Finite Group Databasebeta

← #11792217

Subgroups — #11792217

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63866C211yesmaximal, characteristic, complemented
2#10594856C211yesmaximal, characteristic
3C2×#63827C211yesmaximal, characteristic
4C2×#63651C211yesmaximal, characteristic, complemented
5C2×C3×#825C211yesmaximal, characteristic
6C3×#5120C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70389—31nomaximal
9#70346—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×Dic3⋊Dic3—22no—
18#63962—22no—
19#63866—21no—
20#63866—22no—
21#63866—22no—
22#63860—21no—
23#63857—22no—
24C2×#3718—21no—
25#63827—22no—
26#63827—22no—
27C2×#3715—21no—
28#63651—22no—
29C3×#825—22no—
30C3×#816—22no—
31#5825—31no—
32C2×#951—31no—
33C2×#944—31no—
34C2×#942—31no—
35#5526—31no—
36C2×#869—31no—
37C2×C3×#104—31no—
38C3×#419—31no—
39C2×#825D311yescharacteristic
40C2×#824—31no—
41C2×#824—31no—
42C2×#824—61no—
43#5120D311yescharacteristic, complemented
44#4532—31no—
45#4523—31no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D412yes—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×C3×#67—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6D412yes—
69C2×C3×Dic6D411yescharacteristic
70C32×M16—21no—
71C32×M16—21no—
72C2×C32×C8—21no—
73#3748—21no—
74#3748D412yes—
75C2×C3⋊(C3⋊C8)—21no—
76C3×#217—21no—
77C3×C4⋊Dic3D412yes—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3D412yes—
81Dic3⋊Dic3—24no—
82Dic3⋊Dic3—28no—
83(C2×D3)⋊Dic3—24no—
84#3718—24no—
85#3715—24no—
86#2005—91noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—31no—
89C2×#235C2×D311yescharacteristic
90C22×Dic6—31no—
91C22×Dic6—31no—
92C22×Dic6—61no—
93C22×Dic6C2×D311yescharacteristic
94C2×C3×M16—21no—
95C2×C3×M16C2×D311yescharacteristic
96C2×C3×M16C2×D311yescharacteristic
97C3×#117—31no—
98C2×C3×C42—31no—
99#951—62no—
100#951—62no—
101#944—62no—
102#944—61no—
103#944—62no—
104C2×#216—61no—
105C2×#216—61no—
106#942—62no—
107#942—62no—
108C2×#215—61no—
109#936—61no—
110#935—62no—
111C2×#214—61no—
112#926C2×D311yescharacteristic
113C2×C4⋊Dic3—62no—
114#924—62no—
115C2×Dic3⋊C4—62no—
116C2×C4×Dic3C2×D311yescharacteristic
117C2×#208—31no—
118C2×#208—31no—
119C2×#208—61no—
120#897—62no—
121#886—62no—
122#875—61no—
123#869—62no—
124#869—62no—
125#869—61no—
126C3×#104—62no—
127C3×#103—62no—
128#825—22no—
129#824—62no—
130#824—62no—
131#824—64no—
132#816—22no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144#634—41no—
145#634—41no—
146#634—41no—
147#634—41no—
148C3×#67—41no—
149C3×#67—41no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—22no—
164C3×Dic6—21no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C32×C8—41no—
168C3⋊(C3⋊C8)—22no—
169C2×#137—91no—
170#536—91no—
171C2×C4⋊Q8—91no—
172C2×#104—31no—
173#419—31no—
174C2×#101—91no—
175#339—91no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—32no—
181C2×C3×Q8—31no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×D4—31no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—21no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—62no—
201#235—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205C2×D12D1211yescharacteristic
206C2×C4×D3—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—121no—
227C2×Dic6—121no—
228C2×Dic6—121no—
229C2×Dic6—121no—
230C2×Dic6D1211yescharacteristic
231C2×Dic6D1212yes—
232C3×M16—22no—
233C3×M16—21no—
234C3×M16—21no—
235C3×M16—21no—
236C3×M16—21no—
237C3×M16—41no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—41no—
241C3×C4⋊C4—32no—
242C3×C22⋊C4—61no—
243C3×C42—32no—
244C3×C42—61no—
245C3×C42—61no—
246#217—21no—
247#217—64no—
248#216—64no—
249#216—64no—
250#215—64no—
251#214—64no—
252(C2×D3)⋊C4—64no—
253C4⋊Dic3—68no—
254C4⋊Dic3—64no—
255C4⋊Dic3#6712yes—
256Dic3⋊C4—68no—
257Dic3⋊C4—64no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260C4×Dic3#6712yes—
261#208—32no—
262#208—32no—
263#208—62no—
264#208—61no—
265#208—61no—
266#208—121no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—121no—
270C22×C32—22no—
271C22×C32#12011yescharacteristic
272C22×C32#12011yescharacteristic
273C22×C32#12111yescharacteristic
274C2×C3×D3—41no—
275C2×C3×D3—42no—
276C32×C4#12011yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12711yescharacteristic
280C3⋊Dic3—42no—
281C3×Dic3—24no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C3×Dic3—42no—
285C2×#41—31no—
286C22×Q8—31no—
287C22×Q8—91no—
288#137—182no—
289#137—182no—
290C2×Q16—181no—
291C2×SD16—181no—
292C2×M16—91no—
293C2×M16D3211yescharacteristic
294C4⋊Q8—182no—
