Finite Group Databasebeta

← #11775409

Subgroups — #11775409

Order 1152.

568 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 57 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
2#10593845C211yesmaximal, characteristic, complemented
3#10591720C211yesmaximal, characteristic, complemented
4#10590072C212yesmaximal, complemented
5#10590071C212yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C2×#3805C411yescharacteristic, complemented
8C2×#3792—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—
17C2×#3724—21no—
18#63962—21no—
19#63957C411yescharacteristic, complemented
20C22⋊#622—21no—
21C22⋊#622C2212yes—
22#63579C2212yes—
23#5586—61no—
24#4942—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—
41#3792—42no—
42C2×#622—22no—
43C3×#217—21no—
44C3×#217—21no—
45C3×#217—21no—
46C3×#217—42no—
47#3724—42no—
48#3724C2×C411yescharacteristic
49#3724C2×C411yescharacteristic
50Dic3⋊Dic3—21no—
51Dic3⋊Dic3—21no—
52(C2×D3)⋊Dic3—21no—
53(C2×D3)⋊Dic3—21no—
54Dic32—21no—
55#1513—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×Dic3⋊C4—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—21no—
77C23×C32—21no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32C22⋊C411yescharacteristic
81C23×C32C22⋊C411yescharacteristic
82C23×C32C2×D411yescharacteristic
83C22×C3×D3—21no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22×C411yescharacteristic
93C2×C3⋊Dic3C2×D411yescharacteristic
94C3×#67—42no—
95C3×#67—42no—
96C3×#67—41no—
97C3×#67—41no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C2×C3×Dic3—42no—
104#627—41no—
105#625—41no—
106D3×Dic3—42no—
107#622—42no—
108#525—91no—
109#407—91no—
110#380—91no—
111#328—92no—
112#327—92no—
113C24×C3—21no—
114C24×C3—21no—
115C2×C3×D4—61no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C22×C3×C4—62no—
119C2×#67—21no—
120C2×#67—21no—
121C2×#67—21no—
122C2×#67—61no—
123C22×Dic3—22no—
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—61no—
136C22×Dic3—61no—
137C22×Dic3—124no—
138C22×Dic3—124no—
139#237—124no—
140C2×C4×D3—61no—
141C2×Dic6—61no—
142C3×C22⋊C4—61no—
143C3×C22⋊C4—61no—
144C3×C22⋊C4—61no—
145C3×C22⋊C4—122no—
146#217—21no—
147#217—21no—
148#217—21no—
149#217—42no—
150#217—61no—
151#217—61no—
152(C2×D3)⋊C4—61no—
153(C2×D3)⋊C4—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156Dic3⋊C4—61no—
157Dic3⋊C4—61no—
158Dic3⋊C4—61no—
159Dic3⋊C4—61no—
160Dic3⋊C4—124no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32—42no—
172C22×C32—42no—
173C22×C32C2×C22⋊C411yescharacteristic
174C22×C32AGL(1,ℤ/8)11yescharacteristic
175C22×C32#13711yescharacteristic
176C2×C3×D3—41no—
177C2×C3×D3—41no—
178C2×C3×D3—41no—
179C3⋊Dic3—21no—
180C3⋊Dic3—21no—
181C3⋊Dic3—21no—
182C3⋊Dic3#9912yes—
183C3×Dic3—41no—
184C3×Dic3—41no—
185C3×Dic3—41no—
186C3×Dic3—82no—
187C2×#41—91no—
188C23×C4—91no—
189C2×M16—181no—
190#123—181no—
191C22⋊Q8—91no—
192C22⋊Q8—91no—
193#121—91no—
194#121—91no—
195#120—61no—
196C4×D4—181no—
197C4×D4—181no—
198#117—91no—
199C2×C4⋊C4—181no—
200C2×C22⋊C4—61no—
201C22⋊C8—92no—
202C22⋊C8—181no—
203#95—92no—
204C23×C3—22no—
205C23×C3—22no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3—41no—
213C23×C3—41no—
214C23×C3—42no—
215C23×C3—42no—
216C23×C3—42no—
217C23×C3—42no—
218C23×C3—61no—
219C22×D3—21no—
220C3×D4—122no—
221C3×D4—122no—
222C3×D4—121no—
223C3×D4—121no—
224C2×C3×C4—61no—
