Finite Group Databasebeta

← #30600669

Subgroups — #30600669

Order 15616.

528 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#11758217C211yesmaximal, characteristic
2#21461962C211yesmaximal, characteristic, complemented
3#21461328C211yesmaximal, characteristic, complemented
4#21461144C211yesmaximal, characteristic
5#21460689C211yesmaximal, characteristic, complemented
6#21460664C211yesmaximal, characteristic, complemented
7C2×#16840040C211yesmaximal, characteristic
8C22×#11758217—21no—
9#16840797—21no—
10#16840793—22no—
11D4×#92420—21no—
12#16840779C2211yescharacteristic
13#16840765C2211yescharacteristic
14#16840765C2211yescharacteristic
15C2×#14519838—21no—
16C2×#14519838—21no—
17#16840732—21no—
18C4×#11758217C2211yescharacteristic
19#16840621—22no—
20D4⋊#92420—21no—
21D4⋊#92420—21no—
22C2×#14519776C2211yescharacteristic
23C2×D4×Dic61C2211yescharacteristic
24#16840040—21no—
25#16840040—21no—
26#16840040—21no—
27#16840040—21no—
28C2×#14519711C411yescharacteristic
29C2×#14519710C411yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519698C411yescharacteristic
32C2×#102×C61C411yescharacteristic
33C2×#11758217—22no—
34C2×#11758217—21no—
35C2×#11758217—21no—
36C2×#11758217—42no—
37C2×#11758217—42no—
38C2×#11758217D411yescharacteristic
39C2×#11758217D411yescharacteristic
40C22×#92420—22no—
41#14519844—21no—
42#14519844—21no—
43#14519844D412yes—
44C4⋊#92420—21no—
45C4⋊#92420—21no—
46#14519838—42no—
47#14519838—42no—
48C22⋊#92420—22no—
49C22⋊#92420—22no—
50C22⋊#92420—21no—
51#14519832—21no—
52C4×#92420—21no—
53C4×#92420—21no—
54C22×Dic122—21no—
55C23×Dic61—21no—
56C22×#92418C2×C411yescharacteristic
57#14519776—21no—
58#14519776—21no—
59#14519776—21no—
60#14519776—21no—
61D4×Dic61—21no—
62D4×Dic61—21no—
63D4×Dic61D411yescharacteristic
64D4×Dic61D411yescharacteristic
65D4×Dic61D411yescharacteristic
66D4×Dic61D411yescharacteristic
67C2×C4⋊Dic61C2×C411yescharacteristic
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×#11758196—21no—
70C2×C22⋊Dic61—21no—
71C2×C4×Dic61C2311yescharacteristic
72#14519711—21no—
73#14519711—21no—
74#14519710—21no—
75#14519710—21no—
76#14519706—21no—
77#14519706—21no—
78#14519698—21no—
79#14519698—21no—
80C22×D4×C61C2×C411yescharacteristic
81C22×C8×C61C2×C411yescharacteristic
82C2×C4⋊C4×C61C2×C411yescharacteristic
83#102×C61—21no—
84#102×C61—21no—
85C24×C61—21no—
86C2×D4×C61—22no—
87C2×D4×C61—21no—
88C2×D4×C61—41no—
89C2×D4×C61C22⋊C411yescharacteristic
90C2×D4×C61C22⋊C411yescharacteristic
91C22×C4×C61—21no—
92C22×C4×C61C22×C411yescharacteristic
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61C2×D411yescharacteristic
104C22×Dic61#4111yescharacteristic
105C2×Dic122—41no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111#11758217—21no—
112#11758217—21no—
113#11758217—21no—
114#11758217—44no—
115#11758217—41no—
116#11758217—41no—
117#11758217—41no—
118#11758217—41no—
119#11758217D812yes—
120C2×#92420—21no—
121C2×#92420—21no—
122C2×#92420—22no—
123C2×#92420—44no—
124C2×#92420—41no—
125C2×#92420—41no—
126C2×C8×C61—21no—
127C2×C8×C61—41no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C22⋊Dic61—21no—
131C22⋊Dic61—21no—
