Finite Group Databasebeta

← #11785906

Subgroups — #11785906

Order 1152.

697 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595510C211yesmaximal, characteristic
2C2×#63633C211yesmaximal, characteristic
3C2×#63581C211yesmaximal, characteristic
4C3×#4527C211yesmaximal, characteristic, complemented
5C3×#4526C211yesmaximal, characteristic, complemented
6#10589187C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#68960—31nomaximal
9#68960—31nomaximal
10C22×#638C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17#63974C412yescomplemented
18#63957C412yescomplemented
19#63952—22no—
20#63952—22no—
21#63633—22no—
22#63581—22no—
23#5486—31no—
24#5486—31no—
25C2×#806—31no—
26C2×#806—31no—
27C2×#806—31no—
28C2×#806—31no—
29C2×#806—61no—
30C3×#342—31no—
31C3×#342—31no—
32#4527—31no—
33#4527—31no—
34#4527—31no—
35#4527D311yescharacteristic, complemented
36#4526—31no—
37#4526D311yescharacteristic, complemented
38C24×C32C2311yescharacteristic
39C23×C3⋊D3C2×C411yescharacteristic
40C22×C32×C4—21no—
41C2×#638—21no—
42C2×#638—21no—
43C2×#638—21no—
44C2×#638—21no—
45C2×#638D412yes—
46C2×#638D412yes—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3C2×C411yescharacteristic
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×#624—22no—
54C32×C22⋊C4—21no—
55C32×C22⋊C4—21no—
56#3757—21no—
57#3757—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#217C2×C412yes—
65C3×#217C2×C412yes—
66#3724—22no—
67#3722—22no—
68Dic32—22no—
69#1828—91noSylow
70C22×#67—31no—
71C22×#67—31no—
72C22×#67—61no—
73C2×C3×C22⋊C4—21no—
74C2×C3×C22⋊C4—31no—
75C2×C3×C22⋊C4—31no—
76C2×C3×C22⋊C4—31no—
77C2×C3×C22⋊C4—31no—
78C2×C3×C22⋊C4C2×D311yescharacteristic
79C2×C3×C22⋊C4C2×D311yescharacteristic
80C2×#217—31no—
81C2×#217—31no—
82C2×#217—61no—
83C2×#217C2×D311yescharacteristic
84C2×#217C2×D311yescharacteristic
85C2×#217C2×D311yescharacteristic
86C2×#217C2×D311yescharacteristic
87C4×#67—62no—
88C4×#67—62no—
89#67⋊C4—62no—
90#67⋊C4—62no—
91D3×C22⋊C4—32no—
92D3×C22⋊C4—32no—
93#877—32no—
94#877—32no—
95#806—62no—
96#806—62no—
97#806—62no—
98#806—62no—
99#806—64no—
100C23×C32—81no—
101C23×C32C22×C411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C23×C32#4111yescharacteristic
105C23×C32#4111yescharacteristic
106C23×C32#4111yescharacteristic
107C23×C32#4111yescharacteristic
108C22×C3⋊D3—21no—
109C22×C3⋊D3—21no—
110C22×C3⋊D3—81no—
111C22×C3⋊D3C22⋊C412yes—
112C2×C32×C4—41no—
113C2×C32×C4—81no—
114#638—22no—
115#638—22no—
116#638—22no—
117#638—22no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—81no—
122C2×C3⋊Dic3C22⋊C412yes—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—81no—
128C2×C3×Dic3—81no—
129C2×C3×Dic3—81no—
130C2×C3×Dic3—81no—
131#624—82no—
132#518—91no—
133C2×#99—91no—
134C2×#99—91no—
135#342—31no—
136#342—31no—
137#342—91no—
138#342—91no—
139C24×C3—21no—
140C24×C3C22×D311yescharacteristic
141C24×C3C22×D311yescharacteristic
142C23×D3—31no—
143C23×D3—31no—
144C23×D3—61no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—41no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C2×#67—32no—
153C2×#67—32no—
154C2×#67—32no—
155C2×#67—32no—
156C2×#67—62no—
157C2×#67—62no—
158C2×#67—61no—
159C2×#67—61no—
160C2×#67—61no—
161C2×#67—61no—
162C2×#67—61no—
163C2×#67—61no—
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—121no—
