Finite Group Databasebeta

← #11792204

Subgroups — #11792204

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596287C211yesmaximal, characteristic
2C2×C3×#944C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic
4C2×C3×#836C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6#10591100C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#71795—31nomaximal
9#70119—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13#64156—21no—
14#64155—22no—
15#64153—21no—
16#64138—22no—
17#64135C2211yescharacteristic
18C3×#944—22no—
19C3×#944—22no—
20C2×C3×Dic3⋊C4—22no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×#3719—21no—
25#63833—22no—
26#63833—22no—
27C2×#3717—21no—
28C3×#836—22no—
29#63570—22no—
30#63566—22no—
31C2×C3×C4⋊Q8—31no—
32#5816—31no—
33#5816—31no—
34#5816—61no—
35C2×#944D311yescharacteristic, complemented
36C2×#942—31no—
37C2×#909—31no—
38C2×C3×#101—31no—
39C2×#836D311yescharacteristic, complemented
40#5225—31no—
41C2×#825—31no—
42#5120—31no—
43C2×#805—31no—
44#4555—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×Q8—21no—
52C22×C32×C4D412yes—
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×Dic3—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6D412yes—
70#3757—21no—
71#3752—24no—
72C4⋊(C3⋊Dic3)D412yes—
73#3750—24no—
74C4×C3⋊Dic3—21no—
75C3×Dic3⋊C4—28no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3D412yes—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208—21no—
81C3×#208D412yes—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84#3719—24no—
85#3717—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—
96C2×C3×M16—31no—
97C3×C4⋊Q8—62no—
98C3×C4⋊Q8—62no—
99C2×C3×C4⋊C4—62no—
100C2×C3×C42—31no—
101#947—61no—
102#947—61no—
103#947—62no—
104#946—62no—
105#946—62no—
106#946—64no—
107#944—22no—
108#944—22no—
109#944—61no—
110#944—61no—
111#944—62no—
112C2×#216—61no—
113#942—62no—
114#942—62no—
115C2×#215—61no—
116#929—64no—
117#929—62no—
118#929—62no—
119#926—31no—
120#926—31no—
121#926—61no—
122C2×Dic3⋊C4—22no—
123C2×C4×Dic3C2×D311yescharacteristic
124C2×#208C2×D311yescharacteristic
125C2×#208C2×D311yescharacteristic
126#909—62no—
127#909—62no—
128C2×Dic12—61no—
129C2×#204—61no—
130C3×#101—62no—
131#836—22no—
132#835—62no—
133#825—62no—
134#816—62no—
135#805—62no—
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—21no—
138C32×Q8—41no—
139C32×Q8—41no—
140C32×Q8—41no—
141C32×Q8—41no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4—22no—
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—22no—
154C2×C3⋊Dic3—21no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)—21no—
157C4×C3⋊D3—41no—
158C4×C3⋊D3—41no—
159#634—21no—
160#634—21no—
161C2×C3×Dic3—24no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—41no—
165C2×C3×Dic3—41no—
166C3×Dic6—22no—
167C3×Dic6—22no—
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—91no—
177C2×#101—31no—
178#339—91no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—21no—
182C2×C3×Q8—21no—
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—32no—
194C2×C3×Q8—41no—
195C2×C3×Q8—41no—
196C2×C3×Q8—41no—
197C2×C3×Q8—41no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4D1212yes—
208C22×C3×C4#6712yes—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—62no—
212C2×#67—61no—
213C2×#67—61no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216#235—61no—
217#235—61no—
218#235—61no—
219#235—61no—
220#235—61no—
221#235—61no—
222#235—61no—
223#235—61no—
224#235—121no—
225#235—121no—
226#235—121no—
227#235—121no—
228C2×D12—31no—
229C2×D12—31no—
230C2×D12—61no—
231C2×C4×D3—62no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6—21no—
237C2×Dic6—21no—
238C2×Dic6—21no—
239C2×Dic6—31no—
240C2×Dic6—31no—
241C2×Dic6—61no—
242C2×Dic6#6712yes—
243C3×M16—32no—
244C3×M16—61no—
245C3×M16—61no—
246C3×M16—61no—
247C2×C3×C8—61no—
248C2×C3×C8—61no—
249C3×C4⋊C4—68no—
250C3×C42—32no—
251C3×C42—61no—
252#217—62no—
253#217—61no—
254#217—61no—
255#216—64no—
256#215—64no—
257(C2×D3)⋊C4—68no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260C4⋊Dic3—32no—
261C4⋊Dic3—32no—
262C4⋊Dic3—62no—
263Dic3⋊C4—28no—
264Dic3⋊C4—68no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—21no—
268C4×Dic3—62no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3#6712yes—
272#208—21no—
273#208—21no—
274#208—21no—
275#208#6712yes—
276C2×C3⋊C8—21no—
277C2×C3⋊C8—21no—
278Dic12—64no—
279#204—64no—
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—42no—
293C3×Dic3—24no—
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—31no—
304C4⋊Q8—62no—
