×C22⋊D157C2×C414yescomplemented
71C22×Dic157—22no—
72C22×Dic157—41no—
73C22×Dic157—41no—
74C22×Dic157C2311yescharacteristic
75C22×Dic157C2311yescharacteristic
76C22×Dic157C2311yescharacteristic
77C22×Dic157C2311yescharacteristic
78C22×Dic157C2311yescharacteristic
79C22×Dic157C2311yescharacteristic
80C2×C4×D157—22no—
81C2×C4×D157—22no—
82C2×C4×D157—41no—
83C2×C4×D157—41no—
84C2×C4×D157—41no—
85C2×C4×D157—41no—
86#14578933—22no—
87#14578933—22no—
88C22⋊Dic157—22no—
89C22⋊Dic157—41no—
90C22⋊Dic157—41no—
91#14578931—22no—
92#14578931—22no—
93#14578931—41no—
94#14578931—41no—
95#14578931—41no—
96#14578931—41no—
97C4×Dic157—22no—
98C4×Dic157C2×C414yescomplemented
99C4×Dic157D414yescomplemented
100C24×C157C2311yescharacteristic
101C24×C157C2311yescharacteristic
102C2×D4×C157—41no—
103C2×D4×C157—41no—
104C2×D4×C157C2×C414yescomplemented
105C22×C4×C157—22no—
106C22×C4×C157—41no—
107C22×C4×C157—41no—
108C22×C4×C157C2311yescharacteristic
109C22×C4×C157C2311yescharacteristic
110C22×C4×C157C2311yescharacteristic
111C22×C4×C157C2311yescharacteristic
112C22×C4×C157C2311yescharacteristic
113C22⋊C4×C157—22no—
114C22⋊C4×C157—41no—
115C22⋊C4×C157—41no—
116C22×D157—21no—
117C22×D157—21no—
118C22×D157—21no—
119C22×D157—21no—
120C22×D157—21no—
121C22×D157—21no—
122C22×D157—21no—
123C22×D157—21no—
124C22×D157—21no—
125C22×D157—21no—
126C22×D157—21no—
127C22×D157—21no—
128C22×D157C22×C412yes—
129C22×D157C22×C412yes—
130D628—44no—
131C22⋊D157—28no—
132C22⋊D157—28no—
133C22⋊D157—44no—
134C22⋊D157—44no—
135C2×Dic157—21no—
136C2×Dic157—21no—
137C2×Dic157—21no—
138C2×Dic157—21no—
139C2×Dic157—21no—
140C2×Dic157—21no—
141C2×Dic157—21no—
142C2×Dic157—21no—
143C2×Dic157—21no—
144C2×Dic157—21no—
145C2×Dic157—21no—
146C2×Dic157—21no—
147C2×Dic157—21no—
148C2×Dic157—44no—
149C2×Dic157C22×C412yes—
150C2×Dic157C22×C412yes—
151C2×Dic157C2×D412yes—
152C2×Dic157C2×D412yes—
153C2×Dic157#4112yes—
154C4×D157—44no—
155C4×D157—44no—
156C23×C157—21no—
157C23×C157—21no—
158C23×C157—21no—
159C23×C157—21no—
160C23×C157—21no—
161C23×C157—21no—
162C23×C157—21no—
163C23×C157—21no—
164C23×C157—21no—
165C23×C157—21no—
166C23×C157—21no—
167C23×C157—21no—
168C23×C157C22×C412yes—
169C23×C157C22×C412yes—
170C23×C157C2411yescharacteristic
171D4×C157—44no—
172C2×C4×C157—21no—
173C2×C4×C157—21no—
174C2×C4×C157—21no—
175C2×C4×C157—21no—
176C2×C4×C157—21no—
177C2×C4×C157—21no—
178C2×C4×C157—21no—
179C2×C4×C157—21no—
180C2×C4×C157—21no—
181C2×C4×C157—21no—
182C2×C4×C157—21no—
183C2×C4×C157—21no—
184C2×C4×C157—21no—
185C2×C4×C157—44no—
186C2×C4×C157C22×C412yes—
187C2×C4×C157C2×D412yes—
188C22×C157—22no—
189C22×C157—22no—
190C22×C157—22no—
191C22×C157—22no—
192C22×C157—22no—
193C22×C157—22no—
194C22×C157—41no—
195C22×C157—41no—
196C22×C157—41no—
197C22×C157—41no—
198C22×C157—41no—
199C22×C157—41no—
200C22×C157—41no—
201C22×C157—41no—
202C22×C157C23×C411yescharacteristic
203C22×C157C22×D411yescharacteristic
204C22×C157C2×#4111yescharacteristic
205C22×C157H(5,𝔽2)11yescharacteristic
206C22×C157H(5,𝔽2)11yescharacteristic
207C22×C157H(5,𝔽2)11yescharacteristic
