Finite Group Databasebeta

← #11789717

Subgroups — #11789717

Order 1152.

503 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3748C211yesmaximal, characteristic, complemented
2C2×C3×#805C211yesmaximal, characteristic
3#10591141C211yesmaximal, characteristic, complemented
4#10591111C211yesmaximal, characteristic
5#10591076C211yesmaximal, characteristic
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#70378—31nomaximal
9#68750—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63630—21no—
18C4×C3⋊(C3⋊C8)—21no—
19C3×#805—21no—
20C3×#805—21no—
21#63577—22no—
22#63569—22no—
23#63560C412yescomplemented
24#63558C412yescomplemented
25C2×C3×#104—31no—
26#5237—31no—
27#5236—31no—
28#5132—31no—
29#5125—31no—
30#5124—31no—
31#5005—31no—
32C2×#805D311yescharacteristic
33C4×#208—31no—
34C4×#208—31no—
35C4×#208—61no—
36C3×#339—31no—
37#4556—31no—
38#4533—31no—
39#4523D311yescharacteristic, complemented
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C32×C42—21no—
51C32×C42D411yescharacteristic
52C32×C42D411yescharacteristic
53#3748—21no—
54#3748—21no—
55#3748C2×C412yes—
56#3748D412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4×Dic3—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208C2×C412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C3×#117—31no—
74C2×C3×C42—21no—
75C2×C3×C42C2×D311yescharacteristic
76C2×C3×C42C2×D311yescharacteristic
77#926C2×D311yescharacteristic
78C2×#208—31no—
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#104—61no—
87C3×#104—61no—
88#837—62no—
89#836—32no—
90#833—32no—
91#824—32no—
92#823—32no—
93#822—62no—
94#819—62no—
95#805—21no—
96#805—21no—
97#805—62no—
98#803—62no—
99#803—61no—
100#803—61no—
101C4×C3⋊C8—62no—
102C4×C3⋊C8—61no—
103C4×C3⋊C8—61no—
104C23×C32#4111yescharacteristic
105C22×C3×D3—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—42no—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C3×#67—41no—
116C3×#67—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—41no—
119C3×D12—21no—
120C3×D12—21no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—21no—
124C3×Dic6—21no—
125C3⋊(C3⋊C8)—22no—
126C3⋊(C3⋊C8)—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129#430—91no—
130#421—91no—
131C2×#104—31no—
132#413—91no—
133C4×M16—91no—
134#344—91no—
135#339—31no—
136C3×#41—61no—
137C3×#41—61no—
138C3×#41—61no—
139C3×#41—61no—
140C2×C3×Q8—31no—
141C2×C3×D4—31no—
142C2×C3×D4—61no—
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—61no—
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C2×#67—21no—
151#235—21no—
152#235—21no—
153#235—21no—
154#235—21no—
155C2×D12C4×D311yescharacteristic
156C2×C4×D3—21no—
157C2×Dic6C4×D311yescharacteristic
158C3×M16—32no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—61no—
165C3×C22⋊C4—61no—
166C3×C42—22no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—21no—
170C3×C42—21no—
171C3×C42—61no—
172C3×C42D1211yescharacteristic
173C3×C42D1211yescharacteristic
174C3×C42#6711yescharacteristic
175C3×C42#6711yescharacteristic
176#217—21no—
177C4⋊Dic3—21no—
178C4×Dic3—21no—
179#208—21no—
180#208—21no—
181#208—21no—
182#208—32no—
183#208—32no—
184#208—32no—
185#208—32no—
186#208—62no—
187#208—62no—
188#208—62no—
189#208—62no—
190#208—61no—
191#208—61no—
192#208—61no—
193#208—61no—
194#208C4×D312yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—62no—
198C2×C3⋊C8—62no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C22×C32—41no—
204C22×C32#11711yescharacteristic
205C22×C32#12311yescharacteristic
206C22×C32#12411yescharacteristic
207C2×C3×D3—41no—
208C2×C3×D3—81no—
209C32×C4—22no—
210C32×C4—41no—
211C32×C4C4×D411yescharacteristic
212C32×C4C4×D411yescharacteristic
213C32×C4#12111yescharacteristic
214C32×C4#12611yescharacteristic
215C3×Dic3—41no—
216C3×Dic3—81no—
217C2×#41—31no—
218C2×M16—31no—
219C2×M16—31no—
220C2×M16—91no—
221C2×M16—91no—
222#117—31no—
223C2×C42D3211yescharacteristic
224#108—182no—
225#104—61no—
226#104—61no—
227#104—182no—
228#101—92no—
229#100—92no—
230#97—181no—
231C4×C8—181no—
