Finite Group Databasebeta

← #15673339

Subgroups — #15673339

Order 2944.

618 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 103 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×#41×D23C211yesmaximal, characteristic
2C2×#10624987C211yesmaximal, characteristic, complemented
3C2×#10625019C211yesmaximal, characteristic, complemented
4C2×#10625007C211yesmaximal, characteristic, complemented
5#13092380C211yesmaximal, characteristic, complemented
6C4×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
7C2×C23×#104C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9#41×D23—22no—
10#41×D23—22no—
11#41×D23—22no—
12#41×D23—22no—
13C2×#67292C411yescharacteristic, complemented
14C2×Q8×D23C411yescharacteristic, complemented
15C2×#67290—21no—
16C2×#67290C411yescharacteristic, complemented
17C2×D4×D23—21no—
18C2×D4×D23C411yescharacteristic, complemented
19C2×#67288—21no—
20C2×#67288C2211yescharacteristic
21C22×C4×D23—21no—
22C22×C4×D23C2211yescharacteristic
23C2×M16×C23C2211yescharacteristic, complemented
24C2×C42×C23C2211yescharacteristic, complemented
25C2×(C2×D23)⋊C4—21no—
26C2×C4×Dic23C2211yescharacteristic, complemented
27C2×#67267C2211yescharacteristic, complemented
28C23×#104—22no—
29#10625019—22no—
30C23⋊#95—21no—
31#10625007—22no—
32(C2×D23)⋊C8—21no—
33(C2×D23)⋊C8—21no—
34#10624987—22no—
35C23×D23—21no—
36C23×D23D411yescharacteristic
37#41×C23—21no—
38#41×C23—21no—
39#41×C23D412yes—
40#41×C23D412yes—
41C2×Q8×C23C2×C411yescharacteristic
42C2×D4×C23—21no—
43C2×D4×C23C2×C411yescharacteristic
44C22×C4×C23—21no—
45C22×C4×C23—21no—
46C22×C4×C23C2311yescharacteristic
47C2×C22⋊D23—21no—
48C2×C22⋊D23—21no—
49C2×C22⋊D23—21no—
50C22×Dic23—21no—
51C22×Dic23—21no—
52C22×Dic23D411yescharacteristic
53#67292—22no—
54#67292—22no—
55Q8×D23—22no—
56Q8×D23—22no—
57#67290—24no—
58#67290—24no—
59#67290—22no—
60#67290—22no—
61D4×D23—24no—
62D4×D23—24no—
63D4×D23—22no—
64D4×D23—22no—
65#67288—24no—
66#67288—24no—
67#67288—21no—
68#67288—21no—
69#67288D412yes—
70#67288D412yes—
71C2×D92—21no—
72C2×D92C2×C411yescharacteristic
73C2×C4×D23—24no—
74C2×C4×D23—24no—
75C2×C4×D23—21no—
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23—21no—
79C2×C4×D23—21no—
80C2×C4×D23—21no—
81C2×C4×D23—21no—
82C2×C4×D23C2×C411yescharacteristic
83C2×C4×D23C2×C411yescharacteristic
84C2×C4×D23D411yescharacteristic
85C2×C4×D23D411yescharacteristic
86C2×Dic46—21no—
87C2×Dic46C2×C411yescharacteristic
88M16×C23—21no—
89M16×C23—21no—
90C2×C8×C23—21no—
91C42×C23—21no—
92C42×C23—21no—
93(C2×D23)⋊C4—24no—
94C4×Dic23—21no—
95C4×Dic23—21no—
96#67267—21no—
97#67267—21no—
98C2×C23⋊C8—21no—
99C23×C23—21no—
100C23×C23C2×D411yescharacteristic
101C22×D23—24no—
102C22×D23—21no—
103C22×D23—21no—
104C22×D23—21no—
105C22×D23—22no—
106C22×D23—41no—
107C22×D23—42no—
108C22×D23—42no—
109C22×D23C22⋊C411yescharacteristic
110C22×D23C22⋊C411yescharacteristic
111Q8×C23—21no—
112Q8×C23C22⋊C412yescomplemented
113D4×C23—22no—
114D4×C23—22no—
115D4×C23—21no—
116D4×C23C22⋊C412yescomplemented
117C2×C4×C23—21no—
118C2×C4×C23—22no—
119C2×C4×C23—22no—
120C2×C4×C23—22no—
