Finite Group Databasebeta

← #11792202

Subgroups — #11792202

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3#10594856C211yesmaximal, characteristic
4C3×#5225C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic
6C2×#63561C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#72108—31nomaximal
9#70346—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13#64153—22no—
14#64153—22no—
15C2×#3750—22no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×#216—21no—
18C3×#942—22no—
19C3×#942—22no—
20C2×C3×#215—21no—
21C3×#926C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24#63962—22no—
25#63866—21no—
26#63860—21no—
27#63857—22no—
28C3×#835—22no—
29#63568—22no—
30#63561—22no—
31C2×C3×#137—31no—
32#5825—31no—
33C2×#944—31no—
34C2×#944—31no—
35C2×#944—61no—
36C2×#942D311yescharacteristic
37#5526—31no—
38C3×#419—31no—
39C2×#837—31no—
40#5225D311yescharacteristic, complemented
41C2×#825—31no—
42C2×#824—31no—
43C2×#824—31no—
44#4555—31no—
45#4532—31no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8D412yes—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3D412yes—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634—21no—
62C2×C3×#67—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235—21no—
67C2×C3×D12D411yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6D411yescharacteristic
70#3750—28no—
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3D412yes—
73C3×#217—21no—
74C3×#216—24no—
75C3×#215—24no—
76C3×C4⋊Dic3D412yes—
77C3×C4×Dic3—21no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208—21no—
81C3×#208D412yes—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84Dic3⋊Dic3—24no—
85(C2×D3)⋊Dic3—24no—
86#2005—91noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—21no—
89C22×C3×Q8C2×D311yescharacteristic
90C22×C3×Q8C2×D311yescharacteristic
91C2×#235C2×D311yescharacteristic
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C3×#137—62no—
96C3×#137—62no—
97C2×C3×Q16—61no—
98C2×C3×SD16—61no—
99C2×C3×M16—31no—
100C2×C3×M16—31no—
101C3×#117—31no—
102#944—61no—
103#944—62no—
104#944—62no—
105#944—64no—
106#944—64no—
107#944—62no—
108#944—62no—
109C2×#216—21no—
110#942—22no—
111#942—22no—
112C2×#215—21no—
113#936—61no—
114#935—62no—
115#926C2×D311yescharacteristic
116#924—62no—
117C2×Dic3⋊C4—62no—
118C2×Dic3⋊C4—62no—
119C2×Dic3⋊C4—64no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—61no—
123C2×#208C2×D311yescharacteristic
124C2×#208C2×D311yescharacteristic
125#897—62no—
126#886—62no—
127#875—61no—
128#869—61no—
129C3×#103—62no—
130#837—62no—
131#835—22no—
132#825—62no—
133#824—62no—
134#824—62no—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—21no—
137C32×Q8—22no—
138C32×Q8—22no—
139C32×Q8—41no—
140C32×Q8—41no—
141C2×C32×C4—22no—
142C2×C32×C4—41no—
143C2×C32×C4—41no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4#4111yescharacteristic
150C2×C3⋊Dic3—24no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155#634—41no—
156#634—41no—
157#634—41no—
158#634—41no—
159C3×#67—41no—
160C3×#67—41no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C3×D12—21no—
164C3×D12—21no—
165C3×C4×D3—41no—
166C3×C4×D3—41no—
167C3×Dic6—21no—
168C3×Dic6—21no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—41no—
171C2×#137—31no—
172#536—91no—
173C2×C4⋊Q8—91no—
174C2×#104—91no—
175#419—31no—
