Finite Group Databasebeta

← #11792199

Subgroups — #11792199

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#10596296C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C2×#63866C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic
5#10591100C211yesmaximal, characteristic, complemented
6C2×#63561C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#72108—31nomaximal
9#70389—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13#64153—21no—
14#64145—21no—
15#64144—22no—
16#64135C2211yescharacteristic
17#64133—22no—
18C3×#951—22no—
19C3×#951—22no—
20C2×C3×#216—21no—
21C2×C3×#214—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×Dic3⋊Dic3—22no—
26#63866—22no—
27#63866—22no—
28C3×#837—22no—
29#63566—22no—
30#63561—22no—
31C2×C3×#137—31no—
32#5825—31no—
33#5825—31no—
34#5825—61no—
35C2×#951D311yescharacteristic
36C2×#944—31no—
37C2×#869—31no—
38C2×C3×#104—31no—
39C2×#837D311yescharacteristic
40#5225—31no—
41C2×#824—31no—
42C2×#824—31no—
43#5120—31no—
44#4555—31no—
45#4523—31no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41—21no—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3D412yes—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634—21no—
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—24no—
71#3757—21no—
72C4⋊(C3⋊Dic3)D412yes—
73#3750—24no—
74C4×C3⋊Dic3—21no—
75C3×#216—24no—
76C3×#214—24no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3D412yes—
79C3×#208—21no—
80C3×#208—21no—
81C3×#208—21no—
82C3×#208D412yes—
83C2×C3×C3⋊C8—21no—
84C2×C3×C3⋊C8—21no—
85Dic3⋊Dic3—28no—
86#2005—91noSylow
87C2×C3×#41—21no—
88C2×C3×#41C2×D311yescharacteristic
89C2×C3×#41C2×D311yescharacteristic
90C22×C3×Q8—31no—
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C3×#137—62no—
96C3×#137—62no—
97C2×C3×Q16—61no—
98C2×C3×SD16—61no—
99C2×C3×M16—31no—
100C2×C3×M16—31no—
101C2×C3×C42—31no—
102#951—22no—
103#951—22no—
104#944—62no—
105#944—62no—
106#944—61no—
107#944—61no—
108#944—62no—
109C2×#216—21no—
110#936—62no—
111#936—61no—
112#936—61no—
113#935—62no—
114#935—62no—
115#935—64no—
116C2×#214—21no—
117#926—31no—
118#926—31no—
119#926—61no—
120C2×C4⋊Dic3—62no—
121#924—62no—
122#924—62no—
123#924—64no—
124C2×Dic3⋊C4—62no—
125C2×C4×Dic3C2×D311yescharacteristic
126C2×#208C2×D311yescharacteristic
127C2×#208C2×D311yescharacteristic
128#869—62no—
129#869—62no—
130C3×#104—62no—
131#837—22no—
132#835—62no—
133#824—62no—
134#824—62no—
135#816—62no—
136C23×C32—21no—
137C23×C32C2×D411yescharacteristic
138C32×Q8—21no—
139C32×Q8—21no—
140C32×D4—21no—
141C32×D4—21no—
142C32×D4—41no—
143C32×D4—41no—
144C2×C32×C4—21no—
145C2×C32×C4—41no—
146C2×C32×C4—41no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157#634—41no—
158#634—41no—
159#634—41no—
160#634—41no—
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—31no—
173#536—91no—
174C2×C4⋊Q8—91no—
175C2×#104—31no—
176#419—91no—
177C2×#101—91no—
178#339—91no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—21no—
186C3×#41—21no—
187C3×#41—41no—
188C3×#41—41no—
189C3×#41—41no—
190C3×#41—41no—
191C2×C3×Q8—21no—
192C2×C3×Q8—32no—
193C2×C3×Q8—61no—
194C2×C3×Q8—61no—
195C2×C3×Q8—61no—
196C2×C3×Q8—61no—
197C2×C3×Q8—61no—
198C2×C3×Q8D1211yescharacteristic
199C2×C3×Q8#6711yescharacteristic
200C2×C3×D4—22no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4D1211yescharacteristic
205C2×C3×D4#6711yescharacteristic
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—62no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—62no—
225C2×Dic6—62no—
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—61no—
238C2×Dic6—121no—
239C2×Dic6—121no—
240C2×Dic6—121no—
241C2×Dic6—121no—
242C2×Dic6#6712yes—
243C3×Q16—64no—
244C3×SD16—64no—
245C3×M16—32no—
246C3×M16—61no—
247C3×M16—61no—
248C3×M16—61no—
249C2×C3×C8—61no—
250C2×C3×C8—61no—
251C3×C42—32no—
252C3×C42—61no—
253#217—68no—
254#217—64no—
255#217—64no—
256#217—62no—
257#217—61no—
258#217—61no—
259#216—24no—
260#214—24no—
261C4⋊Dic3—32no—
262C4⋊Dic3—32no—
263C4⋊Dic3—62no—
264C4⋊Dic3—68no—
265Dic3⋊C4—68no—
266Dic3⋊C4—68no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—21no—
270C4×Dic3—62no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C4×Dic3#6712yes—
274#208—21no—
275#208—21no—
276#208—21no—
277#208#6712yes—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—21no—
280C22×C32—22no—
281C22×C32—41no—
282C22×C32—42no—
283C22×C32#12011yescharacteristic
284C22×C32#12011yescharacteristic
285C22×C32#12111yescharacteristic
286C32×C4—41no—
287C32×C4#12011yescharacteristic
288C32×C4#12111yescharacteristic
289C32×C4#12111yescharacteristic
290C32×C4#12711yescharacteristic
291C3⋊Dic3—42no—
292C3⋊Dic3—42no—
293C3×Dic3—24no—
294C3×Dic3—42no—
295C2×#41D3211yescharacteristic
296C22×Q8—31no—
297C22×Q8—91no—
298#137—62no—