121C2×C4×C23—41no—
122C2×C4×C23—41no—
123C2×C4×C23C22×C411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C22⋊D23—24no—
130C22⋊D23—24no—
131C22⋊D23—22no—
132C22⋊D23—22no—
133C2×Dic23—24no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—22no—
138C2×Dic23—41no—
139C2×Dic23—41no—
140C2×Dic23C22⋊C411yescharacteristic
141C2×Dic23C22⋊C411yescharacteristic
142D92—24no—
143D92—21no—
144D92C22⋊C412yescomplemented
145C4×D23—24no—
146C4×D23—24no—
147C4×D23—21no—
148C4×D23—21no—
149C4×D23—21no—
150C4×D23—21no—
151C4×D23—21no—
152C4×D23—21no—
153C4×D23—22no—
154C4×D23—22no—
155C4×D23—21no—
156C4×D23—21no—
157Dic46—24no—
158Dic46—21no—
159Dic46C22⋊C412yescomplemented
160C8×C23—41no—
161C23⋊C8—41no—
162#1789—231nomaximal, Sylow
163C22×C23—21no—
164C22×C23—21no—
165C22×C23—22no—
166C22×C23—41no—
167C22×C23—41no—
168C22×C23C2×C22⋊C411yescharacteristic
169C22×C23#12011yescharacteristic
170C22×C23#12011yescharacteristic
171C2×D23—21no—
172C2×D23—21no—
173C2×D23—21no—
174C2×D23—22no—
175C2×D23—21no—
176C2×D23—21no—
177C2×D23—42no—
178C2×D23—42no—
179C2×D23—48no—
180C2×D23—41no—
181C2×D23—41no—
182C2×D23#10412yescomplemented
183C4×C23—22no—
184C4×C23—42no—
185C4×C23C2×C22⋊C411yescharacteristic
186C4×C23C2×C22⋊C411yescharacteristic
187C4×C23#12011yescharacteristic
188C4×C23#12011yescharacteristic
189Dic23—21no—
190Dic23—22no—
191Dic23—21no—
192Dic23—42no—
193C22×#41—231no—
194C2×#104—231no—
195C2×#104—231no—
196C2×#104—231no—
197C2×#104D2311yescharacteristic, complemented
198#407—231no—
199C4×C22⋊C4—231no—
200C2×C23—21no—
201C2×C23—21no—
202C2×C23—42no—
203C2×C23#37911yescharacteristic
204C2×C23C2×#10411yescharacteristic
205C2×C23#42111yescharacteristic
206D23—22no—
207D23—41no—
208D23—42no—
209C2×#41—231no—
210C2×#41—231no—
211C2×#41—231no—
212C2×#41—461no—
213C2×#41—461no—
214C2×#41—462no—
215C2×#41—462no—
216C2×#41—462no—
217C2×#41—462no—
218C2×#41C2×D2311yescharacteristic
219C22×Q8—231no—
220C22×D4—231no—
221C22×D4—461no—
222C23×C4—231no—
223C23×C4—461no—
224C2×M16—231no—
225C2×M16C2×D2311yescharacteristic, complemented
226C2×C22⋊C4—461no—
227C2×C42—231no—
228C2×C42C2×D2311yescharacteristic, complemented
229#104—22no—
230#104—462no—
231#104—462no—
232#104—462no—
233C22⋊C8—461no—
234C22⋊C8—461no—
235#95—461no—
236C23#178911yescharacteristic, complemented, Sylow
237C24—231no—
238C24—461no—
239#41—21no—
240#41—21no—
241#41—232no—
242#41—232no—
243#41—464no—
244#41—464no—
245#41—462no—
246#41—464no—
247#41—464no—
248#41—462no—
249#41—462no—
250#41—462no—
251#41—461no—
252#41—461no—
253#41D9212yes—
254#41C22⋊D2312yes—
255C2×Q8—231no—
256C2×Q8—461no—
257C2×Q8—462no—
258C2×Q8—462no—
259C2×Q8C4×D2311yescharacteristic
260C2×D4—21no—
261C2×D4—231no—
262C2×D4—461no—
263C2×D4—461no—
264C2×D4—462no—
265C2×D4—464no—
266C2×D4—464no—
267C2×D4—461no—
268C2×D4—461no—
269C2×D4—462no—
270C2×D4C4×D2311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—231no—
274C22×C4—231no—
275C22×C4—231no—
276C22×C4—231no—
277C22×C4—231no—
278C22×C4—461no—
279C22×C4—461no—
280C22×C4—464no—
281C22×C4—464no—
282C22×C4—461no—
