Finite Group Databasebeta

← #11794342

Subgroups — #11794342

Order 1152.

513 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592801C211yesmaximal, characteristic, complemented
2C2×C3×#821C211yesmaximal, characteristic
3C2×C3×#819C211yesmaximal, characteristic, complemented
4#10591130C211yesmaximal, characteristic, complemented
5#10591086C211yesmaximal, characteristic
6C2×#63558C211yesmaximal, characteristic
7#10589167C211yesmaximal, characteristic, complemented
8#70715—31nomaximal
9#70197—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63641—22no—
18C3×#821—22no—
19C3×#819—22no—
20#63575—21no—
21#63573—21no—
22#63563—21no—
23#63563—21no—
24#63558—22no—
25C2×C3×#108—31no—
26C2×C3×#102—31no—
27C2×#833—31no—
28#5215—31no—
29#5131—31no—
30C2×#823—31no—
31#5121—31no—
32C2×#821D311yescharacteristic
33C2×#819D311yescharacteristic, complemented
34#5102—31no—
35#5102—31no—
36#5102—61no—
37#4964—31no—
38#4554—31no—
39#4530—31no—
40C23×C3×D3—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12Q812yes—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C2×C32×C8D412yes—
52#3757—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C4×C3⋊Dic3—21no—
56#3748—21no—
57#3748—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#2063—91noSylow
68C22×C3×D4—31no—
69C22×D12C2×D311yescharacteristic
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C22×C3×C8—21no—
73C22×C3×C8C2×D311yescharacteristic
74C22×C3×C8C2×D311yescharacteristic
75C2×C3×C4⋊C4—31no—
76#926—31no—
77#926—31no—
78#926—61no—
79C2×C4⋊Dic3C2×D311yescharacteristic
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C3×#108—62no—
86C3×#102—62no—
87#833—62no—
88#832—61no—
89#832—61no—
90#823—62no—
91#821—22no—
92#821—61no—
93#821—61no—
94#819—22no—
95#818—61no—
96#817—61no—
97Dic3⋊C8—64no—
98Dic3⋊C8—62no—
99Dic3⋊C8—62no—
100#808—61no—
101#807—61no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—22no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—81no—
107C22×C3×D3—81no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—21no—
116C2×C3×Dic3—41no—
117C2×C3×Dic3—81no—
118C3×D12—22no—
119C3×D12—22no—
120C3×D12—41no—
121C3×D12—41no—
122C32×C8—22no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C2×#108—31no—
127#428—91no—
128#424—91no—
129#418—91no—
130C2×#102—31no—
131C2×#100—91no—
132#343—91no—
133C24×C3—61no—
134C23×D3—21no—
135C2×C3×D4—32no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×Dic3—21no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12Dic612yes—
152C3×M16—32no—
153C3×M16—61no—
154C3×M16—61no—
155C3×M16—61no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—22no—
161C2×C3×C8—41no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C2×C3×C8D1212yes—
166C2×C3×C8#6712yes—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169#217—62no—
170#217—61no—
171#217—61no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4×Dic3—62no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183#208—21no—
184#208—21no—
185#208—21no—
186#208—61no—
187#208—61no—
188#208—61no—
189#208—61no—
190#208—121no—
191#208—121no—
192#208#6712yes—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—62no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C22×C32—21no—
199C22×C32—21no—
200C22×C32#12111yescharacteristic
201C22×C32C22⋊Q811yescharacteristic
202C22×C32#12611yescharacteristic
203C2×C3×D3—42no—
204C2×C3×D3—82no—
205C2×C3×D3—81no—
206C2×C3×D3—81no—
207C2×C3×D3—82no—
208C32×C4#12111yescharacteristic
209C32×C4#12111yescharacteristic
210C32×C4C22⋊Q811yescharacteristic
211C32×C4C22⋊Q811yescharacteristic
212C3⋊Dic3—41no—
213C3⋊Dic3—41no—
214C3×Dic3—81no—
215C22×D4—31no—
216C2×M16—31no—
217C2×M16—31no—
218C2×M16—91no—
219C22×C8D3211yescharacteristic
220#117—91no—
221C2×C4⋊C4—31no—
222#108—62no—
223#107—181no—
224#106—181no—
225C4⋊C8—182no—
226#102—62no—
227#102—181no—
228#102—181no—
229#100—182no—
230C23×C3—21no—
231C23×C3—62no—
232C23×C3—121no—
233C23×C3—121no—
234C23×C3—241no—
235C23×C3—241no—
236C23×C3#23711yescharacteristic