167C2×#67—121no—
168C2×#67—121no—
169C2×#67—121no—
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—121no—
180C2×C4×D3—62no—
181C2×C4×D3—62no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—32no—
188C3×C22⋊C4—32no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196#217—21no—
197#217—21no—
198#217—21no—
199#217—21no—
200#217—21no—
201#217—21no—
202#217—62no—
203#217—61no—
204#217—61no—
205#217—61no—
206#217—61no—
207#217—121no—
208#217C4×D312yes—
209#217C4×D312yes—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—62no—
214C4×Dic3—62no—
215C4×Dic3—62no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32—41no—
223C22×C32C2×C22⋊C411yescharacteristic
224C22×C32#11711yescharacteristic
225C22×C32#11711yescharacteristic
226C22×C32#12311yescharacteristic
227C22×C32#12311yescharacteristic
228C22×C32#12311yescharacteristic
229C22×C32#12311yescharacteristic
230C2×C3⋊D3—22no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—81no—
233C2×C3⋊D3—81no—
234C32×C4—81no—
235C3⋊Dic3—22no—
236C3⋊Dic3—81no—
237C3×Dic3—42no—
238C3×Dic3—42no—
239C3×Dic3—81no—
240C3×Dic3—81no—
241C22×D4—91no—
242C4×D4—182no—
243C4×D4—182no—
244#117—92no—
245C2×C22⋊C4—31no—
246C2×C22⋊C4—31no—
247C2×C22⋊C4—31no—
248C2×C22⋊C4—31no—
249C2×C22⋊C4—92no—
250C2×C22⋊C4—91no—
251C2×C22⋊C4D3211yescharacteristic
252#99—182no—
253#99—182no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—81no—
262C23×C3—81no—
263C23×C3—82no—
264C23×C3C2×C4×D311yescharacteristic
265C23×C3C2×C4×D311yescharacteristic
266C23×C3#23511yescharacteristic
267C23×C3#23511yescharacteristic
268C23×C3#23511yescharacteristic
269C23×C3#23511yescharacteristic
270C23×C3D3×D411yescharacteristic
271C23×C3D3×D411yescharacteristic
272C23×C3D3×D411yescharacteristic
273C23×C3D3×D411yescharacteristic
274C23×C3#23711yescharacteristic
275C23×C3#23711yescharacteristic
276C23×C3#23911yescharacteristic
277C23×C3#23911yescharacteristic
278C22×D3—32no—
279C22×D3—32no—
280C22×D3—62no—
281C22×D3—61no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—121no—
286C22×D3—121no—
287C22×D3—241no—
288C22×D3—241no—
289C22×D3—242no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—82no—
296C2×C3×C4—81no—
297C2×C3×C4—81no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—241no—
301C2×C3×C4—241no—
302C2×C3×C4—241no—
303C2×C3×C4—241no—
304#67—62no—
305#67—62no—
306#67—62no—
307#67—62no—
308#67—62no—
309#67—62no—
310#67—62no—
311#67—62no—
312#67—122no—
313#67—122no—
314#67—122no—
315#67—122no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—32no—
319C2×Dic3—32no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—62no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—81no—
328C2×Dic3—81no—
329C2×Dic3—81no—
330C2×Dic3—81no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—122no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—242no—
337C2×Dic3—241no—
338C2×Dic3—241no—
339C4×D3—242no—
340C4×D3—242no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32#38111yescharacteristic
349C3⋊D3—42no—
350C24—91no—
351C24C2×D3211yescharacteristic
352C2×D4—92no—
353C2×D4—92no—
354C2×D4—181no—
355C2×D4—181no—
356C2×D4—181no—
357C2×D4—181no—
358C22×C4—21no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—91no—
364C22×C4—182no—
365C22×C4—181no—
