Finite Group Databasebeta

← #11778752

Subgroups — #11778752

Order 1152.

461 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 461 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594980C211yesmaximal, characteristic
2C3×#4659C211yesmaximal, characteristic, complemented
3#10591132C211yesmaximal, characteristic, complemented
4#10591125C211yesmaximal, characteristic
5#10589317C211yesmaximal, characteristic
6C3×#4452C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#69717—31nomaximal
9#68330—31nomaximal
10#64139C2211yescharacteristic
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14#63966—21no—
15#63952—21no—
16#63897—21no—
17#63888—21no—
18#63848—21no—
19#63845—21no—
20C32×#95C2211yescharacteristic
21#63657C2211yescharacteristic
22C3×C3⋊#95—21no—
23C3×C3⋊#95—21no—
24C3×#830C2211yescharacteristic
25#63576—21no—
26#63573—21no—
27#63565—21no—
28#63564—21no—
29#5645—31no—
30#5515—31no—
31C3×#400—31no—
32#5044—31no—
33#4970—31no—
34#4968—31no—
35#4735—31no—
36#4659D311yescharacteristic, complemented
37C3×#328—31no—
38#4528—31no—
39#4469—31no—
40#4452D311yescharacteristic, complemented
41#4451—31no—
42#4451—31no—
43#4451—61no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#624—21no—
53#3752—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C2×C3⋊(C3⋊C8)—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—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68#3722—21no—
69#3722—21no—
70Dic32—21no—
71#1615—91noSylow
72C3×C22⋊Q8—31no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75#946—61no—
76#930—31no—
77#930—31no—
78#930—61no—
79#929—61no—
80C4×#67—61no—
81C2×C4⋊Dic3C2×D311yescharacteristic
82#924C2×D311yescharacteristic
83C2×Dic3⋊C4C2×D311yescharacteristic
84#898—61no—
85#898—61no—
86#896—61no—
87#894—61no—
88#894—61no—
89#890—61no—
90#889—61no—
91#886—61no—
92#67⋊C4—61no—
93C3×C22⋊C8—31no—
94C3×#95—21no—
95C3×#95—61no—
96C3×#95—61no—
97C3×#95C2×D311yescharacteristic
98C3×#95C2×D311yescharacteristic
99#835—61no—
100C3⋊#95—21no—
101C3⋊#95—21no—
102#830—31no—
103#830—31no—
104#830—61no—
105#830C2×D311yescharacteristic
106#821—61no—
107#817—61no—
108#810—61no—
109#809—61no—
110#808—61no—
111#807—61no—
112#807—61no—
113C23×C32C2×D411yescharacteristic
114C22×C3⋊D3—21no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121#638—41no—
122#638—41no—
123C2×C3⋊Dic3—21no—
124C4⋊(C3⋊D3)—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—41no—
134C3×Dic6—41no—
135#624—81no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—41no—
138#539—91no—
139#484—91no—
140#481—91no—
141#400—31no—
142#328—31no—
143#327—91no—
144#324—91no—
145C2×C3×Q8—31no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—41no—
152C22×C3×C4—61no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C2×#67—61no—
156C2×#67—61no—
157C2×#67—121no—
158C22×Dic3—21no—
159C22×Dic3#6711yescharacteristic
160C22×Dic3#6711yescharacteristic
161C2×D12—31no—
162C2×D12—31no—
163C2×D12—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×Dic6D1211yescharacteristic
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(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—121no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3D1211yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#12011yescharacteristic
209C22×C32#13511yescharacteristic
210C22×C32#13711yescharacteristic
211C2×C3⋊D3—41no—
212C2×C3⋊D3—41no—
213C2×C3⋊D3—41no—
214C32×C4—21no—
215C32×C4—21no—
216C32×C4—81no—
217C3⋊Dic3—41no—
218C3×Dic3—41no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223#126—181no—
224#125—181no—
225#123—181no—
226#123—181no—
227C22⋊Q8—31no—
228C22⋊Q8—181no—
229#121—91no—
230C4×D4—181no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233#107—181no—
234#106—181no—
235#103—181no—
