Finite Group Databasebeta

← #29575079

Subgroups — #29575079

Order 15616.

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

normal subgroups only

This group has 534 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
1#21454847C211yesmaximal, characteristic
2#21449102C211yesmaximal, characteristic
3C4×#14519693C211yesmaximal, characteristic
4#21444266C211yesmaximal, characteristic, complemented
5#21443713C211yesmaximal, characteristic, complemented
6#21443711C211yesmaximal, characteristic, complemented
7C61×#1491C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16839835—22no—
10#16839832—22no—
11#16839819C2211yescharacteristic
12C2×#14519693—21no—
13#16839724—21no—
14C22⋊C8×D61—21no—
15C4×#11758194C2211yescharacteristic
16#16839701—21no—
17#16839688C411yescharacteristic
18#16839688C411yescharacteristic
19#16839679—21no—
20#16839673C411yescharacteristic
21#16839673C411yescharacteristic
22C4×#11758198—21no—
23C4×#11758198—21no—
24#16839608C2211yescharacteristic
25#16839530—21no—
26Q8⋊#92418—22no—
27C2×C4×Q8×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×D244D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×#11758194—21no—
35C2×#11758189—22no—
36C2×C8×D61—22no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198C2×C411yescharacteristic
48C2×C4×Dic61—21no—
49C4⋊#92418D412yes—
50#14519693—24no—
51C22⋊#92418—21no—
52#14519689—22no—
53#14519689—22no—
54#14519688—21no—
55#14519688—21no—
56C4×#92418—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C22×Q8×C61C2×C411yescharacteristic
65C2×M16×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C42×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61D412yes—
75C22⋊C8×C61—21no—
76#97×C61—21no—
77#97×C61—21no—
78C4×C8×C61—21no—
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—42no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61C22×C411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C2×D244—22no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—41no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103M16×C61—22no—
104M16×C61—41no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C42×C61—41no—
112C42×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C42×C61#4111yescharacteristic
117#11758198—21no—
118#11758198—21no—
119#11758198—21no—
120#11758198—21no—
121#11758198—42no—
122#11758198—42no—
123#11758198—42no—
124#11758198—42no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4×Dic61—42no—
128#11758194—22no—
129#11758194—41no—
130C2×#92418—22no—
131C2×#92418—41no—
132#11758189—82no—
133C8×D61—82no—
134C23×C61C2×C22⋊C411yescharacteristic
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61#10412yes—
145Q8×C61—22no—
146Q8×C61—22no—
147Q8×C61—41no—
148Q8×C61—41no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61C4×D411yescharacteristic
161C2×C4×C61#12011yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12311yescharacteristic
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175D244—42no—
176D244—42no—
177C4×D61—42no—
178C4×D61—42no—
179C4×D61—81no—
180C4×D61—81no—
181C8×C61—42no—
182C8×C61—42no—
183#92418—42no—
184#92418—42no—
185#9029—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61#38611yescharacteristic
189C22×C61C2×#10411yescharacteristic
190C22×C61#42111yescharacteristic
191C2×D61—22no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—42no—
195C2×D61—42no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—81no—
200C2×D61—81no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—42no—
207C4×C61—81no—
208C4×C61#45512yes—
209Dic61—41no—
210Dic61—41no—
211Dic61—81no—
212Dic61—81no—
213#2973—611no—
214#2398—611no—
215C4×#100—611no—
216#1491—611no—
217#1491D6111yescharacteristic, complemented
218#1300—611no—
219#1300—611no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61#187111yescharacteristic
