Finite Group Databasebeta

← #11794061

Subgroups — #11794061

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic
2#10592920C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591221C211yesmaximal, characteristic, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#72051—31nomaximal
9#70217—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×#3757—21no—
13C2×#3757—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×#214—22no—
17C2×C3×#214—22no—
18C2×C3×#214—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#832—22no—
23#63579—21no—
24#63579—21no—
25#63572—22no—
26#63566—22no—
27C22×C3×SD16—31no—
28C22×#214D311yescharacteristic
29C2×C3×#102—31no—
30#5229—31no—
31C2×#835—31no—
32#5221—31no—
33#5221—31no—
34#5221—61no—
35C2×#832D311yescharacteristic
36C2×#816—31no—
37C2×Dic3⋊C8—31no—
38C2×Dic3⋊C8—31no—
39#4973—31no—
40#4551—31no—
41#4529—31no—
42C24×C32—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4D412yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61#3757—42no—
62#3757—42no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C3×#214—28no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D412yes—
76#2055—91noSylow
77C22×C3×Q8—31no—
78C22×C3×D4—21no—
79C22×C3×D4C2×D311yescharacteristic
80C22×C3×D4C2×D311yescharacteristic
81C22×Dic6C2×D311yescharacteristic
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C2×C3×SD16—62no—
85C22×C3×C8—31no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—31no—
88C2×#217—61no—
89C2×#217—61no—
90C2×#217—61no—
91C2×#217—61no—
92C2×#217—62no—
93C2×#217—62no—
94C2×#214—22no—
95C2×#214—22no—
96C2×#214—22no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4×Dic3—31no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—61no—
104C22×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C3×#102—62no—
107#835—62no—
108#832—22no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113#816—62no—
114Dic3⋊C8—62no—
115Dic3⋊C8—62no—
116C23×C32—22no—
117C23×C32—41no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32C2×D411yescharacteristic
124C32×D4—22no—
125C32×D4—22no—
126C32×D4—41no—
127C32×D4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3SD1612yescomplemented
143C2×C3×Dic3—22no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—41no—
152C3×Dic6—41no—
153C3×C3⋊C8—22no—
154C3×C3⋊C8—41no—
155C22×SD16—31no—
156C2×C4⋊C8—91no—
157C2×#103—91no—
158C2×#102—31no—
159#391—91no—
160#390—91no—
161#340—91no—
162C24×C3—22no—
163C24×C3—21no—
164C24×C3—21no—
165C2×C3×Q8—32no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—22no—
183C2×C3×D4—41no—
184C2×C3×D4—41no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4#6712yes—
188C2×C3×D4#6712yes—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—31no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—62no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6#6712yes—
211C3×SD16—68no—
212C2×C3×C8—32no—
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220#217—122no—
221#217—122no—
222#217—124no—
223#217—124no—
224#217—122no—
225#217—122no—
226#214—28no—
227C4⋊Dic3—21no—
228C4⋊Dic3—21no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—121no—
234C4⋊Dic3—121no—
235C4×Dic3—61no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C4×Dic3—61no—
239C4×Dic3—121no—
240C4×Dic3—121no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8#6712yes—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—81no—
251C22×C32—81no—
252C22×C32—81no—
253C22×C32—81no—
254C22×C32#12111yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#12111yescharacteristic
257C22×C32C2×SD1611yescharacteristic
258C22×C32#13511yescharacteristic
259C22×C32AGL(1,ℤ/8)11yescharacteristic
260C22×C32#13711yescharacteristic
261C32×C4#12011yescharacteristic
262C32×C4#12311yescharacteristic
263C32×C4#12311yescharacteristic
264C32×C4#12411yescharacteristic
265C3⋊Dic3—22no—
266C3⋊Dic3—41no—
267C3⋊Dic3—81no—
268C3×Dic3—42no—
269C3×Dic3—81no—
270C22×Q8—31no—
271C22×D4D3211yescharacteristic
272C2×SD16—62no—
273C2×SD16—62no—
274C2×SD16—62no—
275C22×C8—31no—
276C22×C8—31no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4—91no—
279C2×C22⋊C4—181no—
280C2×C22⋊C4—181no—
281C2×C42—91no—
282C4⋊C8—182no—
283#103—182no—
284#102—62no—
285#95—181no—
286#95—181no—
287C23×C3—24no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—21no—
291C23×C3—42no—
292C23×C3—42no—
293C23×C3—42no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3D3×D411yescharacteristic
310C23×C3D3×D411yescharacteristic
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—121no—
