Finite Group Databasebeta

← #11775039

Subgroups — #11775039

Order 1152.

598 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 61 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#10595501C211yesmaximal, characteristic
2C2×C22⋊#622C211yesmaximal, characteristic, complemented
3#10591705C211yesmaximal, characteristic, complemented
4#10590072C212yesmaximal, complemented
5#10590071C212yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C2×#3805C411yescharacteristic, complemented
8C22×#622—21no—
9C3×#953—21no—
10C2×C3×#217—21no—
11#63982C411yescharacteristic, complemented
12#63982C2211yescharacteristic
13#63980C411yescharacteristic, complemented
14#63980C2211yescharacteristic
15#67⋊Dic3—21no—
16#67⋊Dic3—21no—
17#63962—21no—
18#63957C411yescharacteristic, complemented
19C2×Dic32—21no—
20C22⋊#622—21no—
21C22⋊#622C2212yes—
22#63579C2212yes—
23#5586—61no—
24Dic3×C22⋊C4—61no—
25C24×C32D411yescharacteristic
26C22×C3⋊Dic3—42no—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3C2311yescharacteristic
33C2×C3×#67—21no—
34C2×C3×#67—21no—
35C2×C3×#67—21no—
36C22×C3×Dic3—22no—
37C2×#627C2×C411yescharacteristic
38C2×#625C2×C411yescharacteristic
39#3805—42no—
40C2×D3×Dic3—21no—
41C2×#622—22no—
42C2×#622—42no—
43C3×#217—24no—
44C3×#217—21no—
45C3×#217—21no—
46C3×#217—21no—
47#3724C2×C411yescharacteristic
48#3724C2×C411yescharacteristic
49Dic3⋊Dic3—21no—
50Dic3⋊Dic3—21no—
51(C2×D3)⋊Dic3—21no—
52(C2×D3)⋊Dic3—21no—
53Dic32—21no—
54Dic32—42no—
55#1501—91nomaximal, Sylow
56C23×Dic3—61no—
57C23×Dic3—61no—
58C2×#237—61no—
59C3×#120—61no—
60C2×C3×C22⋊C4—61no—
61#953—21no—
62C2×#217—21no—
63#939—61no—
64#939—61no—
65#935—61no—
66D4×Dic3—61no—
67D4×Dic3—61no—
68C2×C4×Dic3—62no—
69#886—61no—
70#67⋊C4—61no—
71#67⋊C4—61no—
72#878—61no—
73#878—61no—
74#877—61no—
75C3⋊#95—62no—
76C23×C32—22no—
77C23×C32—22no—
78C23×C32—41no—
79C23×C32C22⋊C411yescharacteristic
80C23×C32C22⋊C411yescharacteristic
81C23×C32C2×D411yescharacteristic
82C22×C3×D3—21no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22×C411yescharacteristic
92C2×C3⋊Dic3C2×D411yescharacteristic
93C3×#67—42no—
94C3×#67—42no—
95C3×#67—42no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102#627—41no—
103#625—41no—
104D3×Dic3—42no—
105#622—42no—
106#525—91no—
107C2×C22⋊C8—91no—
108C4×C22⋊C4—91no—
109#328—92no—
110#327—92no—
111C24×C3—21no—
112C24×C3—21no—
113C2×C3×D4—61no—
114C2×C3×D4—61no—
115C2×C3×D4—61no—
116C22×C3×C4—62no—
117C2×#67—21no—
118C2×#67—21no—
119C2×#67—21no—
120C2×#67—61no—
121C22×Dic3—22no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—124no—
136C22×Dic3—124no—
137#237—124no—
138C2×C4×D3—61no—
139C2×Dic6—61no—
140C3×C22⋊C4—61no—
141C3×C22⋊C4—61no—
142C3×C22⋊C4—61no—
143C3×C22⋊C4—64no—
144#217—21no—
145#217—21no—
146#217—21no—
147#217—24no—
148#217—61no—
149#217—61no—
150(C2×D3)⋊C4—61no—
151(C2×D3)⋊C4—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154Dic3⋊C4—61no—
155Dic3⋊C4—61no—
156Dic3⋊C4—61no—
157Dic3⋊C4—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—124no—
161C22×C32—21no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32—44no—
169C22×C32#10412yes—
170C22×C32C2×C22⋊C411yescharacteristic
171C22×C32#13512yes—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C2×C3×D3—41no—
175C3⋊Dic3—21no—
176C3⋊Dic3—21no—
177C3⋊Dic3—21no—
178C3⋊Dic3#9912yes—
179C3×Dic3—44no—
180C3×Dic3—41no—
181C3×Dic3—41no—
182C3×Dic3—41no—
183C2×#41—91no—
184C23×C4—91no—
185C22×C8—181no—
186#123—181no—
187C22⋊Q8—91no—
188C22⋊Q8—91no—
189#121—91no—
190#121—91no—
191#120—61no—
192C4×D4—181no—
193C4×D4—181no—
194#117—91no—
195C2×C22⋊C4—61no—
196C2×C42—181no—
197C22⋊C8—92no—
198C22⋊C8—181no—
199#95—92no—
