Finite Group Databasebeta

← #11775093

Subgroups — #11775093

Order 1152.

520 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594808C211yesmaximal, characteristic
2C3×#4718C211yesmaximal, characteristic
3#10591242C211yesmaximal, characteristic
4#10589333C211yesmaximal, characteristic
5C3×#4467C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic
7#10589152C211yesmaximal, characteristic
8#70792—31nomaximal
9#68309—31nomaximal
10#64133C2211yescharacteristic
11C3×#924C2211yescharacteristic
12C2×C3×C4×Dic3C2211yescharacteristic
13C2×Dic3⋊Dic3—21no—
14#63964—21no—
15#63955—21no—
16C2×Dic32—21no—
17#63918C411yescharacteristic, complemented
18#63867—21no—
19#63866C411yescharacteristic, complemented
20#63844C411yescharacteristic, complemented
21Dic3×Dic6C411yescharacteristic, complemented
22#63837—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63658C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×Dic3⋊C8—21no—
28C3×C8×Dic3—21no—
29#5622—31no—
30#5470—31no—
31C3×#431—31no—
32C4×C4⋊Dic3—31no—
33#4718D311yescharacteristic
34#4649—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—24no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70Dic32—21no—
71Dic32—21no—
72Dic32—42no—
73#1503—91noSylow
74C3×C22⋊Q8—31no—
75C2×C3×C42—31no—
76Q8×Dic3—31no—
77#944—31no—
78#926—61no—
79C2×C4⋊Dic3—61no—
80#924—31no—
81#924—31no—
82#924—61no—
83#924—61no—
84#924C2×D311yescharacteristic
85C2×Dic3⋊C4—61no—
86C2×C4×Dic3—61no—
87C2×C4×Dic3—61no—
88C2×C4×Dic3C2×D311yescharacteristic
89#889—61no—
90#888—31no—
91#887—31no—
92#887—61no—
93#878—61no—
94#877—61no—
95#870—61no—
96#869—31no—
97#869—31no—
98C4×Dic6—31no—
99C4×Dic6—31no—
100C4×Dic6—61no—
101C3×C4⋊C8—61no—
102C3×C22⋊C8—21no—
103C3×C22⋊C8—31no—
104C3×C22⋊C8C2×D311yescharacteristic
105C3×C22⋊C8C2×D311yescharacteristic
106C3×C4×C8—61no—
107C3×#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830C2×D311yescharacteristic
113Dic3⋊C8—21no—
114C8×Dic3—21no—
115C23×C32C2×D411yescharacteristic
116C2×C32×C4—41no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124#634—41no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3SD1612yes—
136C2×C3×Dic3Q1612yes—
137C3×Dic6—41no—
138#627—42no—
139C32×C8—41no—
140C3×C3⋊C8—41no—
141#533—91no—
142#431—31no—
143C4×C4⋊C4—91no—
144#328—31no—
145#328—91no—
146#328—91no—
147#328—91no—
148C2×C3×Q8—31no—
149C22×C3×C4—21no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—61no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3—21no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158C22×Dic3—121no—
159C22×Dic3D1211yescharacteristic
160C22×Dic3D1211yescharacteristic
161C2×Dic6—31no—
162C2×Dic6—31no—
163C2×Dic6—61no—
164C2×Dic6—61no—
165C2×Dic6—61no—
166C2×Dic6C4×D311yescharacteristic
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—41no—
170C2×C3×C8—61no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C42—31no—
175C3×C42—31no—
176C3×C42—31no—
177C3×C42—31no—
178#217—21no—
179#217—61no—
180#217—61no—
181#217—121no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—64no—
189C4⋊Dic3—61no—
190C4⋊Dic3C4×D311yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—64no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—121no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—122no—
207C4×Dic3—122no—
208C4×Dic3C4×D311yescharacteristic
209C4×Dic3C4×D311yescharacteristic
210C4×Dic3#6711yescharacteristic
211C4×Dic3#6711yescharacteristic
212C2×C3⋊C8—21no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32C2×SD1611yescharacteristic
217C22×C32C2×Q1611yescharacteristic
218C32×C4—21no—
219C32×C4—21no—
220C3⋊Dic3—42no—
221C3⋊Dic3—41no—
222C3⋊Dic3—41no—
223C3×Dic3—21no—
224C3×Dic3—42no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C3×Dic3#10312yes—
228C3×Dic3#10312yes—
229C3×Dic3#10412yes—
230C4⋊Q8—91no—
231C4⋊Q8—91no—
232#125—181no—
233C22⋊Q8—31no—
234C22⋊Q8—91no—
235C22⋊Q8—181no—
236C4×Q8—91no—
237C4×Q8—91no—
238C4×Q8—181no—
239#117—181no—
240C2×C4⋊C4—181no—
241C2×C42—31no—
242C2×C42—181no—
243C4⋊C8—61no—
