Finite Group Databasebeta

← #11792198

Subgroups — #11792198

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×#64160C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic
3C2×#63866C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic
5#10591107C211yesmaximal, characteristic, complemented
6C2×#63560C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71868—31nomaximal
9#70389—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13#64160—22no—
14#64160—22no—
15C2×#3756—21no—
16C2×#3754—21no—
17C2×#3748C2211yescharacteristic
18C3×#944—21no—
19C3×#936—21no—
20C3×#935—22no—
21C3×#926C2211yescharacteristic
22C3×#924—22no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×Dic3⋊Dic3—22no—
26#63866—22no—
27#63866—22no—
28C3×#837—22no—
29#63567—22no—
30#63560—22no—
31C3×#536—31no—
32#5825D311yescharacteristic
33C2×#951—31no—
34C2×#951—31no—
35C2×#951—61no—
36C2×#944—31no—
37C2×#869—31no—
38C2×C3×#104—31no—
39C2×#837D311yescharacteristic
40C2×#836—31no—
41C2×#824—31no—
42#5120—31no—
43#5004—31no—
44#4532—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⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634D412yes—
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#3754—24no—
72#3748—21no—
73#3748D412yes—
74C2×C3⋊(C3⋊C8)—21no—
75C3×#217—24no—
76C3×#217—21no—
77C3×C4⋊Dic3D412yes—
78C3×Dic3⋊C4—24no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3—21no—
81C3×C4×Dic3D412yes—
82C3×#208—21no—
83C3×#208—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
95C2×C3×M16—31no—
96C3×C4⋊Q8—61no—
97C3×#124—61no—
98C3×#123—62no—
99C3×C22⋊Q8—62no—
100C3×#117—31no—
101C2×C3×C42—31no—
102#951—62no—
103#951—62no—
104#951—62no—
105#951—62no—
106#951—64no—
107#951—64no—
108#944—21no—
109#944—62no—
110#944—62no—
111C2×#216—62no—
112C2×#216—61no—
113C2×#216—61no—
114#936—21no—
115#935—22no—
116C2×#214—62no—
117C2×#214—61no—
118C2×#214—61no—
119#926C2×D311yescharacteristic
120C2×C4⋊Dic3—62no—
121#924—22no—
122C2×Dic3⋊C4—62no—
123C2×C4×Dic3C2×D311yescharacteristic
124C2×#208—31no—
125C2×#208—31no—
126C2×#208—61no—
127C2×#208C2×D311yescharacteristic
128#869—62no—
129#869—62no—
130C3×#104—62no—
131#837—22no—
132#836—62no—
133#824—62no—
134#816—62no—
135#810—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—41no—
155C2×C3⋊Dic3—41no—
156#634—22no—
157#634—22no—
158#634—41no—
159#634—41no—
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—31no—
174C2×C4⋊Q8—91no—
175C2×#104—31no—
176#419—91no—
177C2×#101—91no—
178#339—91no—
179C3×#41—22no—
180C3×#41—22no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—21no—
186C3×#41—21no—
187C3×#41—21no—
188C3×#41—21no—
189C3×#41—41no—
190C3×#41—41no—
191C2×C3×Q8—21no—
192C2×C3×Q8—61no—
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—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—41no—
204C2×C3×D4D1211yescharacteristic
205C2×C3×D4#6711yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—32no—
210C22×C3×C4—41no—
211C22×C3×C4—61no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×Dic3—21no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3—121no—
218C22×Dic3#6712yes—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—32no—
226C2×Dic6—32no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6—62no—
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—61no—
239C2×Dic6—61no—
240C2×Dic6—121no—
241C2×Dic6—121no—
242C2×Dic6—121no—
243C3×M16—61no—
244C3×M16—61no—
245C2×C3×C8—61no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—64no—
248C3×C22⋊C4—64no—
249C3×C22⋊C4—61no—
250C3×C42—32no—
251C3×C42—61no—
252C3×C42—61no—
253#217—24no—
254#217—21no—
255#216—68no—
256#216—64no—
257#216—64no—
258#214—68no—
259#214—64no—
260#214—64no—
261C4⋊Dic3—68no—
262C4⋊Dic3#6712yes—
263Dic3⋊C4—24no—
264Dic3⋊C4—68no—
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—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—24no—