225C2×C3×C4—61no—
226C2×C3×C4—61no—
227C2×C3×C4—122no—
228C2×C3×C4—122no—
229C2×C3×C4—122no—
230#67—42no—
231#67—42no—
232#67—41no—
233#67—41no—
234#67—122no—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—42no—
239C2×Dic3—42no—
240C2×Dic3—42no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—122no—
252C2×Dic3—122no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—122no—
258C2×Dic3—122no—
259C2×Dic3—122no—
260C2×Dic3—122no—
261C2×Dic3—122no—
262C4×D3—122no—
263Dic6—122no—
264C2×C32—21no—
265C2×C32—21no—
266C2×C32—41no—
267C2×C32—41no—
268C2×C32C2×#9911yescharacteristic
269C2×C32#41711yescharacteristic
270C2×C32#42111yescharacteristic
271C3×D3—81no—
272C24GO+(4,𝔽2)11yescharacteristic
273#41—362no—
274C2×Q8—91no—
275C2×D4—61no—
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—91no—
279C22×C4—62no—
280C22×C4—91no—
281C22×C4—91no—
282C22×C4—91no—
283C22×C4—91no—
284C22×C4—91no—
285C22×C4—91no—
286C22×C4—181no—
287C22×C4—362no—
288M16—362no—
289C2×C8—182no—
290C4⋊C4—91no—
291C4⋊C4—91no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4—362no—
295C22⋊C4—61no—
296C22⋊C4—61no—
297C22⋊C4—61no—
298C22⋊C4—122no—
299C22⋊C4—181no—
300C22⋊C4—181no—
301C42—181no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—44no—
325C22×C3—44no—
326C22×C3—44no—
327C22×C3—44no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3—121no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C3×C4—121no—
335C3×C4—121no—
336C3×C4—121no—
337C3×C4—242no—
338Dic3—41no—
339Dic3—41no—
340Dic3—41no—
341Dic3—62no—
342Dic3—62no—
343Dic3—62no—
344Dic3—62no—
345Dic3—82no—
346Dic3—121no—
347Dic3—121no—
348Dic3—121no—
349Dic3—121no—
350C32#151311yescharacteristic, complemented, Sylow
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—61no—
356C23D32⋊C411yescharacteristic
357C23D32⋊C411yescharacteristic
358C23C2×GO+(4,𝔽2)11yescharacteristic
359Q8—361no—
360D4—122no—
361D4—122no—
362D4—121no—
363D4—121no—
364D4—361no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—122no—
373C2×C4—122no—
374C2×C4—122no—
375C2×C4—182no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—362no—
379C2×C4—361no—
380C2×C4—361no—
381C2×C4—361no—
382C8—362no—
383C2×C3—22no—
384C2×C3—22no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—41no—
392C2×C3—41no—
393C2×C3—42no—
394C2×C3—42no—
395C2×C3—42no—
396C2×C3—42no—
397C2×C3—241no—
398D3—81no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—42no—
409C22—121no—
410C22—121no—
411C22—121no—
412C22C2×D32⋊C411yescharacteristic
413C22#6423611yescharacteristic
414C22#6423911yescharacteristic
415C4—92no—
416C4—121no—
417C4—121no—
418C4—121no—
419C4—181no—
420C4—181no—
421C4—181no—
422C4—242no—
423C3—21no—
424C3—21no—
425C2—21no—
426C2—21no—
427C2—41no—
428C2—41no—
429C2—241no—
430C2#1059349011yescharacteristic
431C2#1059349611yescharacteristic
432C2#1059350611yescharacteristic
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#1513
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. #10593845C2semidirect
3. #10591720C2semidirect
4. #10590072C2semidirect
5. #10590071C2semidirect
7. C2×#3805C4semidirect
11. #63982C4semidirect
13. #63980C4semidirect
19. #63957C4semidirect
350. C32#1513semidirect

Maximal subgroups

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

subgroupindex
#105955012
#105938452
#105917202
#105900722
#105900712
#15139