Finite Group Databasebeta

← #30600922

Subgroups — #30600922

Order 15616.

440 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 82 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
1#21462746C211yesmaximal, characteristic
2#21462012C211yesmaximal, characteristic, complemented
3#21461328C211yesmaximal, characteristic, complemented
4#21461156C211yesmaximal, characteristic
5#21460727C211yesmaximal, characteristic, complemented
6#21460703C211yesmaximal, characteristic, complemented
7#21455632C211yesmaximal, characteristic
8#16840812—21no—
9#16840794—22no—
10#16840790—21no—
11#16840785—21no—
12#16840779C2211yescharacteristic
13#16840765C2211yescharacteristic
14#16840765C2211yescharacteristic
15D61⋊(C4⋊C8)—21no—
16C4×#11758217C2211yescharacteristic
17#16840642—22no—
18#16840621—21no—
19#16840621—21no—
20#16840612—21no—
21#16840610—21no—
22C2×#14519776C2211yescharacteristic
23#16840230C2211yescharacteristic
24#16840056—21no—
25#16840051—21no—
26#16840046—21no—
27#16840041—21no—
28#16839805C411yescharacteristic
29#16839785C2211yescharacteristic
30#16839764C411yescharacteristic
31#16839761C411yescharacteristic
32C61×#428C411yescharacteristic
33C2×#11758217—21no—
34C2×#11758217—21no—
35C2×#11758217D412yes—
36C2×D61⋊C8—22no—
37#14519844—21no—
38#14519844—21no—
39#14519844D411yescharacteristic
40#14519844D411yescharacteristic
41C4⋊#92420—22no—
42C4⋊#92420—21no—
43C4⋊#92420—21no—
44#14519834—22no—
45C22⋊#92420—21no—
46#14519832—22no—
47#14519832—21no—
48C4×#92420—21no—
49C4×#92420—21no—
50C2×#11758222C2×C411yescharacteristic
51C22×Dic122—21no—
52C2×#11758194C2×C411yescharacteristic
53#14519776—21no—
54#14519776—21no—
55#14519776—21no—
56#14519776—21no—
57#14519742D411yescharacteristic
58#14519742D411yescharacteristic
59#14519739D411yescharacteristic
60#14519739D411yescharacteristic
61#14519737—21no—
62#14519737—21no—
63#14519734—21no—
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×#11758196—21no—
66C2×C4×Dic61C2311yescharacteristic
67C42×D61—21no—
68#14519710—21no—
69#14519708—21no—
70#14519706—21no—
71#14519706—21no—
72#14519702—21no—
73#14519700—21no—
74#14519699—21no—
75#14519697—21no—
76C2×M16×C61C2×C411yescharacteristic
77#117×C61C2×C411yescharacteristic
78C2×C4⋊C4×C61C2×C411yescharacteristic
79#107×C61—21no—
80#106×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C2×C22⋊D61—21no—
84C22×Dic61—21no—
85C22×Dic61C2×D411yescharacteristic
86C22×Dic61#4111yescharacteristic
87#11758222—22no—
88#11758222—41no—
89C2×D244C22⋊C411yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—81no—
96C2×Dic122—81no—
97C2×Dic122C22⋊C411yescharacteristic
98#11758217—22no—
99#11758217—41no—
100#11758217—42no—
101#11758217—81no—
102C2×#92420—21no—
103C2×#92420—21no—
104C2×#92420—22no—
105C2×#92420—41no—
106C2×#92420—41no—
107D61⋊C8—82no—
108M16×C61—41no—
109C2×C8×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61C22⋊C411yescharacteristic
113C4⋊C4×C61C22⋊C411yescharacteristic
114C22⋊C4×C61—21no—
115C42×C61—21no—
116#11758198—21no—
117#11758198—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120#11758196—21no—
121#11758196—21no—
122#11758196—41no—
123#11758196—41no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61C2×D411yescharacteristic
127C4×Dic61C2×D411yescharacteristic
128C4×Dic61C2×D411yescharacteristic
129C4×Dic61#4111yescharacteristic
130#11758194—41no—
131C2×#92418—21no—
132C23×C61C4×D411yescharacteristic
133C22×D61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C22⋊D61—42no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—81no—
150C2×Dic61#12011yescharacteristic
151C2×Dic61#12111yescharacteristic
152C2×Dic61#12111yescharacteristic
153C2×Dic61#12311yescharacteristic
154D244—21no—
155D244#10112yes—
156C4×D61—42no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—41no—
161Dic122—21no—
162Dic122—21no—
163Dic122—82no—
164Dic122—81no—
165Dic122—81no—
166#92420—42no—
167#92420—41no—
168#92420—42no—
169#92420—41no—
170#92420—81no—
171C8×C61—41no—
172#92418—41no—
173#9355—611nomaximal, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61#38611yescharacteristic
178C2×D61—22no—