200C23×C3—22no—
201C23×C3—22no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—42no—
209C23×C3—42no—
210C23×C3—42no—
211C23×C3—42no—
212C23×C3—42no—
213C23×C3—61no—
214C22×D3—21no—
215C3×D4—122no—
216C3×D4—122no—
217C3×D4—122no—
218C2×C3×C4—61no—
219C2×C3×C4—61no—
220C2×C3×C4—61no—
221C2×C3×C4—64no—
222C2×C3×C4—122no—
223C2×C3×C4—122no—
224#67—42no—
225#67—42no—
226#67—42no—
227#67—122no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—24no—
232C2×Dic3—42no—
233C2×Dic3—42no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246C2×Dic3—122no—
247C2×Dic3—122no—
248C2×Dic3—122no—
249C2×Dic3—122no—
250C2×Dic3—122no—
251C2×Dic3—122no—
252C2×Dic3—122no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C4×D3—122no—
256Dic6—122no—
257C2×C32—22no—
258C2×C32—22no—
259C2×C32—41no—
260C2×C32C2×#9911yescharacteristic
261C2×C32#41611yescharacteristic
262C2×C32C2×#10411yescharacteristic
263C3×D3—81no—
264C24GO+(4,𝔽2)11yescharacteristic
265#41—362no—
266C2×Q8—91no—
267C2×D4—61no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—91no—
271C22×C4—62no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4—181no—
279C22×C4—362no—
280C2×C8—182no—
281C2×C8—362no—
282C4⋊C4—91no—
283C4⋊C4—91no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C22⋊C4—64no—
287C22⋊C4—61no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4—181no—
291C22⋊C4—181no—
292C42—181no—
293C42—362no—
294C22×C3—21no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—22no—
298C22×C3—22no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—44no—
316C22×C3—44no—
317C22×C3—48no—
318C22×C3—121no—
319C22×C3—121no—
320C22×C3—121no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C3×C4—121no—
325C3×C4—124no—
326C3×C4—121no—
327C3×C4—121no—
328Dic3—41no—
329Dic3—44no—
330Dic3—41no—
331Dic3—41no—
332Dic3—62no—
333Dic3—62no—
334Dic3—62no—
335Dic3—62no—
336Dic3—121no—
337Dic3—121no—
338Dic3—121no—
339Dic3—121no—
340C32#150111yescharacteristic, complemented, Sylow
341C23—22no—
342C23—22no—
343C23—41no—
344C23—61no—
345C23D32⋊C411yescharacteristic
346C23D32⋊C411yescharacteristic
347C23C2×GO+(4,𝔽2)11yescharacteristic
348Q8—361no—
349D4—122no—
350D4—122no—
351D4—122no—
352D4—361no—
353C2×C4—64no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—91no—
358C2×C4—91no—
359C2×C4—91no—
360C2×C4—91no—
361C2×C4—122no—
362C2×C4—122no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—362no—
367C2×C4—361no—
368C2×C4—361no—
369C2×C4—361no—
370C8—362no—
371C2×C3—22no—
372C2×C3—22no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—42no—
380C2×C3—42no—
381C2×C3—42no—
382C2×C3—42no—
383C2×C3—42no—
384C2×C3—241no—
385D3—81no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—121no—
395C22—121no—
396C22—121no—
397C22#6374112yes—
398C22C2×D32⋊C411yescharacteristic
399C22#6423712yes—
400C4—92no—
401C4—124no—
402C4—121no—
403C4—121no—
404C4—121no—
405C4—181no—
406C4—181no—
407C4—181no—
408C3—21no—
409C3—21no—
410C2—22no—
411C2—22no—
412C2—41no—
413C2—241no—
414C2#1059349011yescharacteristic
415C2#1059349811yescharacteristic
416C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC24×C32D4
socleC22×C32C2×C22⋊C4
prime radical#10595501C2
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1501
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#622C2semidirect
3. #10591705C2semidirect
4. #10590072C2semidirect
5. #10590071C2semidirect
7. C2×#3805C4semidirect
11. #63982C4semidirect
13. #63980C4semidirect
18. #63957C4semidirect
340. C32#1501semidirect

Maximal subgroups

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

subgroupindex
#105955012
C2×C22⋊#6222
#105917052
#105900722
#105900712
#15019