293C3×Dic3—42no—
294C3×Dic3—42no—
295C2×#41D3211yescharacteristic
296C22×Q8—31no—
297C22×Q8—91no—
298#137—182no—
299#137—182no—
300C2×Q16—181no—
301C2×SD16—181no—
302C2×M16—31no—
303C2×M16—91no—
304C4⋊Q8—61no—
305C4⋊Q8—182no—
306C4⋊Q8—182no—
307#124—61no—
308#123—62no—
309C22⋊Q8—62no—
310#117—31no—
311C2×C4⋊C4—182no—
312C2×C42—31no—
313#104—62no—
314#103—182no—
315#101—182no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—41no—
320C23×C3D3×D411yescharacteristic
321C23×C3C2×#6711yescharacteristic
322C3×Q8—22no—
323C3×Q8—21no—
324C3×Q8—21no—
325C3×Q8—21no—
326C3×Q8—21no—
327C3×Q8—41no—
328C3×Q8—121no—
329C3×Q8—121no—
330C3×Q8—121no—
331C3×Q8—121no—
332C3×D4—22no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—41no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—41no—
344C2×C3×C4—21no—
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—41no—
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—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4C2×D1211yescharacteristic
366C2×C3×C4#23511yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4#23711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C2×#6711yescharacteristic
377C2×Dic3—24no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392Dic6—41no—
393Dic6—41no—
394Dic6—41no—
395Dic6—41no—
396Dic6—64no—
397Dic6—62no—
398Dic6—62no—
399Dic6—62no—
400Dic6—62no—
401Dic6—122no—
402Dic6—122no—
403Dic6—122no—
404Dic6—121no—
405Dic6—121no—
406Dic6—121no—
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—81no—
416C2×C32#39211yescharacteristic
417C2×C32#45612yes—
418#41—21no—
419#41—21no—
420#41—21no—
421#41—21no—
422C2×Q8—61no—
423C2×Q8—61no—
424C2×Q8—61no—
425C2×Q8—61no—
426C2×Q8—61no—
427C2×Q8—61no—
428C2×Q8—92no—
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—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—64no—
452C4⋊C4—188no—
453C22⋊C4—64no—
454C22⋊C4—61no—
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—42no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—82no—
470C22×C3#88211yescharacteristic
471C22×C3#88411yescharacteristic
472C22×C3#93711yescharacteristic
473C22×C3#93711yescharacteristic
474C22×C3#93911yescharacteristic
475C22×C3#95311yescharacteristic
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—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—124no—
498Dic3—122no—
499Dic3—122no—
500C32#200511yescharacteristic, complemented, Sylow
501C23—21no—
502C23D3×#6711yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—121no—
506Q8—121no—
507Q8—121no—
508Q8—121no—
509Q8—182no—
510Q8—182no—
511Q8—361no—
512Q8—361no—
513D4—21no—
514D4—21no—
515D4—41no—
516D4—41no—
517C2×C4—21no—
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—182no—
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—82no—
546C2×C3—81no—
547C2×C3—81no—
548C2×C3#482612yes—
549C2×C3#496011yescharacteristic
550C2×C3#522311yescharacteristic
551C2×C3#524612yes—
552C22—22no—
553C22—42no—
554C22—41no—
555C22#6397111yescharacteristic
556C22#6397711yescharacteristic
557C22#6398311yescharacteristic
558C4—41no—
559C4—64no—
560C4—122no—
561C4—122no—
562C4—362no—
563C4#6395811yescharacteristic
564C4#6397811yescharacteristic
565C4#6397911yescharacteristic
566C4#6398111yescharacteristic
567C3—21no—
568C3#7038911yescharacteristic, complemented
569C3#7186811yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—81no—
573C2#1059168912yes—
574C2#1059172411yescharacteristic
subgroupG/H
centerC22#63977
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. #10591107C2semidirect
6. C2×#63560C2semidirect
7. #10589161C2semidirect
500. C32#2005semidirect
568. C3#70389semidirect
569. C3#71868semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C3×#58252
C2×#638662
C2×C3×#8372
#105911072
C2×#635602
#105891612
#718683
#703893