Finite Group Databasebeta

← #11774621

Subgroups — #11774621

Order 1152.

647 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 647 conjugacy classes of subgroups — too many to draw. Only its 110 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×#3830C211yesmaximal, characteristic
2#10590297C211yesmaximal, characteristic, complemented
3#10590260C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
5#10589085C212yesmaximal, complemented
6#68173—32nomaximal
7C2×#3830C411yescharacteristic
8C32×C4×D4C2211yescharacteristic
9D4×C3⋊Dic3C411yescharacteristic
10C4×#638—21no—
11C2×C4×C3⋊Dic3—21no—
12#64101C411yescharacteristic
13#64096C411yescharacteristic
14#64090—21no—
15#64086—21no—
16C42×C3⋊D3C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2212yes—
19C3×C4×C3⋊C8C2212yes—
20#63572—21no—
21#63557—21no—
22#63557—21no—
23#63555—21no—
24C4×#237—32no—
25C4×#237—61no—
26#4835—32no—
27#4685—32no—
28C3×D4⋊C8—32no—
29D4⋊(C3⋊C8)D312yescomplemented
30#4484—32no—
31#4456—32no—
32C2×C32×D4C2×C411yescharacteristic
33C22×C32×C4—21no—
34C2×#638—21no—
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37#3830—22no—
38#3830—22no—
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×#634C2×C411yescharacteristic
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C22⋊C4—21no—
45C32×C42C2311yescharacteristic
46#3757—21no—
47#3752—21no—
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49#3750—21no—
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59#1488—91noSylow
60C2×#237—32no—
61C2×#237—61no—
62C3×C4×D4—21no—
63C3×C4×D4C2×D312yes—
64D4×Dic3—32no—
65D4×Dic3—61no—
66C4×#67—62no—
67C4×#67—62no—
68C2×C4×Dic3—62no—
69C2×C4×Dic3—62no—
70#892—32no—
71#892—61no—
72#887—32no—
73#887—61no—
74#67⋊C4—62no—
75#67⋊C4—62no—
76#877—62no—
77#877—62no—
78C42×D3—32no—
79C42×D3—61no—
80C4×Dic6—32no—
81C4×Dic6—61no—
82C3×C4⋊C8—32no—
83C3×C4×C8—32no—
84(C2×D3)⋊C8—62no—
85(C2×D3)⋊C8—62no—
86#815—62no—
87Dic3⋊C8—62no—
88C4⋊(C3⋊C8)C2×D312yes—
89C4×C3⋊C8C2×D312yes—
90C23×C32—21no—
91C22×C3⋊D3C22⋊C411yescharacteristic
92C32×D4—21no—
93C32×D4M1612yes—
94C2×C32×C4—21no—
95C2×C32×C4—42no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99#638—24no—
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—42no—
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C4×C3⋊D3—21no—
108C4×C3⋊D3—21no—
109C4×C3⋊D3—22no—
110C4×C3⋊D3—41no—
111#634—21no—
112#634M1612yes—
113C3×C3⋊C8—42no—
114C3×C3⋊C8—42no—
115C4×#41—91no—
116#432—91no—
117#431—91no—
118Q8⋊C8—92no—
119D4⋊C8—32no—
120C2×C3×D4—21no—
121C2×C3×D4C4×D312yes—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C2×#67—62no—
125C2×#67—62no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130#237—64no—
131#237—64no—
132#237—64no—
133#237—64no—
134C2×C4×D3—32no—
135C2×C4×D3—32no—
136C2×C4×D3—32no—
137C2×C4×D3—61no—
138C2×C4×D3—61no—
139C2×C4×D3—61no—
140C2×Dic6—32no—
141C2×Dic6—61no—
142C2×C3×C8—62no—
143C2×C3×C8—62no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4C4×D312yes—
146C3×C22⋊C4—22no—
147C3×C22⋊C4—22no—
148C3×C42—21no—
149C3×C42C22×D312yes—
150#217—62no—
151#217—62no—
152(C2×D3)⋊C4—62no—
153(C2×D3)⋊C4—62no—
154C4⋊Dic3—32no—
155C4⋊Dic3—61no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160C4×Dic3—32no—
161C4×Dic3—32no—
162C4×Dic3—32no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172C2×C3⋊C8—22no—
173C2×C3⋊C8—22no—
174C22×C32—22no—
175C22×C32—41no—
176C22×C32—41no—
177C22×C32C2×C22⋊C411yescharacteristic
178C2×C3⋊D3—21no—
179C2×C3⋊D3—21no—
180C2×C3⋊D3—21no—
181C32×C4—21no—
182C32×C4—41no—
183C32×C4C2×M1611yescharacteristic
184C32×C4C2×M1611yescharacteristic
185C32×C4#13512yes—
186C3⋊Dic3—22no—
187C3⋊Dic3—21no—
188C3⋊Dic3—21no—
189C3⋊Dic3—21no—
190C3⋊Dic3—41no—
191C2×#41—91no—
