Finite Group Databasebeta

← #11794614

Subgroups — #11794614

Order 1152.

525 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63660C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic
3C2×C3×#833C211yesmaximal, characteristic
4#10591143C211yesmaximal, characteristic, complemented
5#10591141C211yesmaximal, characteristic, complemented
6#10591141C211yesmaximal, characteristic, complemented
7#10589159C211yesmaximal, characteristic, complemented
8#70077—31nomaximal
9#70077—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×#208C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63660—22no—
18C3×#833—22no—
19C3×#833—22no—
20#63578—22no—
21#63577—22no—
22#63577—22no—
23C2×C3×#100—31no—
24C2×C3×#100—31no—
25C2×#833—31no—
26C2×#833—31no—
27C2×#833—61no—
28C2×#833D311yescharacteristic
29C2×#833D311yescharacteristic
30#5125—31no—
31#5125—31no—
32#5124—31no—
33#5124—31no—
34#5124—31no—
35#5124—31no—
36C3⋊#338—31no—
37C3⋊#338—31no—
38C24×C32Q812yes—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C22×C32×C4C2311yescharacteristic
46#3748—21no—
47#3748—21no—
48#3748—21no—
49#3748D412yes—
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×#208—21no—
53C3×#208—21no—
54C3×#208—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208D412yes—
59C3×#208D412yes—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#2069—91noSylow
65C22×C3×D4—21no—
66C22×C3×D4C2×D311yescharacteristic
67C22×C3×D4C2×D311yescharacteristic
68C2×C3×M16—31no—
69C2×C3×M16—31no—
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C2×#208—31no—
73C2×#208—31no—
74C2×#208—31no—
75C2×#208—31no—
76C2×#208—61no—
77C2×#208—61no—
78C2×#208C2×D311yescharacteristic
79C2×#208C2×D311yescharacteristic
80C2×#208C2×D311yescharacteristic
81C2×#208C2×D311yescharacteristic
82C3×#100—62no—
83C3×#100—62no—
84#833—22no—
85#833—22no—
86#833—62no—
87#833—62no—
88#833—64no—
89#822—62no—
90#822—62no—
91#822—62no—
92#822—62no—
93#819—62no—
94#819—62no—
95C23×C32—22no—
96C23×C32—22no—
97C23×C32—22no—
98C23×C32—82no—
99C23×C32C2×Q811yescharacteristic
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—41no—
103C32×D4—41no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C3⋊(C3⋊C8)—22no—
111C3⋊(C3⋊C8)—41no—
112C3×C3⋊C8—22no—
113C3×C3⋊C8—22no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#430—91no—
117#430—91no—
118#430—91no—
119C2×#100—31no—
120C2×#100—31no—
121C2×#100—91no—
122#338—91no—
123C24×C3—22no—
124C24×C3Dic612yes—
125C24×C3Dic612yes—
126C2×C3×D4—22no—
127C2×C3×D4—22no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—41no—
141C2×C3×D4—41no—
142C2×C3×D4—41no—
143C2×C3×D4—41no—
144C22×C3×C4—21no—
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C3×M16—32no—
148C3×M16—32no—
149C3×M16—61no—
150C3×M16—61no—
151C3×M16—61no—
152C3×M16—61no—
153C3×M16—61no—
154C3×M16—61no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C2×C3×C8—61no—
159#208—21no—
160#208—21no—
161#208—21no—
162#208—21no—
163#208—21no—
164#208—21no—
165#208—32no—
166#208—32no—
167#208—62no—
168#208—61no—
169#208—61no—
170#208—62no—
171#208—61no—
172#208—61no—
173#208—61no—
174#208—61no—
175#208—121no—
176#208—121no—
177#208#6712yes—
178#208#6712yes—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—121no—
188C2×C3⋊C8—121no—
189C22×C32—41no—
190C22×C32—42no—
191C22×C32—82no—
192C22×C32—82no—
193C22×C32—82no—
194C22×C32C22⋊Q811yescharacteristic
195C22×C32C22⋊Q811yescharacteristic
196C22×C32C22⋊Q811yescharacteristic
197C32×C4#12111yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12111yescharacteristic
200C32×C4#12611yescharacteristic
201C22×D4D3211yescharacteristic
202C2×M16—31no—
203C2×M16—31no—
204C2×M16—31no—
205C2×M16—31no—
206C2×M16—91no—
207C2×M16—91no—
208#108—182no—
209#108—182no—
210#108—182no—
211#100—62no—
212#100—62no—
213#100—182no—