299#137—62no—
300C2×Q16—61no—
301C2×SD16—61no—
302C2×M16—31no—
303C2×M16—31no—
304C4⋊Q8—182no—
305C4⋊Q8—182no—
306C4⋊Q8—181no—
307#124—181no—
308#123—182no—
309C22⋊Q8—182no—
310#117—91no—
311C2×C4⋊C4—182no—
312C2×C42—31no—
313#104—62no—
314#103—182no—
315#101—182no—
316C23×C3—22no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3D3×D411yescharacteristic
321C23×C3D3×D411yescharacteristic
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—21no—
325C3×Q8—21no—
326C3×Q8—41no—
327C3×Q8—41no—
328C3×Q8—62no—
329C3×Q8—62no—
330C3×Q8—121no—
331C3×Q8—121no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—41no—
337C3×D4—41no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—41no—
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—21no—
352C2×C3×C4—21no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—64no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4#23511yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376C2×Dic3—24no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—64no—
382C2×Dic3—64no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393Dic6—22no—
394Dic6—22no—
395Dic6—41no—
396Dic6—41no—
397Dic6—122no—
398Dic6—122no—
399Dic6—122no—
400Dic6—122no—
401Dic6—121no—
402Dic6—121no—
403Dic6—121no—
404Dic6—121no—
405Dic6—121no—
406Dic6—121no—
407Dic6—121no—
408Dic6—121no—
409C3×C8—62no—
410C3×C8—121no—
411C3⋊C8—22no—
412C3⋊C8—41no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—81no—
416C2×C32#39211yescharacteristic
417C2×C32#45612yes—
418#41—21no—
419#41—21no—
420#41—21no—
421#41—21no—
422C2×Q8—32no—
423C2×Q8—61no—
424C2×Q8—61no—
425C2×Q8—61no—
426C2×Q8—61no—
427C2×Q8—61no—
428C2×Q8—181no—
429C2×Q8—181no—
430C2×Q8—181no—
431C2×Q8—181no—
432C2×Q8—181no—
433C2×Q8—181no—
434C2×Q8#62611yescharacteristic
435C2×D4—21no—
436C2×D4#62611yescharacteristic
437C22×C4—21no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—92no—
441C22×C4C2×D3211yescharacteristic
442Q16—64no—
443SD16—64no—
444M16—32no—
445M16—61no—
446M16—61no—
447M16—61no—
448C2×C8—61no—
449C2×C8—61no—
450C4⋊C4—92no—
451C4⋊C4—184no—
452C4⋊C4—188no—
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—42no—
465C22×C3—44no—
466C22×C3—42no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—42no—
470C22×C3#88211yescharacteristic
471C22×C3#88411yescharacteristic
472C22×C3#93711yescharacteristic
473C22×C3#93711yescharacteristic
474C22×C3#93711yescharacteristic
475C22×C3#93811yescharacteristic
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—42no—
481C3×C4—41no—
482C3×C4—41no—
483C3×C4—64no—
484C3×C4—122no—
485C3×C4#88211yescharacteristic
486C3×C4#88411yescharacteristic
487C3×C4#93011yescharacteristic
488C3×C4#93911yescharacteristic
489C3×C4#93911yescharacteristic
490C3×C4#94011yescharacteristic
491C3×C4#94011yescharacteristic
492C3×C4#95311yescharacteristic
493Dic3—24no—
494Dic3—42no—
495Dic3—124no—
496Dic3—124no—
497Dic3—122no—
498Dic3—122no—
499Dic3—122no—
500Dic3—122no—
501C32#200511yescharacteristic, complemented, Sylow
502C23—21no—
503C23#381111yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—62no—
507Q8—62no—
508Q8—121no—
509Q8—121no—
510Q8—361no—
511Q8—361no—
512Q8—361no—
513Q8—361no—
514D4—21no—
515D4—21no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—64no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—182no—
527C2×C4—182no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4#380411yescharacteristic
531C2×C4C2×#62611yescharacteristic
532C2×C4D3×#6711yescharacteristic
533C2×C4D3×#6711yescharacteristic
534C2×C4D3×#6711yescharacteristic
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—82no—
547C2×C3—81no—
548C2×C3—81no—
549C2×C3#482612yes—
550C2×C3#496011yescharacteristic
551C2×C3#520512yes—
552C2×C3#522311yescharacteristic
553C22—22no—
554C22—42no—
555C22—41no—
556C22#6395811yescharacteristic
557C22#6398111yescharacteristic
558C22#6398311yescharacteristic
559C4—41no—
560C4—64no—
561C4—122no—
562C4—362no—
563C4—362no—
564C4#6397111yescharacteristic
565C4#6397711yescharacteristic
566C4#6397811yescharacteristic
567C4#6397911yescharacteristic
568C3—21no—
569C3#7038911yescharacteristic, complemented
570C3#7210811yescharacteristic, complemented
571C2—21no—
572C2—21no—
573C2—81no—
574C2#1059166812yes—
575C2#1059172411yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#120
hypercenterC2×#41D32
hypocenterC32#2005
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. C2×#63866C2semidirect
5. #10591100C2semidirect
6. C2×#63561C2semidirect
7. #10589162C2semidirect
501. C32#2005semidirect
569. C3#70389semidirect
570. C3#72108semidirect

Maximal subgroups

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

subgroupindex
#105962962
C2×C3×#9512
C2×#638662
C2×C3×#8372
#105911002
C2×#635612
#105891622
#721083
#703893