208C22×C157H(5,𝔽2)11yescharacteristic
209C2×D157—22no—
210C2×D157—22no—
211C2×D157—22no—
212C2×D157—22no—
213C2×D157—22no—
214C2×D157—22no—
215C2×D157—41no—
216C2×D157—41no—
217C2×D157—41no—
218C2×D157—41no—
219C2×D157—41no—
220C2×D157—41no—
221C2×D157—41no—
222C2×D157—41no—
223C4×C157—22no—
224C4×C157—22no—
225C4×C157—41no—
226C4×C157—41no—
227C4×C157—41no—
228Dic157—22no—
229Dic157—22no—
230Dic157—41no—
231Dic157—41no—
232Dic157—41no—
233Dic157C4×D414yes—
234C2×C157—42no—
235C2×C157—42no—
236C2×C157C2×C4×D411yescharacteristic
237C2×C157#51811yescharacteristic
238C2×C157#51811yescharacteristic
239C2×C157#53511yescharacteristic
240C2×C157#53511yescharacteristic
241C2×C157#54011yescharacteristic
242C2×C157#54011yescharacteristic
243D157—42no—
244D157—42no—
245C157#232811yescharacteristic, complemented, Sylow
246#2328—1571nomaximal, Sylow
247C2×#127—1571no—
248C2×C4×D4—1571no—
249C2×C4×D4—1571no—
250#390—1571no—
251#390—1571no—
252#386—1571no—
253#386—1571no—
254#386—1571no—
255#386—1571no—
256#386—1571no—
257#386—1571no—
258#386—1571no—
259#386D15711yescharacteristic, complemented
260#382—1571no—
261#376—1571no—
262C22×D4—1571no—
263C22×D4—1571no—
264C22×D4—1571no—
265C22×D4—1571no—
266C22×D4—1571no—
267C22×D4C2×D15711yescharacteristic
268C23×C4—1571no—
269C23×C4—1571no—
270C23×C4—1571no—
271C23×C4C2×D15711yescharacteristic
272#127—1578no—
273C4×D4—3144no—
274C4×D4—3144no—
275C2×C4⋊C4—1571no—
276C2×C4⋊C4—1571no—
277C2×C22⋊C4—1571no—
278C2×C22⋊C4—1571no—
279C2×C22⋊C4—1571no—
280C2×C22⋊C4—1571no—
281C2×C22⋊C4—1571no—
282C2×C22⋊C4—1571no—
283C2×C22⋊C4—1571no—
284C2×C22⋊C4—1571no—
285C2×C22⋊C4—1571no—
286C2×C22⋊C4C2×D15711yescharacteristic
287C2×C22⋊C4C2×D15711yescharacteristic
288C2×C22⋊C4C2×D15711yescharacteristic
289C2×C42—1571no—
290C2×C42—1571no—
291C2×C42—1571no—
292#95—1571no—
293#95—1571no—
294#95—1571no—
295#95—1571no—
296#95—1571no—
297#95—1571no—
298#95C2×D15711yescharacteristic
299#95C2×D15711yescharacteristic
300C24—1571no—
301C24—1571no—
302C24C22×D15711yescharacteristic
303C24C22×D15711yescharacteristic
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—3142no—
307C2×D4—3142no—
308C2×D4—3142no—
309C2×D4—3142no—
310C2×D4—6281no—
311C2×D4—6281no—
312C2×D4—6281no—
313C2×D4—6281no—
314C2×D4—6281no—
315C2×D4—6281no—
316C2×D4—1574no—
317C2×D4—1574no—
318C2×D4—1574no—
319C2×D4—1574no—
320C2×D4—1574no—
321C2×D4C4×D15714yescomplemented
322C22×C4—22no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—3142no—
326C22×C4—3142no—
327C22×C4—3142no—
328C22×C4—6281no—
329C22×C4—6281no—
330C22×C4—6281no—
331C22×C4—6281no—
332C22×C4—6281no—
333C22×C4—6281no—
334C22×C4—1571no—
335C22×C4—1571no—
336C22×C4—1571no—
337C22×C4—1571no—
338C22×C4—1571no—
339C22×C4—1571no—
340C22×C4C22×D15711yescharacteristic
341C22×C4C22×D15711yescharacteristic
342C22×C4C22×D15711yescharacteristic
343C22×C4C22×D15711yescharacteristic
344C22×C4C22×D15711yescharacteristic
345C4⋊C4—3142no—
346C4⋊C4—3142no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—3142no—
351C22⋊C4—3142no—
352C22⋊C4—3142no—
353C22⋊C4—6281no—
