Finite Group Databasebeta

← #11775408

Subgroups — #11775408

Order 1152.

568 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 59 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#10595016C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic, complemented
3#10591325C211yesmaximal, characteristic, complemented
4#10590072C212yesmaximal, complemented
5#10590071C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3798C411yescharacteristic, complemented
8C2×#3788—21no—
9C3×C4×#67—21no—
10C2×C3×C4⋊Dic3—21no—
11#63982C2211yescharacteristic
12#63981—21no—
13#63980C2211yescharacteristic
14C2×#3722—21no—
15#63912C411yescharacteristic, complemented
16C4×#626—21no—
17#63874C411yescharacteristic, complemented
18#63865C411yescharacteristic, complemented
19#63853—21no—
20C22⋊#622C2212yes—
21#63778—21no—
22#63579C2212yes—
23#5547—61no—
24#4987—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C4×C3⋊D3—42no—
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C3×#67—21no—
34C22×C3×Dic3—22no—
35C2×C3×C4×D3—21no—
36C2×#627C2×C411yescharacteristic
37C2×#626—21no—
38C2×#626—21no—
39C2×#625C2×C411yescharacteristic
40#3798—42no—
41C2×#622—22no—
42#3788—42no—
43C3×#217—21no—
44C3×(C2×D3)⋊C4—21no—
45C3×C4⋊Dic3—42no—
46C3×Dic3⋊C4—21no—
47C3×C4×Dic3—21no—
48#3724C2×C411yescharacteristic
49#3724C2×C411yescharacteristic
50Dic3⋊Dic3—21no—
51#3722—21no—
52#3722—21no—
53#3722—42no—
54(C2×D3)⋊Dic3—21no—
55#1513—91nomaximal, Sylow
56C2×#235—61no—
57C22×C4×D3—61no—
58C22×C4×D3—61no—
59C3×C4×D4—61no—
60C2×C3×C4⋊C4—61no—
61#939—61no—
62#937—61no—
63C4×#67—21no—
64C4×#67—61no—
65C2×(C2×D3)⋊C4—62no—
66C2×C4⋊Dic3—21no—
67#896—61no—
68#894—61no—
69#884—61no—
70#883—61no—
71#882—61no—
72#878—61no—
73C4×D12—61no—
74#872—61no—
75C3⋊#95—62no—
76C23×C32C2×D411yescharacteristic
77C22×C3⋊D3—21no—
78C22×C3⋊D3—21no—
79C22×C3⋊D3—41no—
80C22×C3⋊D3—41no—
81C22×C3⋊D3C22⋊C411yescharacteristic
82C22×C3⋊D3C22⋊C411yescharacteristic
83C22×C3×D3—21no—
84C2×C32×C4—22no—
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3C22×C411yescharacteristic
89C2×C3⋊Dic3C2×D411yescharacteristic
90C4×C3⋊D3—22no—
91C4×C3⋊D3—22no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—41no—
94C3×#67—41no—
95C3×#67—41no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102C3×C4×D3—42no—
103#627—41no—
104#626—42no—
105#626—42no—
106#625—41no—
107#622—42no—
108#525—91no—
109#407—91no—
110#380—91no—
111#328—92no—
112#327—92no—
113C23×D3—61no—
114C23×D3—61no—
115C2×C3×D4—61no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—61no—
119C22×C3×C4—62no—
120C2×#67—21no—
121C2×#67—61no—
122C2×#67—61no—
123C2×#67—61no—
124C22×Dic3—22no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127#235—124no—
128C2×D12—61no—
129C2×D12—61no—
130C2×C4×D3—21no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—61no—
139C2×C4×D3—124no—
140C2×C4×D3—122no—
141C2×C4×D3—122no—
142C2×Dic6—61no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—122no—
145C3×C22⋊C4—61no—
146C3×C22⋊C4—61no—
147C3×C42—61no—
148#217—21no—
149#217—61no—
150(C2×D3)⋊C4—21no—
151(C2×D3)⋊C4—61no—
152(C2×D3)⋊C4—61no—
153(C2×D3)⋊C4—61no—
154(C2×D3)⋊C4—61no—
155(C2×D3)⋊C4—61no—
156(C2×D3)⋊C4—124no—
157C4⋊Dic3—42no—
158C4⋊Dic3—61no—
159Dic3⋊C4—21no—
160Dic3⋊C4—61no—
161Dic3⋊C4—61no—
162Dic3⋊C4—61no—
163C4×Dic3—21no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32C2×C22⋊C411yescharacteristic
167C22×C32AGL(1,ℤ/8)11yescharacteristic
168C22×C32#13711yescharacteristic
169C2×C3⋊D3—21no—
170C2×C3⋊D3—21no—
171C2×C3⋊D3—21no—
172C2×C3⋊D3—21no—
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3—42no—
176C2×C3⋊D3—42no—
177C2×C3×D3—41no—
178C2×C3×D3—41no—
179C2×C3×D3—41no—
180C32×C4—21no—
181C32×C4#9912yes—
182C3⋊Dic3—21no—
183C3⋊Dic3—21no—
184C3×Dic3—41no—
185C3×Dic3—41no—
186C3×Dic3—41no—
187C3×Dic3—82no—
188C2×#41—91no—
189C23×C4—91no—
190C2×M16—181no—
191#123—181no—
192C22⋊Q8—91no—
193C22⋊Q8—91no—
194#121—91no—
195#121—91no—
196#120—181no—
197C4×D4—61no—
198C4×D4—181no—
199#117—91no—
200C2×C4⋊C4—61no—
201C2×C22⋊C4—181no—
202C22⋊C8—92no—
203C22⋊C8—181no—