236#102—181no—
237C22⋊C8—31no—
238C22⋊C8—91no—
239#95—61no—
240#95—61no—
241#95D3211yescharacteristic
242C23×C3—21no—
243C23×C3D3×D411yescharacteristic
244C23×C3C2×#6711yescharacteristic
245C22×D3—61no—
246C22×D3—61no—
247C22×D3—121no—
248C3×Q8—121no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—81no—
267C2×C3×C4—81no—
268C2×C3×C4—81no—
269C2×C3×C4—121no—
270C2×C3×C4—122no—
271C2×C3×C4—121no—
272C2×C3×C4C2×D1211yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276#67—121no—
277#67—121no—
278#67—121no—
279#67—121no—
280#67—241no—
281#67—241no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—41no—
289C2×Dic3—42no—
290C2×Dic3—41no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—121no—
294D12—121no—
295D12—121no—
296D12—241no—
297C4×D3—241no—
298C4×D3—241no—
299Dic6—41no—
300C3×C8—121no—
301C3⋊C8—41no—
302C3⋊C8—121no—
303C3⋊C8—121no—
304C3⋊C8—241no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32#45211yescharacteristic
308C2×C32#45411yescharacteristic
309C2×C32#45811yescharacteristic
310C3⋊D3—81no—
311C2×Q8—31no—
312C2×D4—91no—
313C2×D4—181no—
314C22×C4—21no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—61no—
318C22×C4—181no—
319C22×C4C2×D3211yescharacteristic
320C2×C8—61no—
321C2×C8—181no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—91no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C22⋊C4—61no—
333C22⋊C4—181no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—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#91611yescharacteristic
349C22×C3#91811yescharacteristic
350C22×C3#93711yescharacteristic
351C22×C3#94211yescharacteristic
352C22×C3#95011yescharacteristic
353C2×D3—121no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—241no—
360C2×D3—241no—
361C2×D3—241no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—81no—
369C3×C4—81no—
370C3×C4—82no—
371C3×C4—121no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4—121no—
375C3×C4—241no—
376Dic3—41no—
377Dic3—41no—
378Dic3—41no—
379Dic3—41no—
380Dic3—81no—
381Dic3—121no—
382Dic3—121no—
383Dic3—241no—
384C32#161511yescharacteristic, complemented, Sylow
385C23—181no—
386C23D3×#6711yescharacteristic
387Q8—121no—
388D4—361no—
389D4—361no—
390D4—361no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—121no—
402C2×C4—122no—
403C2×C4—121no—
404C2×C4—181no—
405C2×C4—721no—
406C2×C4D3×D1211yescharacteristic
407C2×C4#380211yescharacteristic
408C8—121no—
409C8—361no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3#474211yescharacteristic
420C2×C3#480811yescharacteristic
421C2×C3#482711yescharacteristic
422C2×C3#504711yescharacteristic
423C2×C3#505311yescharacteristic
424C2×C3#506211yescharacteristic
425D3—241no—
426D3—241no—
427D3—481no—
428C22—21no—
429C22—21no—
430C22—361no—
431C22—361no—
432C22—361no—
433C22#6392211yescharacteristic
434C22#6393511yescharacteristic
435C22#6394811yescharacteristic
436C4—21no—
437C4—21no—
438C4—81no—
439C4—121no—
440C4—121no—
441C4—121no—
442C4—121no—
443C4—241no—
444C4—361no—
445C3—21no—
446C3#6833011yescharacteristic, complemented
447C3#6971711yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—721no—
451C2#1059040011yescharacteristic
452C2#1059040811yescharacteristic
453C2#1059061611yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#64139C22
hypercenter#95D32
hypocenterC32#1615
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#4659C2semidirect
3. #10591132C2semidirect
6. C3×#4452C2semidirect
7. #10589147C2semidirect
36. #4659D3semidirect
40. #4452D3semidirect
384. C32#1615semidirect
446. C3#68330semidirect
447. C3#69717semidirect

Maximal subgroups

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

subgroupindex
#105949802
C3×#46592
#105911322
#105911252
#105893172
C3×#44522
#105891472
#697173
#683303