Finite Group Databasebeta

← #30603799

Subgroups — #30603799

Order 15616.

532 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 94 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#21462047C211yesmaximal, characteristic, complemented
2D61⋊(C22⋊C16)C211yesmaximal, characteristic, complemented
3#21460740C212yesmaximal, complemented
4#21460739C212yesmaximal, complemented
5C2×#16839727C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×D61⋊C16—21no—
8#16840657—21no—
9#16840657—21no—
10C22⋊#11758187C2212yes—
11C22⋊#11758187C2212yes—
12C22×#11758222C411yescharacteristic
13C22×#11758189C411yescharacteristic
14C22×C8×D61C2211yescharacteristic
15#16839727—21no—
16#16839727—21no—
17#16839727—21no—
18#16839727—21no—
19C2×C22⋊#92418C2211yescharacteristic
20C2×#14519689C411yescharacteristic
21C2×#14519689C2211yescharacteristic
22C2×C22⋊C8×C61C411yescharacteristic
23#14519852—42no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×#11758222—21no—
28C2×#11758222—21no—
29C2×#11758222—21no—
30C2×#11758222—21no—
31C2×#11758222—42no—
32C2×#11758222—42no—
33C22×Dic122C811yescharacteristic
34C22×D244C811yescharacteristic
35C22×C22⋊D61C811yescharacteristic
36C22×C22⋊D61C811yescharacteristic
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61C2×C411yescharacteristic
39C2×#11758189—21no—
40C2×#11758189—21no—
41C2×#11758189—42no—
42C22×#92418C2×C411yescharacteristic
43C22×#92418C2311yescharacteristic
44C2×C8×D61—42no—
45C2×C8×D61D411yescharacteristic
46C2×C8×D61D411yescharacteristic
47C2×C8×D61D411yescharacteristic
48C2×C8×D61D411yescharacteristic
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519689—21no—
52#14519689—21no—
53#14519689—21no—
54#14519689—21no—
55C23×C4×C61C2×C411yescharacteristic
56C22×C8×C61C2×C411yescharacteristic
57C22×C8×C61C2×C411yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60C24×C61C2×C811yescharacteristic
61C23×D61C2×C811yescharacteristic
62C23×D61C2×C811yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61C2×C811yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C22×Dic61C2×C811yescharacteristic
76C22×Dic61C2×C811yescharacteristic
77#11758222—44no—
78#11758222—42no—
79#11758222—42no—
80#11758222—44no—
81#11758222—42no—
82#11758222—42no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—42no—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61C22⋊C411yescharacteristic
93C2×C4×D61C22⋊C411yescharacteristic
94C2×C4×D61M1611yescharacteristic
95C2×C4×D61M1611yescharacteristic
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—42no—
99C2×C8×C61—21no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61C22⋊C411yescharacteristic
103C2×C8×C61C22⋊C411yescharacteristic
104C2×#92418—21no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418C2×D411yescharacteristic
108C2×#92418C2×D411yescharacteristic
109#11758189—42no—
110#11758189—42no—
111C8×D61—22no—
112C8×D61—22no—
113C8×D61—41no—
114C8×D61—41no—
115#11758187—42no—
116#11758187—42no—
117C23×C61—21no—
118C23×C61—22no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61C22×C811yescharacteristic
122C22×D61—22no—
123C22×D61—22no—
124C22×D61—21no—
125C22×D61—22no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61C22⋊C811yescharacteristic
130C22×D61C22⋊C811yescharacteristic
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C2×M1611yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—42no—
143C22⋊D61—42no—
144C2×Dic61—22no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61C22⋊C811yescharacteristic
148C2×Dic61C22⋊C811yescharacteristic
149D244—42no—
150D244—42no—
151C4×D61—22no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—22no—
155C4×D61—42no—
156C4×D61—41no—
157C4×D61—41no—
158C4×D61#9912yes—
159C4×D61#10012yes—
160Dic122—42no—
161Dic122—42no—
162C8×C61—21no—
163C8×C61—21no—
164C8×C61—41no—
165#92418—21no—
166#92418—21no—
167#92418—41no—
168#11419—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—82no—
175C22×C61C2×C22⋊C811yescharacteristic
176C22×C61#50412yes—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—44no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—82no—
