Finite Group Databasebeta

← #30600635

Subgroups — #30600635

Order 15616.

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

normal subgroups only

This group has 452 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#21462509C211yesmaximal, characteristic
2#21461725C211yesmaximal, characteristic
3#21461218C211yesmaximal, characteristic
4#21461097C211yesmaximal, characteristic
5#21460691C211yesmaximal, characteristic
6#21460661C211yesmaximal, characteristic
7C2×#16840105C211yesmaximal, characteristic
8#16840787—22no—
9#16840782—21no—
10#16840778—21no—
11#16840769—21no—
12#16840733C2211yescharacteristic
13#16840733C2211yescharacteristic
14D61⋊(C22⋊C8)C2211yescharacteristic
15#16840727—21no—
16C4×C22⋊#6923C2211yescharacteristic
17#16840632—21no—
18#16840632—21no—
19#16840615—22no—
20#16840607—21no—
21#16840607—21no—
22C2×#14519757C2211yescharacteristic
23C2×#14519735C2211yescharacteristic
24#16840105—21no—
25#16840105—21no—
26#16840105—21no—
27#16840105—21no—
28C2×#14519708C411yescharacteristic, complemented
29C2×#14519702C411yescharacteristic, complemented
30C2×#14519700C411yescharacteristic, complemented
31C2×#14519689C2211yescharacteristic
32C2×#107×C61C411yescharacteristic, complemented
33C2×#11758213—21no—
34C2×#11758213—21no—
35C2×D61⋊C8—21no—
36C2×C22⋊#6923—21no—
37C2×C4×#6923—21no—
38#14519844—22no—
39C4⋊#92420—22no—
40#14519834—21no—
41#14519834—21no—
42#14519834D412yes—
43C22⋊#92420—21no—
44C22⋊#92420—21no—
45C22⋊#92420D411yescharacteristic
46C22⋊#92420D411yescharacteristic
47#14519832—22no—
48C4×#92420—22no—
49(C2×#6923)⋊C4—21no—
50C22×Dic122C2×C411yescharacteristic
51C22×C4×D61C2311yescharacteristic
52C22×#92418C2×C411yescharacteristic
53#14519757—21no—
54#14519757—21no—
55#14519757—21no—
56#14519757—21no—
57#14519735—21no—
58#14519735—21no—
59#14519735D411yescharacteristic
60#14519735D411yescharacteristic
61#14519735D411yescharacteristic
62#14519735D411yescharacteristic
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×#11758198—21no—
66C2×#11758198—21no—
67C2×C4×Dic61—21no—
68#14519708—21no—
69#14519708—21no—
70#14519702—21no—
71#14519702—21no—
72#14519700—21no—
73#14519700—21no—
74#14519689—21no—
75#14519689—21no—
76C22×C8×C61C2×C411yescharacteristic
77C2×C4⋊C4×C61C2×C411yescharacteristic
78C2×C4⋊C4×C61C2×C411yescharacteristic
79#107×C61—21no—
80#107×C61—21no—
81C23×D61#4111yescharacteristic
82C22×#6923—41no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61C22×C411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61C2×D411yescharacteristic
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61C2×D411yescharacteristic
92C2×C4×D61C2×D411yescharacteristic
93C2×C4×D61C2×D411yescharacteristic
94C2×C4×D61#4111yescharacteristic
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122—41no—
98C2×Dic122—41no—
99C22⋊#6923—22no—
100C22⋊#6923—41no—
101C2×#92420—21no—
102C2×#92420—22no—
103C2×#92420—21no—
104C2×#92420—41no—
105C4×#6923—41no—
106C4×#6923—41no—
107#11758213—41no—
108#11758213—41no—
109#11758213—41no—
110#11758213—41no—
111D61⋊C8—41no—
112D61⋊C8—41no—
113C2×C8×C61—21no—
114C2×C8×C61—41no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61C22⋊C411yescharacteristic
119C4⋊C4×C61C22⋊C411yescharacteristic
120#11758198—21no—
121#11758198—21no—
122#11758198—21no—
123#11758198—21no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—21no—
127C4⋊Dic61—41no—
128C4⋊Dic61—41no—
129C4⋊Dic61C22⋊C411yescharacteristic
130C4⋊Dic61C22⋊C411yescharacteristic
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C2×#92418—21no—
136C2×#92418—41no—
137C23×C61C4×D411yescharacteristic
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61#12111yescharacteristic
143C22×D61#12311yescharacteristic
144C2×#6923—42no—
145C2×#6923—81no—
146C2×#6923—81no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61C2×C22⋊C411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—81no—
163C2×Dic61—81no—
164C2×Dic61#12011yescharacteristic
165C2×Dic61#12111yescharacteristic
166C4×D61—21no—
167C4×D61—21no—
168C4×D61—21no—
169C4×D61—21no—
170C4×D61—41no—
171C4×D61—41no—
172Dic122—41no—
173Dic122—41no—
174Dic122—81no—
175#92420—41no—
176#92420—41no—
177#92420—42no—
178#92420—81no—
179C8×C61—41no—
180#92418—41no—
181#9240—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61#38611yescharacteristic
185C22×C61#44311yescharacteristic
