Finite Group Databasebeta

← #11772565

Subgroups — #11772565

Order 1152.

470 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 43 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×#63774C211yesmaximal, characteristic
2#10591380C211yesmaximal, characteristic
3C2×#63559C211yesmaximal, characteristic
4C22×C4⋊(C3⋊D3)C2211yescharacteristic
5C22×#624C411yescharacteristic, complemented
6C2×C22⋊#157—21no—
7C2×C3×#208—21no—
8C2×#3722—21no—
9C2×#3722C411yescharacteristic, complemented
10#63774—21no—
11#63774C412yescomplemented
12C3×C3⋊#95—21no—
13#63559—21no—
14#63559C412yescomplemented
15C2×#823—61no—
16#4665—61no—
17C23×C3⋊D3C2×C411yescharacteristic
18C23×C3⋊D3D411yescharacteristic
19C22×#157—41no—
20C22×C32×C4D411yescharacteristic
21C2×C4⋊(C3⋊D3)—41no—
22C2×C4⋊(C3⋊D3)—41no—
23C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
24C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
25C2×C4⋊(C3⋊D3)D411yescharacteristic
26C2×C4⋊(C3⋊D3)Q811yescharacteristic
27C22×C3×Dic3—21no—
28C22×C3×Dic3—21no—
29C2×#624—41no—
30C2×#624—42no—
31C22⋊#157—22no—
32C22⋊#157—41no—
33C3×#208—22no—
34C3×#208—41no—
35C2×C3×C3⋊C8—41no—
36#3722—42no—
37#3722—41no—
38#1390—91nomaximal, Sylow
39C22×D12—61no—
40C22×D12—61no—
41C22×C4×D3—61no—
42C2×C3×M16—61no—
43C2×(C2×D3)⋊C4—61no—
44C2×(C2×D3)⋊C4—61no—
45C2×(C2×D3)⋊C4—61no—
46C2×#208—21no—
47C3×#95—61no—
48C3⋊#95—21no—
49#823—62no—
50#823—62no—
51C23×C32C22⋊C411yescharacteristic
52C22×C3⋊D3—21no—
53C22×C3⋊D3—21no—
54C22×C3⋊D3—21no—
55C22×C3⋊D3—21no—
56C22×C3⋊D3—41no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3—41no—
59C22×C3⋊D3—41no—
60C22×C3⋊D3C4211yescharacteristic
61C22×C3⋊D3C22⋊C411yescharacteristic
62C22×C3⋊D3C4⋊C411yescharacteristic
63C22×C3⋊D3C4⋊C411yescharacteristic
64C2×#157—42no—
65C2×#157—81no—
66C2×#157—81no—
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C4⋊C411yescharacteristic
71C4⋊(C3⋊D3)—41no—
72C4⋊(C3⋊D3)—41no—
73C4⋊(C3⋊D3)—41no—
74C4⋊(C3⋊D3)—41no—
75C2×C3×Dic3—22no—
76C2×C3×Dic3—41no—
77C2×C3×Dic3—41no—
78C2×C3×Dic3—41no—
79C2×C3×Dic3—41no—
80C2×C3×Dic3—41no—
81#624—42no—
82#624—42no—
83C3×C3⋊C8—42no—
84C2×#100—91no—
85C2×#99—91no—
86#386—91no—
87C23×D3—61no—
88C23×D3—61no—
89C23×D3—61no—
90C23×D3—61no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—61no—
94C22×C3×C4—61no—
95C22×Dic3—21no—
96C22×Dic3—21no—
97C2×D12—61no—
98C2×D12—61no—
99C2×D12—61no—
100C2×D12—61no—
101C2×D12—61no—
102C2×D12—61no—
103C2×D12—61no—
104C2×D12—61no—
105C2×D12—121no—
106C2×D12—121no—
107C2×D12—121no—
108C2×D12—121no—
109C2×D12—122no—
110C2×D12—122no—
111C2×C4×D3—122no—
112C2×C4×D3—122no—
113C2×C4×D3—122no—
114C3×M16—62no—
115C3×M16—121no—
116C2×C3×C8—121no—
117(C2×D3)⋊C4—122no—
118(C2×D3)⋊C4—122no—
119(C2×D3)⋊C4—122no—
120#208—22no—
121#208—41no—
122C2×C3⋊C8—41no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32#9511yescharacteristic
126C22×C32#9911yescharacteristic
127C22×C32#9911yescharacteristic
128C2×C3⋊D3—21no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—42no—
133C2×C3⋊D3—41no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3—41no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C2×C3⋊D3—41no—
139C2×C3⋊D3—41no—
140C2×C3⋊D3—41no—
141C2×C3⋊D3—81no—
142#157—82no—
143C32×C4—21no—
144C32×C4—21no—
145C3×Dic3—42no—
146C3×Dic3—81no—
147C22×D4—91no—
148C23×C4—91no—
149C2×M16—61no—
150C2×C22⋊C4—91no—
151C2×C22⋊C4—181no—
152C2×C22⋊C4—181no—
153#100—92no—
154#100—181no—
155#99—92no—
156#99—181no—
157#95—61no—
158C23×C3—21no—
159C23×C3—21no—
160C22×D3—61no—
161C22×D3—61no—
162C22×D3—61no—
163C22×D3—61no—
164C22×D3—61no—
165C22×D3—61no—
166C22×D3—61no—
167C22×D3—61no—
168C22×D3—62no—
169C22×D3—62no—
170C22×D3—121no—
171C22×D3—121no—
172C22×D3—121no—
173C22×D3—121no—
174C22×D3—121no—
175C22×D3—121no—
176C22×D3—121no—
177C22×D3—121no—
