Finite Group Databasebeta

← C4×#16837833 #28741968

Subgroups — C4×#16837833 #28741968

Order 15104.

690 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837833C211yesmaximal, characteristic
2C4×#14273750C211yesmaximal, characteristic, complemented
3C4×#14273746C211yesmaximal, characteristic, complemented
4C4×#14273673C211yesmaximal, characteristic, complemented
5#21425952C211yesmaximal, characteristic, complemented
6C4×#14273672C211yesmaximal, characteristic, complemented
7SD32×Dic59C211yesmaximal, characteristic, complemented
8#21425947C211yesmaximal, characteristic, complemented
9C4×#14273668C211yesmaximal, characteristic, complemented
10#21425940C211yesmaximal, characteristic, complemented
11#21425879C211yesmaximal, characteristic, complemented
12#21425802C211yesmaximal, characteristic, complemented
13#21425800C211yesmaximal, characteristic, complemented
14C4×C16×D59C211yesmaximal, characteristic, complemented
15C4×SD32×C59C211yesmaximal, characteristic, complemented
16C2×#14273750C2211yescharacteristic
17C2×#14273746C2211yescharacteristic
18C4×#11745689—21no—
19C4×#11745687—21no—
20#16837833C418yesdirect product factor
21C2×#14273673C2211yescharacteristic
22C2×#14273672C2211yescharacteristic
23C2×#14273668C2211yescharacteristic
24C2×C16×D59C2211yescharacteristic
25C2×C16×D59C2211yescharacteristic
26C4×Dic236C2211yescharacteristic
27Q16×Dic59C2211yescharacteristic
28#16837496C2211yescharacteristic
29#16837493—21no—
30C4×#11745671—21no—
31C4×#11745670—21no—
32#16837487—21no—
33C4×D472C2211yescharacteristic
34D8×Dic59C2211yescharacteristic
35#16837484C2211yescharacteristic
36#16837439C2211yescharacteristic
37#16837439C2211yescharacteristic
38#16837397—21no—
39#16837395—21no—
40C4×C8×D59C2211yescharacteristic
41#16837230C2211yescharacteristic
42#16837227C2211yescharacteristic
43#16837227C2211yescharacteristic
44#16837207C2211yescharacteristic
45#16837206C2211yescharacteristic
46#16837205C2211yescharacteristic
47#16837204C2211yescharacteristic
48#16837203C2211yescharacteristic
49#16837202C2211yescharacteristic
50C4×C59⋊C16C2211yescharacteristic
51C16×Dic59C2211yescharacteristic
52C16×Dic59C2211yescharacteristic
53C2×SD32×C59C2211yescharacteristic
54C4×Q16×C59C2211yescharacteristic
55C4×D8×C59C2211yescharacteristic
56C59×#367C2211yescharacteristic
57C59×#358C2211yescharacteristic
58C59×#357C2211yescharacteristic
59C4×C16×C59C2211yescharacteristic
60C2×#11745689—21no—
61C2×#11745687—21no—
62#14273750—22no—
63#14273750C2×C414yescomplemented
64#14273746—22no—
65#14273746C2×C414yescomplemented
66C2×Dic236C2311yescharacteristic
67C2×#11745670—21no—
68C2×#11745671—21no—
69C2×D472C2311yescharacteristic
70C2×C8×D59D411yescharacteristic
71C2×C8×D59C2311yescharacteristic
72Q8×Dic59—21no—
73C4×Dic118—21no—
74#14273692—21no—
75C4×D236—21no—
76C4×D236—41no—
77D4×Dic59—21no—
78#14273689—21no—
79#14273689—41no—
80C4×C22⋊D59—41no—
81(C22⋊D59)⋊C4—41no—
82#14273685—21no—
83#14273685—21no—
84#14273685—41no—
85#14273683—41no—
86C2×C4×Dic59—41no—
87C42×D59—41no—
88C42×D59D411yescharacteristic
89#14273673C2×C414yescomplemented
90#14273672C2×C414yescomplemented
91#14273668C2×C414yescomplemented
92C2×C59⋊C16C2311yescharacteristic
93C2×C59⋊C16C2311yescharacteristic