354C22⋊C4—6281no—
355C22⋊C4—6281no—
356C22⋊C4—6281no—
357C22⋊C4—6281no—
358C22⋊C4—6281no—
359C42—3142no—
360C42—1574no—
361C42—1574no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—3141no—
375C23—3141no—
376C23—3141no—
377C23—3141no—
378C23—3141no—
379C23—3141no—
380C23—3141no—
381C23—3141no—
382C23—3141no—
383C23—3141no—
384C23—3141no—
385C23—3141no—
386C23—1572no—
387C23—1572no—
388C23C2×C4×D15712yes—
389C23C2×C4×D15712yes—
390C23C23×D15711yescharacteristic
391D4—44no—
392D4—3148no—
393D4—3148no—
394D4—6284no—
395D4—6284no—
396D4—6284no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—44no—
411C2×C4—3141no—
412C2×C4—3141no—
413C2×C4—3141no—
414C2×C4—3141no—
415C2×C4—3141no—
416C2×C4—3141no—
417C2×C4—3141no—
418C2×C4—3141no—
419C2×C4—3141no—
420C2×C4—3141no—
421C2×C4—3141no—
422C2×C4—3141no—
423C2×C4—3141no—
424C2×C4—6284no—
425C2×C4—6284no—
426C2×C4—6284no—
427C2×C4—1572no—
428C2×C4—1572no—
429C2×C4—1572no—
430C2×C4—1572no—
431C2×C4—1572no—
432C2×C4C2×C4×D15712yes—
433C2×C4D4×D15712yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—3142no—
449C22—3142no—
450C22—3142no—
451C22—3142no—
452C22—3142no—
453C22—3142no—
454C22—6281no—
455C22—6281no—
456C22—6281no—
457C22—6281no—
458C22—6281no—
459C22—6281no—
460C22—6281no—
461C22—6281no—
462C22C22×C4×D15711yescharacteristic
463C22C2×D4×D15711yescharacteristic
464C22#41×D15711yescharacteristic
465C22#1909781611yescharacteristic
466C22#1909781611yescharacteristic
467C22#1909781611yescharacteristic
468C22#1909781711yescharacteristic
469C4—22no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—3142no—
475C4—3142no—
476C4—6281no—
477C4—6281no—
478C4—6281no—
479C4—1574no—
480C2—42no—
481C2—42no—
482C2—6282no—
483C2—6282no—
484C2C4×D4×D15711yescharacteristic
485C2#2375774511yescharacteristic
486C2#2375774611yescharacteristic
487C2#2375783811yescharacteristic
488C2#2375783911yescharacteristic
489C2#2375787311yescharacteristic
490C2#2375787511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutatorC22×C157C23×C4
Fitting#386×C157C2
socle, cosocleC23×C157C24
prime radicalC2×#19097767C2
hypercenter#386D157
hypocenterC157#2328
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D157C2semidirect
3. C2×#19097731C2semidirect
4. #23757173C2semidirect
5. #23757173C2semidirect
6. #23757153C2semidirect
7. #23757152C2semidirect
8. #23757151C2semidirect
9. #23757151C2semidirect
10. #23757150C2semidirect
11. #23757149C2semidirect
12. #23757149C2semidirect
13. #23757137C2semidirect
14. #23757118C2semidirect
15. #386×C157C2semidirect
24. #19097767C4semidirect
58. C2×D628C2×C4semidirect
67. C2×C22⋊D157C2×C4semidirect
68. C2×C22⋊D157C2×C4semidirect
69. C2×C22⋊D157C2×C4semidirect
70. C2×C22⋊D157C2×C4semidirect
98. C4×Dic157C2×C4semidirect
99. C4×Dic157D4semidirect
104. C2×D4×C157C2×C4semidirect
245. C157#2328semidirect
259. #386D157semidirect
321. C2×D4C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977672
C2×C4×C22⋊D1572
C2×#190977312
#237571732
#237571532
#237571522
#237571512
#237571502
#237571492
#237571372
#237571182
#386×C1572
#2328157