Finite Group Databasebeta

← #29596013

Subgroups — #29596013

Order 15616.

468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C4×#14519775C211yesmaximal, characteristic
2C2×#16839560C212yesmaximal
3#21445815C211yesmaximal, characteristic
4#21443945C212yesmaximal
5C61×#1801C211yesmaximal, characteristic
6C2×#14519775C2211yescharacteristic
7C2×C4×Dic122C411yescharacteristic
8#16839786—21no—
9C2×#14519696C2212yes—
10#16839669C2211yescharacteristic
11#16839667C411yescharacteristic
12#16839657—21no—
13#16839657—21no—
14#16839631C411yescharacteristic
15C4×#11758196—21no—
16C4×#11758196—21no—
17C42×Dic61C411yescharacteristic
18#16839560—24no—
19#16839531—21no—
20C2×C4×Q8×C61C2211yescharacteristic
21C61×#423—21no—
22C2×#101×C61C2212yes—
23C61×#343—21no—
24C22×Dic122C2×C411yescharacteristic
25C2×#11758194—22no—
26#14519775—21no—
27#14519775—21no—
28#14519775D412yes—
29#14519775Q812yes—
30C4×Dic122—41no—
31C4×Dic122—41no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C4⋊#92418—41no—
44C4⋊#92418—41no—
45#14519696—22no—
46#14519696—22no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61C2311yescharacteristic
52C2×M16×C61—22no—
53C4×Q8×C61—41no—
54C4×Q8×C61—41no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C2×C42×C61D411yescharacteristic
61C4⋊C8×C61—41no—
62C4⋊C8×C61—41no—
63#101×C61—22no—
64#101×C61—22no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61C2×D411yescharacteristic
68C2×Q8×C61C2×Q811yescharacteristic
69C2×Q8×C61#4111yescharacteristic
70C2×Q8×C61#4111yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C2×Dic122—21no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122C4⋊C412yes—
86M16×C61—42no—
87M16×C61—42no—
88C2×C8×C61—42no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C42×C61—21no—
93C42×C61—21no—
94C42×C61—21no—
95C42×C61—21no—
96C42×C61—21no—
97C42×C61—21no—
98C4⋊Dic61—41no—
99#11758196—22no—
100#11758196—22no—
101#11758196—22no—
102#11758196—22no—
103#11758196—42no—
104#11758196—42no—
105#11758196—42no—
106C4×Dic61—24no—
107C4×Dic61—21no—
108C4×Dic61—42no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C4×Dic61—41no—
112C4×Dic61C4⋊C412yes—
113#11758194—42no—
114#11758194—42no—
115C2×#92418—42no—
116C23×C61C2×C22⋊C411yescharacteristic
117Q8×C61—41no—
118Q8×C61—41no—
119Q8×C61—41no—
120Q8×C61—41no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61#9911yescharacteristic
135C2×C4×C61#9911yescharacteristic
136C2×C4×C61C2×C4⋊C411yescharacteristic
137C2×C4×C61#11711yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61C22⋊Q811yescharacteristic
141C2×C4×C61C22⋊Q811yescharacteristic
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154Dic122—42no—
155Dic122—42no—
156C8×C61—82no—
157#92418—82no—
158#12802—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#38011yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61#41011yescharacteristic
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61#35612yescomplemented
175Dic61—24no—
176Dic61—42no—
177Dic61—42no—
178Dic61—81no—
179C4×C4⋊Q8—611no—
180C2×#356—612no—
181#1801—611no—
182#1801D6111yescharacteristic
183#1394—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#179911yescharacteristic
187C2×C61C2×#35611yescharacteristic
188C2×C61#213211yescharacteristic
189C2×C4⋊Q8—611no—
190C2×C4×Q8—611no—
191C2×C4×Q8C2×D6111yescharacteristic
192#423—21no—