94C16×D59—22no—
95C16×D59C2×C414yescomplemented
96#14273661C2311yescharacteristic
97#14273661C2311yescharacteristic
98#14273658—21no—
99#14273658—21no—
100#14273652—21no—
101#14273651—21no—
102#14273650—21no—
103#14273649—21no—
104#14273648—21no—
105#14273647—21no—
106C4×C59⋊C8D411yescharacteristic
107C8×Dic59D411yescharacteristic
108C8×Dic59C2311yescharacteristic
109C2×Q16×C59C2311yescharacteristic
110C2×D8×C59C2311yescharacteristic
111C4×Q8×C59—21no—
112C4×D4×C59—21no—
113SD32×C59C2×C414yescomplemented
114C2×C16×C59C2311yescharacteristic
115C2×C16×C59C2311yescharacteristic
116#107×C59C2311yescharacteristic
117#107×C59C2311yescharacteristic
118#103×C59—21no—
119#102×C59—21no—
120C4×C8×C59C2311yescharacteristic
121C2×Q8×C59—21no—
122C2×D4×C59—21no—
123C22×C4×C59—41no—
124C2×C22⋊D59—41no—
125C22×Dic59—41no—
126C22×Dic59—41no—
127#11745689—24no—
128#11745689—42no—
129#11745687—24no—
130#11745687—42no—
131C2×D236—21no—
132C2×D236—41no—
133C2×C4×D59—41no—
134C2×C4×D59—41no—
135C2×C4×D59—41no—
136C2×C4×D59D811yescharacteristic
137C2×C4×D59D811yescharacteristic
138C2×C4×D59C2×D411yescharacteristic
139C2×Dic118—21no—
140Q16×C59—21no—
141Q16×C59C22×C412yes—
142D8×C59—21no—
143D8×C59C22×C412yes—
144C2×C8×C59C2×D411yescharacteristic
145C2×C8×C59C2411yescharacteristic
146C4⋊C4×C59—21no—
147C4⋊C4×C59—21no—
148C4⋊C4×C59—41no—
149C22⋊C4×C59—41no—
150C42×C59—41no—
151C42×C59C2×D411yescharacteristic
152C22⋊Dic59—41no—
153#11745671—24no—
154#11745670—24no—
155(C2×D59)⋊C4—41no—
156(C2×D59)⋊C4—41no—
157(C2×D59)⋊C4—41no—
158(C2×D59)⋊C4—41no—
159C4⋊Dic59—21no—
160C4⋊Dic59—21no—
161C4⋊Dic59—41no—
162Dic59⋊C4—41no—
163Dic59⋊C4—41no—
164C4×Dic59—41no—
165C4×Dic59—41no—
166C4×Dic59—41no—
167C4×Dic59—41no—
168C4×Dic59—41no—
169C4×Dic59D811yescharacteristic
170C4×Dic59D811yescharacteristic
171C4×Dic59C2×D411yescharacteristic
172C2×C59⋊C8C2×D411yescharacteristic
173C2×C59⋊C8C2×D411yescharacteristic
174Dic236—21no—
175Dic236C22×C412yes—
176D472—21no—
177D472C22×C412yes—
178C8×D59—22no—
179C8×D59C22×C412yes—
180C8×D59#4112yes—
181C16×C59—21no—
182C16×C59C22×C412yes—
183C59⋊C16—21no—
184C59⋊C16C22×C412yes—
185C23×C59—41no—
186C22×D59—41no—
187C22×D59C2×D811yescharacteristic
188Q8×C59—22no—
189Q8×C59—41no—
190D4×C59—22no—
191D4×C59—41no—
192C2×C4×C59—41no—
193C2×C4×C59—41no—
194C2×C4×C59—41no—
195C2×C4×C59—82no—
196C2×C4×C59C2×D811yescharacteristic
197C2×C4×C59C2×D811yescharacteristic
198C2×C4×C59C22×D411yescharacteristic
199C22⋊D59—44no—
200C2×Dic59—41no—
201C2×Dic59—44no—
202C2×Dic59—41no—
203C2×Dic59—41no—
204C2×Dic59—82no—
205C2×Dic59C2×D811yescharacteristic
206C2×Dic59C2×D811yescharacteristic
207C2×Dic59C2×D811yescharacteristic
208D236—22no—
209D236—44no—
210D236—41no—
211C4×D59—22no—
212C4×D59—22no—
213C4×D59—44no—
214C4×D59—82no—
215C4×D59—82no—
216C4×D59C4×D412yes—
217C4×D59#13512yes—
218Dic118—22no—
219Dic118—41no—
220C8×C59—21no—
221C8×C59C23×C411yescharacteristic
222C8×C59C2×#4111yescharacteristic
223C59⋊C8—21no—
224C59⋊C8C4×D412yes—
225C4×#508—591nomaximal, Sylow
226C22×C59—42no—
227C22×C59—81no—
228C22×C59—81no—
229C22×C59C22×D811yescharacteristic
230C2×D59—21no—
231C2×D59—21no—
232C2×D59—42no—
233C2×D59—81no—
234C2×D59—81no—