187C2×D61#32312yes—
188C4×C61—21no—
189C4×C61—41no—
190C4×C61C2×#9911yescharacteristic
191C4×C61C2×#10011yescharacteristic
192Dic61—21no—
193Dic61—41no—
194Dic61#32312yes—
195C2×#408—611no—
196#2112—611no—
197C2×C22⋊C16—611no—
198#1314—612no—
199#1314—612no—
200C2×C61—22no—
201C2×C61—81no—
202C2×C61C2×#32311yescharacteristic
203C2×C61#211311yescharacteristic
204C2×C61#211511yescharacteristic
205D61—22no—
206D61—41no—
207D61—81no—
208C22×#41—611no—
209C22×M16—611no—
210C23×C8—611no—
211C2×M32—1221no—
212C22×C16—1221no—
213#408—1221no—
214#408—1221no—
215#408—1221no—
216#408—1221no—
217C2×C22⋊C8—611no—
218C2×C22⋊C8—611no—
219C2×C22⋊C8—611no—
220C2×C22⋊C8#692311yescharacteristic
221C22⋊C16—612no—
222C22⋊C16—612no—
223C22⋊C16—1221no—
224C22⋊C16—1221no—
225C61#1141911yescharacteristic, complemented, Sylow
226C2×#41—1221no—
227C2×#41—1221no—
228C2×#41—1221no—
229C2×#41—1221no—
230C2×#41—2442no—
231C2×#41—2442no—
232C22×Q8—611no—
233C22×D4—611no—
234C22×D4—611no—
235C22×D4—611no—
236C23×C4—611no—
237C23×C4—611no—
238C23×C4C2×#692311yescharacteristic
239C2×M16—1221no—
240C2×M16—1221no—
241C2×M16—2442no—
242C22×C8—611no—
243C22×C8—611no—
244C22×C8—611no—
245C22×C8—611no—
246C22×C8—611no—
247C22×C8—611no—
248C22×C8—2442no—
249C22×C8C2×#692311yescharacteristic
250C22×C8C2×#692311yescharacteristic
251M32—2442no—
252C2×C16—1222no—
253C2×C16—1222no—
254C2×C16—2442no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—1221no—
258C22⋊C8—1221no—
259C22⋊C8—1221no—
260C22⋊C8—1221no—
261C22⋊C8—1221no—
262C22⋊C8—1221no—
263C24—611no—
264C24—611no—
265C24D61⋊C811yescharacteristic
266#41—2442no—
267#41—2442no—
268#41—2444no—
269#41—2444no—
270#41—2442no—
271#41—2442no—
272C2×Q8—1221no—
273C2×Q8—1221no—
274C2×Q8—2442no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—2442no—
282C2×D4—2442no—
283C2×D4—2442no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4D61⋊C811yescharacteristic
301C22×C4C22×#692311yescharacteristic
302M16—2442no—
303M16—2442no—
304C2×C8—21no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—611no—
308C2×C8—611no—
309C2×C8—1222no—
310C2×C8—1222no—
311C2×C8—1221no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C2×C8C22⋊#692311yescharacteristic
317C2×C8C22⋊#692311yescharacteristic
318C16—2442no—
319C16—2442no—
320C23—21no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—611no—
325C23—611no—
326C23—1222no—
327C23—1222no—
328C23—1222no—
329C23—1221no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23C2×D61⋊C811yescharacteristic
334Q8—2442no—
335Q8—2442no—
336D4—2442no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—611no—
350C2×C4—612no—
351C2×C4—612no—
352C2×C4—611no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—2442no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4C2×C22⋊#692311yescharacteristic
364C2×C4D61⋊M1611yescharacteristic
365C8—21no—
366C8—21no—
367C8—41no—
368C8—1221no—
369C8—1221no—
370C8—2441no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—82no—
377C22—612no—
378C22—1221no—
379C22—1221no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—4882no—
384C22—2444no—
385C22—2441no—
386C22—2441no—
387C22—2441no—
388C22D61⋊(C22⋊C8)11yescharacteristic
389C22#1684082112yes—
390C4—21no—
391C4—41no—
392C4—612no—
393C4—1221no—
394C4—2441no—
395C4D61⋊#9911yescharacteristic
396C4D61⋊#10011yescharacteristic
397C2—22no—
398C2—81no—
399C2—1222no—
400C2—4881no—
401C2—2441no—
402C2D61⋊#32311yescharacteristic
403C2#2146205011yescharacteristic
404C2#2146205611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC22×#11758222C4
cosocleC22×#92418C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#11419
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21462047C2semidirect
2. D61⋊(C22⋊C16)C2semidirect
3. #21460740C2semidirect
4. #21460739C2semidirect
225. C61#11419semidirect

Maximal subgroups

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

subgroupindex
#214620472
D61⋊(C22⋊C16)2
#214607402
#214607392
C2×#168397272
#1141961