Finite Group Databasebeta

← #29590602

Subgroups — #29590602

Order 15616.

482 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 73 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#21450817C211yesmaximal, characteristic
2#21445614C211yesmaximal, characteristic, complemented
3#21444161C211yesmaximal, characteristic, complemented
4#21443823C211yesmaximal, characteristic, complemented
5#21443822C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1345C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic
9C2×#14519763—21no—
10C2×#14519742C2211yescharacteristic
11#16839816—21no—
12C2×#14519695—21no—
13M16×Dic61—21no—
14#16839680C411yescharacteristic
15#16839679C2211yescharacteristic
16#16839676C411yescharacteristic
17#16839662—21no—
18#16839662—21no—
19#16839662—21no—
20#16839613C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C22×C22⋊D61—21no—
31C2×#11758194—21no—
32#14519773—41no—
33#14519773—41no—
34#14519763—42no—
35#14519763—42no—
36#14519742—41no—
37#14519742—41no—
38C2×#11758196—21no—
39C2×#11758196C2×C411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—41no—
52#14519695—24no—
53C22⋊#92418—21no—
54#14519687—41no—
55#14519687—41no—
56C8×Dic61—41no—
57#14519684C2×C411yescharacteristic
58C22×D4×C61C2×C411yescharacteristic
59C2×M16×C61—21no—
60C2×C4⋊C4×C61C2311yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61C2×C411yescharacteristic
65C24×C61—21no—
66C23×D61—21no—
67C2×D4×C61—41no—
68C2×D4×C61—81no—
69C22×C4×C61—21no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—42no—
80C22×Dic61—21no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C2×D244—41no—
86C2×D244—81no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122—22no—
90C2×Dic122—41no—
91M16×C61—22no—
92M16×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—81no—
99C22⋊Dic61—42no—
100C22⋊Dic61—81no—
101#11758198—42no—
102#11758198—41no—
103#11758198—41no—
104#11758198—81no—
105#11758198—81no—
106#11758196—41no—
107#11758196—41no—
108#11758196—42no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—42no—
116#11758194—22no—
117#11758194—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61C2×C22⋊C411yescharacteristic
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135D4×C61—82no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C22⋊D61—82no—
148C22⋊D61—84no—
149C22⋊D61—82no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—22no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61#9911yescharacteristic
162C2×Dic61#9911yescharacteristic
163C2×Dic61#10412yes—
164D244—82no—
165Dic122—42no—
166Dic122—42no—
167C8×C61—42no—
168C8×C61—81no—
169#92418—42no—
170#92418—81no—
171#11781—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61C2×#9911yescharacteristic
182C22×C61#41811yescharacteristic
183C22×C61C2×#10411yescharacteristic
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—41no—
194C4×C61—41no—
195C4×C61—81no—
196Dic61—21no—
197Dic61—22no—
198Dic61—41no—
199Dic61—41no—
200Dic61—81no—
201Dic61#35512yes—
202#2548—611no—
203C4×#101—611no—
204#1467—611no—
205#1345—611no—
206#1345—611no—
207#1345—611no—
208#1345D6111yescharacteristic, complemented
209C2×C61—21no—
210C2×C61—21no—
211C2×C61—161no—
212C2×C61#150711yescharacteristic
213C2×C61#212211yescharacteristic
214C2×C61C2×#35511yescharacteristic
215D61—161no—
216C2×#127—611no—
217C2×#124—1221no—
218C2×C4×Q8—611no—
219#432—1221no—
220C2×#101—1221no—
221C4×M16—1221no—
222#394—611no—
223#394—611no—
224#394—611no—
225#394C2×D6111yescharacteristic
226#390—1221no—
227#390—1221no—
228#390—1221no—
229C4×C4⋊C4—611no—
230#343—611no—
231#343C2×D6111yescharacteristic
232#324—611no—
233#324—1221no—
234#324C2×D6111yescharacteristic
235C61#1178111yescharacteristic, complemented, Sylow
236C22×Q8—611no—
237C22×D4—611no—
238C22×D4—1221no—
239C22×D4—1221no—
240C22×D4C4×D6111yescharacteristic
241C2×M16—21no—
242C2×M16—1221no—
243#127—2441no—
244#127—2441no—
245#124—2442no—
246#124—2442no—
247C4×Q8—2441no—
248C4×Q8—2441no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4C22×D6111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—1221no—
265C4⋊C8—2441no—
266#101—1224no—
267C22⋊C8—21no—
268C22⋊C8—1221no—
269#97—2441no—
270#97—2441no—
271C4×C8—2441no—
272#95—611no—
273#95C4×D6111yescharacteristic
274C24—21no—
275C24—1221no—
276C2×Q8—1222no—
277C2×Q8—1221no—
278C2×Q8—1221no—
279C2×Q8—2441no—
280C2×D4—41no—
281C2×D4—81no—
282C2×D4—4881no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2441no—
286C2×D4—2442no—
287C2×D4—2442no—
288C2×D4—2442no—
289C2×D4—2442no—
290C2×D4—2442no—
291C22×C4—21no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4C2×C4×D6111yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4D4×D6111yescharacteristic
300M16—22no—
301M16—41no—
302M16—1222no—
303M16—2441no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—2441no—
307C2×C8—2441no—
308C4⋊C4—41no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C4⋊C4—2442no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—81no—
315C22⋊C4—4881no—
316C22⋊C4—4881no—
317C22⋊C4—4881no—
318C22⋊C4—2442no—
319C22⋊C4—2442no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C42—1221no—
323C42—1221no—
324C42—1221no—
325C42—1221no—
326C42—1221no—
327C42—1221no—
328C42—2442no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23—2441no—
343C23C22⋊C4×D6111yescharacteristic
344Q8—2442no—
345Q8—2442no—
346D4—82no—
347D4—4882no—
348D4—4882no—
349D4—4882no—
350D4—4884no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—612no—
363C2×C4—1222no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4#1451980111yescharacteristic
375C2×C4#1451980411yescharacteristic
376C8—42no—
377C8—81no—
378C8—4881no—
379C8—2442no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—4881no—
395C22—4881no—
396C22#99×D6111yescharacteristic
397C22#1683976511yescharacteristic
398C22#104×D6111yescharacteristic
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—81no—
404C4—612no—
405C4—1221no—
406C4—1222no—
407C4—4881no—
408C4—2441no—
409C4—2441no—
410C2—21no—
411C2—21no—
412C2—161no—
413C2—9761no—
414C2#2144433311yescharacteristic
415C2#2144746711yescharacteristic
416C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radicalC2×#14519773C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11781
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #21445614C2semidirect
3. #21444161C2semidirect
4. #21443823C2semidirect
5. #21443822C2semidirect
6. #21443821C2semidirect
7. C61×#1345C2semidirect
208. #1345D61semidirect
235. C61#11781semidirect

Maximal subgroups

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

subgroupindex
#214508172
#214456142
#214441612
#214438232
#214438222
#214438212
C61×#13452
#1178161