235C2×D59C4×D812yes—
236C4×C59—21no—
237C4×C59—42no—
238C4×C59—81no—
239C4×C59—81no—
240C4×C59#50812yescomplemented
241C4×C59C2×C4×D411yescharacteristic
242C4×C59C2×#13511yescharacteristic
243Dic59—21no—
244Dic59—42no—
245Dic59—81no—
246Dic59—81no—
247Dic59C4×D812yes—
248Dic59#50812yescomplemented
249C2×#508—591no—
250C4×#135—591no—
251C4×#135—591no—
252C4×Q32—591no—
253C4×Q32—591no—
254C4×SD32—591no—
255C4×SD32—591no—
256C4×SD32—591no—
257C4×SD32D5911yescharacteristic, complemented
258C4×D16—591no—
259C4×D16—591no—
260#2158—591no—
261#2138—591no—
262#2138—591no—
263C2×C4×C16—591no—
264C2×C59—82no—
265C2×C59C2×C4×D811yescharacteristic
266C2×C59C2×#50811yescharacteristic
267C2×C59C2×#50811yescharacteristic
268D59—22no—
269D59—82no—
270C2×#135—591no—
271C2×#135—591no—
272C4×#41—1181no—
273C4×#41—1181no—
274#508—598no—
275C2×Q32—591no—
276C2×SD32—591no—
277C2×SD32C2×D5911yescharacteristic
278C2×D16—591no—
279C22×C16—591no—
280C22×C16—591no—
281C4×Q16—591no—
282C4×Q16—591no—
283C4×Q16—591no—
284C4×Q16C2×D5911yescharacteristic
285C4×SD16—1181no—
286C4×SD16—1181no—
287C4×SD16—1181no—
288C4×SD16—1181no—
289C4×D8—591no—
290C4×D8—591no—
291C4×D8—591no—
292C4×D8C2×D5911yescharacteristic
293#427—591no—
294#427—591no—
295#416—1181no—
296#416—1181no—
297C2×C4×C8—591no—
298#367—591no—
299#367C2×D5911yescharacteristic
300#366—591no—
301#366—591no—
302#358—591no—
303#358—591no—
304#358—591no—
305#358C2×D5911yescharacteristic
306#357—591no—
307#357—591no—
308#357—591no—
309#357C2×D5911yescharacteristic
310C4×C16—591no—
311C4×C16—591no—
312C4×C16—591no—
313C4×C16C2×D5911yescharacteristic
314C59C4×#50811yescharacteristic, complemented, Sylow
315C2×#41—1181no—
316C2×#41—1181no—
317#135—594no—
318#135—594no—
319#135—1182no—
320#135—1182no—
321C2×Q16—591no—
322C2×Q16C22×D5911yescharacteristic
323C2×SD16—1181no—
324C2×SD16—1181no—
325C2×D8—591no—
326C2×D8C22×D5911yescharacteristic
327C22×C8—591no—
328C22×C8—591no—
329C4×Q8—21no—
330C4×Q8—1181no—
331C4×Q8—1181no—
332C4×Q8—1181no—
333C4×D4—21no—
334C4×D4—1181no—
335C4×D4—1181no—
336C4×D4—1181no—
337C4×D4—2361no—
338C4×D4—2361no—
339C4×D4—2361no—
340C4×D4—2361no—
341#117—1181no—
342#117—1181no—
343#117—2361no—
344#117—2361no—
345C2×C42—591no—
346C2×C42—2361no—
347C2×C42—2361no—
348Q32—594no—
349SD32—594no—
350SD32C4×D5914yescomplemented
351D16—594no—
352C2×C16—591no—
353C2×C16—594no—
354C2×C16—591no—
355C2×C16—1182no—
356C2×C16C22×D5911yescharacteristic
357C2×C16C22×D5911yescharacteristic
358#107—591no—
359#107—591no—
360#107C22×D5911yescharacteristic
361#107C22×D5911yescharacteristic
362#106—1181no—
363#106—1181no—
364#103—21no—
365#103—1181no—
366#103—1181no—
367#103—1181no—
368#102—21no—
369#102—1181no—
370#102—1181no—
371#102—1181no—
372C4×C8—591no—
373C4×C8—591no—
374C4×C8—591no—
375C4×C8C22×D5911yescharacteristic
376#41—1184no—
377#41—1184no—
378#41—2362no—
379#41—2362no—
380C2×Q8—21no—
381C2×Q8—1181no—
382C2×D4—21no—
383C2×D4—1181no—
384C2×D4—2361no—
385C2×D4—2361no—
386C22×C4—41no—
387C22×C4—591no—
388C22×C4—591no—
389C22×C4—591no—
390C22×C4—2361no—
391C22×C4—2361no—
392C22×C4—2361no—
393C22×C4—2361no—
394C22×C4—2361no—
395Q16—21no—
396Q16—592no—
397Q16—1181no—
398Q16C2×C4×D5912yes—
399SD16—1184no—
