Finite Group Databasebeta

← #11785555

Subgroups — #11785555

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2#10592935C211yesmaximal, characteristic
3C3×#5236C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591122C211yesmaximal, characteristic, complemented
6#10589171C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#72013—31nomaximal
9#70396—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64135C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#948—21no—
14C3×#948—21no—
15C3×#948C412yescomplemented
16C3×#948C412yescomplemented
17C3×#926C2211yescharacteristic
18C2×C3×#208—21no—
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8—21no—
22C22×C3×C3⋊C8C2211yescharacteristic
23#63664—22no—
24C3×#837—22no—
25#63577—21no—
26#63577—21no—
27#63575—21no—
28#63573—21no—
29C2×C3×#131—31no—
30C2×#948D311yescharacteristic
31C3×#421—31no—
32#5236—31no—
33#5236—31no—
34#5236—61no—
35#5236D311yescharacteristic
36C2×#822—31no—
37C2×#819—31no—
38#5106—31no—
39#4998—31no—
40#4559—31no—
41#4559—31no—
42#4556—31no—
43#4533—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41C2×C412yes—
47C32×#41D412yes—
48C2×C32×Q8Q811yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4Q811yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53#3757—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4×C3⋊Dic3—21no—
56#3748—21no—
57#3748—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4×Dic3—21no—
62C3×#208—21no—
63C3×#208—22no—
64C3×#208—22no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—22no—
70C2×C3×C3⋊C8—22no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8C2×C411yescharacteristic
73C2×C3×C3⋊C8C2×C411yescharacteristic
74C2×C3×C3⋊C8D411yescharacteristic
75C2×C3×C3⋊C8D411yescharacteristic
76C2×C3×C3⋊C8D411yescharacteristic
77C2×C3×C3⋊C8D411yescharacteristic
78#1814—91noSylow
79C2×C3×#41—21no—
80C2×C3×#41C2×D311yescharacteristic
81C2×C3×#41C2×D311yescharacteristic
82C3×#131—32no—
83C3×#131—32no—
84C3×#131—61no—
85C3×#131—61no—
86C2×C3×M16—31no—
87C2×C3×M16—31no—
88C2×C3×M16—61no—
89C22×C3×C8—31no—
90C22×C3×C8—61no—
91C3×#117—31no—
92#948—21no—
93#948—21no—
94#948Dic312yescomplemented
95#948Dic312yescomplemented
96#926—31no—
97#926—31no—
98#926—61no—
99#926C2×D311yescharacteristic
100C2×#208—21no—
101C2×#208—31no—
102C2×#208—31no—
103C2×#208—61no—
104C2×#208C2×D311yescharacteristic
105C2×#208C2×D311yescharacteristic
106C22×C3⋊C8—21no—
107C22×C3⋊C8C2×D311yescharacteristic
108C3×#104—62no—
109#837—22no—
110#837—64no—
111#837—62no—
112#837—62no—
113#822—61no—
114#822—61no—
115#819—61no—
116#819—61no—
117#818—61no—
118#817—61no—
119#808—61no—
120#807—61no—
121C23×C32—21no—
122C23×C32#4111yescharacteristic
123C32×Q8—21no—
124C32×Q8C4⋊C412yes—
125C32×D4—22no—
126C32×D4—22no—
127C32×D4—21no—
128C32×D4C4⋊C412yes—
129C2×C32×C4—21no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×Q811yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—41no—
139C2×C3×Dic3—41no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8C22⋊C411yescharacteristic
144C3×C3⋊C8C22⋊C411yescharacteristic
145C3×C3⋊C8C22⋊C411yescharacteristic
146C3×C3⋊C8C22⋊C411yescharacteristic
147C2×#131—31no—
148C2×#108—91no—
149#427—91no—
150#421—31no—
151#421—91no—
152#344—91no—
153#344—91no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—22no—