366C4⋊C4—182no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—32no—
370C22⋊C4—32no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—182no—
378C22⋊C4—181no—
379C22⋊C4—181no—
380C42—182no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3—81no—
408C22×C3—81no—
409C22×C3#87211yescharacteristic
410C22×C3#87211yescharacteristic
411C22×C3D3×C22⋊C411yescharacteristic
412C22×C3D3×C22⋊C411yescharacteristic
413C22×C3#88311yescharacteristic
414C22×C3#88311yescharacteristic
415C22×C3#88311yescharacteristic
416C22×C3#88311yescharacteristic
417C22×C3#89211yescharacteristic
418C22×C3#89211yescharacteristic
419C22×C3#89411yescharacteristic
420C22×C3#89411yescharacteristic
421C22×C3#89411yescharacteristic
422C22×C3#89411yescharacteristic
423C2×D3—62no—
424C2×D3—62no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—242no—
429C2×D3—241no—
430C2×D3—241no—
431C2×D3—241no—
432C2×D3—241no—
433C2×D3—242no—
434C2×D3—242no—
435C3×C4—81no—
436C3×C4—81no—
437C3×C4—82no—
438C3×C4—122no—
439C3×C4—122no—
440C3×C4—241no—
441C3×C4—241no—
442Dic3—42no—
443Dic3—42no—
444Dic3—62no—
445Dic3—62no—
446Dic3—81no—
447Dic3—81no—
448Dic3—122no—
449Dic3—241no—
450Dic3—241no—
451Dic3—242no—
452C32#182811yescharacteristic, complemented, Sylow
453C23—81no—
454C23—92no—
455C23—181no—
456C23—181no—
457C23—721no—
458C23#379911yescharacteristic
459C23#379911yescharacteristic
460C23C4×D3211yescharacteristic
461C23#380211yescharacteristic
462C23#380411yescharacteristic
463C23#380411yescharacteristic
464C23#381111yescharacteristic
465D4—182no—
466D4—182no—
467D4—182no—
468D4—182no—
469C2×C4—41no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—81no—
473C2×C4—92no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—241no—
479C2×C4—241no—
480C2×C4—241no—
481C2×C4—241no—
482C2×C4—361no—
483C2×C4—722no—
484C2×C4—721no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—41no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—41no—
506C2×C3—41no—
507C2×C3#466411yescharacteristic
508C2×C3#466411yescharacteristic
509D3—122no—
510D3—122no—
511D3—242no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—182no—
520C22—362no—
521C22—721no—
522C22—721no—
523C22#6383611yescharacteristic
524C22#6383611yescharacteristic
525C22#6385411yescharacteristic
526C22#6385411yescharacteristic
527C22#6389711yescharacteristic
528C22#6392111yescharacteristic
529C22#6397511yescharacteristic
530C4—81no—
531C4—122no—
532C4—122no—
533C4—182no—
534C4—241no—
535C4—241no—
536C4—721no—
537C3—21no—
538C3#6896011yescharacteristic, complemented
539C3#6896011yescharacteristic, complemented
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—362no—
548C2#1059137111yescharacteristic
subgroupG/H
centerC2#10591371
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC2×C32#381
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1828
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4527C2semidirect
5. C3×#4526C2semidirect
6. #10589187C2semidirect
7. #10589186C2semidirect
17. #63974C4semidirect
18. #63957C4semidirect
35. #4527D3semidirect
37. #4526D3semidirect
452. C32#1828semidirect
538. C3#68960semidirect
539. C3#68960semidirect

Maximal subgroups

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

subgroupindex
#105955102
C2×#636332
C2×#635812
C3×#45272
C3×#45262
#105891872
#105891862
#689603