283C22×C4—461no—
284C22×C4—461no—
285C22×C4—461no—
286C22×C4—461no—
287C22×C4—461no—
288C22×C4—461no—
289C22×C4C22×D2311yescharacteristic
290M16—21no—
291M16—21no—
292M16—461no—
293M16—461no—
294C2×C8—21no—
295C2×C8—461no—
296C22⋊C4—464no—
297C42—21no—
298C42—21no—
299C42—461no—
300C42—461no—
301C23—21no—
302C23—231no—
303C23—231no—
304C23—462no—
305C23—464no—
306C23—461no—
307C23—461no—
308C23—461no—
309C23—921no—
310C23—922no—
311C23—922no—
312C23D4×D2311yescharacteristic
313Q8—21no—
314Q8—232no—
315Q8—464no—
316Q8—461no—
317Q8(C2×D23)⋊C412yescomplemented
318D4—22no—
319D4—22no—
320D4—21no—
321D4—232no—
322D4—464no—
323D4—464no—
324D4—464no—
325D4—462no—
326D4—462no—
327D4—461no—
328D4(C2×D23)⋊C412yescomplemented
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—231no—
336C2×C4—231no—
337C2×C4—464no—
338C2×C4—464no—
339C2×C4—464no—
340C2×C4—461no—
341C2×C4—461no—
342C2×C4—461no—
343C2×C4—461no—
344C2×C4—461no—
345C2×C4—461no—
346C2×C4—461no—
347C2×C4—462no—
348C2×C4—461no—
349C2×C4—461no—
350C2×C4—461no—
351C2×C4—461no—
352C2×C4—462no—
353C2×C4—462no—
354C2×C4—921no—
355C2×C4—921no—
356C2×C4C2×C4×D2311yescharacteristic
357C2×C4C2×D9211yescharacteristic
358C2×C4D4×D2311yescharacteristic
359C2×C4D4×D2311yescharacteristic
360C2×C4D4×D2311yescharacteristic
361C2×C4C2×C22⋊D2311yescharacteristic
362C8—41no—
363C8—921no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—232no—
370C22—461no—
371C22—461no—
372C22—461no—
373C22—461no—
374C22—462no—
375C22—461no—
376C22—922no—
377C22—922no—
378C22—928no—
379C22—921no—
380C22—921no—
381C22C22⋊C4×D2311yescharacteristic
382C22#1062505311yescharacteristic
383C22#1062510811yescharacteristic
384C4—22no—
385C4—42no—
386C4—461no—
387C4—461no—
388C4—462no—
389C4—922no—
390C4C22⋊C4×D2311yescharacteristic
391C4#1062505311yescharacteristic
392C4C2×(C2×D23)⋊C411yescharacteristic
393C4#1062510811yescharacteristic
394C2—21no—
395C2—21no—
396C2—42no—
397C2—462no—
398C2—921no—
399C2—922no—
400C2#1309227211yescharacteristic
401C2#104×D2311yescharacteristic
402C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#104C2
socleC22×C23C2×C22⋊C4
prime radicalC2×#41×D23C2
cosocleC22×C4×C23C23
hypercenterC2×#104D23
hypocenterC23#1789
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#10624987C2semidirect
3. C2×#10625019C2semidirect
4. C2×#10625007C2semidirect
5. #13092380C2semidirect
6. C4×(C2×D23)⋊C4C2semidirect
7. C2×C23×#104C2semidirect
13. C2×#67292C4semidirect
14. C2×Q8×D23C4semidirect
16. C2×#67290C4semidirect
18. C2×D4×D23C4semidirect
23. C2×M16×C23C22semidirect
24. C2×C42×C23C22semidirect
26. C2×C4×Dic23C22semidirect
27. C2×#67267C22semidirect
112. Q8×C23C22⋊C4semidirect
116. D4×C23C22⋊C4semidirect
144. D92C22⋊C4semidirect
159. Dic46C22⋊C4semidirect
182. C2×D23#104semidirect
197. C2×#104D23semidirect
225. C2×M16C2×D23semidirect
228. C2×C42C2×D23semidirect
236. C23#1789semidirect
317. Q8(C2×D23)⋊C4semidirect
328. D4(C2×D23)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D232
C2×#106249872
C2×#106250192
C2×#106250072
#130923802
C4×(C2×D23)⋊C42
C2×C23×#1042
#178923