Finite Group Databasebeta

← #29576356

Subgroups — #29576356

Order 15616.

464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#16839985C211yesmaximal, characteristic
2#21454909C211yesmaximal, characteristic, complemented
3#21444418C211yesmaximal, characteristic
4#21444265C211yesmaximal, characteristic, complemented
5#21444172C211yesmaximal, characteristic
6#21443669C211yesmaximal, characteristic, complemented
7C61×#1290C211yesmaximal, characteristic, complemented
8C22×Dic244C411yescharacteristic
9C22×#11758190C411yescharacteristic
10C2×#14519765C2211yescharacteristic
11C2×C4×Dic122C2211yescharacteristic
12#16839985—21no—
13#16839985—21no—
14#16839985—21no—
15#16839985—21no—
16#16839890—22no—
17#16839889—21no—
18#16839886—21no—
19#16839816—21no—
20#16839815C2211yescharacteristic
21#16839812—21no—
22C2×#14519702C411yescharacteristic
23C2×#14519699C411yescharacteristic
24C4×#11758194C2211yescharacteristic
25#16839501—22no—
26#16839492—21no—
27#16839492—21no—
28#16839485—21no—
29#16839485—21no—
30C61×#432C2211yescharacteristic
31C61×#432C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C22×Dic122C2×C411yescharacteristic
34C22×Dic122C2×C411yescharacteristic
35C22×D244C2×C411yescharacteristic
36C2×Dic244—21no—
37C2×Dic244—21no—
38C2×Dic244—42no—
39C2×#11758190—21no—
40C2×#11758190—21no—
41C2×#11758190—42no—
42C2×#11758194—21no—
43#14519765—21no—
44#14519765—21no—
45#14519765—21no—
46#14519765—21no—
47C4×Dic122—21no—
48C4×Dic122—21no—
49C4×Dic122D411yescharacteristic
50C4×Dic122D411yescharacteristic
51C4×Dic122D411yescharacteristic
52C4×Dic122D411yescharacteristic
53C2×C4⋊Dic61C2×C411yescharacteristic
54C2×#11758196—21no—
55C2×#11758198—21no—
56C2×#11758198—21no—
57C2×C4×Dic61—21no—
58C4⋊#92418—21no—
59#14519706—22no—
60#14519706—22no—
61#14519702—21no—
62#14519702—21no—
63#14519699—21no—
64#14519699—21no—
65C22⋊#92418D411yescharacteristic
66C22⋊#92418D411yescharacteristic
67#14519688—21no—
68#14519687—22no—
69C4×#92418—21no—
70C4×#92418—21no—
71C8×Dic61—22no—
72C22×C8×C61C2×C411yescharacteristic
73C22×C8×C61C2×C411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81#97×C61—21no—
82#97×C61D412yes—
83C23×D61—21no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—41no—
93C2×D244—41no—
94C2×Dic122—22no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×Dic122—41no—
101C2×Dic122C22⋊C411yescharacteristic
102C2×Dic122C22⋊C411yescharacteristic
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113#11758198—41no—
114#11758198—41no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—21no—
118C4⋊Dic61C22⋊C411yescharacteristic
119C4⋊Dic61C22⋊C411yescharacteristic
120#11758196—21no—
121#11758196—21no—
122#11758196—21no—
123#11758196—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128#11758194—22no—
129#11758194—41no—
130C2×#92418—21no—
131C2×#92418—21no—
132C2×#92418—41no—
133Dic244—42no—
134Dic244—42no—
135#11758190—42no—
136#11758190—42no—
137C23×C61C4×D411yescharacteristic
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—81no—
142C22×D61—81no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—42no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—81no—
163D244—41no—
164D244—41no—
165D244—81no—
166Dic122—21no—
167Dic122—21no—
168Dic122—21no—
169Dic122—42no—
170Dic122—41no—
171Dic122—41no—
172Dic122—81no—
173Dic122#10012yes—
174C8×C61—42no—
175C8×C61—41no—
176C8×C61—41no—
177C8×C61—81no—
178#92418—41no—
179#92418—41no—
180#92418—42no—
181#9244—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61#38611yescharacteristic
185C22×C61#44311yescharacteristic
186C22×C61#44411yescharacteristic
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—161no—
191C2×D61—161no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61C2×#10011yescharacteristic
198C4×C61#41311yescharacteristic
199Dic61—22no—
200Dic61—41no—
201Dic61—41no—
202Dic61—41no—
203Dic61—81no—
204C2×#464—611no—
205#2984—611no—
206#1527—611no—
207#1491—611no—
208#1469—611no—
209#1290D6111yescharacteristic, complemented
210#1283—611no—
211C2×C61—21no—
212C2×C61—21no—
213C2×C61#187611yescharacteristic