192C4×Q8—91no—
193C4×Q8—91no—
194C4×D4—91no—
195C4×D4—181no—
196C4×D4—181no—
197C4×D4D3211yescharacteristic
198#117—91no—
199#117—181no—
200C2×C42—91no—
201C2×C42—181no—
202C4⋊C8—32no—
203C4⋊C8—181no—
204C22⋊C8—181no—
205C22⋊C8—181no—
206#97—181no—
207C4×C8—32no—
208C23×C3—22no—
209C23×C3—22no—
210C22×D3—32no—
211C22×D3—61no—
212C3×D4—22no—
213C3×D4—22no—
214C3×D4—22no—
215C3×D4ΓL(1,𝔽25)14yes—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—44no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4C2×C4×D312yes—
225C2×C3×C4D3×D412yes—
226C2×C3×C4D3×D412yes—
227#67—68no—
228#67—68no—
229C2×Dic3—32no—
230C2×Dic3—32no—
231C2×Dic3—32no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—62no—
236C2×Dic3—68no—
237C2×Dic3—68no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—124no—
242C2×Dic3—124no—
243C4×D3—62no—
244C4×D3—62no—
245C4×D3—62no—
246C4×D3—62no—
247C4×D3—62no—
248C4×D3—62no—
249C4×D3—122no—
250C4×D3—122no—
251C4×D3—122no—
252Dic6—34no—
253Dic6—62no—
254Dic6—62no—
255Dic6—62no—
256C3×C8—122no—
257C3×C8—122no—
258C3⋊C8—42no—
259C3⋊C8—42no—
260C2×C32—42no—
261C2×C32#40711yescharacteristic
262C2×C32#41611yescharacteristic
263C2×C32#42111yescharacteristic
264C3⋊D3—41no—
265#41—182no—
266#41—182no—
267C2×Q8—91no—
268C2×D4—181no—
269C2×D4#62411yescharacteristic
270C22×C4—21no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—181no—
275C22×C4—181no—
276C2×C8—62no—
277C2×C8—62no—
278C4⋊C4—91no—
279C4⋊C4—181no—
280C4⋊C4—181no—
281C4⋊C4#62411yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—181no—
284C22⋊C4—181no—
285C42—91no—
286C42—91no—
287C42—91no—
288C42—181no—
289C42—181no—
290C42—181no—
291C42C2×D3211yescharacteristic
292C22×C3—24no—
293C22×C3—24no—
294C22×C3—21no—
295C22×C3—42no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3D3×C22⋊C412yes—
300C2×D3—62no—
301C2×D3—62no—
302C2×D3—62no—
303C2×D3—62no—
304C2×D3—121no—
305C2×D3—121no—
306C3×C4—22no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—22no—
310C3×C4—41no—
311C3×C4—42no—
312C3×C4—42no—
313C3×C4C2×ΓL(1,𝔽25)12yes—
314C3×C4D3×M1612yes—
315C3×C4#91212yes—
316C3×C4#91612yes—
317Dic3—64no—
318Dic3—62no—
319Dic3—62no—
320Dic3—64no—
321Dic3—62no—
322Dic3—62no—
323Dic3—62no—
324Dic3—121no—
325Dic3—122no—
326Dic3—122no—
327C32#148811yescharacteristic, complemented, Sylow
328C23—21no—
329C23—91no—
330Q8—92no—
331Q8—181no—
332D4—21no—
333D4—184no—
334D4#371212yes—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—91no—
340C2×C4—184no—
341C2×C4—181no—
342C2×C4—181no—
343C2×C4—181no—
344C2×C4—182no—
345C2×C4—181no—
346C2×C4—361no—
347C2×C4—362no—
348C2×C4C2×#62411yescharacteristic
349C2×C4#381111yescharacteristic
350C2×C4#381111yescharacteristic
351C8—122no—
352C8—122no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—44no—
357C2×C3—44no—
358C2×C3#472612yes—
359C2×C3#477212yes—
360C2×C3#482112yes—
361D3—122no—
362D3—122no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—181no—
367C22—181no—
368C22—181no—
369C22#6397411yescharacteristic
370C4—21no—
371C4—41no—
372C4—181no—
373C4—182no—
374C4—181no—
375C4—181no—
376C4—361no—
377C4#6381811yescharacteristic
378C4C2×#371211yescharacteristic
379C4#6393612yes—
380C3—21no—
381C3#6817312yescomplemented
382C2—42no—
383C2—361no—
384C2#1059115911yescharacteristic
385C2#1059142411yescharacteristic
386C2#1059167211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3830C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10590297C2semidirect
3. #10590260C2semidirect
4. C3×D4⋊(C3⋊C8)C2semidirect
5. #10589085C2semidirect
29. D4⋊(C3⋊C8)D3semidirect
327. C32#1488semidirect
381. C3#68173semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105902972
#105902602
C3×D4⋊(C3⋊C8)2
#105890852
#681733