Finite Group Databasebeta

← #30599640

Subgroups — #30599640

Order 15616.

458 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 80 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#21462683C211yesmaximal, characteristic
2#21461797C211yesmaximal, characteristic
3#21461772C211yesmaximal, characteristic, complemented
4#21461771C211yesmaximal, characteristic, complemented
5#21460702C211yesmaximal, characteristic, complemented
6#21460702C211yesmaximal, characteristic, complemented
7#21444134C211yesmaximal, characteristic
8C22×#11758213C2211yescharacteristic
9#16840795—21no—
10#16840795—21no—
11#16840795—21no—
12#16840795—21no—
13#16840779—21no—
14C2×#14519848—21no—
15C2×#14519847—21no—
16#16840733C2211yescharacteristic
17#16840733C2211yescharacteristic
18#16840732—21no—
19C2×#14519834C2211yescharacteristic
20C2×C22⋊#92420—21no—
21#16840638—21no—
22#16840638—21no—
23#16840628—21no—
24C2×#14519737C2211yescharacteristic
25C22⋊C8×D61C2211yescharacteristic
26C22⋊C8×D61C2211yescharacteristic
27#16839487C411yescharacteristic
28#16839487C411yescharacteristic
29#16839486C411yescharacteristic
30C61×#323C411yescharacteristic
31C2×#11758213—21no—
32C2×#11758213—21no—
33C2×#11758213—42no—
34C2×#11758213D411yescharacteristic
35C2×#11758213D411yescharacteristic
36C2×#11758213D411yescharacteristic
37C2×#11758213D411yescharacteristic
38C2×#11758217—21no—
39C2×#11758217—21no—
40C22×#92420—21no—
41C22×#92420—21no—
42#14519848—42no—
43#14519847—42no—
44#14519844—21no—
45#14519844—21no—
46#14519834—21no—
47#14519834—21no—
48#14519834—21no—
49#14519834—21no—
50C22⋊#92420—21no—
51C22⋊#92420—21no—
52C22⋊#92420—21no—
53C22⋊#92420—21no—
54C22⋊#92420—42no—
55C4×#92420—21no—
56C4×#92420—21no—
57C22×C22⋊D61Q811yescharacteristic
58C23×Dic61D411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×C8×D61—21no—
61C2×C8×D61—21no—
62#14519737—21no—
63#14519737—21no—
64#14519737—21no—
65#14519737—21no—
66C2×#11758196C2×C411yescharacteristic
67C2×#11758198Q811yescharacteristic
68C2×C4×Dic61D411yescharacteristic
69C22⋊#92418C2×C411yescharacteristic
70C22⋊#92418C2×C411yescharacteristic
71#14519689—21no—
72#14519689—21no—
73C2×C22⋊C4×C61C2×C411yescharacteristic
74C22⋊C8×C61C2×C411yescharacteristic
75C22⋊C8×C61C2×C411yescharacteristic
76C24×C61C4⋊C411yescharacteristic
77C23×D61C2×Q811yescharacteristic
78C22×C4×C61C4⋊C411yescharacteristic
79C22×C4×C61C22×C411yescharacteristic
80C2×C22⋊D61—21no—
81C2×C22⋊D61—21no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—41no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61C4⋊C411yescharacteristic
89C22×Dic61C4⋊C411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61C2×D411yescharacteristic
94C2×C4×D61C2×D411yescharacteristic
95C2×C4×D61#4111yescharacteristic
96C2×C4×D61#4111yescharacteristic
97#11758217—81no—
98#11758217—81no—
99C2×#92420—22no—
100C2×#92420—21no—
101C2×#92420—21no—
102C2×#92420—21no—
103C2×#92420—21no—
104C2×#92420—41no—
105C2×#92420—41no—
106C2×#92420—41no—
107C2×#92420—41no—
108C2×#92420—41no—
109#11758213—22no—
110#11758213—22no—
111#11758213—41no—
112#11758213—41no—
113#11758213—41no—
114#11758213—41no—
115#11758213—41no—
116#11758213—41no—
117C2×C8×C61—21no—
118C2×C8×C61—21no—
119C22⋊C4×C61—21no—
120C22⋊C4×C61—21no—
121#11758198—21no—
122#11758198—21no—
123#11758196—21no—
124#11758196—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C2×#92418—21no—
128C2×#92418—21no—
129C8×D61—41no—
130C8×D61—41no—
131C8×D61—41no—
132C8×D61—41no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61C2×C4⋊C411yescharacteristic
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61C22⋊Q811yescharacteristic
144C22×D61C22⋊Q811yescharacteristic
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C22⋊D61—42no—
151C22⋊D61—42no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—81no—
161C2×Dic61#10812yescomplemented
162C2×Dic61#12011yescharacteristic
163C2×Dic61#12311yescharacteristic
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—21no—
168C4×D61—41no—
169C4×D61—41no—
170#92420—42no—
171#92420—41no—
172#92420—41no—
173#92420—41no—
174#92420—41no—
175#92420—81no—
176C8×C61—41no—
177C8×C61—41no—
178#92418—41no—
179#92418—41no—
180#8860—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—42no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—81no—
188C22×C61#38511yescharacteristic
189C22×C61C2×#10811yescharacteristic
190C22×C61#43011yescharacteristic