159C3×#41—22no—
160C3×#41—41no—
161C3×#41—41no—
162C3×#41C4×D312yes—
163C3×#41D1212yes—
164C3×#41C2×Dic312yes—
165C3×#41#6712yes—
166C2×C3×Q8—21no—
167C2×C3×Q8Dic611yescharacteristic
168C2×C3×Q8Dic611yescharacteristic
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—41no—
173C2×C3×D4Dic611yescharacteristic
174C2×C3×D4Dic611yescharacteristic
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—41no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C3×M16—32no—
182C3×M16—62no—
183C3×M16—62no—
184C3×M16—61no—
185C3×M16—61no—
186C3×M16—61no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—31no—
190C2×C3×C8—31no—
191C2×C3×C8—31no—
192C2×C3×C8—31no—
193C2×C3×C8—62no—
194C2×C3×C8—62no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C42—61no—
200#217—21no—
201#217—61no—
202#217—61no—
203#217—121no—
204C4⋊Dic3—21no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—121no—
208C4×Dic3—21no—
209C4×Dic3—62no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212#208—21no—
213#208—22no—
214#208—22no—
215#208—21no—
216#208—21no—
217#208—62no—
218#208—61no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—121no—
223#208C2×Dic312yes—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—22no—
226C2×C3⋊C8—22no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C2×C3⋊C8C2×Dic311yescharacteristic
232C2×C3⋊C8C2×Dic311yescharacteristic
233C2×C3⋊C8#6711yescharacteristic
234C2×C3⋊C8#6711yescharacteristic
235C2×C3⋊C8#6711yescharacteristic
236C2×C3⋊C8#6711yescharacteristic
237C22×C32—22no—
238C22×C32—41no—
239C22×C32—42no—
240C22×C32#11711yescharacteristic
241C22×C32#12111yescharacteristic
242C22×C32C22⋊Q811yescharacteristic
243C32×C4—22no—
244C32×C4C2×C22⋊C411yescharacteristic
245C32×C4C2×C4⋊C411yescharacteristic
246C32×C4#12111yescharacteristic
247C32×C4C22⋊Q811yescharacteristic
248C3⋊Dic3—81no—
249C3×Dic3—81no—
250C2×#41D3211yescharacteristic
251#131—32no—
252#131—32no—
253#131—61no—
254#131—61no—
255C2×M16—31no—
256C2×M16—31no—
257C2×M16—61no—
258C2×M16—91no—
259C22×C8—31no—
260C22×C8—61no—
261#117—31no—
262#117—91no—
263#108—181no—
264#108—181no—
265#107—181no—
266#106—181no—
267#104—62no—
268#104—182no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—41no—
273C23×C3#23511yescharacteristic
274C23×C3#23711yescharacteristic
275C3×Q8—21no—
276C3×Q8—21no—
277C3×Q8—22no—
278C3×Q8—41no—
279C3×Q8Dic3⋊C412yes—
280C3×Q8C4⋊Dic312yes—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—22no—
284C3×D4—22no—
285C3×D4—21no—
286C3×D4—21no—
287C3×D4—22no—
288C3×D4—41no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4Dic3⋊C412yes—
292C3×D4C4⋊Dic312yes—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—121no—
309C2×C3×C4C2×Dic611yescharacteristic
310C2×C3×C4C2×Dic611yescharacteristic
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4#23511yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4C22×Dic311yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×Dic3—41no—
322C2×Dic3—122no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C3×C8—31no—
326C3×C8—31no—
327C3×C8—31no—
328C3×C8—31no—
329C3×C8—62no—
330C3×C8—121no—
331C3⋊C8—22no—
332C3⋊C8—41no—
333C3⋊C8—122no—
334C3⋊C8—121no—
335C3⋊C8—121no—
336C3⋊C8#21711yescharacteristic
337C3⋊C8#21711yescharacteristic
