Finite Group Databasebeta

← #11794553

Subgroups — #11794553

Order 1152.

498 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4⋊#622C211yesmaximal, characteristic, complemented
2C2×#63743C211yesmaximal, characteristic, complemented
3C2×#63739C211yesmaximal, characteristic
4C2×#63739C211yesmaximal, characteristic
5#10591385C211yesmaximal, characteristic
6#10591337C211yesmaximal, characteristic, complemented
7#10590075C211yesmaximal, characteristic, complemented
8C22×#625C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×Dic3⋊C4—21no—
14C2×#3724C2211yescharacteristic
15C2×#3724C2211yescharacteristic
16C2×#3724C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—21no—
18C4⋊#622—22no—
19#63743—22no—
20#63739—22no—
21#63739—22no—
22#63579—21no—
23#4976—61no—
24#4957—61no—
25C23×C3×D3—21no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C22×C3×Dic3—21no—
32C2×#625—21no—
33C2×#625—21no—
34C2×#625—21no—
35C2×#625—21no—
36C2×#625—21no—
37C2×#625Q812yes—
38C2×#622—21no—
39C2×#622—21no—
40C2×#622—21no—
41C2×#622—21no—
42C2×#622—21no—
43C2×#622D412yes—
44C4×C3⋊Dic3—21no—
45C4×C3⋊Dic3—21no—
46C3×(C2×D3)⋊C4—42no—
47C3×Dic3⋊C4—42no—
48#3724—21no—
49#3724—21no—
50#3724—21no—
51#3724—21no—
52#3724—21no—
53#3724D412yes—
54(C2×D3)⋊Dic3—42no—
55#2067—91nomaximal, Sylow
56C22×#67—61no—
57C2×C3×C4⋊C4—61no—
58C2×C3×C22⋊C4—61no—
59C2×#217—61no—
60C2×(C2×D3)⋊C4—21no—
61C2×(C2×D3)⋊C4—61no—
62C2×Dic3⋊C4—21no—
63C2×Dic3⋊C4—61no—
64C2×Dic3⋊C4—61no—
65C2×Dic3⋊C4—61no—
66C2×C4×Dic3—61no—
67C2×C4×Dic3—61no—
68C3⋊#95—61no—
69C3⋊#95—61no—
70C23×C32C2×D411yescharacteristic
71C22×C3×D3—22no—
72C22×C3×D3—41no—
73C22×C3×D3—41no—
74C22×C3×D3—41no—
75C22×C3×D3—41no—
76C22×C3×D3—41no—
77C22×C3×D3—41no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4D812yes—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3C2×D411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C2×C3⋊Dic3C2×Q811yescharacteristic
87C2×C3⋊Dic3#4111yescharacteristic
88C2×C3⋊Dic3#4111yescharacteristic
89C2×C3⋊Dic3#4111yescharacteristic
90C2×C3×Dic3—22no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99#625—22no—
100#625—22no—
101#625—41no—
102#625—41no—
103#622—22no—
104#622—41no—
105C2×#107—91no—
106C2×C4⋊C8—91no—
107C2×#102—91no—
108C2×#102—91no—
109#390—91no—
110#389—91no—
111#340—91no—
112C24×C3—61no—
113C23×D3—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C22×C3×C4—61no—
119C2×#67—62no—
120C2×#67—62no—
121C2×#67—121no—
122C2×#67—121no—
123C2×#67—121no—
124C2×#67—121no—
125C22×Dic3—21no—
126C22×Dic3—21no—
127C22×Dic3—21no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C3×C4⋊C4—122no—
133C3×C22⋊C4—122no—
134#217—122no—
135(C2×D3)⋊C4—42no—
136(C2×D3)⋊C4—122no—
137Dic3⋊C4—42no—
138Dic3⋊C4—62no—
139Dic3⋊C4—62no—
140Dic3⋊C4—121no—
141Dic3⋊C4—121no—
142Dic3⋊C4—121no—
143Dic3⋊C4—121no—
144C4×Dic3—121no—
145C4×Dic3—121no—
146C4×Dic3—121no—
147C4×Dic3—121no—
148C22×C32#12111yescharacteristic
149C22×C32#12111yescharacteristic
150C22×C32C22⋊Q811yescharacteristic
151C22×C32C2×D811yescharacteristic
152C22×C32#13511yescharacteristic
153C22×C32AGL(1,ℤ/8)11yescharacteristic
154C22×C32#13711yescharacteristic
155C2×C3×D3—42no—
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158C2×C3×D3—81no—
159C2×C3×D3—81no—
160C2×C3×D3—81no—
161C2×C3×D3—81no—
162C32×C4—22no—
163C3⋊Dic3—41no—
164C3⋊Dic3#12111yescharacteristic
165C3⋊Dic3C22⋊Q811yescharacteristic
166C3⋊Dic3C22⋊Q811yescharacteristic
167C3⋊Dic3#12611yescharacteristic
168C3×Dic3—42no—
169C3×Dic3—81no—
170C3×Dic3—81no—
171C22×D4—91no—
172C22×C8—91no—
173C22×C8—91no—
174C2×C4⋊C4—61no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—91no—
177C2×C4⋊C4—91no—
178C2×C22⋊C4—61no—
179C2×C22⋊C4—181no—
180C2×C42—91no—
181#107—182no—
182C4⋊C8—182no—
183#102—182no—
184#102—182no—
185#95—181no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—62no—
189C23×C3—121no—
