Finite Group Databasebeta

← #11778596

Subgroups — #11778596

Order 1152.

472 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 82 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#10594812C211yesmaximal, characteristic
2#10592420C211yesmaximal, characteristic
3#10591353C211yesmaximal, characteristic
4#10591126C211yesmaximal, characteristic
5C3×#4469C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic
7#10589154C211yesmaximal, characteristic
8#68329—31nomaximal
9#68140—31nomaximal
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14C2×Dic3⋊Dic3—21no—
15#63964—21no—
16#63955—21no—
17#63846—21no—
18#63845—21no—
19#63840—21no—
20#63839—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63644—21no—
23#63643—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27#63573—21no—
28#63566—21no—
29#5623—31no—
30#5500—31no—
31#5043—31no—
32#4981—31no—
33#4721—31no—
34#4721—31no—
35#4721—31no—
36#4721—61no—
37#4661—31no—
38C3×#328—31no—
39C3×#324—31no—
40#4469D311yescharacteristic
41#4467—31no—
42#4467D311yescharacteristic
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#627—21no—
52C2×C32×C8—21no—
53#3757—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C3×#217—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—42no—
70Dic32—21no—
71Dic32—21no—
72#1611—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C4⋊C4—31no—
75#944—61no—
76#926—61no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—61no—
80C2×C4⋊Dic3—61no—
81#924—31no—
82#924—31no—
83#924—61no—
84#924—61no—
85#924C2×D311yescharacteristic
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4C2×D311yescharacteristic
88#890—61no—
89#890—61no—
90#889—61no—
91#889—61no—
92#888—61no—
93#888—61no—
94#888—61no—
95#878—61no—
96#877—61no—
97C3×C22⋊C8—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×#95—31no—
102#835—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830C2×D311yescharacteristic
107#817—61no—
108#817—61no—
109#817—62no—
110#817—61no—
111#816—61no—
112#816—61no—
113#816—62no—
114#816—61no—
115#808—61no—
116C23×C32C2×D411yescharacteristic
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125#634—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3SD1612yes—
136C3×Dic6—41no—
137#627—81no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#544—91no—
141#483—91no—
142#483—91no—
143#398—91no—
144#328—31no—
145#328—91no—
146#324—31no—
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×Dic6D1211yescharacteristic
166C2×C3×C8—22no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—61no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C22⋊C4—61no—
175#217—21no—
176#217—61no—
177#217—61no—
178#217—121no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—62no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—121no—
192C4⋊Dic3—122no—
193C4⋊Dic3D1211yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—121no—
206Dic3⋊C4—122no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C2×C3⋊C8—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32#12011yescharacteristic
215C22×C32C2×SD1611yescharacteristic
216C22×C32#13711yescharacteristic
217C32×C4—21no—
218C32×C4—21no—
219C3⋊Dic3—41no—
220C3⋊Dic3—41no—
221C3⋊Dic3—81no—
222C3×Dic3—22no—
223C3×Dic3—42no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C4⋊Q8—181no—
228C4⋊Q8—181no—
229#125—181no—
230#125—181no—
231C22⋊Q8—31no—
232C22⋊Q8—91no—
233C22⋊Q8—181no—
234#117—181no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—181no—
238#106—181no—
239#106—181no—
240#103—181no—
241#103—181no—
242C22⋊C8—31no—
243C22⋊C8D3211yescharacteristic
244#95—31no—
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—32no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—42no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—62no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—22no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—41no—
276C2×Dic3—41no—
277C2×Dic3—41no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—121no—
283C2×Dic3—121no—
284C2×Dic3—122no—
285C2×Dic3—121no—
286C2×Dic3—121no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—241no—
292C2×Dic3—241no—
293C2×Dic3#20412yes—
294Dic6—41no—
295Dic6—121no—
296Dic6—121no—
297Dic6—122no—
298Dic6—241no—
299Dic6—241no—
300C3×C8—42no—
301C3×C8—41no—
302C3×C8—41no—
303C3×C8—121no—
304C3⋊C8—41no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32#44811yescharacteristic
308C2×C32#45611yescharacteristic
309C2×C32#45811yescharacteristic
310C2×Q8—31no—
311C2×Q8—91no—
312C2×Q8—181no—
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—61no—
316C22×C4—181no—
317C22×C4C2×D3211yescharacteristic
318C2×C8—21no—
319C2×C8—61no—
320C4⋊C4—31no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—91no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4—362no—
334C22⋊C4—61no—
335C22⋊C4—181no—
336C42—181no—
337C42—181no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3#88211yescharacteristic
348C22×C3#88211yescharacteristic
349C22×C3C2×#20411yescharacteristic
350C22×C3#90911yescharacteristic
351C22×C3D3×SD1611yescharacteristic
352C22×C3#91811yescharacteristic
353C3×C4—22no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—62no—
360C3×C4—122no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4—121no—
364Dic3—22no—
365Dic3—42no—
366Dic3—41no—
367Dic3—41no—
368Dic3—41no—
369Dic3—121no—
370Dic3—121no—
371Dic3—121no—
372Dic3—121no—
373Dic3—241no—
374Dic3—241no—
375Dic3—242no—
376Dic3—241no—
377Dic3—241no—
378C32#161111yescharacteristic, complemented, Sylow
379C23D3×D1211yescharacteristic
380Q8—121no—
381Q8—361no—
382Q8—721no—
383C2×C4—32no—
384C2×C4—41no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—62no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—121no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—181no—
395C2×C4—181no—
396C2×C4—361no—
397C2×C4—361no—
398C2×C4—361no—
399C2×C4D3×D1211yescharacteristic
400C2×C4#381111yescharacteristic
401C8—41no—
402C8—121no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3#473811yescharacteristic
413C2×C3#474211yescharacteristic
414C2×C3#474211yescharacteristic
415C2×C3#475211yescharacteristic
416C2×C3#480611yescharacteristic
417C2×C3#482611yescharacteristic
418C22—21no—
419C22—21no—
420C22D3×#20411yescharacteristic
421C22#6380111yescharacteristic
422C22#6392311yescharacteristic
423C4—21no—
424C4—21no—
425C4—62no—
426C4—122no—
427C4—121no—
428C4—121no—
429C4—121no—
430C4—361no—
431C4—361no—
432C4—721no—
433C3—21no—
434C3#6814011yescharacteristic, complemented
435C3#6832911yescharacteristic, complemented
436C2—21no—
437C2—21no—
438C2#1059040911yescharacteristic
439C2#1059095111yescharacteristic
440C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊C8D32
hypocenterC32#1611
LCSG ▷ C22×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
378. C32#1611semidirect
434. C3#68140semidirect
435. C3#68329semidirect

Maximal subgroups

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

subgroupindex
#105948122
#105924202
#105913532
#105911262
C3×#44692
C3×#44672
#105891542
#683293
#681403