179C2×D61—41no—
180C2×D61—41no—
181C4×C61—21no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—81no—
185C4×C61C2×#10111yescharacteristic
186C4×C61#41311yescharacteristic
187Dic61—21no—
188Dic61—21no—
189Dic61—41no—
190Dic61—81no—
191Dic61#45511yescharacteristic
192Dic61#45611yescharacteristic
193Dic61#47111yescharacteristic
194Dic61#47211yescharacteristic
195#3079—611no—
196#2990—611no—
197#1997—611no—
198#1546—611no—
199#1489—611no—
200#1309—611no—
201#1299—611no—
202C2×C61—41no—
203C2×C61#188211yescharacteristic
204C2×C61#190111yescharacteristic
205C2×C61#190711yescharacteristic
206D61—42no—
207C2×C4⋊Q8—611no—
208C4×#41—611no—
209#477—1221no—
210#476—1221no—
211#475—1221no—
212#474—1221no—
213#446—1221no—
214#435—1222no—
215C8×D4—1221no—
216#432—1221no—
217#431—611no—
218#428—611no—
219#428#692311yescharacteristic
220#423—611no—
221#423—611no—
222#423—611no—
223C2×C4⋊C8—1221no—
224#417—611no—
225#417—611no—
226C4×M16—611no—
227#343—1222no—
228#332—1221no—
229#332—1221no—
230Q8⋊C8—1221no—
231D4⋊C8—1221no—
232C61#935511yescharacteristic, complemented, Sylow
233C2×#41—611no—
234C22×Q8—1221no—
235C2×M16—612no—
236C2×M16—611no—
237C2×M16—1221no—
238C2×M16—1221no—
239C2×M16C2×#692311yescharacteristic
240C22×C8—1222no—
241C4⋊Q8—1221no—
242C4⋊Q8—1221no—
243C4⋊Q8—1221no—
244C4⋊Q8—1221no—
245C4×Q8—611no—
246C4×Q8—611no—
247C4×D4—611no—
248C4×D4—611no—
249C4×D4—1221no—
250C4×D4—1221no—
251#117—1221no—
252#117C2×#692311yescharacteristic
253C2×C4⋊C4—611no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4C2×#692311yescharacteristic
256C2×C42—611no—
257C2×C42—1221no—
258#107—21no—
259#107—1221no—
260#106—21no—
261#106—1221no—
262C4⋊C8—611no—
263C4⋊C8—611no—
264C4⋊C8—1221no—
265C4⋊C8—1221no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270C4⋊C8—1222no—
271#103—1221no—
272#103—1221no—
273#102—1221no—
274#102—1221no—
275C22⋊C8—1221no—
276C22⋊C8—1222no—
277#97—1221no—
278#97—1222no—
279C4×C8—1221no—
280C4×C8—1221no—
281#41—1222no—
282#41—2441no—
283C2×Q8—611no—
284C2×Q8—4881no—
285C2×Q8—4881no—
286C2×Q8—2441no—
287C2×Q8—2441no—
288C2×D4—611no—
289C2×D4—1221no—
290C22×C4—21no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4C22×#692311yescharacteristic
298M16—41no—
299M16—1222no—
300M16—4881no—
301M16—2441no—
302M16—2441no—
303M16—2442no—
304C2×C8—21no—
305C2×C8—1221no—
306C2×C8—1221no—
307C2×C8—1222no—
308C2×C8—1221no—
309C2×C8—4882no—
310C2×C8—2441no—
311C2×C8—2441no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4C22⋊#692311yescharacteristic
321C4⋊C4C22⋊#692311yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C42—21no—
326C42—611no—
327C42—611no—
328C42—611no—
329C42—611no—
330C42—1221no—
331C42—1221no—
332C23—1221no—
333C23D4×#692311yescharacteristic
334Q8—1221no—
335Q8—1221no—
336Q8—4881no—
337Q8—4881no—
338Q8—4882no—
339D4—612no—
340D4—1221no—
341D4—2442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4881no—
358C2×C4—2442no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4C2×C22⋊#692311yescharacteristic
365C2×C4D4×#692311yescharacteristic
366C8—41no—
367C8—4881no—
368C8—2441no—
369C8—2441no—
370C8—2442no—
371C8—2442no—
372C8—2441no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—1222no—
377C22—2441no—
378C22—2441no—
379C22#1684071011yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—81no—
384C4—611no—
385C4—611no—
386C4—611no—
387C4—611no—
388C4—1221no—
389C4—1221no—
390C4—4881no—
391C4—2441no—
392C4D61⋊#10111yescharacteristic
393C4#1684074811yescharacteristic
394C2—41no—
395C2—2442no—
396C2#2146181811yescharacteristic
397C2#2146184711yescharacteristic
398C2#2146185811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#428C4
socleC22×C61#386
prime radicalC2×#11758222C2×C4
cosocleC2×C4×Dic61C23
hypercenter#428#6923
hypocenterC61#9355
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #21462012C2semidirect
3. #21461328C2semidirect
5. #21460727C2semidirect
6. #21460703C2semidirect
232. C61#9355semidirect

Maximal subgroups

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

subgroupindex
#214627462
#214620122
#214613282
#214611562
#214607272
#214607032
#214556322
#935561