132C22⋊Dic61—21no—
133C22⋊Dic61—21no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61C22⋊C411yescharacteristic
138C4⋊Dic61C22⋊C411yescharacteristic
139#11758196—41no—
140#11758196—41no—
141C4×Dic61C2×D411yescharacteristic
142C4×Dic61C2×D411yescharacteristic
143C4×Dic61C2×D411yescharacteristic
144C4×Dic61#4111yescharacteristic
145C2×#92418—21no—
146C2×#92418—41no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—42no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—81no—
153C23×C61C4×D411yescharacteristic
154D4×C61—21no—
155D4×C61—21no—
156D4×C61—21no—
157D4×C61—42no—
158D4×C61#10112yescomplemented
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61C2×C22⋊C411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61#12011yescharacteristic
183C2×Dic61#12111yescharacteristic
184C2×Dic61#12111yescharacteristic
185C2×Dic61#12311yescharacteristic
186C2×Dic61C2×D811yescharacteristic
187C2×Dic61#13511yescharacteristic
188C2×Dic61AGL(1,ℤ/8)11yescharacteristic
189C2×Dic61AGL(1,ℤ/8)11yescharacteristic
190Dic122—81no—
191Dic122—81no—
192Dic122—81no—
193Dic122—81no—
194#92420—22no—
195#92420—42no—
196#92420—41no—
197#92420—81no—
198#92420—81no—
199C8×C61—41no—
200#92418—41no—
201#9251—611nomaximal, Sylow
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—22no—
205C22×C61—41no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—82no—
211C22×C61—82no—
212C22×C61#38611yescharacteristic
213C22×C61C4×D811yescharacteristic
214C22×C61#44211yescharacteristic
215C4×C61—21no—
216C4×C61—81no—
217C4×C61C2×#10111yescharacteristic
218C4×C61#41311yescharacteristic
219Dic61—21no—
220Dic61—21no—
221Dic61—41no—
222Dic61—41no—
223Dic61—81no—
224Dic61#44711yescharacteristic
225Dic61#44911yescharacteristic
226Dic61#45911yescharacteristic
227Dic61#46311yescharacteristic
228C2×#474—611no—
229D4×M16—611no—
230#1966—611no—
231#1546—611no—
232#1486—611no—
233#1292—611no—
234#1283—611no—
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—42no—
238C2×C61—81no—
239C2×C61#187911yescharacteristic
240C2×C61#190111yescharacteristic
241C2×C61#190211yescharacteristic
242C22×M16—1221no—
243C2×C4⋊Q8—611no—
244C2×C4×D4—611no—
245#474—1221no—
246#474—1221no—
247#474—1221no—
248#474—1221no—
249#436—1221no—
250#435—1222no—
251C8×D4—1221no—
252#431—611no—
253C2×#107—611no—
254C2×#107—611no—
255#423—611no—
256#423—611no—
257C2×C4⋊C8—611no—
258C2×#102—611no—
259C2×#102#692311yescharacteristic
260C2×#101—1221no—
261C2×#101—1221no—
262#407—1221no—
263C4×M16—611no—
264#332—1222no—
265D4⋊C8—1221no—
266D4⋊C8—1221no—
267C61#925111yescharacteristic, complemented, Sylow
268C22×Q8—1221no—
269C22×D4C2×#692311yescharacteristic
270C23×C4—1221no—
271C2×M16—611no—
272C2×M16—611no—
273C2×M16—1221no—
274C2×M16—1222no—
275C2×M16—1221no—
276C2×M16—2442no—
277C2×M16—2442no—
278C22×C8—611no—
279C22×C8—1222no—
280C22×C8C2×#692311yescharacteristic
281C4⋊Q8—1221no—
282C4⋊Q8—1221no—
283C4⋊Q8—1221no—
284C4⋊Q8—1221no—
285C4×D4—611no—
286C4×D4—611no—
287C4×D4—611no—
288C4×D4—611no—
289C4×D4—1221no—
290C4×D4—1221no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—611no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4C2×#692311yescharacteristic