400SD16—1184no—
401D8—21no—
402D8—592no—
403D8—1181no—
404D8C2×C4×D5912yes—
405C2×C8—591no—
406C2×C8—592no—
407C2×C8—592no—
408C2×C8—591no—
409C2×C8—1182no—
410C2×C8D4×D5911yescharacteristic
411C2×C8C23×D5911yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—41no—
415C4⋊C4—1181no—
416C4⋊C4—1181no—
417C4⋊C4—2361no—
418C4⋊C4—2361no—
419C4⋊C4—2361no—
420C22⋊C4—41no—
421C22⋊C4—2361no—
422C22⋊C4—2361no—
423C22⋊C4—2361no—
424C22⋊C4—2361no—
425C22⋊C4—2361no—
426C42—41no—
427C42—591no—
428C42—591no—
429C42—591no—
430C42—2361no—
431C42—2361no—
432C42—2361no—
433C42—2361no—
434C42—2361no—
435C42D4×D5911yescharacteristic
436C16—21no—
437C16—592no—
438C16—1181no—
439C16C2×C4×D5912yes—
440C23—41no—
441C23—591no—
442C23—2361no—
443Q8—22no—
444Q8—41no—
445Q8—1182no—
446Q8—2361no—
447D4—22no—
448D4—41no—
449D4—1182no—
450D4—2364no—
451D4—2364no—
452D4—2361no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—82no—
457C2×C4—591no—
458C2×C4—591no—
459C2×C4—592no—
460C2×C4—592no—
461C2×C4—591no—
462C2×C4—1182no—
463C2×C4—1182no—
464C2×C4—4722no—
465C2×C4—4722no—
466C2×C4—4722no—
467C2×C4—2364no—
468C2×C4—2364no—
469C2×C4—2361no—
470C2×C4—2361no—
471C2×C4—2361no—
472C2×C4D8×D5911yescharacteristic
473C2×C4D8×D5911yescharacteristic
474C2×C4C2×D4×D5911yescharacteristic
475C8—21no—
476C8—592no—
477C8—1181no—
478C8C22×C4×D5911yescharacteristic
479C8#41×D5911yescharacteristic
480C22—42no—
481C22—81no—
482C22—81no—
483C22—592no—
484C22—1181no—
485C22—1181no—
486C22—4721no—
487C22—4721no—
488C22—2362no—
489C22C2×D8×D5911yescharacteristic
490C4—21no—
491C4—42no—
492C4—81no—
493C4—81no—
494C4—592no—
495C4—592no—
496C4—1181no—
497C4—4721no—
498C4—4721no—
499C4—2362no—
500C4#1683783312yesdirect product factor
501C4C4×D4×D5911yescharacteristic
502C4#135×D5911yescharacteristic
503C2—82no—
504C2—1182no—
505C2—4722no—
506C2C4×D8×D5911yescharacteristic
507C2#508×D5911yescharacteristic
508C2C2×#1683783311yescharacteristic
subgroupG/H
centerC2×C4D8×D59
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
FittingC4×SD32×C59C2
socleC22×C59C22×D8
prime radicalC2×#16837833C2
cosocleC2×C8×C59C24
hypercenterC4×SD32D59
hypocenterC59C4×#508
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. C4×#14273750C2semidirect
3. C4×#14273746C2semidirect
4. C4×#14273673C2semidirect
5. #21425952C2semidirect
6. C4×#14273672C2semidirect
7. SD32×Dic59C2semidirect
8. #21425947C2semidirect
9. C4×#14273668C2semidirect
10. #21425940C2semidirect
11. #21425879C2semidirect
12. #21425802C2semidirect
13. #21425800C2semidirect
14. C4×C16×D59C2semidirect
15. C4×SD32×C59C2semidirect
20. #16837833C4direct (N × H)
63. #14273750C2×C4semidirect
65. #14273746C2×C4semidirect
89. #14273673C2×C4semidirect
90. #14273672C2×C4semidirect
91. #14273668C2×C4semidirect
95. C16×D59C2×C4semidirect
113. SD32×C59C2×C4semidirect
240. C4×C59#508semidirect
248. Dic59#508semidirect
257. C4×SD32D59semidirect
314. C59C4×#508semidirect
350. SD32C4×D59semidirect
500. C4#16837833direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168378332
C4×#142737502
C4×#142737462
C4×#142736732
#214259522
C4×#142736722
SD32×Dic592
#214259472
C4×#142736682
#214259402
#214258792
#214258022
#214258002
C4×C16×D592
C4×SD32×C592
C4×#50859