214C23×C3—24no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3—22no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—21no—
222C23×C3—42no—
223C23×C3—42no—
224C23×C3—82no—
225C23×C3—82no—
226C23×C3—84no—
227C23×C3C2×Dic611yescharacteristic
228C23×C3C2×Dic611yescharacteristic
229C3×D4—42no—
230C3×D4—42no—
231C3×D4—42no—
232C3×D4—42no—
233C3×D4—41no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4#23511yescharacteristic
248C2×C3×C4#23511yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4#23711yescharacteristic
254C2×C3×C4#23711yescharacteristic
255C2×C3×C4#23711yescharacteristic
256C2×C3×C4#23711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C3×C8—62no—
260C3×C8—62no—
261C3×C8—121no—
262C3×C8—121no—
263C3⋊C8—22no—
264C3⋊C8—22no—
265C3⋊C8—41no—
266C3⋊C8—41no—
267C3⋊C8—62no—
268C3⋊C8—62no—
269C3⋊C8—122no—
270C3⋊C8—122no—
271C3⋊C8—121no—
272C3⋊C8—121no—
273C2×C32—21no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32—82no—
277C2×C32#39611yescharacteristic
278C24#62712yes—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C22×C4C2×D3211yescharacteristic
286M16—32no—
287M16—32no—
288M16—61no—
289M16—61no—
290M16—61no—
291M16—61no—
292M16—61no—
293M16—61no—
294M16—92no—
295M16—181no—
296M16—181no—
297M16—181no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8—61no—
302C2×C8—181no—
303C2×C8—181no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—42no—
310C22×C3—44no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—82no—
314C22×C3—82no—
315C22×C3—82no—
316C22×C3—82no—
317C22×C3—82no—
318C22×C3—82no—
319C22×C3—84no—
320C22×C3—84no—
321C22×C3—84no—
322C22×C3#87811yescharacteristic
323C22×C3#87811yescharacteristic
324C22×C3#87811yescharacteristic
325C22×C3#87811yescharacteristic
326C22×C3#92411yescharacteristic
327C22×C3#92411yescharacteristic
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4#87911yescharacteristic
333C3×C4#87911yescharacteristic
334C3×C4#88411yescharacteristic
335C3×C4#88411yescharacteristic
336C3×C4#93811yescharacteristic
337C3×C4#93811yescharacteristic
338C3×C4#93911yescharacteristic
339C3×C4#93911yescharacteristic
340C32#206911yescharacteristic, complemented, Sylow
341C23—22no—
342C23—22no—
343C23—22no—
344C23—82no—
345C23C2×#62711yescharacteristic
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350C2×C4#380411yescharacteristic
351C2×C4#380411yescharacteristic
352C2×C4#380511yescharacteristic
353C2×C4D3×#6711yescharacteristic
354C2×C4D3×#6711yescharacteristic
355C2×C4#381111yescharacteristic
356C8—62no—
357C8—62no—
358C8—121no—
359C8—121no—
360C8—182no—
361C8—361no—
362C2×C3—22no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—41no—
371C2×C3—41no—
372C2×C3—84no—
373C2×C3—82no—
374C2×C3—82no—
375C2×C3#494811yescharacteristic
376C2×C3#494811yescharacteristic
377C22—41no—
378C22—42no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22#6396411yescharacteristic
383C22#6396411yescharacteristic
384C22#6398211yescharacteristic
385C4#6395611yescharacteristic
386C4#6395811yescharacteristic
387C4#6397011yescharacteristic
388C4#6397111yescharacteristic
389C3—21no—
390C3#7007711yescharacteristic, complemented
391C3#7007711yescharacteristic, complemented
392C2—21no—
393C2—21no—
394C2—21no—
395C2—82no—
396C2#1059169111yescharacteristic
subgroupG/H
centerC2#10591691
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC2×C32#396
hypercenterC22×D4D32
hypocenterC32#2069
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591143C2semidirect
5. #10591141C2semidirect
6. #10591141C2semidirect
7. #10589159C2semidirect
340. C32#2069semidirect
390. C3#70077semidirect
391. C3#70077semidirect

Maximal subgroups

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

subgroupindex
C2×#636602
C2×C3×#8332
#105911432
#105911412
#105891592
#700773