Finite Group Databasebeta

← #11794345

Subgroups — #11794345

Order 1152.

551 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592914C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591130C211yesmaximal, characteristic, complemented
6#10591119C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70197—31nomaximal
9#70075—31nomaximal
10C22×C32×D4C2211yescharacteristic
11#64135C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63659—21no—
18#63659—21no—
19C3×#833—22no—
20C3×#832—22no—
21#63577—22no—
22#63575—21no—
23#63573—21no—
24#63572—22no—
25C2×C3×#102—31no—
26C2×C3×#100—31no—
27C2×#833D311yescharacteristic
28#5215—31no—
29#5215—31no—
30#5215—61no—
31C2×#832D311yescharacteristic
32C2×#822—31no—
33#5121—31no—
34#5119—31no—
35C2×#819—31no—
36#5102—31no—
37#4964—31no—
38#4554—31no—
39#4530—31no—
40C24×C32—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4Q812yes—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49#3757—21no—
50C4⋊(C3⋊Dic3)D411yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C4×C3⋊Dic3—21no—
53#3748—21no—
54#3748—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208D412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#2063—91noSylow
68C22×C3×D4—21no—
69C22×C3×D4C2×D311yescharacteristic
70C22×C3×D4C2×D311yescharacteristic
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C22×C3×C8—31no—
74C2×C3×C4⋊C4—31no—
75#926—31no—
76#926—31no—
77#926—61no—
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—61no—
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#102—62no—
86C3×#100—62no—
87#833—22no—
88#832—22no—
89#832—61no—
90#832—61no—
91#832—61no—
92#832—61no—
93#832—62no—
94#832—62no—
95#822—62no—
96#819—62no—
97#818—61no—
98#817—61no—
99Dic3⋊C8—62no—
100Dic3⋊C8—62no—
101#808—61no—
102#807—61no—
103C23×C32—22no—
104C23×C32—41no—
105C23×C32—41no—
106C23×C32—81no—
107C23×C32—81no—
108C23×C32#4111yescharacteristic
109C32×D4—22no—
110C32×D4—22no—
111C32×D4—41no—
112C32×D4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×Q811yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—81no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127C2×#108—91no—
128#428—91no—
129#424—91no—
130#418—91no—
131C2×#102—31no—
132C2×#100—31no—
133#343—91no—
134C24×C3—21no—
135C24×C3—21no—
136C24×C3—41no—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—22no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4—41no—
153C2×C3×D4Dic612yes—
154C2×C3×D4Dic612yes—
155C22×C3×C4—21no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×Dic3—21no—
160C3×M16—32no—
161C3×M16—61no—
162C3×M16—61no—
163C3×M16—61no—
164C2×C3×C8—32no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171#217—61no—
172#217—61no—
173#217—121no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—121no—
185#208—21no—
186#208—21no—
187#208—21no—
188#208—61no—
189#208—61no—
190#208—61no—
191#208—61no—
192#208—121no—
193#208—121no—
194#208#6712yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—62no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8#6712yes—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32—42no—
206C22×C32—82no—
207C22×C32—82no—
208C22×C32—81no—
209C22×C32—81no—
210C22×C32#12111yescharacteristic
211C22×C32C22⋊Q811yescharacteristic
212C22×C32#12611yescharacteristic
213C32×C4#12111yescharacteristic
214C32×C4#12111yescharacteristic
215C32×C4C22⋊Q811yescharacteristic
216C32×C4C22⋊Q811yescharacteristic
217C3⋊Dic3—41no—
218C3⋊Dic3—41no—
219C3×Dic3—81no—
220C22×D4D3211yescharacteristic
221C2×M16—31no—
222C2×M16—31no—
223C2×M16—91no—
224C22×C8—31no—
225#117—91no—
226C2×C4⋊C4—31no—
227#108—182no—
228#107—181no—
229#106—181no—
230C4⋊C8—182no—
231#102—62no—
232#102—181no—
233#102—181no—
234#100—62no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—21no—
238C23×C3—42no—
239C23×C3—42no—
240C23×C3—42no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3—81no—
246C23×C3—81no—
247C23×C3—81no—
248C23×C3—81no—
249C23×C3—82no—
250C23×C3—82no—
251C23×C3#23511yescharacteristic
252C23×C3#23711yescharacteristic
253C3×D4—24no—
