Finite Group Databasebeta

← #11792768

Subgroups — #11792768

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3756C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic
4C2×C3×#836C211yesmaximal, characteristic, complemented
5C2×#63561C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic
7#10589165C211yesmaximal, characteristic, complemented
8#72109—31nomaximal
9#70125—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×#3756—22no—
14C2×#3756—22no—
15C2×#3756—22no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#216—21no—
18C3×#942—22no—
19C3×#942—22no—
20C2×C3×#215—21no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×#3719—21no—
25#63831—22no—
26#63831—22no—
27C2×#3716—21no—
28C3×#836—22no—
29#63561—22no—
30(C2×D3)⋊(C3⋊C8)—22no—
31C2×C3×#137—31no—
32C2×#951—31no—
33C22×#216—31no—
34C22×#216—31no—
35C22×#216—61no—
36C2×#942D311yescharacteristic
37C2×#909—31no—
38C2×C3×#101—31no—
39#5234—31no—
40C2×#836D311yescharacteristic, complemented
41C2×#824—31no—
42C2×#824—31no—
43#5129—31no—
44#4558—31no—
45#4558—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—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634D412yes—
61C2×C3×#67—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C2×C3×D12D411yescharacteristic
67C2×C3×C4×D3—21no—
68C2×C3×Dic6D411yescharacteristic
69#3756—28no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)D412yes—
73C3×#216—24no—
74C3×#215—24no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208D412yes—
80C3×#208D412yes—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84#3719—24no—
85#3716—24no—
86#2020—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—
101C2×C3×M16—31no—
102#951—62no—
103#951—62no—
104C2×#216—21no—
105C2×#216—61no—
106C2×#216—62no—
107C2×#216—62no—
108C2×#216—62no—
109C2×#216—62no—
110C2×#216—64no—
111C2×#216—64no—
112C2×#216—64no—
113C2×#216—62no—
114C2×#216—62no—
115#942—22no—
116#942—22no—
117C2×#215—21no—
118C2×#214—61no—
119C2×#208C2×D311yescharacteristic
120C2×#208C2×D311yescharacteristic
121C2×#208C2×D311yescharacteristic
122C22×C3⋊C8—31no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—61no—
125#909—62no—
126#909—62no—
127C2×Dic12—61no—
128C2×#204—61no—
129C3×#101—62no—
130#836—22no—
131#830—62no—
132#824—62no—
133#824—62no—
134(C2×D3)⋊C8—62no—
135C23×C32#4111yescharacteristic
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×C4C2×D411yescharacteristic
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—41no—
153#634—22no—
154#634—22no—
155#634—41no—
156#634—41no—
157C3×#67—41no—
158C3×#67—41no—
159C2×C3×Dic3—21no—
160C3×D12—21no—
161C3×D12—21no—
162C3×C4×D3—41no—
163C3×C4×D3—41no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—41no—
170C2×#137—31no—
171C2×#137—91no—
172C22×Q16—91no—
173C2×#101—31no—
174C2×#101—91no—
175#408—91no—
176#341—91no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C3×#41—61no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
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×Q8D1212yes—
199C2×C3×Q8#6712yes—
200C2×C3×D4—31no—
201C2×C3×D4—61no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—41no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C2×#67—21no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—121no—
213#235—21no—
214#235—21no—
215#235—21no—
216#235—21no—
217C2×D12#6711yescharacteristic
218C2×C4×D3—21no—
219C2×Dic6—32no—
220C2×Dic6—32no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—61no—
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—121no—
235C2×Dic6—121no—
236C2×Dic6—121no—
237C2×Dic6#6711yescharacteristic
238C3×Q16—64no—
239C3×SD16—64no—
240C3×M16—32no—
241C3×M16—32no—
242C3×M16—61no—
243C3×M16—61no—
244C3×M16—61no—
245C3×M16—61no—
246C2×C3×C8—61no—
247C2×C3×C8—61no—
248C2×C3×C8—61no—
249#216—24no—
250#216—64no—
251#216—616no—
252#216—68no—
253#216—68no—
254#215—24no—
255#214—64no—
256#208—21no—
257#208—21no—
258#208—21no—
259#208—21no—
260#208#6712yes—
261#208#6712yes—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274Dic12—64no—
275#204—64no—
276C22×C32—22no—
277C22×C32#12111yescharacteristic
278C22×C32#12111yescharacteristic
279C22×C32#12111yescharacteristic
280C2×C3×D3—41no—
281C2×C3×D3—42no—
282C32×C4—42no—
283C32×C4#12011yescharacteristic
284C32×C4#12011yescharacteristic
285C32×C4#12011yescharacteristic
286C32×C4#12711yescharacteristic
287C3⋊Dic3—42no—
288C3×Dic3—41no—
289C2×#41—31no—
290C22×Q8—91no—
291C22×Q8D3211yescharacteristic
292#137—62no—
293#137—62no—
294#137—182no—
295#137—182no—
296C2×Q16—61no—
297C2×Q16—181no—
298C2×Q16—182no—