204#95—92no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—61no—
208C22×D3—21no—
209C22×D3—61no—
210C22×D3—61no—
211C22×D3—61no—
212C22×D3—61no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—121no—
216C22×D3—121no—
217C22×D3—122no—
218C22×D3—122no—
219C22×D3—121no—
220C22×D3—121no—
221C22×D3—121no—
222C22×D3—121no—
223C3×D4—121no—
224C3×D4—121no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—42no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—122no—
236C2×C3×C4—122no—
237C2×C3×C4—122no—
238C2×C3×C4—122no—
239#67—41no—
240#67—41no—
241#67—122no—
242#67—122no—
243#67—122no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—42no—
248C2×Dic3—42no—
249C2×Dic3—42no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—122no—
255C2×Dic3—121no—
256C2×Dic3—121no—
257D12—122no—
258D12—122no—
259C4×D3—42no—
260C4×D3—64no—
261C4×D3—122no—
262C4×D3—122no—
263C4×D3—122no—
264C4×D3—122no—
265C4×D3—122no—
266C4×D3—122no—
267C4×D3—122no—
268Dic6—122no—
269C2×C32—21no—
270C2×C32—21no—
271C2×C32C2×#9911yescharacteristic
272C2×C32#41711yescharacteristic
273C2×C32#42111yescharacteristic
274C3⋊D3—41no—
275C3⋊D3—41no—
276C3×D3—81no—
277C24—91no—
278#41—362no—
279C2×Q8—91no—
280C2×D4—61no—
281C2×D4—91no—
282C2×D4—181no—
283C2×D4—181no—
284C22×C4—61no—
285C22×C4—62no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—362no—
292C22×C4GO+(4,𝔽2)11yescharacteristic
293M16—362no—
294C2×C8—182no—
295C4⋊C4—61no—
296C4⋊C4—91no—
297C4⋊C4—91no—
298C4⋊C4—122no—
299C4⋊C4—181no—
300C22⋊C4—61no—
301C22⋊C4—61no—
302C22⋊C4—181no—
303C22⋊C4—181no—
304C22⋊C4—181no—
305C22⋊C4—362no—
306C42—61no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3—121no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—121no—
330C2×D3—121no—
331C2×D3—121no—
332C2×D3—121no—
333C2×D3—121no—
334C2×D3—121no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—122no—
338C2×D3—122no—
339C2×D3—122no—
340C2×D3—122no—
341C2×D3—124no—
342C2×D3—124no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—41no—
347C3×C4—121no—
348C3×C4—121no—
349C3×C4—121no—
350C3×C4—242no—
351Dic3—41no—
352Dic3—41no—
353Dic3—41no—
354Dic3—62no—
355Dic3—82no—
356Dic3—121no—
357Dic3—121no—
358Dic3—121no—
359C32#151311yescharacteristic, complemented, Sylow
360C23—61no—
361C23—91no—
362C23—91no—
363C23—181no—
364C23—181no—
365C23—361no—
366C23—361no—
367C23C2×GO+(4,𝔽2)11yescharacteristic
368Q8—361no—
369D4—121no—
370D4—121no—
371D4—362no—
372D4—362no—
373D4—361no—
374C2×C4—22no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—91no—
379C2×C4—91no—
380C2×C4—122no—
381C2×C4—122no—
382C2×C4—122no—
383C2×C4—122no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4—361no—
387C2×C4—361no—
388C2×C4—361no—
389C2×C4D32⋊C411yescharacteristic
390C2×C4D32⋊C411yescharacteristic
391C8—362no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—41no—
403C2×C3—41no—
404C2×C3—241no—
405D3—81no—
406D3—122no—
407D3—122no—
408D3—122no—
409D3—122no—
410C22—21no—
411C22—21no—
412C22—121no—
413C22—121no—
414C22—121no—
415C22—181no—
416C22—181no—
417C22—181no—
418C22—181no—
419C22—181no—
420C22—181no—
421C22—362no—
422C22—362no—
423C22#6422411yescharacteristic
424C22#6422611yescharacteristic
425C22C2×D32⋊C411yescharacteristic
426C4—21no—
427C4—121no—
428C4—121no—
429C4—121no—
430C4—181no—
431C4—181no—
432C4—242no—
433C4#6373812yes—
434C3—21no—
435C3—21no—
436C2—21no—
437C2—21no—
438C2—241no—
439C2—361no—
440C2—361no—
441C2#1059336011yescharacteristic
442C2#1059338111yescharacteristic
443C2C2×#6373811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595016C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1513
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593803C2semidirect
3. #10591325C2semidirect
4. #10590072C2semidirect
5. #10590071C2semidirect
7. C2×#3798C4semidirect
15. #63912C4semidirect
17. #63874C4semidirect
18. #63865C4semidirect
359. C32#1513semidirect

Maximal subgroups

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

subgroupindex
#105950162
#105938032
#105913252
#105900722
#105900712
#15139