Finite Group Databasebeta

← #11792201

Subgroups — #11792201

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic
2C2×C3×#944C211yesmaximal, characteristic, complemented
3#10594866C211yesmaximal, characteristic
4C3×#5225C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6C2×#63560C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71795—31nomaximal
9#70346—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3756—21no—
14#64151—22no—
15#64151—22no—
16C2×#3755—21no—
17C2×#3748C2211yescharacteristic
18C3×#944—22no—
19C3×#944—22no—
20C3×#926C2211yescharacteristic
21C2×C3×Dic3⋊C4—22no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24#63966—22no—
25#63871—22no—
26#63866—21no—
27#63864—21no—
28C3×#835—22no—
29#63570—22no—
30#63560—22no—
31C2×C3×C4⋊Q8—31no—
32#5816—31no—
33C2×#944D311yescharacteristic, complemented
34C2×#942—31no—
35C2×#942—31no—
36C2×#942—61no—
37#5526—31no—
38C3×#419—31no—
39C2×#836—31no—
40#5225D311yescharacteristic, complemented
41C2×#825—31no—
42C2×#824—31no—
43C2×#805—31no—
44#4532—31no—
45#4523—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
54C2×#638—21no—
55#3828—21no—
56#3828—21no—
57#3828—21no—
58#3828—21no—
59C2×C4⋊(C3⋊D3)D411yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×#634D411yescharacteristic
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70#3756—24no—
71#3755—24no—
72#3748—21no—
73#3748D412yes—
74C2×C3⋊(C3⋊C8)—21no—
75C3×#217—21no—
76C3×C4⋊Dic3D412yes—
77C3×Dic3⋊C4—28no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3D412yes—
81C3×#208—21no—
82C3×#208—21no—
83C2×C3×C3⋊C8—21no—
84Dic3⋊Dic3—24no—
85#3722—24no—
86#2005—91noSylow
87C22×C3×Q8—21no—
88C22×C3×Q8—31no—
89C22×C3×Q8C2×D311yescharacteristic
90C22×C3×Q8C2×D311yescharacteristic
91C2×#235—31no—
92C2×#235—31no—
93C2×#235—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×M16—31no—
96C3×C4⋊Q8—62no—
97C3×C4⋊Q8—62no—
98C3×#117—31no—
99C2×C3×C4⋊C4—62no—
100C2×C3×C42—31no—
101#947—61no—
102#946—62no—
103#944—22no—
104#944—22no—
105#944—61no—
106C2×#216—61no—
107C2×#216—61no—
108C2×#216—62no—
109#942—62no—
110#942—62no—
111#942—64no—
112#942—64no—
113#942—62no—
114#942—62no—
115C2×#215—61no—
116C2×#215—61no—
117C2×#215—62no—
118#929—62no—
119#926C2×D311yescharacteristic
120C2×Dic3⋊C4—22no—
121C2×C4×Dic3C2×D311yescharacteristic
122C2×#208—31no—
123C2×#208—31no—
124C2×#208—61no—
125C2×#208C2×D311yescharacteristic
126#897—62no—
127#886—62no—
128#875—61no—
129#869—61no—
130C3×#103—62no—
131#836—62no—
132#835—22no—
133#825—62no—
134#824—62no—
135#805—62no—
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—21no—
138C32×Q8—22no—
139C32×Q8—22no—
140C32×Q8—41no—
141C32×Q8—41no—
142C2×C32×C4—22no—
143C2×C32×C4—41no—
144C2×C32×C4—41no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151#638—41no—
152#638—41no—
153C2×C3⋊Dic3—21no—
154C4⋊(C3⋊D3)—21no—
155C4⋊(C3⋊D3)—21no—
156C4×C3⋊D3—41no—
157C4×C3⋊D3—41no—
158#634—21no—
159#634—21no—
160C2×C3×Dic3—24no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C3×Dic6—41no—
167C3×Dic6—41no—
168C3×Dic6—41no—
169C3×Dic6—41no—
170C3⋊(C3⋊C8)—22no—
171C3×C3⋊C8—41no—
172C2×#137—91no—
173#536—91no—
174C2×C4⋊Q8—31no—
175C2×#104—91no—
176#419—31no—
177C2×#101—91no—
178#339—91no—
179C2×C3×Q8—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—22no—
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—22no—
192C2×C3×Q8—41no—