176C2×#101—91no—
177#339—91no—
178C3×#41—61no—
179C3×#41—61no—
180C3×#41—61no—
181C3×#41—61no—
182C2×C3×Q8—22no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—22no—
194C2×C3×Q8—31no—
195C2×C3×Q8—41no—
196C2×C3×Q8—41no—
197C2×C3×Q8—41no—
198C2×C3×Q8—41no—
199C2×C3×Q8D1212yes—
200C2×C3×Q8#6712yes—
201C2×C3×D4—31no—
202C2×C3×D4—61no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—21no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—62no—
214C22×Dic3—62no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217#235—21no—
218#235—21no—
219#235—21no—
220#235—21no—
221C2×D12#6711yescharacteristic
222C2×C4×D3—21no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C2×Dic6—61no—
231C2×Dic6—61no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C2×Dic6—61no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—121no—
238C2×Dic6—121no—
239C2×Dic6—121no—
240C2×Dic6—121no—
241C2×Dic6#6711yescharacteristic
242C3×Q16—64no—
243C3×SD16—64no—
244C3×M16—32no—
245C3×M16—61no—
246C3×M16—61no—
247C3×M16—61no—
248C2×C3×C8—61no—
249C2×C3×C8—61no—
250C3×C4⋊C4—32no—
251C3×C22⋊C4—61no—
252C3×C42—61no—
253#217—21no—
254#217—64no—
255#216—24no—
256#215—24no—
257(C2×D3)⋊C4—64no—
258C4⋊Dic3—64no—
259C4⋊Dic3#6712yes—
260Dic3⋊C4—64no—
261Dic3⋊C4—616no—
262Dic3⋊C4—68no—
263Dic3⋊C4—68no—
264C4×Dic3—21no—
265C4×Dic3—32no—
266C4×Dic3—32no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271#208—21no—
272#208—21no—
273#208—21no—
274#208#6712yes—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—21no—
277C22×C32—22no—
278C22×C32#12011yescharacteristic
279C22×C32#12011yescharacteristic
280C22×C32#12111yescharacteristic
281C2×C3×D3—41no—
282C2×C3×D3—42no—
283C32×C4—42no—
284C32×C4#12011yescharacteristic
285C32×C4#12111yescharacteristic
286C32×C4#12111yescharacteristic
287C32×C4#12711yescharacteristic
288C3⋊Dic3—24no—
289C3⋊Dic3—42no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C2×#41—31no—
293C22×Q8—91no—
294C22×Q8D3211yescharacteristic
295#137—62no—
296#137—62no—
297C2×Q16—61no—
298C2×SD16—61no—
299C2×M16—31no—
300C2×M16—31no—
301C4⋊Q8—181no—
302C4⋊Q8—182no—
303C4⋊Q8—182no—
304#124—181no—
305#123—182no—
306C22⋊Q8—182no—
307#117—31no—
308C2×C4⋊C4—182no—
309C2×C42—91no—
310#104—182no—
311#103—62no—
312#101—182no—
313C23×C3—21no—
314C23×C3—61no—
315C23×C3D3×D411yescharacteristic
316C23×C3D3×D411yescharacteristic
317C22×D3—21no—
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—42no—
323C3×Q8—42no—
324C3×Q8—42no—
325C3×Q8—42no—
326C3×Q8—41no—
327C3×Q8—41no—
328C3×Q8—41no—
329C3×Q8—41no—
330C3×Q8—61no—
331C3×Q8—61no—
332C3×D4—61no—
333C3×D4—61no—
334C3×D4—121no—
335C3×D4—121no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4#23511yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367#67—41no—
368#67—41no—
369C2×Dic3—22no—
370C2×Dic3—21no—
371C2×Dic3—64no—
372C2×Dic3—68no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—64no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—122no—
385C2×Dic3—122no—
386D12—21no—
387D12—21no—
388C4×D3—41no—
389C4×D3—41no—
390Dic6—21no—
391Dic6—21no—
392Dic6—122no—
393Dic6—122no—
394Dic6—122no—
395Dic6—122no—
396Dic6—121no—
397Dic6—121no—
398Dic6—121no—
399Dic6—121no—
400Dic6—121no—
401Dic6—121no—
402Dic6—121no—
403Dic6—121no—
404C3×C8—62no—
405C3×C8—121no—
406C3⋊C8—22no—