191C2×D61—21no—
192C2×D61—21no—
193C2×D61—21no—
194C2×D61—21no—
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—81no—
198C2×D61—81no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—41no—
202Dic61—22no—
203Dic61—21no—
204Dic61—41no—
205Dic61B(4,𝔽2)11yescharacteristic
206Dic61#45811yescharacteristic
207#2975—611no—
208#1870—611no—
209#1855—611no—
210#1855—611no—
211#1459—611no—
212#1298—611no—
213#1298—611no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—81no—
217C2×C61#185511yescharacteristic
218C2×C61#185811yescharacteristic
219C2×C61#186711yescharacteristic
220D61—41no—
221D61—41no—
222C22×M16—611no—
223C2×C4×D4—611no—
224#436—1221no—
225#436—1221no—
226#436—1221no—
227#436—1221no—
228#431—1221no—
229C2×#108—1221no—
230C2×#108—1221no—
231#407—611no—
232#407—611no—
233#407—1221no—
234C2×C22⋊C8—611no—
235C2×C22⋊C8—611no—
236C2×C22⋊C8—611no—
237C2×C22⋊C8—1221no—
238#341—1221no—
239#341—1221no—
240#336—1221no—
241#324—611no—
242#324—611no—
243#323—611no—
244#323#692311yescharacteristic
245C61#886011yescharacteristic, complemented, Sylow
246C22×D4—611no—
247C23×C4—611no—
248C23×C4—611no—
249C2×M16—611no—
250C2×M16—611no—
251C2×M16—611no—
252C2×M16—611no—
253C2×M16—1221no—
254C2×M16—1221no—
255C2×M16—1221no—
256C2×M16—1221no—
257C2×M16—2442no—
258C22×C8—1221no—
259C22×C8—1221no—
260C22×C8—1221no—
261C22×C8—1221no—
262C4×D4—1221no—
263C4×D4—1221no—
264C4×D4—1221no—
265C4×D4—1221no—
266C2×C4⋊C4—611no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4C2×#692311yescharacteristic
269C2×C42—611no—
270#108—2442no—
271#108—2442no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C22⋊C8—611no—
275C22⋊C8—611no—
276C22⋊C8—1221no—
277C22⋊C8—1221no—
278C22⋊C8—1221no—
279C22⋊C8—1221no—
280C22⋊C8—1221no—
281C22⋊C8—1221no—
282C22⋊C8—1221no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286C22⋊C8—2442no—
287C22⋊C8C2×#692311yescharacteristic
288C22⋊C8C2×#692311yescharacteristic
289C4×C8—1221no—
290C4×C8—1221no—
291C24—611no—
292C24C4⋊#692311yescharacteristic
293C2×D4—1222no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—2441no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4C4⋊#692311yescharacteristic
311C22×C4C22×#692311yescharacteristic
312M16—1222no—
313M16—1222no—
314M16—4881no—
315M16—4881no—
316M16—2441no—
317M16—2441no—
318M16—2441no—
319M16—2441no—
320M16—2441no—
321M16—2441no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—1221no—
325C2×C8—1221no—
326C2×C8—1221no—
327C2×C8—1221no—
328C2×C8—1222no—
329C2×C8—1221no—
330C2×C8—1221no—
331C2×C8—2441no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8—2441no—
336C2×C8—2441no—
337C2×C8—2441no—
338C2×C8—2441no—
339C2×C8—2441no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C42—1221no—
347C42—1221no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—611no—
354C23—611no—
355C23—1221no—
356C23—1221no—
357C23—2441no—
358C23—2441no—
359C23C2×C4⋊#692311yescharacteristic
360D4—2442no—
361D4—2442no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—612no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—4881no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4D4×#692311yescharacteristic
384C2×C4D4×#692311yescharacteristic
385C8—41no—
386C8—41no—
387C8—4881no—
388C8—2441no—
389C8—2441no—
390C8—2442no—
391C8—2441no—
392C8—2441no—
393C8—2441no—
394C8—2441no—
395C22—21no—
396C22—21no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—1221no—
403C22—1221no—
404C22—1221no—
405C22—1221no—
406C22—1221no—
407C22—1221no—
408C22—4881no—
409C22—4881no—
410C22#1684070911yescharacteristic
411C22D61⋊#10811yescharacteristic
412C22#1684077711yescharacteristic
413C4—21no—
414C4—21no—
415C4—41no—
416C4—611no—
417C4—611no—
418C4—1222no—
419C4—1221no—
420C4—2441no—
421C2—21no—
422C2—21no—
423C2—81no—
424C2—2441no—
425C2—2441no—
426C2#2146177311yescharacteristic
427C2#2146177611yescharacteristic
428C2#2146179011yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#323C4
socleC22×C61#385
prime radicalC22×C22⋊D61Q8
cosocleC22×C4×D61C23
hypercenter#323#6923
hypocenterC61#8860
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
3. #21461772C2semidirect
4. #21461771C2semidirect
5. #21460702C2semidirect
6. #21460702C2semidirect
161. C2×Dic61#108semidirect
245. C61#8860semidirect

Maximal subgroups

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

subgroupindex
#214626832
#214617972
#214617722
#214617712
#214607022
#214441342
#886061