Finite Group Databasebeta

← #29593117

Subgroups — #29593117

Order 15616.

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

normal subgroups only

This group has 468 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#21446983C211yesmaximal, characteristic
2#21444809C211yesmaximal, characteristic, complemented
3#21444775C211yesmaximal, characteristic, complemented
4#21443840C211yesmaximal, characteristic, complemented
5#21443819C211yesmaximal, characteristic, complemented
6#21443747C211yesmaximal, characteristic
7C61×#2736C211yesmaximal, characteristic
8#16840388C2211yescharacteristic
9#16840092—21no—
10#16839918—21no—
11#16839618—21no—
12#16839529C2211yescharacteristic
13#16839528—21no—
14#16839498—21no—
15#16839498—21no—
16#16839486C2211yescharacteristic
17#16839486C2211yescharacteristic
18C61×#397—21no—
19C61×#397C2211yescharacteristic
20C61×#393—21no—
21C61×#393C2211yescharacteristic
22C61×#388—21no—
23C61×#388—21no—
24C61×#388—21no—
25C61×#379—21no—
26C61×#379C2211yescharacteristic
27C2×#11758202—41no—
28#14519756—21no—
29#14519756—21no—
30#14519754—41no—
31#14519754—41no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—41no—
35C2×C22⋊Dic61—41no—
36#14519708—41no—
37#14519701—41no—
38#14519700—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C25×C61D411yescharacteristic
42C22×Q8×C61D411yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61—21no—
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61D411yescharacteristic
54C2×C22⋊C4×C61C2311yescharacteristic
55C2×C42×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61D411yescharacteristic
61#95×C61D411yescharacteristic
62C24×C61—21no—
63C24×C61—21no—
64C24×C61—21no—
65C24×C61—41no—
66C24×C61—41no—
67C24×C61—42no—
68C24×C61—81no—
69C24×C61C2×D411yescharacteristic
70C2×Q8×C61—41no—
71C2×Q8×C61—81no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C2×Dic122—21no—
83C2×Dic122—21no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—81no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—81no—
93C22⋊C4×C61—81no—
94C22⋊C4×C61—81no—
95C22⋊C4×C61—81no—
96C22⋊C4×C61—81no—
97C42×C61—81no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102C22⋊Dic61—82no—
103C22⋊Dic61—82no—
104#11758202—82no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107#11758196—41no—
108#11758196—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—22no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—42no—
120C23×C61—42no—
121C23×C61—42no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—81no—
126C23×C61—82no—
127C23×C61—81no—
128C23×C61—84no—
129C23×C61—82no—
130C23×C61—81no—
131C23×C61#12011yescharacteristic
132C23×C61#13511yescharacteristic
133C23×C61#13711yescharacteristic
134Q8×C61—42no—
135Q8×C61—81no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
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—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—81no—
158C2×Dic61—81no—
159C2×Dic61—81no—
160C2×Dic61—81no—
161C2×Dic61—81no—
162Dic122—81no—
163Dic122—81no—
164#92418—81no—
165#92418—81no—
166#12264—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—44no—
178C22×C61—42no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—82no—
183C22×C61—82no—
184C22×C61—82no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61#45211yescharacteristic
188C22×C61#45511yescharacteristic
189C22×C61B(4,𝔽2)11yescharacteristic
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—81no—
193C4×C61—81no—
194C4×C61—81no—
195C4×C61—81no—
196C4×C61—81no—
197Dic61—81no—
198Dic61—81no—
199Dic61—161no—
200#2736D6111yescharacteristic
201#2029—611no—
202#1608—611no—
203#1602—611no—
204#1351—611no—
205#1344—611no—
206#1316—611no—
207C2×C61—21no—
208C2×C61—21no—
209C2×C61—41no—
210C2×C61—41no—
211C2×C61—82no—
212C2×C61#160611yescharacteristic
213C2×C61#219711yescharacteristic
214C2×C61#219911yescharacteristic
215#543—611no—
216#483—1221no—
217#451—1221no—
218#397—21no—
219#397C2×D6111yescharacteristic
220#393—21no—
221#393C2×D6111yescharacteristic
222#388—21no—
223#388—21no—
224#388—21no—
225#379—21no—
226#379—1221no—
227#379C2×D6111yescharacteristic
228#342—611no—
229#342—1221no—
230#328—1221no—
231#328—1221no—
232#323—611no—
233#323—611no—
234C61#1226411yescharacteristic, complemented, Sylow
235C25C22⋊D6111yescharacteristic
236C22×Q8C22⋊D6111yescharacteristic
237C2×Q16—2441no—
238C22⋊Q8—1221no—
239C22⋊Q8—1221no—
240C22⋊Q8—2441no—
241C22⋊Q8—2441no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C22⋊D6111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
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×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—2441no—
255C2×C22⋊C4—2441no—
256C2×C22⋊C4C22⋊D6111yescharacteristic
257C2×C22⋊C4C22×D6111yescharacteristic
258C2×C42—21no—
259#106—2441no—
260#103—2441no—
261#103—2441no—
262C22⋊C8—1221no—
263C22⋊C8—1221no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95C22⋊D6111yescharacteristic
269#95C22⋊D6111yescharacteristic
270C24—21no—
271C24—21no—
272C24—21no—
273C24—41no—
274C24—41no—
275C24—42no—
276C24—81no—
277C24C2×C22⋊D6111yescharacteristic
278C2×Q8—41no—
279C2×Q8—81no—
280C2×Q8—1221no—
281C2×Q8—1221no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4C2×C22⋊D6111yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292Q16—4882no—
293C2×C8—2441no—
294C2×C8—2441no—
295C4⋊C4—41no—
296C4⋊C4—81no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C22⋊C4—41no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C22⋊C4—4882no—
313C22⋊C4—4882no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C42—81no—
319C23—21no—
320C23—21no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—81no—
334C23—82no—
335C23—81no—
336C23—82no—
337C23—84no—
338C23—81no—
339C23#1451974611yescharacteristic
340C23#1451979711yescharacteristic
341C23#1451980711yescharacteristic
342Q8—42no—
343Q8—81no—
344Q8—4881no—
345Q8—4881no—
346C2×C4—21no—
347C2×C4—21no—
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—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—4881no—
366C2×C4—4881no—
367C2×C4—4881no—
368C2×C4—4881no—
369C2×C4—4881no—
370C2×C4—2441no—
371C2×C4—2441no—
372C8—4881no—
373C8—4881no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—44no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—81no—
393C22—81no—
394C22#1683992411yescharacteristic
395C22#1683994011yescharacteristic
396C22#1683994911yescharacteristic
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—9761no—
405C4—4881no—
406C4—4881no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—82no—
412C2#2144479911yescharacteristic
413C2#2144780911yescharacteristic
414C2#2144782011yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2736C2
socleC22×C61B(4,𝔽2)
prime radicalC25×C61D4
hypercenter#2736D61
hypocenterC61#12264
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2736

Complements

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

NH ≅ G/Ntype
2. #21444809C2semidirect
3. #21444775C2semidirect
4. #21443840C2semidirect
5. #21443819C2semidirect
234. C61#12264semidirect

Maximal subgroups

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

subgroupindex
#214469832
#214448092
#214447752
#214438402
#214438192
#214437472
C61×#27362
#1226461