214C2×C61#190011yescharacteristic
215C2×C61#190511yescharacteristic
216D61—161no—
217C22×Q16—611no—
218C22×SD16—611no—
219C2×#124—611no—
220C2×C4×Q8—611no—
221#464—1221no—
222#464—1221no—
223#464—1221no—
224#464—1221no—
225#446—1221no—
226#446—1222no—
227C8×Q8—1221no—
228#432—1221no—
229#432C2×D6111yescharacteristic
230#432C2×D6111yescharacteristic
231#431—611no—
232#431—1221no—
233C2×C4⋊C8C2×D6111yescharacteristic
234C2×#103—611no—
235C2×#102—611no—
236C4×M16—611no—
237#329—1222no—
238Q8⋊C8—1221no—
239Q8⋊C8—1221no—
240#323—1221no—
241#323—1221no—
242C61#924411yescharacteristic, complemented, Sylow
243C22×Q8—611no—
244C22×Q8—611no—
245C22×D4—611no—
246C2×Q16—1221no—
247C2×Q16—1221no—
248C2×Q16—2442no—
249C2×SD16—1221no—
250C2×SD16—1221no—
251C2×SD16—2442no—
252C2×M16—1221no—
253C22×C8C4×D6111yescharacteristic
254C22×C8C4×D6111yescharacteristic
255#124—1221no—
256#124—1221no—
257#124—1221no—
258#124—1221no—
259C4×Q8—611no—
260C4×Q8—611no—
261C4×Q8—611no—
262C4×Q8—611no—
263C4×Q8—1221no—
264C4×Q8—1221no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C42—1221no—
270C2×C42C22×D6111yescharacteristic
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—1222no—
276C4⋊C8—1222no—
277C4⋊C8—1221no—
278#103—1221no—
279#103—1221no—
280#102—1221no—
281#102—1221no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—611no—
285C22⋊C8—611no—
286#97—21no—
287#97—1222no—
288#97—1221no—
289#97D24412yes—
290C4×C8—1222no—
291C4×C8—1221no—
292C4×C8—1221no—
293C24—1221no—
294C2×Q8—611no—
295C2×Q8—611no—
296C2×Q8—1222no—
297C2×Q8—1221no—
298C2×Q8—1221no—
299C2×Q8—1221no—
300C2×Q8—2441no—
301C2×Q8—2441no—
302C2×Q8—2441no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—2441no—
306C2×D4—2441no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4C2×C4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4#1175822611yescharacteristic
313Q16—2442no—
314Q16—2442no—
315SD16—2442no—
316SD16—2442no—
317M16—1222no—
318M16—2441no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—1221no—
326C2×C8—1221no—
327C2×C8—2441no—
328C4⋊C4—611no—
329C4⋊C4—611no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C42—1221no—
340C42—1221no—
341C42—1221no—
342C42—1221no—
343C42C2×D24411yescharacteristic
344C42#1175822211yescharacteristic
345C42D4×D6111yescharacteristic
346C42D4×D6111yescharacteristic
347C23—4881no—
348C23—4881no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23#1451973911yescharacteristic
353Q8—612no—
354Q8—1221no—
355Q8—1221no—
356Q8—1221no—
357Q8—4881no—
358Q8—2442no—
359Q8—2441no—
360Q8—2441no—
361D4—4881no—
362D4—2441no—
363D4—2441no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—4881no—
374C2×C4—2442no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4C22⋊C4×D6111yescharacteristic
379C2×C4C4×D24411yescharacteristic
380C2×C4#1451974711yescharacteristic
381C2×C4#1451975011yescharacteristic
382C2×C4#1451975211yescharacteristic
383C2×C4#1451976211yescharacteristic
384C8—42no—
385C8—41no—
386C8—41no—
387C8—81no—
388C8—2441no—
389C8—2441no—
390C8—2442no—
391C22—21no—
392C22—21no—
393C22—9761no—
394C22—9761no—
395C22—4881no—
396C22—4881no—
397C22—4881no—
398C22#1683964011yescharacteristic
399C22#1683987811yescharacteristic
400C22#1683988311yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—1222no—
407C4—4881no—
408C4—2441no—
409C4—2441no—
410C4—2441no—
411C4#100×D6111yescharacteristic
412C4#1683974511yescharacteristic
413C2—21no—
414C2—21no—
415C2—9761no—
416C2#2144614711yescharacteristic
417C2#2144628111yescharacteristic
418C2#2144631411yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1290C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1290D61
hypocenterC61#9244
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
2. #21454909C2semidirect
4. #21444265C2semidirect
6. #21443669C2semidirect
7. C61×#1290C2semidirect
209. #1290D61semidirect
242. C61#9244semidirect

Maximal subgroups

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

subgroupindex
C2×#168399852
#214549092
#214444182
#214442652
#214441722
#214436692
C61×#12902
#924461