190C23×C3—121no—
191C23×C3—121no—
192C23×C3—121no—
193C23×C3—121no—
194C23×C3—121no—
195C22×D3—22no—
196C22×D3—41no—
197C22×D3—41no—
198C22×D3—41no—
199C22×D3—41no—
200C22×D3—41no—
201C22×D3—41no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—62no—
209C2×C3×C4—121no—
210C2×C3×C4—121no—
211C2×C3×C4—121no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4—121no—
216C2×C3×C4—121no—
217#67—122no—
218#67—122no—
219#67—122no—
220#67—122no—
221C2×Dic3—22no—
222C2×Dic3—41no—
223C2×Dic3—41no—
224C2×Dic3—41no—
225C2×Dic3—41no—
226C2×Dic3—41no—
227C2×Dic3—41no—
228C2×Dic3—41no—
229C2×Dic3—41no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
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—62no—
243C2×Dic3—62no—
244C2×Dic3—121no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248C2×C32#39611yescharacteristic
249C2×C32#45911yescharacteristic
250C2×C32#46411yescharacteristic
251C2×C32#46611yescharacteristic
252C2×C32#46811yescharacteristic
253C2×C32#47411yescharacteristic
254C2×C32#47811yescharacteristic
255C3×D3—82no—
256C24—61no—
257C2×D4—92no—
258C2×D4—181no—
259C2×D4—181no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263C22×C4—61no—
264C22×C4—61no—
265C22×C4—61no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4GO+(4,𝔽2)11yescharacteristic
269C2×C8—92no—
270C2×C8—181no—
271C2×C8—181no—
272C2×C8—181no—
273C2×C8—181no—
274C2×C8—181no—
275C4⋊C4—92no—
276C4⋊C4—122no—
277C4⋊C4—181no—
278C4⋊C4—181no—
279C4⋊C4—181no—
280C4⋊C4—181no—
281C4⋊C4—181no—
282C22⋊C4—122no—
283C22⋊C4—362no—
284C42—181no—
285C42—181no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—122no—
303C22×C3—241no—
304C22×C3—241no—
305C22×C3—241no—
306C22×C3—241no—
307C2×D3—42no—
308C2×D3—42no—
309C2×D3—42no—
310C2×D3—81no—
311C2×D3—81no—
312C2×D3—81no—
313C2×D3—81no—
314C3×C4—42no—
315C3×C4—42no—
316C3×C4—122no—
317C3×C4—241no—
318C3×C4—241no—
319Dic3—42no—
320Dic3—61no—
321Dic3—61no—
322Dic3—61no—
323Dic3—61no—
324Dic3—61no—
325Dic3—61no—
326Dic3—61no—
327Dic3—61no—
328Dic3—81no—
329Dic3—81no—
330Dic3—122no—
331Dic3—122no—
332C32#206711yescharacteristic, complemented, Sylow
333C23—62no—
334C23—121no—
335C23—121no—
336C23—121no—
337C23—121no—
338C23—121no—
339C23—121no—
340C23C2×GO+(4,𝔽2)11yescharacteristic
341D4—182no—
342D4—182no—
343D4—361no—
344D4—361no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—62no—
348C2×C4—91no—
349C2×C4—91no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—91no—
354C2×C4—121no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4—121no—
358C2×C4—121no—
359C2×C4—121no—
360C2×C4—121no—
361C2×C4—121no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4#377412yes—
366C8—182no—
367C8—361no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—242no—
383D3—82no—
384C22—122no—
385C22—122no—
386C22—122no—
387C22—241no—
388C22—241no—
389C22—241no—
390C22—241no—
391C22D32⋊Q811yescharacteristic
392C22#6422411yescharacteristic
393C22#6422611yescharacteristic
394C22#6423011yescharacteristic
395C22C2×#377411yescharacteristic
396C22#6423711yescharacteristic
397C22#6424211yescharacteristic
398C4—22no—
399C4—91no—
400C4—91no—
401C4—91no—
402C4—91no—
403C4—122no—
404C4—241no—
405C4—241no—
406C4—361no—
407C3—21no—
408C3—21no—
409C2—242no—
410C2#1059334711yescharacteristic
411C2#1059336411yescharacteristic
412C2#1059340611yescharacteristic
413C2#1059341711yescharacteristic
414C2#1059344011yescharacteristic
415C2#1059344111yescharacteristic
416C2#1059352011yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊Dic3C23
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2067
LCSG ▷ C22×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#622C2semidirect
2. C2×#63743C2semidirect
6. #10591337C2semidirect
7. #10590075C2semidirect
332. C32#2067semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#6222
C2×#637432
C2×#637392
#105913852
#105913372
#105900752
#20679