Finite Group Databasebeta

← #11792200

Subgroups — #11792200

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5825C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C2×#63873C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic
5#10591099C211yesmaximal, characteristic, complemented
6C2×#63560C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#72108—31nomaximal
9#71868—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#951—22no—
16C3×#951—22no—
17C3×#944—21no—
18C2×C3×#216—21no—
19C3×#936—21no—
20C3×#935—22no—
21C2×C3×#214—21no—
22C3×#926C2211yescharacteristic
23C3×#924—22no—
24C2×C3×#208C2211yescharacteristic
25C2×#3724—22no—
26#63873—22no—
27#63873—22no—
28#63664—22no—
29#63565—22no—
30#63560—22no—
31C2×C3×#137—31no—
32C3×#536—31no—
33#5825D311yescharacteristic
34C2×#951D311yescharacteristic
35C2×#944—31no—
36C2×#944—31no—
37C2×#837—31no—
38C2×#837—31no—
39C2×#837—61no—
40C2×#836—31no—
41#5225—31no—
42C2×#824—31no—
43#5004—31no—
44#4555—31no—
45#4532—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—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D412yes—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6D412yes—
70C4×C3⋊Dic3—21no—
71C4×C3⋊Dic3D412yes—
72#3748—21no—
73#3748—21no—
74C2×C3⋊(C3⋊C8)—21no—
75C3×#217—24no—
76C3×#217—21no—
77C3×#216—24no—
78C3×#214—24no—
79C3×C4⋊Dic3D412yes—
80C3×Dic3⋊C4—24no—
81C3×C4×Dic3—21no—
82C3×#208—21no—
83C3×#208D412yes—
84C2×C3×C3⋊C8—21no—
85#3724—28no—
86#2005—91noSylow
87C2×C3×#41—21no—
88C2×C3×#41C2×D311yescharacteristic
89C2×C3×#41C2×D311yescharacteristic
90C22×C3×Q8—31no—
91C22×C3×Q8—31no—
92C22×Dic6C2×D311yescharacteristic
93C22×Dic6C2×D311yescharacteristic
94C3×#137—62no—
95C3×#137—62no—
96C2×C3×Q16—61no—
97C2×C3×SD16—61no—
98C2×C3×M16—31no—
99C3×C4⋊Q8—61no—
100C3×#124—61no—
101C3×#123—62no—
102C3×C22⋊Q8—62no—
103C3×#117—31no—
104#951—22no—
105#951—22no—
106#944—21no—
107#944—62no—
108#944—62no—
109#944—62no—
110#944—62no—
111C2×#216—21no—
112#936—21no—
113#935—22no—
114C2×#214—21no—
115#926C2×D311yescharacteristic
116#924—22no—
117C2×Dic3⋊C4—62no—
118C2×Dic3⋊C4—62no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—61no—
122C2×#208—31no—
123C2×#208—31no—
124C2×#208—61no—
125C2×#208C2×D311yescharacteristic
126#837—62no—
127#837—62no—
128#837—64no—
129#836—62no—
130#835—62no—
131#824—62no—
132#810—62no—
133C23×C32—21no—
134C23×C32C2×D411yescharacteristic
135C32×Q8—21no—
136C32×Q8—21no—
137C32×D4—21no—
138C32×D4—21no—
139C32×D4—41no—
140C32×D4—41no—
141C2×C32×C4—21no—
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×C4#4111yescharacteristic
150C2×C3⋊Dic3—24no—
151C2×C3⋊Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—41no—
162C3×Dic6—41no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C3⋊(C3⋊C8)—41no—
168C3×C3⋊C8—22no—
169C2×#137—31no—
170#536—31no—
171C2×C4⋊Q8—91no—
172C2×#104—91no—
173#419—91no—
174C2×#101—91no—
175#339—91no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—21no—
186C3×#41—41no—
187C3×#41—41no—
188C2×C3×Q8—21no—
189C2×C3×Q8—32no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
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×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8#6711yescharacteristic
202C2×C3×Q8#6711yescharacteristic
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—41no—
207C2×C3×D4#6711yescharacteristic
208C2×C3×D4#6711yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—32no—
213C22×C3×C4—41no—
214C22×C3×C4—61no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×Dic3—21no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—121no—
221C22×Dic3#6712yes—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6#6712yes—
234C3×Q16—64no—
235C3×SD16—64no—
236C3×M16—32no—
237C3×M16—61no—
238C2×C3×C8—61no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—64no—
241C3×C22⋊C4—64no—
242C3×C22⋊C4—61no—
243C3×C42—61no—
244#217—24no—
245#217—21no—
246#216—24no—
247#214—24no—
248C4⋊Dic3#6712yes—
249Dic3⋊C4—24no—
250Dic3⋊C4—68no—
251Dic3⋊C4—68no—
252C4×Dic3—21no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—62no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—121no—
259#208—21no—
260#208—62no—
261#208—61no—
262#208—61no—
263#208—61no—
264#208—61no—
265#208—121no—
266#208#6712yes—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—121no—
271C22×C32—22no—
272C22×C32—41no—
273C22×C32—42no—
274C22×C32#12011yescharacteristic
275C22×C32#12011yescharacteristic
276C22×C32#12111yescharacteristic
277C32×C4—41no—
278C32×C4#12011yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12711yescharacteristic
282C3⋊Dic3—24no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C3×Dic3—42no—