193C2×C3×Q8—41no—
194C2×C3×Q8—41no—
195C2×C3×Q8—61no—
196C2×C3×Q8—61no—
197C2×C3×Q8—61no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8D1212yes—
202C2×C3×Q8#6712yes—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—32no—
207C22×C3×C4—41no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—61no—
212C2×#67—61no—
213C2×#67—121no—
214C22×Dic3—21no—
215C22×Dic3#6712yes—
216#235—62no—
217#235—62no—
218#235—61no—
219#235—61no—
220#235—61no—
221#235—61no—
222#235—61no—
223#235—61no—
224#235—61no—
225#235—61no—
226#235—121no—
227#235—121no—
228C2×D12—31no—
229C2×D12—31no—
230C2×D12—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—121no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6—21no—
237C2×Dic6—21no—
238C2×Dic6—21no—
239C2×Dic6—21no—
240C2×Dic6—31no—
241C2×Dic6—31no—
242C2×Dic6—61no—
243C3×M16—61no—
244C3×M16—61no—
245C2×C3×C8—61no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—68no—
248C3×C22⋊C4—61no—
249C3×C42—32no—
250C3×C42—61no—
251C3×C42—61no—
252#217—21no—
253#216—68no—
254#216—64no—
255#216—64no—
256#215—68no—
257#215—64no—
258#215—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261C4⋊Dic3—64no—
262C4⋊Dic3#6712yes—
263Dic3⋊C4—28no—
264Dic3⋊C4—64no—
265C4×Dic3—21no—
266C4×Dic3—21no—
267C4×Dic3#6712yes—
268#208—21no—
269#208—21no—
270#208—32no—
271#208—32no—
272#208—62no—
273#208—62no—
274#208—61no—
275#208—61no—
276C2×C3⋊C8—21no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—61no—
280C22×C32—22no—
281C22×C32#12011yescharacteristic
282C22×C32#12011yescharacteristic
283C22×C32#12111yescharacteristic
284C2×C3⋊D3—41no—
285C2×C3⋊D3—42no—
286C32×C4—42no—
287C32×C4#12011yescharacteristic
288C32×C4#12111yescharacteristic
289C32×C4#12111yescharacteristic
290C32×C4#12711yescharacteristic
291C3⋊Dic3—41no—
292C3×Dic3—24no—
293C3×Dic3—42no—
294C3×Dic3—42no—
295C2×#41—91no—
296C22×Q8—31no—
297C22×Q8D3211yescharacteristic
298#137—182no—
299#137—182no—
300C2×Q16—181no—
301C2×SD16—181no—
302C2×M16—31no—
303C2×M16—91no—
304C4⋊Q8—62no—
305C4⋊Q8—62no—
306C4⋊Q8—181no—
307#124—181no—
308#123—182no—
309C22⋊Q8—182no—
310#117—31no—
311C2×C4⋊C4—62no—
312C2×C42—31no—
313#104—182no—
314#103—62no—
315#101—182no—
316C23×C3—21no—
317C23×C3D3×D411yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—121no—
322C3×Q8—24no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—22no—
327C3×Q8—42no—
328C3×Q8—42no—
329C3×Q8—42no—
330C3×Q8—41no—
331C3×Q8—41no—
332C3×Q8—41no—
333C3×Q8—41no—
334C3×Q8—121no—
335C3×Q8—121no—
336C3×Q8—121no—
337C3×Q8—121no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—64no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4C2×D1211yescharacteristic
360C2×C3×C4#23511yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4#23711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371#67—122no—
372#67—122no—
373#67—121no—
374#67—121no—
375#67—121no—
376#67—121no—
377C2×Dic3—24no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—121no—
386D12—62no—
387D12—61no—
388D12—61no—
389D12—61no—
390D12—61no—
391D12—121no—
392C4×D3—122no—
393C4×D3—122no—
394C4×D3—121no—
395C4×D3—121no—
396C4×D3—121no—
397C4×D3—121no—
398Dic6—41no—
399Dic6—41no—
400Dic6—41no—
401Dic6—41no—
402Dic6—62no—
403Dic6—61no—
404Dic6—61no—
405Dic6—61no—
406Dic6—61no—
407Dic6—121no—
408C3×C8—121no—
409C3⋊C8—41no—
410C3⋊C8—64no—
411C3⋊C8—62no—
