Finite Group Databasebeta

← #29592710

Subgroups — #29592710

Order 15616.

434 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 59 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#21446865C211yesmaximal, characteristic, complemented
2#21444787C211yesmaximal, characteristic, complemented
3#21444753C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic, complemented
6#21443753C211yesmaximal, characteristic, complemented
7C61×#2832C211yesmaximal, characteristic, complemented
8C2×#14519808—21no—
9#16840343C2211yescharacteristic
10#16839901—21no—
11#16839896—21no—
12C2×#14519705—21no—
13#16839531C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#400—21no—
19C61×#397—21no—
20C61×#395C2211yescharacteristic
21C61×#394—21no—
22C61×#394C2211yescharacteristic
23C61×#393—21no—
24C61×#393—21no—
25C61×#391C2211yescharacteristic
26C61×#388—21no—
27C2×#11758222—21no—
28#14519808—42no—
29#14519808—42no—
30C2×#11758202—41no—
31C2×#11758201—41no—
32C2×#11758201—41no—
33C2×#11758199—41no—
34C2×#11758194—21no—
35#14519757—41no—
36#14519752—41no—
37#14519751—21no—
38#14519751—21no—
39#14519705—42no—
40#14519701—41no—
41#14519698—41no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22×Q8×C61D411yescharacteristic
45C22×Q8×C61D411yescharacteristic
46C22×D4×C61D411yescharacteristic
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61C2311yescharacteristic
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C42×C61D411yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C24×C61—21no—
66C2×Q8×C61—21no—
67C2×Q8×C61—21no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—81no—
72C2×D4×C61—41no—
73C2×D4×C61—81no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×C4×D61—41no—
91C2×Dic122—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—81no—
94C4⋊C4×C61—81no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—81no—
98C22⋊C4×C61—81no—
99C22⋊C4×C61—81no—
100C22⋊C4×C61—81no—
101C22⋊C4×C61—81no—
102C42×C61—41no—
103#11758202—44no—
104#11758201—44no—
105#11758201—82no—
106#11758199—82no—
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111#11758194—22no—
112#11758194—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61#12011yescharacteristic
124C22×D61—41no—
125Q8×C61—42no—
126Q8×C61—42no—
127Q8×C61—81no—
128Q8×C61—81no—
129D4×C61—42no—
130D4×C61—81no—
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—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61#13511yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C22⋊D61—81no—
155C22⋊D61—81no—
156C2×Dic61—41no—
157D244—41no—
158D244—41no—
159D244—81no—
160D244—81no—
161C4×D61—81no—
162C4×D61—81no—
163Dic122—41no—
164Dic122—41no—
165#92418—42no—
166#92418—81no—
167#92418—81no—
168#12199—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61#44911yescharacteristic
179C22×C61#45311yescharacteristic
180C22×C61B(4,𝔽2)11yescharacteristic
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—81no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—81no—
189C4×C61—81no—
190C4×C61—81no—
191C4×C61—81no—
192C4×C61—81no—
193Dic61—81no—
194#2832D6111yescharacteristic, complemented
195#2007—611no—
196#1604—611no—
197#1598—611no—
198#1354—611no—
199#1345—611no—
200#1319—611no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—161no—
204C2×C61#160011yescharacteristic
205C2×C61#219911yescharacteristic
206C2×C61#220311yescharacteristic
207D61—161no—
208C2×#137—1221no—
209#537—611no—
210#448—1221no—
211#447—1221no—
212C2×#104—1221no—
213#400—21no—
214#397—21no—
215#395C2×D6111yescharacteristic
216#394—21no—
217#394C2×D6111yescharacteristic
218#393—21no—
219#393—21no—
220#391C2×D6111yescharacteristic
221#388—21no—
222#343—611no—
223#327—1221no—
224#327—1221no—
225#324—611no—
226#324—611no—
227C61#1219911yescharacteristic, complemented, Sylow
228C2×#41—1221no—
229C22×Q8C22⋊D6111yescharacteristic
230C22×Q8C22⋊D6111yescharacteristic
231C22×D4C22⋊D6111yescharacteristic
232#137—2442no—
233#137—2442no—
234C2×Q16—2441no—
235C2×SD16—2441no—
236C2×SD16—2441no—
237C2×D8—2441no—
238C2×M16—1221no—
239C22⋊Q8—2441no—
240#121—1221no—
241#121—1221no—
242#121—2441no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C22×D6111yescharacteristic
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C42C22⋊D6111yescharacteristic
253#104—2442no—
254#103—2441no—
255#102—2441no—
256C22⋊C8—1221no—
257C22⋊C8—1221no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95C22⋊D6111yescharacteristic
265#95C22⋊D6111yescharacteristic
266C24—21no—
267#41—2441no—
268#41—2441no—
269#41—2441no—
270#41—2441no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—81no—
277C2×Q8—1221no—
278C2×D4—41no—
279C2×D4—81no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—2441no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—2441no—
290C22×C4C2×C22⋊D6111yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292C22×C4C2×C22⋊D6111yescharacteristic
293Q16—2444no—
294SD16—4882no—
295SD16—2444no—
296D8—4882no—
297M16—1222no—
298M16—2441no—
299C2×C8—2441no—
300C2×C8—2441no—
301C2×C8—2441no—
302C4⋊C4—41no—
303C4⋊C4—81no—
304C4⋊C4—81no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C22⋊C4—81no—
313C22⋊C4—81no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C42—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—2441no—
325C23#1451974611yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—81no—
329Q8—81no—
330Q8—2441no—
331Q8—2441no—
332D4—42no—
333D4—81no—
334D4—4881no—
335D4—4881no—
336D4—4881no—
337D4—4881no—
338D4—2441no—
339D4—2441no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—4881no—
362C2×C4—4881no—
363C2×C4—2441no—
364C2×C4#1451979711yescharacteristic
365C2×C4#1451980211yescharacteristic
366C8—4881no—
367C8—4881no—
368C8—2442no—
369C22—21no—
370C22—21no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—4881no—
379C22—4881no—
380C22—4881no—
381C22#1683990711yescharacteristic
382C22#1683993011yescharacteristic
383C22#1683994911yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—4881no—
394C2—21no—
395C2—21no—
396C2—161no—
397C2—9761no—
398C2#2144476511yescharacteristic
399C2#2144782011yescharacteristic
400C2#2144784011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2832C2
socleC22×C61B(4,𝔽2)
prime radical#21444753C2
hypercenter#2832D61
hypocenterC61#12199
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2832

Complements

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

NH ≅ G/Ntype
1. #21446865C2semidirect
2. #21444787C2semidirect
4. #21443849C2semidirect
5. #21443822C2semidirect
6. #21443753C2semidirect
7. C61×#2832C2semidirect
194. #2832D61semidirect
227. C61#12199semidirect

Maximal subgroups

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

subgroupindex
#214468652
#214447872
#214447532
#214438492
#214438222
#214437532
C61×#28322
#1219961