Finite Group Databasebeta

← #11780499

Subgroups — #11780499

Order 1152.

490 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593985C211yesmaximal, characteristic, complemented
2C3×#4712C211yesmaximal, characteristic, complemented
3#10590354C211yesmaximal, characteristic, complemented
4#10590275C211yesmaximal, characteristic, complemented
5#10589331C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71327—31nomaximal
9#68351—31nomaximal
10#64079C2211yescharacteristic
11C2×C3×D24—21no—
12C2×C3×#204—21no—
13C3×#875C2211yescharacteristic
14C3×#875C2211yescharacteristic
15C3×#874C2211yescharacteristic
16#63891—21no—
17#63891—21no—
18#63887—21no—
19#63887—21no—
20#63885—21no—
21#63885—21no—
22C2×#3715—21no—
23C2×#3713—21no—
24C32×#97C2211yescharacteristic
25#63630C2211yescharacteristic
26C3×#803C2211yescharacteristic
27#63563—21no—
28#63563—21no—
29#5684—31no—
30#5684—31no—
31C3×#496—31no—
32#5074—31no—
33#5071—31no—
34#5058—31no—
35#4713—31no—
36#4712D311yescharacteristic, complemented
37C3×#329—31no—
38#4540—31no—
39#4465—31no—
40#4465—31no—
41#4465—61no—
42#4464—31no—
43#4464D311yescharacteristic, complemented
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12D411yescharacteristic
48C2×C3×D12D411yescharacteristic
49C2×C3×Dic6D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#625—21no—
52C2×#625—21no—
53C2×D3×Dic3—21no—
54C2×D3×Dic3—21no—
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60#3750—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C2×C3×C3⋊C8—21no—
67C3×D24—42no—
68C3×#204—42no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73#3715—42no—
74#3713—42no—
75#1656—91noSylow
76C2×C3×SD16—61no—
77C2×C3×D8—61no—
78C3×#127—31no—
79C3×#124—31no—
80C3×#124—31no—
81#946—61no—
82#946—61no—
83C2×#215—61no—
84#939—61no—
85#939—61no—
86C2×#214—61no—
87C2×#213—61no—
88C2×#213—61no—
89C2×D24—21no—
90C2×#204—21no—
91#886—61no—
92#886—61no—
93#884—61no—
94#884—61no—
95#883—61no—
96#883—61no—
97#878—61no—
98#878—61no—
99#875C2×D311yescharacteristic
100#875C2×D311yescharacteristic
101#874C2×D311yescharacteristic
102#870—31no—
103#870—31no—
104#870—61no—
105C3×#97—21no—
106C3×#97—31no—
107C3×#97C2×D311yescharacteristic
108C3×#97C2×D311yescharacteristic
109#832—61no—
110#832—61no—
111#821—61no—
112#821—61no—
113#803—31no—
114#803—31no—
115#803—61no—
116#803C2×D311yescharacteristic
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C3×D12—41no—
128C3×D12—41no—
129C3×D12—41no—
130C3×D12—41no—
131C3×D12—41no—
132C3×D12—41no—
133C3×D12—42no—
134C3×Dic6—41no—
135C3×Dic6—41no—
136#625—81no—
137#625—81no—
138D3×Dic3—81no—
139D3×Dic3—81no—
140C32×C8—22no—
141C3⋊(C3⋊C8)—22no—
142C3×C3⋊C8—41no—
143#562—91no—
144#496—31no—
145#496—91no—
146#490—91no—
147#330—91no—
148#329—31no—
149#329—91no—
150C2×C3×Q8—31no—
151C2×C3×Q8—31no—
152C2×C3×D4—31no—
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C2×#67—61no—
158C2×#67—61no—
159C2×#67—61no—
160C2×#67—61no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C2×D12—21no—
164C2×D12—21no—
165C2×D12—21no—
166C2×D12D1211yescharacteristic
167C2×D12#6711yescharacteristic
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×Dic6D1211yescharacteristic
171C2×Dic6#6711yescharacteristic
172C3×SD16—122no—
173C3×D8—122no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—41no—
177C2×C3×C8—61no—
178C3×C22⋊C4—61no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C42—21no—
183C3×C42C22×D311yescharacteristic
184C3×C42C22×D311yescharacteristic
185#217—61no—
186#217—61no—
187#215—122no—
188#214—122no—
189#213—122no—
190#213—122no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197C4⋊Dic3—31no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200C4⋊Dic3—31no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—121no—
212Dic3⋊C4—121no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—121no—
217D24—42no—
218#204—42no—
219C22×C32#12011yescharacteristic
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—81no—
227C2×C3×D3—81no—
228C2×C3×D3—81no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—21no—
232C3⋊Dic3—41no—
233C3⋊Dic3—41no—
234C3×Dic3—41no—
235C3×Dic3—41no—
236C2×SD16—61no—
237C2×SD16—181no—