305C4⋊Q8—62no—
306C4⋊Q8—181no—
307#124—181no—
308#123—182no—
309C22⋊Q8—182no—
310#117—91no—
311C2×C4⋊C4—62no—
312C2×C42—31no—
313#104—182no—
314#103—182no—
315#101—62no—
316C23×C3—21no—
317C23×C3C2×D1211yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C22×D3—62no—
320C22×D3—61no—
321C22×D3—61no—
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—41no—
331C3×Q8—41no—
332C3×Q8—41no—
333C3×Q8—41no—
334C3×Q8—62no—
335C3×Q8—62no—
336C3×Q8—121no—
337C3×Q8—121no—
338C2×C3×C4—24no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—64no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—121no—
357C2×C3×C4—121no—
358C2×C3×C4#23511yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4#23711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370#67—122no—
371#67—122no—
372#67—121no—
373#67—121no—
374#67—121no—
375#67—121no—
376C2×Dic3—24no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—61no—
385C2×Dic3—62no—
386C2×Dic3—61no—
387D12—61no—
388D12—61no—
389D12—61no—
390D12—61no—
391D12—121no—
392D12—121no—
393C4×D3—122no—
394C4×D3—122no—
395C4×D3—121no—
396C4×D3—121no—
397C4×D3—121no—
398C4×D3—121no—
399Dic6—22no—
400Dic6—22no—
401Dic6—41no—
402Dic6—41no—
403Dic6—61no—
404Dic6—61no—
405Dic6—61no—
406Dic6—61no—
407Dic6—121no—
408Dic6—121no—
409C3×C8—62no—
410C3×C8—121no—
411C3⋊C8—22no—
412C3⋊C8—41no—
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—21no—
428C2×Q8—32no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—61no—
433C2×Q8—61no—
434C2×Q8—91no—
435C2×D4—91no—
436C2×D4—181no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—181no—
440C22×C4#62612yes—
441C22×C4C2×D3211yescharacteristic
442Q16—184no—
443SD16—184no—
444M16—32no—
445M16—61no—
446M16—61no—
447M16—61no—
448C2×C8—61no—
449C2×C8—61no—
450C4⋊C4—68no—
451C4⋊C4—92no—
452C4⋊C4—184no—
453C22⋊C4—184no—
454C22⋊C4—181no—
455C42—32no—
456C42—61no—
457C42—181no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—42no—
464C22×C3#88211yescharacteristic
465C22×C3#88211yescharacteristic
466C22×C3#93011yescharacteristic
467C22×C3#93711yescharacteristic
468C22×C3#93911yescharacteristic
469C22×C3#95311yescharacteristic
470C2×D3—122no—
471C2×D3—124no—
472C2×D3—121no—
473C2×D3—121no—
474C2×D3—122no—
475C2×D3—122no—
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#88411yescharacteristic
486C3×C4#88411yescharacteristic
487C3×C4#93711yescharacteristic
488C3×C4#93711yescharacteristic
489C3×C4#93811yescharacteristic
490C3×C4#93911yescharacteristic
491C3×C4#94011yescharacteristic
492C3×C4#94011yescharacteristic
493Dic3—24no—
494Dic3—42no—
495Dic3—122no—
496Dic3—124no—
497Dic3—121no—
498Dic3—121no—
499Dic3—122no—
500Dic3—122no—
501C32#200511yescharacteristic, complemented, Sylow
502C23—181no—
503C23C2×#62611yescharacteristic
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—62no—
509Q8—62no—
510Q8—121no—
511Q8—121no—
512Q8—181no—
513Q8—181no—
514D4—181no—
515D4—181no—
516D4—361no—
517D4—361no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—64no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—182no—
527C2×C4—181no—
528C2×C4—361no—
529C2×C4—361no—
530C2×C4#380411yescharacteristic
531C2×C4D3×#6711yescharacteristic
532C2×C4D3×#6711yescharacteristic
533C2×C4D3×#6711yescharacteristic
534C2×C4#381111yescharacteristic
535C2×C4#381111yescharacteristic
536C8—62no—
537C8—121no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—41no—
545C2×C3—41no—
546C2×C3#475212yes—
547C2×C3#496011yescharacteristic
548C2×C3#509512yes—
549C2×C3#522311yescharacteristic
550D3—242no—
551D3—241no—
552D3—241no—
553C22—22no—
554C22—362no—
555C22—361no—
556C22#6397711yescharacteristic
557C22#6397811yescharacteristic
558C22#6398111yescharacteristic
559C4—42no—
560C4—64no—
561C4—122no—
562C4—362no—
563C4—361no—
564C4#6395811yescharacteristic
565C4#6397111yescharacteristic
566C4#6397911yescharacteristic
567C4#6398311yescharacteristic
568C3—21no—
569C3#7011911yescharacteristic, complemented
570C3#7179511yescharacteristic, complemented
571C2—21no—
572C2—21no—
573C2—721no—
574C2#1059165012yes—
575C2#1059172411yescharacteristic
subgroupG/H
centerC22#63981
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. C2×C3×#836C2semidirect
6. #10591100C2semidirect
7. #10589162C2semidirect
35. C2×#944D3semidirect
39. C2×#836D3semidirect
501. C32#2005semidirect
569. C3#70119semidirect
570. C3#71795semidirect

Maximal subgroups

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

subgroupindex
#105962872
C2×C3×#9442
C2×#638332
C2×C3×#8362
C2×#635702
#105911002
#105891622
#717953
#701193