254C3×D4—22no—
255C3×D4—22no—
256C3×D4—22no—
257C3×D4—22no—
258C3×D4—42no—
259C3×D4—42no—
260C3×D4—42no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—41no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—121no—
272C2×C3×C4—241no—
273C2×C3×C4C2×Dic611yescharacteristic
274C2×C3×C4C2×Dic611yescharacteristic
275C2×C3×C4#23511yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4#23711yescharacteristic
281C2×C3×C4#23711yescharacteristic
282C2×C3×C4#23711yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×Dic3—41no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—81no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C3×C8—62no—
294C3×C8—62no—
295C3×C8—121no—
296C3⋊C8—22no—
297C3⋊C8—22no—
298C3⋊C8—41no—
299C3⋊C8—122no—
300C3⋊C8—121no—
301C3⋊C8—121no—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32—82no—
305C2×C32#39611yescharacteristic
306C2×C32#47111yescharacteristic
307C2×C32#47211yescharacteristic
308C24—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4#62712yes—
315C22×C4—61no—
316C22×C4C2×D3211yescharacteristic
317M16—32no—
318M16—61no—
319M16—61no—
320M16—61no—
321M16—181no—
322M16—181no—
323C2×C8—32no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—181no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—91no—
332C4⋊C4—91no—
333C22⋊C4—181no—
334C42—181no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—44no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—82no—
348C22×C3—82no—
349C22×C3—82no—
350C22×C3—82no—
351C22×C3—82no—
352C22×C3—82no—
353C22×C3—84no—
354C22×C3—84no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3#87811yescharacteristic
360C22×C3#87911yescharacteristic
361C22×C3#87911yescharacteristic
362C22×C3#88411yescharacteristic
363C22×C3#92411yescharacteristic
364C22×C3#93811yescharacteristic
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—241no—
370C3×C4#87811yescharacteristic
371C3×C4#87811yescharacteristic
372C3×C4#87811yescharacteristic
373C3×C4#88411yescharacteristic
374C3×C4#92411yescharacteristic
375C3×C4#93811yescharacteristic
376C3×C4#93911yescharacteristic
377C3×C4#93911yescharacteristic
378Dic3—81no—
379Dic3—121no—
380Dic3—121no—
381Dic3—121no—
382Dic3—121no—
383Dic3—241no—
384Dic3—241no—
385C32#206311yescharacteristic, complemented, Sylow
386C23—22no—
387C23—41no—
388C23—41no—
389C23—81no—
390C23—81no—
391C23#380411yescharacteristic
392D4—22no—
393D4—22no—
394D4—41no—
395D4—41no—
396C2×C4—121no—
397C2×C4—181no—
398C2×C4—181no—
399C2×C4—241no—
400C2×C4#380411yescharacteristic
401C2×C4#380511yescharacteristic
402C2×C4C2×#62711yescharacteristic
403C2×C4D3×#6711yescharacteristic
404C2×C4D3×#6711yescharacteristic
405C2×C4#381111yescharacteristic
406C8—62no—
407C8—62no—
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—84no—
420C2×C3—82no—
421C2×C3—82no—
422C2×C3#474811yescharacteristic
423C2×C3#474911yescharacteristic
424C2×C3#494811yescharacteristic
425C2×C3#494811yescharacteristic
426C2×C3#516011yescharacteristic
427C2×C3#517711yescharacteristic
428C22—21no—
429C22—21no—
430C22—42no—
431C22—82no—
432C22—82no—
433C22—81no—
434C22—81no—
435C22#6395611yescharacteristic
436C22#6395811yescharacteristic
437C22#6396411yescharacteristic
438C4—241no—
439C4—361no—
440C4—361no—
441C4#6396411yescharacteristic
442C4#6397011yescharacteristic
443C4#6397111yescharacteristic
444C4#6398211yescharacteristic
445C3—21no—
446C3#7007511yescharacteristic, complemented
447C3#7019711yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—82no—
451C2#1059140611yescharacteristic
452C2#1059140711yescharacteristic
453C2#1059169111yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#121
hypercenterC22×D4D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. #10591130C2semidirect
6. #10591119C2semidirect
7. #10589167C2semidirect
385. C32#2063semidirect
446. C3#70075semidirect
447. C3#70197semidirect

Maximal subgroups

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

subgroupindex
#105929142
C2×C3×#8332
C2×C3×#8322
C2×#635772
#105911302
#105911192
#105891672
#701973
#700753