186C22×C61#44411yescharacteristic
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—21no—
192C2×D61—21no—
193C2×D61—81no—
194C2×D61—81no—
195#6923—82no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—81no—
200C4×C61#41011yescharacteristic
201C4×C61#41011yescharacteristic
202Dic61—21no—
203Dic61—21no—
204Dic61—41no—
205Dic61—41no—
206Dic61—81no—
207C2×#485—611no—
208#2924—611no—
209#1826—611no—
210#1508—611no—
211#1472—611no—
212#1293—611no—
213#1282—611no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61#187611yescharacteristic
217C2×C61#189911yescharacteristic
218C2×C61#190211yescharacteristic
219D61—41no—
220D61—41no—
221C2×C22⋊Q8—611no—
222C2×#117—611no—
223#485—1221no—
224#485—1221no—
225#485—1221no—
226#485—1221no—
227#433—1222no—
228#432—1221no—
229#431—1221no—
230C2×#107#692311yescharacteristic, complemented
231C2×#106—611no—
232#424—1221no—
233C2×#103—611no—
234C2×#103—611no—
235#407—611no—
236#407—611no—
237C2×C22⋊C8—611no—
238C2×C22⋊C8—611no—
239#405—1221no—
240C4×C22⋊C4—611no—
241#339—1221no—
242#339—1221no—
243#328—1222no—
244#324—1221no—
245#324—1221no—
246C61#924011yescharacteristic, complemented, Sylow
247C22×Q8—611no—
248C23×C4—611no—
249C2×M16—1221no—
250C2×M16—1221no—
251C22×C8—611no—
252C22×C8—1221no—
253C22×C8C2×#692311yescharacteristic
254C22⋊Q8—1221no—
255C22⋊Q8—1221no—
256C22⋊Q8—1221no—
257C22⋊Q8—1221no—
258#117—611no—
259#117—611no—
260#117—611no—
261#117—611no—
262#117—1221no—
263#117—1221no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4C2×#692311yescharacteristic
267C2×C4⋊C4C2×#692311yescharacteristic
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C42—1221no—
272C2×C42—1221no—
273#107—21no—
274#107—21no—
275#106—1221no—
276#106—1221no—
277C4⋊C8—1222no—
278C4⋊C8—1222no—
279#103—1221no—
280#103—1221no—
281#103—1221no—
282#103—1221no—
283C22⋊C8—611no—
284C22⋊C8—611no—
285C22⋊C8—612no—
286C22⋊C8—1221no—
287C22⋊C8—1221no—
288C22⋊C8—1221no—
289C22⋊C8—1221no—
290C22⋊C8—1221no—
291C22⋊C8—1221no—
292#97—1222no—
293C4×C8—1222no—
294#95—1221no—
295C24—611no—
296C2×Q8—1221no—
297C2×Q8—1221no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4C22×#692311yescharacteristic
313M16—2441no—
314M16—2441no—
315M16—2441no—
316M16—2441no—
317C2×C8—21no—
318C2×C8—41no—
319C2×C8—1221no—
320C2×C8—1222no—
321C2×C8—1221no—
322C2×C8—1221no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8—2441no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—611no—
331C4⋊C4—611no—
332C4⋊C4—1221no—
333C4⋊C4—2441no—
334C4⋊C4—2441no—
335C4⋊C4C22⋊#692311yescharacteristic
336C4⋊C4C22⋊#692311yescharacteristic
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1222no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C42—1221no—
346C42—1221no—
347C42—1221no—
348C42—1221no—
349C42—2441no—
350C42—2441no—
351C23—611no—
352C23—611no—
353C23—1221no—
354C23—1221no—
355C23—2441no—
356C23—2441no—
357C23D4×#692311yescharacteristic
358Q8—4881no—
359Q8—2441no—
360Q8—2441no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2442no—
386C2×C4—2441no—
387C2×C4C2×C22⋊#692311yescharacteristic
388C2×C4D4×#692311yescharacteristic
389C8—41no—
390C8—4881no—
391C8—2441no—
392C8—2441no—
393C8—2442no—
394C8—2441no—
395C22—21no—
396C22—21no—
397C22—1221no—
398C22—1221no—
399C22—1221no—
400C22—1221no—
401C22—1221no—
402C22—1221no—
403C22—4881no—
404C22—4881no—
405C22#1684071011yescharacteristic
406C22#1684080411yescharacteristic
407C22#1684080911yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—81no—
412C4—1221no—
413C4—1221no—
414C4—4882no—
415C4—4881no—
416C4—2441no—
417C4—2441no—
418C4#1684074111yescharacteristic
419C4#1684074311yescharacteristic
420C2—21no—
421C2—21no—
422C2—2441no—
423C2—2441no—
424C2#2146181011yescharacteristic
425C2#2146184311yescharacteristic
426C2#2146184911yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#107×C61C4
socleC22×C61#386
prime radicalC23×D61#41
cosocleC22×C4×D61C23
hypercenterC2×#107#6923
hypocenterC61#9240
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
28. C2×#14519708C4semidirect
29. C2×#14519702C4semidirect
30. C2×#14519700C4semidirect
32. C2×#107×C61C4semidirect
230. C2×#107#6923semidirect
246. C61#9240semidirect

Maximal subgroups

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

subgroupindex
#214625092
#214617252
#214612182
#214610972
#214606912
#214606612
C2×#168401052
#924061