Finite Group Databasebeta

← #11778598

Subgroups — #11778598

Order 1152.

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

normal subgroups only

This group has 460 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
2C3×#4721C211yesmaximal, characteristic
3#10591214C211yesmaximal, characteristic
4#10591124C211yesmaximal, characteristic
5#10589333C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic
7#10589152C211yesmaximal, characteristic
8#71175—31nomaximal
9#68140—31nomaximal
10#64133C2211yescharacteristic
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14C2×#3724—21no—
15#63964—21no—
16#63955—21no—
17#63846—21no—
18#63845—21no—
19#63840—21no—
20#63839—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63658C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#817—21no—
25C3×#816—21no—
26#63579—21no—
27#63573—21no—
28#63567—21no—
29#5623—31no—
30#5500—31no—
31C3×#483—31no—
32#4983—31no—
33#4981—31no—
34#4971—31no—
35#4721—31no—
36#4721D311yescharacteristic
37C3×#324—31no—
38#4538—31no—
39#4469D311yescharacteristic
40#4467—31no—
41#4467—31no—
42#4467—31no—
43#4467—61no—
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)D411yescharacteristic
55#3750—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65#3724—42no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70Dic32—21no—
71Dic32—21no—
72#1611—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—31no—
76#944—61no—
77#926—61no—
78C2×C4⋊Dic3C2×D311yescharacteristic
79#924—31no—
80#924—31no—
81#924—61no—
82#924—61no—
83#924C2×D311yescharacteristic
84C2×Dic3⋊C4—61no—
85C2×Dic3⋊C4—61no—
86C2×Dic3⋊C4C2×D311yescharacteristic
87#890—61no—
88#890—61no—
89#889—61no—
90#889—61no—
91#888—61no—
92#888—61no—
93#888—61no—
94#878—61no—
95#877—61no—
96C3×#106—61no—
97C3×#103—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8—31no—
100C3×C22⋊C8C2×D311yescharacteristic
101C3×C22⋊C8C2×D311yescharacteristic
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107#830C2×D311yescharacteristic
108#817—21no—
109#817—61no—
110#816—21no—
111#816—61no—
112#810—61no—
113#808—61no—
114C23×C32C2×D411yescharacteristic
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
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—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3SD1612yes—
134C3×Dic6—41no—
135#627—81no—
136C32×C8—41no—
137C3×C3⋊C8—41no—
138#544—91no—
139#483—31no—
140#483—91no—
141#398—91no—
142#328—91no—
143#328—91no—
144#324—31no—
145C2×C3×Q8—31no—
146C22×C3×C4—21no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—61no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×Dic3—21no—
153C22×Dic3—61no—
154C22×Dic3—61no—
155C22×Dic3—121no—
156C22×Dic3D1211yescharacteristic
157C22×Dic3D1211yescharacteristic
158C2×Dic6—31no—
159C2×Dic6—31no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6#6711yescharacteristic
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
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—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3#6711yescharacteristic
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191Dic3⋊C4—21no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—121no—
201Dic3⋊C4—122no—
202Dic3⋊C4—122no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C2×C3⋊C8—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32#12011yescharacteristic
211C22×C32C2×SD1611yescharacteristic
212C22×C32#13711yescharacteristic
213C32×C4—21no—
214C32×C4—21no—
215C3⋊Dic3—42no—
216C3⋊Dic3—41no—
217C3⋊Dic3—41no—
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223C4⋊Q8—181no—
224C4⋊Q8—181no—
225#125—181no—
226#125—181no—
227C22⋊Q8—31no—
228C22⋊Q8—91no—
229C22⋊Q8—181no—
230#117—181no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—181no—
234#106—61no—
235#106—181no—
236#103—61no—
237#103—181no—
238C22⋊C8—31no—
239C22⋊C8D3211yescharacteristic
240#95—91no—
241#95—181no—
242C23×C3—21no—
243C23×C3C2×D1211yescharacteristic
244C23×C3D3×D411yescharacteristic
245C3×Q8—121no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—32no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—61no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—81no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4—121no—
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—41no—
271C2×Dic3—41no—
272C2×Dic3—41no—
273C2×Dic3—41no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—121no—
281C2×Dic3—121no—
282C2×Dic3—122no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3—121no—
287C2×Dic3—241no—
288C2×Dic3—241no—
289C2×Dic3#20412yes—
290Dic6—41no—
291Dic6—121no—
292Dic6—121no—
293Dic6—241no—
294Dic6—241no—
295Dic6—241no—
296C3×C8—41no—
297C3×C8—41no—
298C3×C8—81no—
299C3×C8—121no—
300C3⋊C8—41no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#44811yescharacteristic
304C2×C32#45611yescharacteristic
305C2×C32#45811yescharacteristic
306C2×Q8—31no—
307C2×Q8—91no—
308C2×Q8—181no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—61no—
312C22×C4—181no—
313C22×C4C2×D3211yescharacteristic
314C2×C8—21no—
315C2×C8—61no—
316C4⋊C4—31no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—91no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4—362no—
330C22⋊C4—61no—
331C22⋊C4—181no—
332C42—181no—
333C42—181no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3#88211yescharacteristic
344C22×C3C2×#20411yescharacteristic
345C22×C3#90911yescharacteristic
346C22×C3D3×SD1611yescharacteristic
347C22×C3#91511yescharacteristic
348C22×C3#93711yescharacteristic
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—62no—
356C3×C4—121no—
357C3×C4—121no—
358C3×C4—121no—
359C3×C4—241no—
360Dic3—22no—
361Dic3—41no—
362Dic3—41no—
363Dic3—41no—
364Dic3—81no—
365Dic3—122no—
366Dic3—122no—
367Dic3—121no—
368Dic3—121no—
369Dic3—121no—
370Dic3—121no—
371Dic3—241no—
372Dic3—241no—
373Dic3—242no—
374C32#161111yescharacteristic, complemented, Sylow
375C23D3×D1211yescharacteristic
376Q8—121no—
377Q8—361no—
378Q8—721no—
379C2×C4—32no—
380C2×C4—41no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—182no—
391C2×C4—181no—
392C2×C4—181no—
393C2×C4—361no—
394C2×C4—361no—
395C2×C4#380211yescharacteristic
396C2×C4D3×#6711yescharacteristic
397C8—41no—
398C8—121no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3#473811yescharacteristic
409C2×C3#474211yescharacteristic
410C2×C3#475211yescharacteristic
411C2×C3#505311yescharacteristic
412C2×C3#517011yescharacteristic
413C2×C3#520511yescharacteristic
414C22—21no—
415C22—21no—
416C22D3×#20411yescharacteristic
417C22#6380011yescharacteristic
418C22#6392211yescharacteristic
419C4—21no—
420C4—21no—
421C4—62no—
422C4—121no—
423C4—121no—
424C4—121no—
425C4—241no—
426C4—362no—
427C4—361no—
428C4—361no—
429C3—21no—
430C3#6814011yescharacteristic, complemented
431C3#7117511yescharacteristic, complemented
432C2—21no—
433C2—21no—
434C2#1059040811yescharacteristic
435C2#1059082211yescharacteristic
436C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
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
374. C32#1611semidirect
430. C3#68140semidirect
431. C3#71175semidirect

Maximal subgroups

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

subgroupindex
#105948122
C3×#47212
#105912142
#105911242
#105893332
C3×#44692
#105891522
#711753
#681403