238C2×D8—61no—
239C2×D8—181no—
240#127—31no—
241#125—91no—
242#124—31no—
243#124—31no—
244#123—181no—
245#123—181no—
246C22⋊Q8—181no—
247C22⋊Q8—181no—
248#121—181no—
249#121—181no—
250#102—181no—
251#102—181no—
252#97—31no—
253#97—91no—
254#97D3211yescharacteristic
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—121no—
258C22×D3—21no—
259C22×D3—21no—
260C22×D3—41no—
261C3×Q8—121no—
262C3×Q8—121no—
263C3×D4—121no—
264C3×D4—121no—
265C3×D4—121no—
266C3×D4—121no—
267C3×D4—121no—
268C3×D4—121no—
269C3×D4—122no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4C2×D1211yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281#67—241no—
282#67—241no—
283#67—241no—
284#67—241no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C2×Dic3—241no—
294C2×Dic3—241no—
295D12—41no—
296D12—41no—
297D12—41no—
298D12—41no—
299D12—41no—
300D12—41no—
301D12—42no—
302C4×D3—241no—
303C4×D3—241no—
304Dic6—41no—
305Dic6—41no—
306C3×C8—22no—
307C3×C8—22no—
308C3×C8—42no—
309C3×C8—121no—
310C3⋊C8—41no—
311C3⋊C8—62no—
312C3⋊C8—62no—
313C3⋊C8—122no—
314C2×C32#45311yescharacteristic
315C2×C32#45311yescharacteristic
316C2×C32#45411yescharacteristic
317C3×D3—81no—
318C3×D3—81no—
319C3×D3—161no—
320C2×Q8—31no—
321C2×Q8—31no—
322C2×D4—31no—
323C2×D4—31no—
324C2×D4—61no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4—181no—
328C2×D4—181no—
329C22×C4—181no—
330C22×C4—181no—
331SD16—122no—
332SD16—362no—
333D8—122no—
334D8—362no—
335C2×C8—21no—
336C2×C8—61no—
337C2×C8—181no—
338C4⋊C4—91no—
339C4⋊C4—91no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—181no—
343C4⋊C4—181no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—181no—
349C22⋊C4—181no—
350C42C2×D3211yescharacteristic
351C22×C3—21no—
352C22×C3—121no—
353C22×C3—121no—
354C22×C3—121no—
355C22×C3—121no—
356C22×C3—121no—
357C22×C3—121no—
358C22×C3—241no—
359C22×C3—241no—
360C22×C3—241no—
361C22×C3#88211yescharacteristic
362C22×C3#93711yescharacteristic
363C2×D3—41no—
364C2×D3—41no—
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—41no—
368C2×D3—41no—
369C2×D3—81no—
370C2×D3—81no—
371C2×D3—81no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—121no—
382C3×C4—121no—
383Dic3—41no—
384Dic3—41no—
385Dic3—121no—
386Dic3—121no—
387Dic3—121no—
388Dic3—121no—
389Dic3—241no—
390Dic3—241no—
391C32#165611yescharacteristic, complemented, Sylow
392C23—61no—
393C23—61no—
394C23—121no—
395Q8—121no—
396Q8—121no—
397D4—121no—
398D4—121no—
399D4—121no—
400D4—121no—
401D4—121no—
402D4—121no—
403D4—122no—
404D4—721no—
405D4—721no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—181no—
409C2×C4—181no—
410C2×C4—721no—
411C2×C4—721no—
412C2×C4D3×D1211yescharacteristic
413C2×C4#380211yescharacteristic
414C2×C4D3×#6711yescharacteristic
415C8—22no—
416C8—121no—
417C8—182no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—241no—
422C2×C3—241no—
423C2×C3—481no—
424C2×C3#474711yescharacteristic
425C2×C3#482211yescharacteristic
426C2×C3#482711yescharacteristic
427C2×C3#507711yescharacteristic
428C2×C3#519811yescharacteristic
429C2×C3#520111yescharacteristic
430D3—81no—
431D3—81no—
432D3—161no—
433C22—121no—
434C22—121no—
435C22—121no—
436C22—121no—
437C22—121no—
438C22—121no—
439C22—241no—
440C22—241no—
441C22—241no—
442C22#6392211yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—121no—
447C4—121no—
448C4—361no—
449C4—361no—
450C3—21no—
451C3#6835111yescharacteristic, complemented
452C3#7132711yescharacteristic, complemented
453C2—241no—
454C2—241no—
455C2—481no—
456C2#1059039511yescharacteristic
457C2#1059101411yescharacteristic
458C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
hypercenter#97D32
hypocenterC32#1656
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593985C2semidirect
2. C3×#4712C2semidirect
3. #10590354C2semidirect
4. #10590275C2semidirect
5. #10589331C2semidirect
6. C3×#4464C2semidirect
7. #10589086C2semidirect
36. #4712D3semidirect
43. #4464D3semidirect
391. C32#1656semidirect
451. C3#68351semidirect
452. C3#71327semidirect

Maximal subgroups

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

subgroupindex
#105939852
C3×#47122
#105903542
#105902752
#105893312
C3×#44642
#105890862
#713273
#683513