Finite Group Databasebeta

← #30595681

Subgroups — #30595681

Order 15616.

566 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461735C211yesmaximal, characteristic, complemented
2C4×C4⋊#92420C211yesmaximal, characteristic, complemented
3#21460636C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454173C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×#14519773C411yescharacteristic
14C2×#14519763—21no—
15C2×#14519763—21no—
16#16839665C2211yescharacteristic
17#16839664C411yescharacteristic
18#16839663C2211yescharacteristic
19#16839662—21no—
20#16839662—21no—
21C42×Dic61C2211yescharacteristic
22C61×#390C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C4⋊#92420—24no—
27C4×#92420—42no—
28C22×Dic122—21no—
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—21no—
31C22×C22⋊D61—21no—
32#14519776—42no—
33#14519773—42no—
34#14519763—42no—
35#14519763—42no—
36#14519763—42no—
37#14519763—42no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C24×C61—21no—
58C23×D61—21no—
59C2×D4×C61—22no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—42no—
67C2×C22⋊D61—42no—
68C2×C22⋊D61—42no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61—42no—
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×D244—22no—
78C2×D244—41no—
79C2×D244—41no—
80C2×Dic122—42no—
81C2×Dic122—42no—
82C2×Dic122—42no—
83C2×#92420—24no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—42no—
91C22⋊C4×C61—42no—
92C42×C61—22no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97#11758198—42no—
98#11758198—42no—
99#11758198—41no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103C4⋊Dic61—41no—
104#11758196—42no—
105C4×Dic61—22no—
106C4×Dic61—22no—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C4×Dic61D812yes—
110C4×Dic61D812yes—
111C4×Dic61SD1612yes—
112C4×Dic61SD1612yes—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61C2×C22⋊C411yescharacteristic
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128D4×C61—82no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61#10212yes—
139C2×C4×C61#10212yes—
140C2×C4×C61#13112yes—
141C22⋊D61—84no—
142C22⋊D61—84no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61#10012yes—
153C2×Dic61#10212yes—
154C2×Dic61#10212yes—
155C2×Dic61#10412yes—
156C2×Dic61C2×D811yescharacteristic
157C2×Dic61C2×D811yescharacteristic
158C2×Dic61C2×SD1611yescharacteristic
159C2×Dic61C2×SD1611yescharacteristic
160D244—82no—
161Dic122—84no—
162#92420—44no—
163#92420—82no—
164#7659—611nomaximal, Sylow
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61#40811yescharacteristic
173C22×C61#41011yescharacteristic
174C22×C61C2×#10011yescharacteristic
175C22×C61C2×#10211yescharacteristic
176C22×C61C2×#10211yescharacteristic
177C22×C61C2×#10411yescharacteristic
178C22×C61#42111yescharacteristic
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C4×C61—22no—
187C4×C61—22no—
188C4×C61—22no—
189C4×C61—81no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—22no—
195Dic61—81no—
196Dic61#33114yes—
197#2858—611no—
198#1831—611no—
199C4×C4⋊C8—611no—
200#1270—612no—
201#1270—612no—
202C2×C61—161no—
203C2×C61#146911yescharacteristic
204C2×C61#148011yescharacteristic
205C2×C61#149211yescharacteristic
206C2×C61#150211yescharacteristic
207C2×C61#151711yescharacteristic
208C2×C61#152711yescharacteristic
209C2×C61C2×#33111yescharacteristic
210D61—161no—
211C2×C4⋊Q8—611no—
212C2×#127—611no—
213C2×#124—1221no—
214C2×#124—1221no—
215C2×C4⋊C8—1221no—
216C2×C4⋊C8—1221no—
217C2×C4×C8—1221no—
218#390—611no—
219#390—611no—
220#390—611no—
221#390—1221no—
222#390—1221no—
223#390#692311yescharacteristic
224C43—611no—
225#336—612no—
226#336—612no—
227#336—1221no—
228C61#765911yescharacteristic, complemented, Sylow
229C22×Q8—1221no—
230C22×D4—611no—
231C22×D4—1221no—
232C22×D4—1221no—
233C22×D4C2×#692311yescharacteristic
234C22×C8—1222no—
235C22×C8—1222no—
236C4⋊Q8—2442no—
237#127—2442no—
238#124—2442no—
239#124—2442no—
240#124—2442no—
241#124—2442no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4C2×#692311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42—611no—
258C2×C42—611no—
259C2×C42C2×#692311yescharacteristic
260C4⋊C8—1224no—
261C4⋊C8—2442no—
262C4×C8—2442no—
263C24—21no—
264C24—1221no—
265C2×Q8—2442no—
266C2×Q8—2442no—
267C2×Q8—2442no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—1222no—
272C2×D4—2441no—
273C2×D4—2441no—
274C2×D4—2442no—
275C2×D4—2442no—
276C2×D4—2442no—
277C2×D4—2442no—
278C2×D4—2442no—
279C2×D4—2442no—
280C22×C4—21no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1221no—
286C22×C4C22⋊#692311yescharacteristic
287C22×C4C22⋊#692311yescharacteristic
288C22×C4C22×#692311yescharacteristic
289C2×C8—1224no—
290C2×C8—2442no—
291C2×C8—2442no—
292C2×C8—2442no—
293C2×C8—2442no—
294C2×C8—2442no—
295C4⋊C4—41no—
296C4⋊C4—2441no—
297C4⋊C4—2442no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C42—22no—
311C42—612no—
312C42—612no—
313C42—612no—
314C42—612no—
315C42—1222no—
316C42—1222no—
317C42—2441no—
318C42—2441no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23—2441no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23C2×C22⋊#692311yescharacteristic
334Q8—4884no—
335D4—82no—
336D4—4882no—
337D4—4884no—
338D4—4884no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—612no—
349C2×C4—612no—
350C2×C4—612no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—612no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4#1451983912yes—
366C2×C4#1451983912yes—
367C2×C4#1451986412yes—
368C8—4882no—
369C8—2444no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—4881no—
378C22—4881no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22—4881no—
384C22#1684073511yescharacteristic
385C22#1684074111yescharacteristic
386C22D61⋊#10011yescharacteristic
387C22C2×#1451983911yescharacteristic
388C22C2×#1451983911yescharacteristic
389C22D61⋊#10411yescharacteristic
390C22#1684075911yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—81no—
395C4—614no—
396C4—1221no—
397C4—1221no—
398C4—1222no—
399C4—1221no—
400C4—1221no—
401C4—4881no—
402C2—161no—
403C2—9761no—
404C2#2146108811yescharacteristic
405C2#2146112411yescharacteristic
406C2#2146116411yescharacteristic
407C2#2146119811yescharacteristic
408C2#2146124911yescharacteristic
409C2#2146127911yescharacteristic
410C2D61⋊#33111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#7659
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461735C2semidirect
2. C4×C4⋊#92420C2semidirect
3. #21460636C2semidirect
4. #21460635C2semidirect
228. C61#7659semidirect

Maximal subgroups

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

subgroupindex
#214617352
C4×C4⋊#924202
#214606362
#214606352
#214541732
#765961