232C23×C3—21no—
233C23×C3—61no—
234C23×C3#23711yescharacteristic
235C23×C3#23711yescharacteristic
236C22×D3—21no—
237C3×Q8—61no—
238C3×Q8—61no—
239C3×D4—61no—
240C3×D4—61no—
241C3×D4—121no—
242C3×D4—121no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—22no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—44no—
258C2×C3×C4—61no—
259C2×C3×C4—121no—
260C2×C3×C4—121no—
261C2×C3×C4—121no—
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4C2×C4×D311yescharacteristic
264C2×C3×C4C2×D1211yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4#23911yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274#67—41no—
275#67—41no—
276C2×Dic3—21no—
277C2×Dic3—41no—
278D12—21no—
279D12—21no—
280C4×D3—41no—
281C4×D3—41no—
282Dic6—21no—
283Dic6—21no—
284C3×C8—62no—
285C3×C8—121no—
286C3⋊C8—22no—
287C3⋊C8—41no—
288C3⋊C8—64no—
289C3⋊C8—64no—
290C3⋊C8—62no—
291C3⋊C8—62no—
292C3⋊C8—62no—
293C3⋊C8—62no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32#38811yescharacteristic
298C3×D3—81no—
299#41—61no—
300#41—61no—
301#41—61no—
302#41—61no—
303C2×Q8—31no—
304C2×D4—31no—
305C2×D4—61no—
306C22×C4—21no—
307C22×C4—61no—
308C22×C4C2×D3211yescharacteristic
309M16—32no—
310M16—61no—
311M16—61no—
312M16—61no—
313M16—92no—
314M16—92no—
315M16—181no—
316M16—181no—
317C2×C8—61no—
318C2×C8—61no—
319C2×C8—181no—
320C2×C8—181no—
321C4⋊C4—61no—
322C22⋊C4—61no—
323C42—21no—
324C42—61no—
325C42#62611yescharacteristic
326C42#62611yescharacteristic
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—42no—
333C22×C3—121no—
334C22×C3—241no—
335C22×C3#87711yescharacteristic
336C22×C3#88511yescharacteristic
337C22×C3#88511yescharacteristic
338C22×C3#88611yescharacteristic
339C22×C3#89211yescharacteristic
340C22×C3#93511yescharacteristic
341C2×D3—41no—
342C2×D3—81no—
343C3×C4—24no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—42no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—121no—
354C3×C4—241no—
355C3×C4C4×D1211yescharacteristic
356C3×C4#87911yescharacteristic
357C3×C4#67⋊C411yescharacteristic
358C3×C4#67⋊C411yescharacteristic
359C3×C4#89511yescharacteristic
360C3×C4#89811yescharacteristic
361C3×C4C4×#6711yescharacteristic
362C3×C4#93811yescharacteristic
363Dic3—41no—
364Dic3—81no—
365C32#193211yescharacteristic, complemented, Sylow
366C23—61no—
367C23#380511yescharacteristic
368Q8—61no—
369Q8—61no—
370D4—61no—
371D4—61no—
372D4—121no—
373D4—121no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—61no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4#379611yescharacteristic
382C2×C4#379811yescharacteristic
383C2×C4C4×D3211yescharacteristic
384C2×C4#380211yescharacteristic
385C2×C4#380511yescharacteristic
386C2×C4C2×#62611yescharacteristic
387C8—62no—
388C8—121no—
389C8—182no—
390C8—182no—
391C2×C3—22no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—41no—
400C2×C3—41no—
401C2×C3—241no—
402C2×C3#467011yescharacteristic
403C2×C3#494411yescharacteristic
404D3—81no—
405C22—41no—
406C22—121no—
407C22—241no—
408C22#6387811yescharacteristic
409C22#6391511yescharacteristic
410C22#6396211yescharacteristic
411C4—22no—
412C4—41no—
413C4—121no—
414C4—241no—
415C4#6386211yescharacteristic
416C4#6390211yescharacteristic
417C4C4×#62611yescharacteristic
418C4#6391611yescharacteristic
419C3—21no—
420C3#6875011yescharacteristic, complemented
421C3#7037811yescharacteristic, complemented
422C2—21no—
423C2—21no—
424C2—21no—
425C2—241no—
426C2#1059128711yescharacteristic
subgroupG/H
centerC4#63916
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC2×C32#388
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C4×#3748C2semidirect
3. #10591141C2semidirect
6. C3×#4523C2semidirect
7. #10589169C2semidirect
23. #63560C4semidirect
24. #63558C4semidirect
39. #4523D3semidirect
365. C32#1932semidirect
420. C3#68750semidirect
421. C3#70378semidirect

Maximal subgroups

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

subgroupindex
C4×#37482
C2×C3×#8052
#105911412
#105911112
#105910762
C3×#45232
#105891692
#703783
#687503