Finite Group Databasebeta

← #11793105

Subgroups — #11793105

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595050C211yesmaximal, characteristic, complemented
2C2×#63664C211yesmaximal, characteristic
3C3×#5240C211yesmaximal, characteristic
4C3×#5236C211yesmaximal, characteristic
5#10589169C211yesmaximal, characteristic, complemented
6#10589160C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#70394—31nomaximal
9#70038—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63982—22no—
18#63919—21no—
19C4×#627—22no—
20#63872—21no—
21#63664—21no—
22#63664—21no—
23C3×#837—22no—
24C3×#834—22no—
25#5517—31no—
26#5517—31no—
27C3×#421—31no—
28C3×#410—31no—
29#5240D311yescharacteristic
30#5236D311yescharacteristic
31C2×#837—31no—
32C2×#837—31no—
33C2×#837—61no—
34#4556—31no—
35#4555—31no—
36#4533—31no—
37#4532—31no—
38#4531—31no—
39#4531—31no—
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C32×#41—21no—
44C2×C32×Q8Q811yescharacteristic, complemented
45C2×C32×D4—21no—
46C2×C32×D4Q811yescharacteristic, complemented
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×#627—22no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3D411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54#3748—21no—
55#3748—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—21no—
58C3×#217—21no—
59C3×#217D412yes—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3D412yes—
66C3×#208—21no—
67C3×#208—21no—
68C2×C3×C3⋊C8—21no—
69#3724—22no—
70Dic3⋊Dic3—22no—
71Dic3⋊Dic3—22no—
72#2031—91noSylow
73C2×C3×#41—21no—
74C2×C3×#41C2×D311yescharacteristic
75C2×C3×#41C2×D311yescharacteristic
76C2×C3×M16—31no—
77C3×#117—31no—
78C3×#117—31no—
79C3×#117—31no—
80#926C2×D311yescharacteristic
81#926C2×D311yescharacteristic
82#926C2×D311yescharacteristic
83C2×C4×Dic3—31no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—61no—
86C2×#208—31no—
87C2×#208—31no—
88C2×#208—61no—
89C2×#208C2×D311yescharacteristic
90#890—61no—
91#890—61no—
92#888—61no—
93#888—61no—
94#878—62no—
95#878—62no—
96C4×Dic6—62no—
97C4×Dic6—62no—
98C3×#104—62no—
99C3×#99—62no—
100#837—22no—
101#837—61no—
102#837—61no—
103#837—61no—
104#837—61no—
105#837—62no—
106#837—62no—
107#834—22no—
108C23×C32—21no—
109C23×C32C2×D411yescharacteristic
110C32×Q8—21no—
111C32×Q8—21no—
112C32×D4—21no—
113C32×D4—21no—
114C32×D4—41no—
115C32×D4—41no—
116C2×C32×C4—21no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—42no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—41no—
131#627—44no—
132C3⋊(C3⋊C8)—41no—
133C3×C3⋊C8—41no—
134#533—91no—
135#421—31no—
136C2×#104—91no—
137#410—31no—
138#344—91no—
139#339—91no—
140H(3,ℤ/4)—91no—
141C3×#41—22no—
142C3×#41—22no—
143C3×#41—21no—
144C3×#41—21no—
145C3×#41—21no—
146C3×#41—21no—
147C3×#41—21no—
148C3×#41—21no—
149C3×#41—21no—
150C3×#41—21no—
151C3×#41—41no—
152C3×#41—41no—
153C2×C3×Q8—21no—
154C2×C3×Q8Dic611yescharacteristic, complemented
155C2×C3×Q8Dic611yescharacteristic, complemented
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—41no—
160C2×C3×D4Dic611yescharacteristic, complemented
161C2×C3×D4Dic611yescharacteristic, complemented
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—41no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—121no—
171C2×Dic6—62no—
172C2×Dic6—62no—
173C3×M16—61no—
174C3×M16—61no—
175C2×C3×C8—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C22⋊C4—32no—
180C3×C22⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C42—32no—
183C3×C42—61no—
184C3×C42—61no—
185#217—21no—
186#217—21no—
187#217#6712yes—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—62no—
192C4⋊Dic3—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—62no—
197C4×Dic3—21no—
198C4×Dic3—21no—
199C4×Dic3—31no—
200C4×Dic3—31no—
201C4×Dic3—31no—
202C4×Dic3—31no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—121no—
208C4×Dic3#6712yes—
209#208—21no—
210#208—21no—
211#208—62no—
212#208—61no—
213#208—61no—
214#208—61no—
215#208—61no—
216#208—121no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—121no—
221C22×C32—41no—
222C22×C32—41no—
223C22×C32—81no—
224C22×C32#12011yescharacteristic
225C22×C32C22⋊Q811yescharacteristic
226C22×C32#12411yescharacteristic
227C32×C4—41no—
228C32×C4C22⋊Q811yescharacteristic
229C32×C4C22⋊Q811yescharacteristic
230C32×C4#12411yescharacteristic
231C32×C4#12411yescharacteristic
232C3⋊Dic3—22no—
233C3⋊Dic3—41no—
234C3×Dic3—42no—
235C3×Dic3—42no—
236C3×Dic3—81no—
237C2×#41D3211yescharacteristic
