Finite Group Databasebeta

← #11775186

Subgroups — #11775186

Order 1152.

496 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594808C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic
3#10591239C211yesmaximal, characteristic
4#10589333C211yesmaximal, characteristic
5C3×#4467C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic
7#10589152C211yesmaximal, characteristic
8#70836—31nomaximal
9#68310—31nomaximal
10#64133C2211yescharacteristic
11C3×#924C2211yescharacteristic
12C2×C3×C4×Dic3C2211yescharacteristic
13#63964—21no—
14#63955—21no—
15C2×Dic32—21no—
16#63918C411yescharacteristic, complemented
17#63867—21no—
18#63866C411yescharacteristic, complemented
19#63844C411yescharacteristic, complemented
20Dic3×Dic6C411yescharacteristic, complemented
21#63837—21no—
22C32×C22⋊C8C2211yescharacteristic
23#63658C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#815—21no—
27C3×Dic3⋊C8—21no—
28#63579—21no—
29#5622—31no—
30#5470—31no—
31C3×#432—31no—
32#4932—31no—
33#4719D311yescharacteristic
34#4648—31no—
35C3×#328—31no—
36#4538—31no—
37#4467—31no—
38#4467—31no—
39#4467—31no—
40#4467—31no—
41#4467—61no—
42#4467D311yescharacteristic
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634C2×C411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6C2×C411yescharacteristic
51C2×#627—21no—
52C2×C32×C8—21no—
53#3757—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56C3×#217—21no—
57C3×C4⋊Dic3C2×C411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic32—24no—
70Dic32—21no—
71Dic32—21no—
72#1506—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C42—31no—
75Q8×Dic3—31no—
76#944—31no—
77#926—61no—
78#924—31no—
79#924—31no—
80#924—61no—
81#924—61no—
82#924C2×D311yescharacteristic
83C2×C4×Dic3—61no—
84C2×C4×Dic3—61no—
85C2×C4×Dic3C2×D311yescharacteristic
86#889—61no—
87#888—31no—
88#887—31no—
89#887—61no—
90#878—61no—
91#877—61no—
92#870—61no—
93#869—31no—
94#869—31no—
95C4×Dic6—31no—
96C4×Dic6—31no—
97C4×Dic6—61no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—21no—
100C3×C22⋊C8—31no—
101C3×C22⋊C8C2×D311yescharacteristic
102C3×C22⋊C8C2×D311yescharacteristic
103C3×#97—61no—
104C3×#95—31no—
105C3⋊#95—31no—
106C3⋊#95—31no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95C2×D311yescharacteristic
111#830C2×D311yescharacteristic
112#815—21no—
113Dic3⋊C8—21no—
114C23×C32C2×D411yescharacteristic
115C2×C32×C4—41no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123#634—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C3×Dic6—41no—
137#627—42no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#533—91no—
141#432—31no—
142#376—91no—
143#328—31no—
144#328—91no—
145#328—91no—
146#328—91no—
147C2×C3×Q8—31no—
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×Dic3—21no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C22×Dic3—121no—
158C22×Dic3D1211yescharacteristic
159C22×Dic3D1211yescharacteristic
160C2×Dic6—31no—
161C2×Dic6—31no—
162C2×Dic6—61no—
163C2×Dic6—61no—
164C2×Dic6—61no—
165C2×Dic6C4×D311yescharacteristic
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—41no—
169C2×C3×C8—61no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—31no—
174C3×C42—31no—
175C3×C42—31no—
176C3×C42—31no—
177#217—21no—
178#217—61no—
179#217—61no—
180#217—121no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3C4×D311yescharacteristic
189Dic3⋊C4—21no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—121no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C4×Dic3—64no—
202C4×Dic3—64no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3C4×D311yescharacteristic
206C4×Dic3C4×D311yescharacteristic
207C4×Dic3#6711yescharacteristic
208C4×Dic3#6711yescharacteristic
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32C2×C22⋊C411yescharacteristic
213C22×C32#13711yescharacteristic
214C22×C32#13711yescharacteristic
215C32×C4—21no—
216C32×C4—21no—
217C3⋊Dic3—42no—
218C3⋊Dic3—41no—
219C3⋊Dic3—41no—
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3—21no—
223C3×Dic3—42no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3#10412yes—
227C4⋊Q8—91no—
228C4⋊Q8—91no—
229#125—181no—
230C22⋊Q8—31no—
231C22⋊Q8—91no—
232C22⋊Q8—181no—
233C4×Q8—91no—