338C3⋊C8#21711yescharacteristic
339C3⋊C8#21711yescharacteristic
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—42no—
344C2×C32#38011yescharacteristic
345#41—21no—
346#41—21no—
347#41D3×Dic312yes—
348#41#62612yes—
349C2×Q8#62711yescharacteristic
350C2×D4—21no—
351C2×D4#62711yescharacteristic
352C22×C4—21no—
353C22×C4C2×D3211yescharacteristic
354M16—32no—
355M16—62no—
356M16—62no—
357M16—61no—
358M16—61no—
359M16—61no—
360M16—181no—
361M16—181no—
362C2×C8—31no—
363C2×C8—31no—
364C2×C8—31no—
365C2×C8—31no—
366C2×C8—31no—
367C2×C8—31no—
368C2×C8—62no—
369C2×C8—62no—
370C2×C8—61no—
371C2×C8—61no—
372C2×C8—181no—
373C4⋊C4—61no—
374C4⋊C4—181no—
375C22⋊C4—61no—
376C22⋊C4—181no—
377C42—61no—
378C42—181no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—42no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—81no—
390C22×C3—82no—
391C22×C3#87711yescharacteristic
392C22×C3#87811yescharacteristic
393C22×C3#92411yescharacteristic
394C22×C3#92611yescharacteristic
395C22×C3#93011yescharacteristic
396C22×C3#93911yescharacteristic
397C3×C4—22no—
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—42no—
404C3×C4—241no—
405C3×C4#87811yescharacteristic
406C3×C4D3×C22⋊C411yescharacteristic
407C3×C4C2×Dic3⋊C411yescharacteristic
408C3×C4#92411yescharacteristic
409C3×C4C2×C4⋊Dic311yescharacteristic
410C3×C4#93011yescharacteristic
411C3×C4#93911yescharacteristic
412C3×C4C2×#21711yescharacteristic
413Dic3—81no—
414Dic3—241no—
415Dic3—241no—
416Dic3—242no—
417C32#181411yescharacteristic, complemented, Sylow
418C23—21no—
419C23#380411yescharacteristic
420Q8—21no—
421Q8Dic3⋊Dic312yes—
422D4—22no—
423D4—22no—
424D4—21no—
425D4Dic3⋊Dic312yes—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—121no—
430C2×C4—361no—
431C2×C4C2×D3×Dic311yescharacteristic
432C2×C4#380411yescharacteristic
433C2×C4C2×#62611yescharacteristic
434C2×C4C2×#62711yescharacteristic
435C2×C4D3×#6711yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C8—31no—
438C8—31no—
439C8—31no—
440C8—31no—
441C8—62no—
442C8—121no—
443C8—361no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3—42no—
455C2×C3—42no—
456C2×C3—82no—
457C2×C3#494211yescharacteristic
458C2×C3#521211yescharacteristic
459C22—22no—
460C22—41no—
461C22—42no—
462C22#6395511yescharacteristic
463C22#6396411yescharacteristic
464C22#6397811yescharacteristic
465C4—22no—
466C4—241no—
467C4—721no—
468C4#6396411yescharacteristic
469C4C2×Dic3⋊Dic311yescharacteristic
470C4D3×#21711yescharacteristic
471C4#6397811yescharacteristic
472C3—21no—
473C3#7039611yescharacteristic, complemented
474C3#7201311yescharacteristic, complemented
475C2—21no—
476C2—21no—
477C2—21no—
478C2—42no—
479C2#1059171611yescharacteristic
subgroupG/H
centerC4#63978
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#380
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1814
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. #10591122C2semidirect
6. #10589171C2semidirect
7. #10589170C2semidirect
15. C3×#948C4semidirect
16. C3×#948C4semidirect
94. #948Dic3semidirect
95. #948Dic3semidirect
417. C32#1814semidirect
473. C3#70396semidirect
474. C3#72013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9482
#105929352
C3×#52362
C2×#635772
#105911222
#105891712
#105891702
#720133
#703963