178C22×D3—121no—
179C22×D3—121no—
180C22×D3—121no—
181C22×D3—121no—
182C22×D3—121no—
183C22×D3—121no—
184C22×D3—241no—
185C22×D3—241no—
186C22×D3—241no—
187C22×D3—241no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198C2×C3×C4—62no—
199C2×C3×C4—121no—
200C2×C3×C4—121no—
201C2×C3×C4—121no—
202C2×C3×C4—121no—
203C2×C3×C4—121no—
204C2×Dic3—22no—
205C2×Dic3—41no—
206C2×Dic3—41no—
207C2×Dic3—41no—
208C2×Dic3—41no—
209C2×Dic3—41no—
210D12—121no—
211D12—121no—
212D12—121no—
213D12—121no—
214D12—121no—
215D12—121no—
216D12—121no—
217D12—121no—
218D12—122no—
219D12—122no—
220D12—122no—
221D12—122no—
222C4×D3—124no—
223C4×D3—124no—
224C3×C8—122no—
225C3⋊C8—42no—
226C2×C32—21no—
227C2×C32—21no—
228C2×C32#34211yescharacteristic
229C2×C32AΣL(1,𝔽16)11yescharacteristic
230C2×C32#35211yescharacteristic
231C3⋊D3—41no—
232C3⋊D3—41no—
233C3⋊D3—41no—
234C3⋊D3—41no—
235C24—91no—
236C24—91no—
237C2×D4—91no—
238C2×D4—91no—
239C2×D4—91no—
240C2×D4—91no—
241C2×D4—361no—
242C2×D4—361no—
243C22×C4—61no—
244C22×C4—61no—
245C22×C4—362no—
246C22×C4—361no—
247C22×C4—361no—
248C22×C4GO+(4,𝔽2)11yescharacteristic
249M16—62no—
250M16—121no—
251C2×C8—121no—
252C22⋊C4—182no—
253C22⋊C4—362no—
254C22⋊C4—361no—
255C22⋊C4—361no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—41no—
267C22×C3—41no—
268C2×D3—62no—
269C2×D3—62no—
270C2×D3—121no—
271C2×D3—121no—
272C2×D3—121no—
273C2×D3—121no—
274C2×D3—121no—
275C2×D3—121no—
276C2×D3—122no—
277C2×D3—121no—
278C2×D3—121no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—122no—
282C2×D3—122no—
283C2×D3—122no—
284C2×D3—121no—
285C2×D3—121no—
286C2×D3—121no—
287C2×D3—121no—
288C2×D3—241no—
289C2×D3—241no—
290C2×D3—241no—
291C2×D3—241no—
292C2×D3—241no—
293C2×D3—241no—
294C2×D3—242no—
295C2×D3—241no—
296C2×D3—241no—
297C2×D3—241no—
298C2×D3—241no—
299C2×D3—241no—
300C2×D3—241no—
301C2×D3—242no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—122no—
309C3×C4—241no—
310Dic3—42no—
311Dic3—81no—
312C32#139011yescharacteristic, complemented, Sylow
313C23—91no—
314C23—91no—
315C23—91no—
316C23—91no—
317C23—181no—
318C23—181no—
319C23—181no—
320C23—181no—
321C23—361no—
322C23—361no—
323C23—361no—
324C23—361no—
325C23D32⋊C411yescharacteristic
326D4—361no—
327D4—361no—
328D4—361no—
329D4—361no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—62no—
333C2×C4—121no—
334C2×C4—121no—
335C2×C4—121no—
336C2×C4—121no—
337C2×C4—121no—
338C2×C4—362no—
339C2×C4—362no—
340C2×C4—362no—
341C2×C4—721no—
342C2×C4—721no—
343C2×C4D32⋊C411yescharacteristic
344C2×C4#377311yescharacteristic
345C8—122no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—41no—
357C2×C3—41no—
358D3—122no—
359D3—122no—
360D3—241no—
361D3—241no—
362D3—241no—
363D3—241no—
364D3—241no—
365D3—241no—
366C22—21no—
367C22—21no—
368C22—181no—
369C22—181no—
370C22—181no—
371C22—181no—
372C22—361no—
373C22—361no—
374C22—361no—
375C22—361no—
376C22—362no—
377C22—361no—
378C22—361no—
379C22—361no—
380C22—361no—
381C22—721no—
382C22#6373711yescharacteristic
383C22#6373811yescharacteristic
384C22#6373811yescharacteristic
385C4—21no—
386C4—21no—
387C4—122no—
388C4—241no—
389C4—722no—
390C3—21no—
391C3—21no—
392C2—21no—
393C2—21no—
394C2—361no—
395C2—361no—
396C2—361no—
397C2—361no—
398C2#1059005711yescharacteristic
399C2#1059005811yescharacteristic
400C2#1059007611yescharacteristic
subgroupG/H
centerC22#63738
commutatorC22×C3⋊D3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#99
prime radical, cosocleC22×C4⋊(C3⋊D3)C22
hypocenterC32#1390
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. C22×#624C4semidirect
9. C2×#3722C4semidirect
11. #63774C4semidirect
14. #63559C4semidirect
312. C32#1390semidirect

Maximal subgroups

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

subgroupindex
C2×#637742
#105913802
C2×#635592
#13909