193#423—1221no—
194C2×#101—612no—
195C2×#101C2×D6112yes—
196#391—611no—
197#391—611no—
198#389—1221no—
199#389—1221no—
200#384—611no—
201C4×C4⋊C4—1221no—
202C4×C4⋊C4—1221no—
203C43—611no—
204#356—1224no—
205#343—21no—
206#343—1221no—
207C61#1280211yescharacteristic, complemented, Sylow
208C22×Q8—611no—
209C22×Q8C22×D6111yescharacteristic
210C2×M16—22no—
211C2×M16—1222no—
212C4⋊Q8—612no—
213C4⋊Q8—612no—
214C4⋊Q8—1221no—
215C4⋊Q8—1221no—
216C4×Q8—41no—
217C4×Q8—41no—
218C4×Q8—2441no—
219C4×Q8—2441no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4C4×D6111yescharacteristic
227C2×C4⋊C4D24411yescharacteristic
228C2×C4⋊C4C22⋊D6111yescharacteristic
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—1221no—
232C2×C42—1221no—
233C2×C42—1221no—
234C2×C42C4×D6111yescharacteristic
235C2×C42D24411yescharacteristic
236C2×C42C22⋊D6111yescharacteristic
237C4⋊C8—41no—
238C4⋊C8—41no—
239C4⋊C8—2441no—
240C4⋊C8—2441no—
241#101—22no—
242#101—22no—
243#101—1222no—
244#101—1222no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248#95—1221no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—612no—
252C2×Q8—1221no—
253C2×Q8—2441no—
254C2×Q8—2441no—
255C2×Q8D4×D6111yescharacteristic
256C2×Q8#1175822411yescharacteristic
257C2×Q8Q8×D6111yescharacteristic
258C2×Q8#1175822611yescharacteristic
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4#1175819811yescharacteristic
264C22×C4#1175819811yescharacteristic
265C22×C4#1175819811yescharacteristic
266C22×C4#1175819811yescharacteristic
267C22×C4C2×C4×D6111yescharacteristic
268C22×C4C2×D24411yescharacteristic
269C22×C4C2×C22⋊D6111yescharacteristic
270M16—42no—
271M16—42no—
272M16—2442no—
273M16—2442no—
274C2×C8—42no—
275C2×C8—2442no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—1222no—
280C4⋊C4—1222no—
281C4⋊C4—1222no—
282C4⋊C4—1222no—
283C4⋊C4—2441no—
284C4⋊C4—2442no—
285C4⋊C4—2442no—
286C4⋊C4—2442no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—612no—
294C42—1224no—
295C42—1221no—
296C42—2441no—
297C42—2442no—
298C42—2441no—
299C42—2441no—
300C23C2×#1175819811yescharacteristic
301Q8—41no—
302Q8—41no—
303Q8—41no—
304Q8—41no—
305Q8—2442no—
306Q8—2442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451969111yescharacteristic
333C2×C4#1451969111yescharacteristic
334C2×C4C4⋊C4×D6111yescharacteristic
335C2×C4#1451973511yescharacteristic
336C2×C4#1451974811yescharacteristic
337C2×C4#1451975211yescharacteristic
338C2×C4#1451975311yescharacteristic
339C2×C4#1451975711yescharacteristic
340C8—82no—
341C8—4882no—
342C22—21no—
343C22—21no—
344C22#1683961911yescharacteristic
345C22C2×#1451969111yescharacteristic
346C22#1683973511yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1224no—
358C4—4881no—
359C4—2442no—
360C4—2442no—
361C4#1683956012yescomplemented
362C2—21no—
363C2—21no—
364C2#2144580411yescharacteristic
365C2C2×#1683956011yescharacteristic
366C2#2144750211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1801C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenter#1801D61
hypocenterC61#12802
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
174. C4×C61#356semidirect
207. C61#12802semidirect
361. C4#16839560semidirect

Maximal subgroups

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

subgroupindex
C4×#145197752
C2×#168395602
#214458152
#214439452
C61×#18012
#1280261