286C2×#41D3211yescharacteristic
287C22×Q8—31no—
288C22×Q8—31no—
289#137—62no—
290#137—62no—
291C2×Q16—61no—
292C2×SD16—61no—
293C2×M16—31no—
294C2×M16—91no—
295C4⋊Q8—61no—
296C4⋊Q8—182no—
297C4⋊Q8—182no—
298#124—61no—
299#123—62no—
300C22⋊Q8—62no—
301#117—31no—
302C2×C4⋊C4—182no—
303C2×C42—91no—
304#104—182no—
305#103—182no—
306#101—182no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—41no—
311C23×C3D3×D411yescharacteristic
312C23×C3C2×#6711yescharacteristic
313C3×Q8—22no—
314C3×Q8—21no—
315C3×Q8—21no—
316C3×Q8—21no—
317C3×Q8—21no—
318C3×Q8—41no—
319C3×Q8—62no—
320C3×Q8—62no—
321C3×Q8—121no—
322C3×Q8—121no—
323C3×Q8—121no—
324C3×Q8—121no—
325C3×Q8—121no—
326C3×Q8—121no—
327C3×D4—22no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—41no—
333C3×D4—42no—
334C3×D4—42no—
335C3×D4—41no—
336C3×D4—41no—
337C3×D4—41no—
338C3×D4—41no—
339C2×C3×C4—21no—
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—21no—
347C2×C3×C4—41no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
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×C4#23711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—122no—
385C2×Dic3—124no—
386Dic6—22no—
387Dic6—22no—
388Dic6—41no—
389Dic6—41no—
390Dic6—41no—
391Dic6—41no—
392Dic6—41no—
393Dic6—41no—
394C3×C8—62no—
395C3⋊C8—22no—
396C3⋊C8—122no—
397C3⋊C8—121no—
398C3⋊C8—121no—
399C2×C32—21no—
400C2×C32—21no—
401C2×C32—81no—
402C2×C32#39211yescharacteristic
403C2×C32#45612yes—
404#41—21no—
405#41—21no—
406#41—21no—
407#41—21no—
408C2×Q8—32no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×Q8—61no—
412C2×Q8—61no—
413C2×Q8—61no—
414C2×Q8—61no—
415C2×Q8—61no—
416C2×Q8—61no—
417C2×Q8—61no—
418C2×Q8—61no—
419C2×Q8—61no—
420C2×Q8#62511yescharacteristic
421C2×D4—21no—
422C2×D4#62511yescharacteristic
423C22×C4—21no—
424C22×C4—32no—
425C22×C4—61no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—64no—
429SD16—64no—
430M16—32no—
431M16—61no—
432M16—181no—
433M16—181no—
434C2×C8—61no—
435C2×C8—181no—
436C4⋊C4—32no—
437C4⋊C4—64no—
438C4⋊C4—188no—
439C22⋊C4—64no—
440C22⋊C4—61no—
441C42—61no—
442C42—92no—
443C42—181no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—42no—
455C22×C3—82no—
456C22×C3#93711yescharacteristic
457C22×C3#93711yescharacteristic
458C22×C3#93711yescharacteristic
459C22×C3#93811yescharacteristic
460C22×C3#93911yescharacteristic
461C22×C3#95311yescharacteristic
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—42no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—122no—
470C3×C4—122no—
471C3×C4—122no—
472C3×C4#93711yescharacteristic
473C3×C4#93811yescharacteristic
474C3×C4#93911yescharacteristic
475C3×C4#93911yescharacteristic
476C3×C4#93911yescharacteristic
477C3×C4#94011yescharacteristic
478C3×C4#94011yescharacteristic
479C3×C4#95311yescharacteristic
480Dic3—42no—
481Dic3—42no—
482Dic3—42no—
483Dic3—64no—
484Dic3—64no—
485Dic3—124no—
486C32#200511yescharacteristic, complemented, Sylow
487C23—21no—
488C23D3×#6711yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—62no—
492Q8—62no—
493Q8—121no—
494Q8—121no—
495Q8—121no—
496Q8—121no—
497Q8—121no—
498Q8—121no—
499D4—21no—
500D4—21no—
501D4—41no—
502D4—41no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—184no—
514C2×C4—182no—
515C2×C4#380511yescharacteristic
516C2×C4C2×#62511yescharacteristic
517C2×C4D3×#6711yescharacteristic
518C2×C4D3×#6711yescharacteristic
519C2×C4D3×#6711yescharacteristic
520C2×C4#381111yescharacteristic
521C8—62no—
522C8—361no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—22no—
528C2×C3—21no—
529C2×C3—41no—
530C2×C3—41no—
531C2×C3—82no—
532C2×C3—81no—
533C2×C3—81no—
534C2×C3#520512yes—
535C2×C3#522311yescharacteristic
536C2×C3#522311yescharacteristic
537C2×C3#524612yes—
538C22—22no—
539C22—42no—
540C22—41no—
541C22#6397011yescharacteristic
542C22#6397611yescharacteristic
543C22#6398311yescharacteristic
544C4—41no—
545C4—122no—
546C4—122no—
547C4—122no—
548C4—184no—
549C4#6397011yescharacteristic
550C4#6397611yescharacteristic
551C4#6397911yescharacteristic
552C4#6398011yescharacteristic
553C3—21no—
554C3#7186811yescharacteristic, complemented
555C3#7210811yescharacteristic, complemented
556C2—21no—
557C2—21no—
558C2—81no—
559C2#1059168712yes—
560C2#1059172311yescharacteristic
subgroupG/H
centerC22#63976
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×#63873C2semidirect
5. #10591099C2semidirect
6. C2×#63560C2semidirect
7. #10589160C2semidirect
486. C32#2005semidirect
554. C3#71868semidirect
555. C3#72108semidirect

Maximal subgroups

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

subgroupindex
C3×#58252
C2×C3×#9512
C2×#638732
C2×#636642
#105910992
C2×#635602
#105891602
#721083
#718683