295C4⋊Q8—182no—
296C4⋊Q8—181no—
297#124—181no—
298#123—182no—
299C22⋊Q8—182no—
300#117—31no—
301C2×C4⋊C4—182no—
302C2×C42—31no—
303#104—62no—
304#103—62no—
305#101—182no—
306C23×C3—21no—
307C23×C3—61no—
308C23×C3D3×D411yescharacteristic
309C23×C3D3×D411yescharacteristic
310C22×D3—21no—
311C3×Q8—62no—
312C3×Q8—61no—
313C3×Q8—62no—
314C3×Q8—61no—
315C3×Q8—121no—
316C3×Q8—121no—
317C3×D4—61no—
318C3×D4—61no—
319C3×D4—121no—
320C3×D4—121no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—64no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—62no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348#67—41no—
349#67—41no—
350C2×Dic3—24no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—21no—
354C2×Dic3—22no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—64no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366D12—21no—
367D12—21no—
368C4×D3—41no—
369C4×D3—41no—
370Dic6—22no—
371Dic6—21no—
372Dic6—22no—
373Dic6—21no—
374Dic6—41no—
375Dic6—41no—
376Dic6—122no—
377Dic6—122no—
378Dic6—122no—
379Dic6—122no—
380Dic6—121no—
381Dic6—121no—
382Dic6—121no—
383Dic6—121no—
384Dic6—121no—
385Dic6—121no—
386Dic6—121no—
387Dic6—121no—
388C3×C8—42no—
389C3×C8—41no—
390C3×C8—41no—
391C3⋊C8—62no—
392C3⋊C8—62no—
393C3⋊C8—122no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32#39211yescharacteristic
397C2×C32#45612yes—
398C3×D3—81no—
399#41—61no—
400#41—61no—
401#41—61no—
402#41—61no—
403C2×Q8—31no—
404C2×Q8—32no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—181no—
411C2×Q8—181no—
412C2×Q8—181no—
413C2×Q8—181no—
414C2×Q8—181no—
415C2×Q8—181no—
416C2×D4—31no—
417C2×D4—61no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—92no—
422C22×C4C2×D3211yescharacteristic
423Q16—184no—
424SD16—184no—
425M16—21no—
426M16—21no—
427M16—92no—
428M16—181no—
429C2×C8—21no—
430C2×C8—181no—
431C4⋊C4—32no—
432C4⋊C4—188no—
433C4⋊C4—184no—
434C22⋊C4—61no—
435C22⋊C4—184no—
436C42—32no—
437C42—61no—
438C42—61no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—42no—
445C22×C3—122no—
446C22×C3—121no—
447C22×C3#88211yescharacteristic
448C22×C3#88211yescharacteristic
449C22×C3#88411yescharacteristic
450C22×C3#88411yescharacteristic
451C22×C3#93711yescharacteristic
452C22×C3#93711yescharacteristic
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—64no—
460C3×C4—121no—
461C3×C4—122no—
462C3×C4—122no—
463C3×C4#88211yescharacteristic
464C3×C4#88211yescharacteristic
465C3×C4#88411yescharacteristic
466C3×C4#88411yescharacteristic
467C3×C4#93011yescharacteristic
468C3×C4#93011yescharacteristic
469C3×C4#94011yescharacteristic
470C3×C4#94011yescharacteristic
471Dic3—24no—
472Dic3—42no—
473Dic3—42no—
474Dic3—41no—
475Dic3—124no—
476Dic3—122no—
477Dic3—122no—
478C32#200511yescharacteristic, complemented, Sylow
479C23—61no—
480C23#380211yescharacteristic
481Q8—62no—
482Q8—61no—
483Q8—62no—
484Q8—61no—
485Q8—121no—
486Q8—121no—
487Q8—361no—
488Q8—361no—
489Q8—361no—
490Q8—361no—
491D4—61no—
492D4—61no—
493D4—121no—
494D4—121no—
495C2×C4—64no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4#379811yescharacteristic
508C2×C4D3×D1211yescharacteristic
509C2×C4D3×D1211yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4#381111yescharacteristic
513C8—41no—
514C8—182no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—22no—
520C2×C3—21no—
521C2×C3—41no—
522C2×C3—41no—
523C2×C3—241no—
524C2×C3#482612yes—
525C2×C3#496011yescharacteristic
526C2×C3#496011yescharacteristic
527C2×C3#520512yes—
528D3—81no—
529C22—22no—
530C22—122no—
531C22—121no—
532C22#6391211yescharacteristic
533C22#6392211yescharacteristic
534C22#6392211yescharacteristic
535C4—64no—
536C4—122no—
537C4—121no—
538C4—122no—
539C4—362no—
540C4#6390611yescharacteristic
541C4#6390611yescharacteristic
542C4#6392311yescharacteristic
543C4#6397911yescharacteristic
544C3—21no—
545C3#7034611yescharacteristic, complemented
546C3#7038911yescharacteristic, complemented
547C2—21no—
548C2—21no—
549C2—241no—
550C2#1059101712yes—
551C2#1059139311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC2×M16D32
hypocenterC32#2005
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#63866C2semidirect
4. C2×#63651C2semidirect
6. C3×#5120C2semidirect
7. #10589161C2semidirect
43. #5120D3semidirect
478. C32#2005semidirect
545. C3#70346semidirect
546. C3#70389semidirect

Maximal subgroups

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

subgroupindex
C2×#638662
#105948562
C2×#638272
C2×#636512
C2×C3×#8252
C3×#51202
#105891612
#703893
#703463