407C3⋊C8—41no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32#39211yescharacteristic
411C2×C32#45612yes—
412C3×D3—81no—
413#41—61no—
414#41—61no—
415#41—61no—
416#41—61no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—31no—
423C2×Q8—181no—
424C2×Q8—181no—
425C2×Q8—181no—
426C2×Q8—181no—
427C2×Q8—181no—
428C2×Q8—181no—
429C2×Q8#62612yes—
430C2×D4—31no—
431C2×D4—61no—
432C22×C4—21no—
433C22×C4—61no—
434C22×C4—92no—
435C22×C4—181no—
436C22×C4C2×D3211yescharacteristic
437Q16—64no—
438SD16—64no—
439M16—32no—
440M16—61no—
441M16—61no—
442M16—61no—
443C2×C8—61no—
444C2×C8—61no—
445C4⋊C4—32no—
446C4⋊C4—188no—
447C4⋊C4—184no—
448C22⋊C4—61no—
449C22⋊C4—184no—
450C42—61no—
451C42—92no—
452C42—181no—
453C22×C3—24no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—122no—
460C22×C3—121no—
461C22×C3#88211yescharacteristic
462C22×C3#88411yescharacteristic
463C22×C3#93711yescharacteristic
464C22×C3#93711yescharacteristic
465C22×C3#93711yescharacteristic
466C22×C3#93811yescharacteristic
467C2×D3—42no—
468C2×D3—41no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—44no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—122no—
477C3×C4—121no—
478C3×C4#88211yescharacteristic
479C3×C4#88411yescharacteristic
480C3×C4#93011yescharacteristic
481C3×C4#93911yescharacteristic
482C3×C4#93911yescharacteristic
483C3×C4#94011yescharacteristic
484C3×C4#94011yescharacteristic
485C3×C4#95311yescharacteristic
486Dic3—42no—
487Dic3—41no—
488Dic3—68no—
489Dic3—64no—
490Dic3—64no—
491Dic3—124no—
492Dic3—122no—
493Dic3—122no—
494C32#200511yescharacteristic, complemented, Sylow
495C23—61no—
496C23#381111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501Q8—61no—
502Q8—61no—
503Q8—361no—
504Q8—361no—
505Q8—361no—
506Q8—361no—
507D4—61no—
508D4—61no—
509D4—121no—
510D4—121no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—62no—
515C2×C4—61no—
516C2×C4—121no—
517C2×C4—121no—
518C2×C4—184no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4#380411yescharacteristic
524C2×C4C2×#62611yescharacteristic
525C2×C4D3×#6711yescharacteristic
526C2×C4D3×#6711yescharacteristic
527C2×C4D3×#6711yescharacteristic
528C2×C4#381111yescharacteristic
529C8—62no—
530C8—121no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—21no—
539C2×C3—241no—
540C2×C3#496011yescharacteristic
541C2×C3#520512yes—
542C2×C3#520512yes—
543C2×C3#522311yescharacteristic
544D3—81no—
545C22—22no—
546C22—122no—
547C22—121no—
548C22#6395811yescharacteristic
549C22#6398111yescharacteristic
550C22#6398311yescharacteristic
551C4—42no—
552C4—122no—
553C4—121no—
554C4—184no—
555C4—362no—
556C4#6397111yescharacteristic
557C4#6397711yescharacteristic
558C4#6397811yescharacteristic
559C4#6397911yescharacteristic
560C3—21no—
561C3#7034611yescharacteristic, complemented
562C3#7210811yescharacteristic, complemented
563C2—21no—
564C2—21no—
565C2—241no—
566C2#1059166012yes—
567C2#1059172411yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC22×Q8D32
hypocenterC32#2005
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64153C2semidirect
4. C3×#5225C2semidirect
6. C2×#63561C2semidirect
7. #10589160C2semidirect
40. #5225D3semidirect
494. C32#2005semidirect
561. C3#70346semidirect
562. C3#72108semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9422
#105948562
C3×#52252
C2×#635682
C2×#635612
#105891602
#721083
#703463