295C2×C22⋊C4—1221no—
296C2×C42—611no—
297#107—1221no—
298#107—1221no—
299#107—1221no—
300#107—1221no—
301C4⋊C8—612no—
302C4⋊C8—1221no—
303C4⋊C8—1221no—
304C4⋊C8—1221no—
305C4⋊C8—1221no—
306C4⋊C8—1221no—
307C4⋊C8—1221no—
308#102—21no—
309#102—21no—
310#102—1221no—
311#102—1221no—
312#101—2442no—
313#101—2442no—
314C22⋊C8—1222no—
315C22⋊C8—1222no—
316C22⋊C8—1221no—
317#97—1221no—
318C4×C8—1221no—
319C4×C8—1221no—
320C24—21no—
321C2×Q8—2441no—
322C2×Q8—2441no—
323C2×Q8—2441no—
324C2×Q8—2441no—
325C2×Q8—2441no—
326C2×Q8—2441no—
327C2×D4—22no—
328C2×D4—21no—
329C2×D4—41no—
330C2×D4C22⋊#692311yescharacteristic
331C2×D4C22⋊#692311yescharacteristic
332C22×C4—21no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4C22×#692311yescharacteristic
346M16—612no—
347M16—1221no—
348M16—1221no—
349M16—1221no—
350M16—2444no—
351M16—2441no—
352M16—2441no—
353M16—2441no—
354M16—2441no—
355C2×C8—21no—
356C2×C8—41no—
357C2×C8—1221no—
358C2×C8—1221no—
359C2×C8—1222no—
360C2×C8—1221no—
361C2×C8—2444no—
362C2×C8—2441no—
363C2×C8—2441no—
364C2×C8—2441no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—611no—
368C4⋊C4—611no—
369C4⋊C4—1221no—
370C4⋊C4—1221no—
371C4⋊C4—1221no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C22⋊C4—1221no—
375C22⋊C4—1221no—
376C22⋊C4—1221no—
377C22⋊C4—1221no—
378C42—611no—
379C42—611no—
380C42—611no—
381C42—611no—
382C23—21no—
383C23—21no—
384C23—42no—
385C23—41no—
386C23—41no—
387C23—81no—
388C23D4×#692311yescharacteristic
389Q8—4881no—
390Q8—4881no—
391Q8—4881no—
392Q8—4881no—
393D4—21no—
394D4—21no—
395D4—21no—
396D4—42no—
397D4#1451983812yescomplemented
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—611no—
404C2×C4—611no—
405C2×C4—611no—
406C2×C4—611no—
407C2×C4—611no—
408C2×C4—611no—
409C2×C4—611no—
410C2×C4—611no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4C2×C22⋊#692311yescharacteristic
428C2×C4D4×#692311yescharacteristic
429C8—41no—
430C8—1222no—
431C8—4881no—
432C8—4881no—
433C8—2442no—
434C8—2441no—
435C8—2441no—
436C22—21no—
437C22—21no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—82no—
445C22—82no—
446C22#1684071011yescharacteristic
447C22D8×#692311yescharacteristic
448C22#1684080311yescharacteristic
449C4—21no—
450C4—81no—
451C4—611no—
452C4—611no—
453C4—611no—
454C4—611no—
455C4—1221no—
456C4—1221no—
457C4—4881no—
458C4—2441no—
459C4—2441no—
460C4C2×#1451983811yescharacteristic
461C4#1684074911yescharacteristic
462C2—21no—
463C2—21no—
464C2—42no—
465C2—81no—
466C2#2146181411yescharacteristic
467C2#2146184611yescharacteristic
468C2#2146184811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC22×C61#386
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×#102#6923
hypocenterC61#9251
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. #21461962C2semidirect
3. #21461328C2semidirect
5. #21460689C2semidirect
6. #21460664C2semidirect
158. D4×C61#101semidirect
267. C61#9251semidirect
397. D4#14519838semidirect

Maximal subgroups

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

subgroupindex
D4×#117582172
#214619622
#214613282
#214611442
#214606892
#214606642
C2×#168400402
#925161