234C4×Q8—91no—
235C4×Q8—181no—
236#117—181no—
237C2×C42—31no—
238C2×C42—181no—
239C4⋊C8—61no—
240C22⋊C8—31no—
241C22⋊C8D3211yescharacteristic
242#97—61no—
243#95—31no—
244#95—91no—
245#95—181no—
246C23×C3—21no—
247C23×C3C2×D1211yescharacteristic
248C23×C3D3×D411yescharacteristic
249C3×Q8—121no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—31no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—62no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—62no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—81no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4C2×C4×D311yescharacteristic
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—22no—
274C2×Dic3—22no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—41no—
278C2×Dic3—41no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—121no—
286C2×Dic3—121no—
287C2×Dic3—122no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—121no—
292C2×Dic3—241no—
293C2×Dic3—241no—
294C2×Dic3(C2×D3)⋊C411yescharacteristic
295C2×Dic3(C2×D3)⋊C411yescharacteristic
296C2×Dic3(C2×D3)⋊C411yescharacteristic
297C2×Dic3(C2×D3)⋊C411yescharacteristic
298Dic6—41no—
299Dic6—122no—
300Dic6—122no—
301Dic6—121no—
302Dic6—121no—
303Dic6—241no—
304C3×C8—41no—
305C3×C8—41no—
306C3×C8—81no—
307C3×C8—121no—
308C3⋊C8—41no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32#41011yescharacteristic
312C2×C32#41911yescharacteristic
313C2×C32C2×#10411yescharacteristic
314C2×Q8—31no—
315C2×Q8—91no—
316C2×Q8—181no—
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—61no—
320C22×C4—181no—
321C22×C4C2×D3211yescharacteristic
322C2×C8—21no—
323C2×C8—61no—
324C4⋊C4—31no—
325C4⋊C4—61no—
326C4⋊C4—91no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C22⋊C4—61no—
334C22⋊C4—181no—
335C42—31no—
336C42—31no—
337C42—31no—
338C42—31no—
339C42—181no—
340C42—181no—
341C42—184no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3D3×C22⋊C411yescharacteristic
352C22×C3#90911yescharacteristic
353C22×C3#90911yescharacteristic
354C22×C3#91511yescharacteristic
355C22×C3#91811yescharacteristic
356C22×C3C2×(C2×D3)⋊C411yescharacteristic
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—32no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—61no—
365C3×C4—61no—
366C3×C4—61no—
367C3×C4—122no—
368C3×C4—121no—
369C3×C4—121no—
370Dic3—21no—
371Dic3—21no—
372Dic3—21no—
373Dic3—42no—
374Dic3—41no—
375Dic3—41no—
376Dic3—122no—
377Dic3—122no—
378Dic3—121no—
379Dic3—121no—
380Dic3—121no—
381Dic3—121no—
382Dic3—241no—
383Dic3—241no—
384Dic3—242no—
385Dic3#82512yes—
386C32#150611yescharacteristic, complemented, Sylow
387C23D3×D1211yescharacteristic
388Q8—121no—
389Q8—361no—
390Q8—362no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—31no—
395C2×C4—41no—
396C2×C4—62no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—182no—
405C2×C4—181no—
406C2×C4—181no—
407C2×C4—361no—
408C2×C4—361no—
409C2×C4C4×D3211yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C8—41no—
412C8—121no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3#474011yescharacteristic
423C2×C3#480211yescharacteristic
424C2×C3D3×#10411yescharacteristic
425C2×C3#500611yescharacteristic
426C2×C3#512011yescharacteristic
427C2×C3C2×#82511yescharacteristic
428C22—21no—
429C22—21no—
430C22#6380011yescharacteristic
431C22#6380111yescharacteristic
432C22D3×(C2×D3)⋊C411yescharacteristic
433C4—21no—
434C4—21no—
435C4—32no—
436C4—61no—
437C4—61no—
438C4—61no—
439C4—122no—
440C4—121no—
441C4—121no—
442C4—362no—
443C4—361no—
444C4—361no—
445C3—21no—
446C3#6831011yescharacteristic, complemented
447C3#7083611yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2#1059040511yescharacteristic
451C2#1059094811yescharacteristic
452C2D3×#82511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1506
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
16. #63918C4semidirect
18. #63866C4semidirect
19. #63844C4semidirect
20. Dic3×Dic6C4semidirect
386. C32#1506semidirect
446. C3#68310semidirect
447. C3#70836semidirect

Maximal subgroups

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

subgroupindex
#105948082
C3×#47192
#105912392
#105893332
C3×#44672
#105891542
#105891522
#708363
#683103