238C2×M16—31no—
239C2×M16—91no—
240C4⋊Q8—181no—
241#125—181no—
242C22⋊Q8—182no—
243C4×Q8—182no—
244#117—31no—
245#117—31no—
246#117—31no—
247C2×C42—91no—
248#104—62no—
249#104—181no—
250#104—181no—
251#99—62no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—41no—
256C23×C3D3×D411yescharacteristic
257C23×C3C2×#6711yescharacteristic
258C3×Q8—22no—
259C3×Q8—21no—
260C3×Q8—21no—
261C3×Q8—21no—
262C3×Q8—21no—
263C3×Q8—41no—
264C3×D4—22no—
265C3×D4—21no—
266C3×D4—21no—
267C3×D4—21no—
268C3×D4—21no—
269C3×D4—41no—
270C3×D4—42no—
271C3×D4—42no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—121no—
294C2×C3×C4C2×Dic611yescharacteristic
295C2×C3×C4C2×Dic611yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4#23711yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—41no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—124no—
318Dic6—124no—
319Dic6—124no—
320C3×C8—121no—
321C3⋊C8—41no—
322C3⋊C8—122no—
323C3⋊C8—121no—
324C3⋊C8—121no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32—81no—
329C2×C32#39311yescharacteristic
330#41—21no—
331#41—21no—
332#41—21no—
333#41—21no—
334C2×Q8—182no—
335C2×Q8#62711yescharacteristic, complemented
336C2×D4—21no—
337C2×D4#62711yescharacteristic, complemented
338C22×C4—21no—
339C22×C4—181no—
340C22×C4C2×D3211yescharacteristic
341M16—61no—
342M16—61no—
343M16—181no—
344M16—181no—
345C2×C8—61no—
346C2×C8—181no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—182no—
351C4⋊C4—182no—
352C4⋊C4—182no—
353C22⋊C4—32no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C42—32no—
357C42—61no—
358C42—61no—
359C42—91no—
360C42—91no—
361C42—181no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—81no—
372C22×C3—81no—
373C22×C3—82no—
374C22×C3#87811yescharacteristic
375C22×C3#88511yescharacteristic
376C22×C3#92411yescharacteristic
377C22×C3#93611yescharacteristic
378C22×C3#93711yescharacteristic
379C22×C3#93711yescharacteristic
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—42no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—122no—
388C3×C4—122no—
389C3×C4—241no—
390C3×C4#87811yescharacteristic
391C3×C4#87811yescharacteristic
392C3×C4#87811yescharacteristic
393C3×C4#88511yescharacteristic
394C3×C4#88511yescharacteristic
395C3×C4#88511yescharacteristic
396C3×C4#92411yescharacteristic
397C3×C4#93611yescharacteristic
398Dic3—42no—
399Dic3—42no—
400Dic3—62no—
401Dic3—62no—
402Dic3—81no—
403Dic3—122no—
404Dic3—121no—
405Dic3—121no—
406Dic3—122no—
407C32#203111yescharacteristic, complemented, Sylow
408C23—21no—
409C23D3×#6711yescharacteristic
410Q8—21no—
411Q8—21no—
412Q8—364no—
413D4—21no—
414D4—21no—
415D4—41no—
416D4—41no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—121no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—362no—
426C2×C4#380411yescharacteristic
427C2×C4#380411yescharacteristic
428C2×C4#380511yescharacteristic
429C2×C4C2×#62711yescharacteristic
430C2×C4D3×#6711yescharacteristic
431C2×C4#381111yescharacteristic
432C8—121no—
433C8—361no—
434C2×C3—22no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—82no—
445C2×C3—81no—
446C2×C3—81no—
447C2×C3#494711yescharacteristic
448C2×C3#494711yescharacteristic
449C22—41no—
450C22—41no—
451C22—81no—
452C22#6395911yescharacteristic
453C22#6396411yescharacteristic
454C22#6398311yescharacteristic
455C4—41no—
456C4—122no—
457C4—122no—
458C4—182no—
459C4—241no—
460C4—361no—
461C4#6395311yescharacteristic
462C4#6395911yescharacteristic
463C4#6396411yescharacteristic
464C4#6398211yescharacteristic
465C3—21no—
466C3#7003811yescharacteristic, complemented
467C3#7039411yescharacteristic, complemented
468C2—21no—
469C2—21no—
470C2—21no—
471C2—81no—
472C2#1059169211yescharacteristic
subgroupG/H
centerC4#63959
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#393
hypercenterC2×#41D32
hypocenterC32#2031
LCSG ▷ C22×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
1. #10595050C2semidirect
5. #10589169C2semidirect
6. #10589160C2semidirect
7. #10589157C2semidirect
44. C2×C32×Q8Q8semidirect
46. C2×C32×D4Q8semidirect
154. C2×C3×Q8Dic6semidirect
155. C2×C3×Q8Dic6semidirect
160. C2×C3×D4Dic6semidirect
161. C2×C3×D4Dic6semidirect
335. C2×Q8#627semidirect
337. C2×D4#627semidirect
407. C32#2031semidirect
466. C3#70038semidirect
467. C3#70394semidirect

Maximal subgroups

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

subgroupindex
#105950502
C2×#636642
C3×#52402
C3×#52362
#105891692
#105891602
#105891572
#703943
#700383