237C23×C3#23911yescharacteristic
238C22×D3—22no—
239C22×D3—41no—
240C22×D3—41no—
241C22×D3—81no—
242C22×D3—81no—
243C3×D4—62no—
244C3×D4—62no—
245C3×D4—121no—
246C3×D4—121no—
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—121no—
254C2×C3×C4—241no—
255C2×C3×C4C2×Dic611yescharacteristic
256C2×C3×C4C2×D1211yescharacteristic
257C2×C3×C4#23511yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23711yescharacteristic
264C2×C3×C4D3×Q811yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267C2×Dic3—41no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—81no—
275D12—22no—
276D12—22no—
277D12—41no—
278D12—41no—
279C3×C8—22no—
280C3×C8—22no—
281C3×C8—42no—
282C3×C8—62no—
283C3×C8—121no—
284C3⋊C8—22no—
285C3⋊C8—41no—
286C3⋊C8—122no—
287C3⋊C8—121no—
288C3⋊C8—121no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32#39611yescharacteristic
292C2×C32#47111yescharacteristic
293C2×C32#47211yescharacteristic
294C3×D3—82no—
295C24—61no—
296C2×D4—32no—
297C2×D4—61no—
298C2×D4—61no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C22×C4—61no—
303C22×C4C2×D3211yescharacteristic
304M16—32no—
305M16—61no—
306M16—61no—
307M16—61no—
308M16—181no—
309M16—181no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—181no—
315C2×C8#62612yes—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C22⋊C4—181no—
321C42—181no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—122no—
332C22×C3—242no—
333C22×C3—242no—
334C22×C3—241no—
335C22×C3—241no—
336C22×C3#87811yescharacteristic
337C22×C3#87911yescharacteristic
338C22×C3#89511yescharacteristic
339C22×C3#89811yescharacteristic
340C22×C3#93811yescharacteristic
341C22×C3#94611yescharacteristic
342C2×D3—42no—
343C2×D3—82no—
344C2×D3—81no—
345C2×D3—81no—
346C2×D3—82no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—241no—
352C3×C4#87811yescharacteristic
353C3×C4#88411yescharacteristic
354C3×C4#89611yescharacteristic
355C3×C4#89711yescharacteristic
356C3×C4#92411yescharacteristic
357C3×C4#93011yescharacteristic
358C3×C4#93911yescharacteristic
359C3×C4#93911yescharacteristic
360Dic3—81no—
361Dic3—122no—
362Dic3—122no—
363Dic3—121no—
364Dic3—121no—
365Dic3—121no—
366Dic3—121no—
367C32#206311yescharacteristic, complemented, Sylow
368C23—62no—
369C23—121no—
370C23—121no—
371C23—241no—
372C23—241no—
373C23#379611yescharacteristic
374D4—62no—
375D4—62no—
376D4—121no—
377D4—121no—
378C2×C4—121no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—241no—
382C2×C4D3×Dic611yescharacteristic
383C2×C4#379511yescharacteristic
384C2×C4#380211yescharacteristic
385C2×C4#380411yescharacteristic
386C2×C4C2×#62611yescharacteristic
387C2×C4D3×#6711yescharacteristic
388C8—22no—
389C8—62no—
390C8—121no—
391C8—361no—
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—242no—
402C2×C3#489711yescharacteristic
403C2×C3#489811yescharacteristic
404C2×C3#494811yescharacteristic
405C2×C3#499411yescharacteristic
406C2×C3#516011yescharacteristic
407C2×C3#517711yescharacteristic
408D3—82no—
409C22—21no—
410C22—21no—
411C22—122no—
412C22—242no—
413C22—242no—
414C22—241no—
415C22—241no—
416C22#6385811yescharacteristic
417C22#6388711yescharacteristic
418C22#6391611yescharacteristic
419C4—241no—
420C4—361no—
421C4—361no—
422C4#6385711yescharacteristic
423C4#6388511yescharacteristic
424C4#6389911yescharacteristic
425C4#6397811yescharacteristic
426C3—21no—
427C3#7019711yescharacteristic, complemented
428C3#7071511yescharacteristic, complemented
429C2—21no—
430C2—21no—
431C2—242no—
432C2#1059092811yescharacteristic
433C2#1059092911yescharacteristic
434C2#1059130811yescharacteristic
subgroupG/H
centerC22#63916
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10592801C2semidirect
3. C2×C3×#819C2semidirect
4. #10591130C2semidirect
7. #10589167C2semidirect
33. C2×#819D3semidirect
367. C32#2063semidirect
427. C3#70197semidirect
428. C3#70715semidirect

Maximal subgroups

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

subgroupindex
#105928012
C2×C3×#8212
C2×C3×#8192
#105911302
#105910862
C2×#635582
#105891672
#707153
#701973