244C22⋊C8—31no—
245C22⋊C8D3211yescharacteristic
246C4×C8—61no—
247#95—31no—
248#95—91no—
249C23×C3—21no—
250C23×C3C2×D1211yescharacteristic
251C23×C3D3×D411yescharacteristic
252C3×Q8—121no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—32no—
259C2×C3×C4—32no—
260C2×C3×C4—31no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—81no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×Dic3—22no—
275C2×Dic3—22no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—41no—
279C2×Dic3—41no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—121no—
287C2×Dic3—121no—
288C2×Dic3—122no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C2×Dic3—241no—
294C2×Dic3—241no—
295C2×Dic3#20412yes—
296C2×Dic3Dic1212yes—
297C2×Dic3(C2×D3)⋊C411yescharacteristic
298C2×Dic3(C2×D3)⋊C411yescharacteristic
299C2×Dic3(C2×D3)⋊C411yescharacteristic
300C2×Dic3(C2×D3)⋊C411yescharacteristic
301Dic6—41no—
302Dic6—122no—
303Dic6—122no—
304Dic6—121no—
305Dic6—121no—
306Dic6—241no—
307C3×C8—41no—
308C3×C8—41no—
309C3×C8—81no—
310C3×C8—121no—
311C3⋊C8—41no—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#41011yescharacteristic
315C2×C32C2×#10311yescharacteristic
316C2×C32C2×#10411yescharacteristic
317C2×Q8—31no—
318C2×Q8—91no—
319C2×Q8—181no—
320C22×C4—31no—
321C22×C4—31no—
322C22×C4—61no—
323C22×C4—181no—
324C22×C4C2×D3211yescharacteristic
325C2×C8—21no—
326C2×C8—61no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—91no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—184no—
336C4⋊C4—181no—
337C22⋊C4—61no—
338C22⋊C4—181no—
339C42—31no—
340C42—31no—
341C42—31no—
342C42—31no—
343C42—181no—
344C42—181no—
345C42—362no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3D3×C22⋊C411yescharacteristic
356C22×C3C2×#20411yescharacteristic
357C22×C3C2×Dic1211yescharacteristic
358C22×C3D3×SD1611yescharacteristic
359C22×C3D3×Q1611yescharacteristic
360C22×C3C2×(C2×D3)⋊C411yescharacteristic
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—32no—
366C3×C4—32no—
367C3×C4—32no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—61no—
371C3×C4—122no—
372C3×C4—121no—
373C3×C4—121no—
374Dic3—21no—
375Dic3—42no—
376Dic3—41no—
377Dic3—41no—
378Dic3—122no—
379Dic3—122no—
380Dic3—121no—
381Dic3—121no—
382Dic3—121no—
383Dic3—121no—
384Dic3—241no—
385Dic3—241no—
386Dic3—242no—
387Dic3#81612yes—
388Dic3#81612yes—
389Dic3#82512yes—
390C32#150311yescharacteristic, complemented, Sylow
391C23D3×D1211yescharacteristic
392Q8—121no—
393Q8—361no—
394Q8—362no—
395C2×C4—32no—
396C2×C4—32no—
397C2×C4—31no—
398C2×C4—31no—
399C2×C4—31no—
400C2×C4—31no—
401C2×C4—41no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—182no—
409C2×C4—181no—
410C2×C4—181no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C4C4×D3211yescharacteristic
414C2×C4D3×#6711yescharacteristic
415C8—41no—
416C8—121no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3#474011yescharacteristic
427C2×C3D3×#10311yescharacteristic
428C2×C3D3×#10411yescharacteristic
429C2×C3#500611yescharacteristic
430C2×C3C2×#81611yescharacteristic
431C2×C3C2×#82511yescharacteristic
432C22—21no—
433C22—21no—
434C22D3×#20411yescharacteristic
435C22D3×Dic1211yescharacteristic
436C22D3×(C2×D3)⋊C411yescharacteristic
437C4—21no—
438C4—21no—
439C4—32no—
440C4—32no—
441C4—32no—
442C4—61no—
443C4—122no—
444C4—121no—
445C4—121no—
446C4—362no—
447C4—361no—
448C4—361no—
449C3—21no—
450C3#6830911yescharacteristic, complemented
451C3#7079211yescharacteristic, complemented
452C2—21no—
453C2—21no—
454C2#1059040511yescharacteristic
455C2D3×#81611yescharacteristic
456C2D3×#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#1503
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
17. #63918C4semidirect
19. #63866C4semidirect
20. #63844C4semidirect
21. Dic3×Dic6C4semidirect
390. C32#1503semidirect
450. C3#68309semidirect
451. C3#70792semidirect

Maximal subgroups

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

subgroupindex
#105948082
C3×#47182
#105912422
#105893332
C3×#44672
#105891542
#105891522
#707923
#683093