223C2×C61#188511yescharacteristic
224C2×C61#189111yescharacteristic
225D61—42no—
226D61—81no—
227C2×C4×Q8C2×D6111yescharacteristic
228C2×C4×D4—611no—
229#435—1222no—
230#435—1222no—
231#432—611no—
232#432C2×D6111yescharacteristic
233C2×#100—1221no—
234#407—1221no—
235C2×C22⋊C8—1221no—
236C4×M16—611no—
237C4×M16C2×D6111yescharacteristic
238#400—1221no—
239#397—611no—
240#397—611no—
241#394—1221no—
242#393—611no—
243#393—611no—
244C4×C22⋊C4—1221no—
245C4×C22⋊C4—1221no—
246#376—611no—
247#343—1221no—
248Q8⋊C8—22no—
249Q8⋊C8—1222no—
250C61#902911yescharacteristic, complemented, Sylow
251C22×Q8C4×D6111yescharacteristic
252C22×D4—611no—
253C23×C4—611no—
254C23×C4—611no—
255C2×M16—21no—
256C2×M16—1222no—
257C2×M16—1221no—
258C22×C8—1222no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×D4—1221no—
264C4×D4—1221no—
265C4×D4—1221no—
266C4×D4—1221no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4C4×D6111yescharacteristic
270C2×C22⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C42—21no—
277C2×C42—1221no—
278C2×C42C22×D6111yescharacteristic
279C4⋊C8—612no—
280C4⋊C8C22⋊D6112yes—
281#100—1224no—
282C22⋊C8—21no—
283C22⋊C8—1222no—
284C22⋊C8—1222no—
285C22⋊C8—1221no—
286#97—21no—
287#97—21no—
288#97—1221no—
289#97—1221no—
290C4×C8—21no—
291C4×C8—1221no—
292#95—611no—
293#95—611no—
294#95—1221no—
295#95—1221no—
296#95—1221no—
297#95—1221no—
298#95—1221no—
299C24—611no—
300C24—611no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—42no—
304C2×D4—1222no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—2441no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—2442no—
319C22×C4—2442no—
320C22×C4C2×C4×D6111yescharacteristic
321C22×C4D4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323M16—22no—
324M16—41no—
325M16—1222no—
326M16—4882no—
327M16—2441no—
328C2×C8—22no—
329C2×C8—41no—
330C2×C8—1222no—
331C2×C8—4882no—
332C2×C8—2441no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—2442no—
344C22⋊C4—2442no—
345C22⋊C4—2442no—
346C22⋊C4—2442no—
347C42—41no—
348C42—41no—
349C42—2442no—
350C42#1175822211yescharacteristic
351C42D4×D6111yescharacteristic
352C42#1175822411yescharacteristic
353C42C2×C22⋊D6111yescharacteristic
354C23—612no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23—1221no—
359C23—1221no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23C22⋊C4×D6111yescharacteristic
365Q8—22no—
366Q8—22no—
367Q8—41no—
368Q8—41no—
369D4—2442no—
370D4—2442no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4#1451973711yescharacteristic
396C2×C4C4×C22⋊D6111yescharacteristic
397C2×C4#1451974511yescharacteristic
398C2×C4#1451974811yescharacteristic
399C2×C4#1451975011yescharacteristic
400C2×C4#1451975911yescharacteristic
401C8—42no—
402C8—42no—
403C8—2442no—
404C8—2442no—
405C22—21no—
406C22—21no—
407C22—1222no—
408C22—4881no—
409C22—4881no—
410C22—2442no—
411C22—2442no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22—2441no—
417C22#1683963811yescharacteristic
418C22#104×D6111yescharacteristic
419C22#1683977711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—42no—
426C4—81no—
427C4—4881no—
428C4—4881no—
429C4—2441no—
430C4—2441no—
431C4#1683993812yes—
432C2—21no—
433C2—21no—
434C2—4881no—
435C2—2442no—
436C2#2144611811yescharacteristic
437C2#2144620411yescharacteristic
438C2#2144623411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1491C2
socleC22×C61#386
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1491D61
hypocenterC61#9029
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
4. #21444266C2semidirect
5. #21443713C2semidirect
6. #21443711C2semidirect
7. C61×#1491C2semidirect
217. #1491D61semidirect
250. C61#9029semidirect

Maximal subgroups

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

subgroupindex
#214548472
#214491022
C4×#145196932
#214442662
#214437132
#214437112
C61×#14912
#902961