412C3⋊C8—62no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32#39211yescharacteristic
416C2×C32#45612yes—
417C3⋊D3—81no—
418#41—181no—
419#41—181no—
420#41—181no—
421#41—181no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—61no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—61no—
433C2×Q8—91no—
434C2×Q8#62612yes—
435C2×D4—91no—
436C2×D4—181no—
437C22×C4—21no—
438C22×C4—32no—
439C22×C4—61no—
440C22×C4—181no—
441C22×C4C2×D3211yescharacteristic
442Q16—184no—
443SD16—184no—
444M16—61no—
445M16—61no—
446M16—92no—
447M16—181no—
448C2×C8—61no—
449C2×C8—181no—
450C4⋊C4—32no—
451C4⋊C4—68no—
452C4⋊C4—184no—
453C22⋊C4—61no—
454C22⋊C4—184no—
455C42—32no—
456C42—61no—
457C42—61no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—42no—
464C22×C3#88211yescharacteristic
465C22×C3#88411yescharacteristic
466C22×C3#93711yescharacteristic
467C22×C3#93711yescharacteristic
468C22×C3#93911yescharacteristic
469C22×C3#95311yescharacteristic
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—121no—
473C2×D3—121no—
474C2×D3—122no—
475C2×D3—242no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—44no—
481C3×C4—42no—
482C3×C4—42no—
483C3×C4—64no—
484C3×C4—122no—
485C3×C4—122no—
486C3×C4#88211yescharacteristic
487C3×C4#88411yescharacteristic
488C3×C4#93011yescharacteristic
489C3×C4#93711yescharacteristic
490C3×C4#93811yescharacteristic
491C3×C4#93911yescharacteristic
492C3×C4#94011yescharacteristic
493C3×C4#94011yescharacteristic
494Dic3—24no—
495Dic3—42no—
496Dic3—42no—
497Dic3—122no—
498Dic3—121no—
499Dic3—121no—
500C32#200511yescharacteristic, complemented, Sylow
501C23—181no—
502C23D3×#6711yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507Q8—121no—
508Q8—121no—
509Q8—121no—
510Q8—121no—
511Q8—181no—
512Q8—181no—
513D4—181no—
514D4—181no—
515D4—361no—
516D4—361no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—64no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—181no—
527C2×C4—361no—
528C2×C4—361no—
529C2×C4#380411yescharacteristic
530C2×C4C2×#62611yescharacteristic
531C2×C4D3×#6711yescharacteristic
532C2×C4D3×#6711yescharacteristic
533C2×C4#381111yescharacteristic
534C2×C4#381111yescharacteristic
535C8—121no—
536C8—182no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—41no—
544C2×C3—41no—
545C2×C3#496011yescharacteristic
546C2×C3#509512yes—
547C2×C3#520512yes—
548C2×C3#522311yescharacteristic
549D3—242no—
550D3—241no—
551D3—241no—
552C22—22no—
553C22—362no—
554C22—361no—
555C22#6397111yescharacteristic
556C22#6397711yescharacteristic
557C22#6398311yescharacteristic
558C4—42no—
559C4—64no—
560C4—122no—
561C4—122no—
562C4—361no—
563C4#6395811yescharacteristic
564C4#6397811yescharacteristic
565C4#6397911yescharacteristic
566C4#6398111yescharacteristic
567C3—21no—
568C3#7034611yescharacteristic, complemented
569C3#7179511yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—721no—
573C2#1059166112yes—
574C2#1059172411yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC2×#3828C22
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
2. C2×C3×#944C2semidirect
4. C3×#5225C2semidirect
6. C2×#63560C2semidirect
7. #10589161C2semidirect
33. C2×#944D3semidirect
40. #5225D3semidirect
500. C32#2005semidirect
568. C3#70346semidirect
569. C3#71795semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C2×C3×#9442
#105948662
C3×#52252
C2×#635702
C2×#635602
#105891612
#717953
#703463