299C2×Q16—182no—
300C2×Q16—182no—
301C2×SD16—61no—
302C2×SD16—181no—
303C2×M16—31no—
304C2×M16—31no—
305C2×M16—31no—
306C22×C8—91no—
307#101—62no—
308#101—182no—
309C22⋊C8—182no—
310C23×C3—21no—
311C23×C3—61no—
312C23×C3#23511yescharacteristic
313C23×C3#23711yescharacteristic
314C22×D3—21no—
315C3×Q8—24no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—42no—
321C3×Q8—42no—
322C3×Q8—42no—
323C3×Q8—41no—
324C3×Q8—41no—
325C3×Q8—41no—
326C3×Q8—41no—
327C3×Q8—61no—
328C3×Q8—61no—
329C3×D4—61no—
330C3×D4—61no—
331C3×D4—121no—
332C3×D4—121no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—61no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363#67—41no—
364#67—41no—
365C2×Dic3—21no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—122no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375D12—21no—
376D12—21no—
377C4×D3—41no—
378C4×D3—41no—
379Dic6—21no—
380Dic6—21no—
381Dic6—64no—
382Dic6—62no—
383Dic6—62no—
384Dic6—62no—
385Dic6—62no—
386Dic6—122no—
387Dic6—122no—
388Dic6—122no—
389Dic6—121no—
390Dic6—121no—
391Dic6—121no—
392Dic6—121no—
393C3×C8—62no—
394C3×C8—62no—
395C3×C8—121no—
396C3⋊C8—22no—
397C3⋊C8—22no—
398C3⋊C8—41no—
399C3⋊C8—64no—
400C3⋊C8—62no—
401C3⋊C8—62no—
402C2×C32—21no—
403C2×C32—21no—
404C2×C32#39211yescharacteristic
405C2×C32#47312yes—
406C3×D3—81no—
407#41—61no—
408#41—61no—
409#41—61no—
410#41—61no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—31no—
417C2×Q8—92no—
418C2×Q8—181no—
419C2×Q8—181no—
420C2×Q8—181no—
421C2×Q8—181no—
422C2×Q8—181no—
423C2×Q8#62612yes—
424C2×D4—31no—
425C2×D4—61no—
426C22×C4—21no—
427C22×C4—61no—
428C22×C4—181no—
429C22×C4C2×D3211yescharacteristic
430Q16—64no—
431Q16—184no—
432Q16—188no—
433SD16—64no—
434SD16—184no—
435M16—32no—
436M16—32no—
437M16—61no—
438M16—61no—
439M16—61no—
440M16—61no—
441C2×C8—61no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—92no—
445C2×C8—181no—
446C2×C8—181no—
447C22×C3—24no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—121no—
454C22×C3—122no—
455C22×C3#88411yescharacteristic
456C22×C3#88411yescharacteristic
457C22×C3#93011yescharacteristic
458C22×C3#93811yescharacteristic
459C22×C3#93911yescharacteristic
460C22×C3#93911yescharacteristic
461C2×D3—42no—
462C2×D3—41no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—44no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—121no—
471C3×C4#88211yescharacteristic
472C3×C4#88211yescharacteristic
473C3×C4#93711yescharacteristic
474C3×C4#93711yescharacteristic
475C3×C4#93711yescharacteristic
476C3×C4#94011yescharacteristic
477C3×C4#94011yescharacteristic
478C3×C4#95311yescharacteristic
479Dic3—41no—
480Dic3—124no—
481Dic3—122no—
482Dic3—122no—
483C32#202011yescharacteristic, complemented, Sylow
484C23—61no—
485C23#380411yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—41no—
489Q8—41no—
490Q8—61no—
491Q8—61no—
492Q8—182no—
493Q8—182no—
494Q8—361no—
495Q8—361no—
496D4—61no—
497D4—61no—
498D4—121no—
499D4—121no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—61no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—182no—
507C2×C4—361no—
508C2×C4—361no—
509C2×C4C2×#62611yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4D3×#6711yescharacteristic
513C2×C4#381111yescharacteristic
514C2×C4#381111yescharacteristic
515C8—62no—
516C8—62no—
517C8—121no—
518C8—182no—
519C2×C3—22no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—241no—
528C2×C3#475512yes—
529C2×C3#496011yescharacteristic
530C2×C3#520412yes—
531C2×C3#522311yescharacteristic
532D3—81no—
533C22—22no—
534C22—122no—
535C22—121no—
536C22#6395811yescharacteristic
537C22#6397111yescharacteristic
538C22#6397811yescharacteristic
539C4—42no—
540C4—121no—
541C4—362no—
542C4#6397711yescharacteristic
543C4#6397911yescharacteristic
544C4#6398111yescharacteristic
545C4#6398311yescharacteristic
546C3—21no—
547C3#7012511yescharacteristic, complemented
548C3#7210911yescharacteristic, complemented
549C2—21no—
550C2—21no—
551C2—241no—
552C2#1059164412yes—
553C2#1059172411yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#121
prime radicalC2×C3×#235C22
hypercenterC22×Q8D32
hypocenterC32#2020
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. C22×#3756C2semidirect
4. C2×C3×#836C2semidirect
5. C2×#63561C2semidirect
7. #10589165C2semidirect
40. C2×#836D3semidirect
483. C32#2020semidirect
547. C3#70125semidirect
548. C3#72109semidirect

Maximal subgroups

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

subgroupindex
C22×#37562
C2×C3×#9422
C2×#638312
C2×C3×#8362
C2×#635612
#105910712
#105891652
#721093
#701253