314C3×Q8—121no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—42no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—41no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—62no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4#23511yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4#23711yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×Dic3—22no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—62no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—62no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384Dic6—22no—
385Dic6—22no—
386Dic6—41no—
387Dic6—41no—
388C3×C8—62no—
389C3×C8—121no—
390C3⋊C8—22no—
391C3⋊C8—41no—
392C2×C32—82no—
393C2×C32#39411yescharacteristic
394C2×C32#46011yescharacteristic
395C2×C32#46111yescharacteristic
396C2×C32#46311yescharacteristic
397C2×C32#46411yescharacteristic
398C2×C32#46511yescharacteristic
399C2×C32#46811yescharacteristic
400C24—21no—
401C2×Q8—32no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4#62512yes—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—181no—
418C22×C4C2×D3211yescharacteristic
419SD16—68no—
420C2×C8—32no—
421C2×C8—61no—
422C2×C8—61no—
423C2×C8—61no—
424C2×C8—61no—
425C2×C8—61no—
426C4⋊C4—61no—
427C4⋊C4—61no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C22⋊C4—362no—
431C22⋊C4—362no—
432C42—181no—
433C42—181no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—82no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—82no—
454C22×C3—81no—
455C22×C3—81no—
456C22×C3—81no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3#88411yescharacteristic
463C22×C3#88411yescharacteristic
464C22×C3#91111yescharacteristic
465C22×C3#91211yescharacteristic
466C22×C3D3×SD1611yescharacteristic
467C22×C3D3×SD1611yescharacteristic
468C22×C3#91411yescharacteristic
469C22×C3#91511yescharacteristic
470C22×C3#91511yescharacteristic
471C22×C3#91611yescharacteristic
472C22×C3#93811yescharacteristic
473C22×C3#93911yescharacteristic
474C22×C3#93911yescharacteristic
475C22×C3#93911yescharacteristic
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—122no—
481C3×C4—241no—
482C3×C4#88311yescharacteristic
483C3×C4#88511yescharacteristic
484C3×C4#92911yescharacteristic
485C3×C4#93511yescharacteristic
486C3×C4#93511yescharacteristic
487C3×C4#93611yescharacteristic
488C3×C4#93711yescharacteristic
489C3×C4#95311yescharacteristic
490Dic3—42no—
491Dic3—62no—
492Dic3—62no—
493Dic3—81no—
494Dic3—122no—
495Dic3—122no—
496Dic3—121no—
497Dic3—121no—
498Dic3—242no—
499Dic3—241no—
500Dic3—241no—
501C32#205511yescharacteristic, complemented, Sylow
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23#381111yescharacteristic
510Q8—62no—
511Q8—62no—
512Q8—121no—
513Q8—121no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—62no—
519C2×C4—92no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4—181no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—361no—
531C2×C4—361no—
532C2×C4—361no—
533C2×C4#380411yescharacteristic
534C2×C4#380411yescharacteristic
535C2×C4#380511yescharacteristic
536C2×C4C2×#62511yescharacteristic
537C2×C4D3×#6711yescharacteristic
538C2×C4D3×#6711yescharacteristic
539C8—62no—
540C8—121no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—84no—
549C2×C3—82no—
550C2×C3—82no—
551C2×C3#476211yescharacteristic
552C2×C3#476711yescharacteristic
553C2×C3#477811yescharacteristic
554C2×C3#478011yescharacteristic
555C2×C3#495911yescharacteristic
556C2×C3#515311yescharacteristic
557C2×C3#516211yescharacteristic
558C2×C3#516211yescharacteristic
559C2×C3#516311yescharacteristic
560C2×C3#516511yescharacteristic
561C2×C3#516611yescharacteristic
562C2×C3#517111yescharacteristic
563C2×C3#517411yescharacteristic
564C2×C3#522211yescharacteristic
565C22—42no—
566C22—42no—
567C22—42no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22#6393011yescharacteristic
573C22#6393111yescharacteristic
574C22#6393611yescharacteristic
575C22#6393711yescharacteristic
576C22#6395811yescharacteristic
577C22#6397111yescharacteristic
578C22#6398011yescharacteristic
579C4—122no—
580C4—182no—
581C4—241no—
582C4—361no—
583C4—721no—
584C4#6395911yescharacteristic
585C4#6396111yescharacteristic
586C4#6396911yescharacteristic
587C4#6397611yescharacteristic
588C3—21no—
589C3#7021711yescharacteristic, complemented
590C3#7205111yescharacteristic, complemented
591C2—82no—
592C2#1059144311yescharacteristic
593C2#1059144411yescharacteristic
594C2#1059146411yescharacteristic
595C2#1059146511yescharacteristic
596C2#1059147611yescharacteristic
597C2#1059149711yescharacteristic
598C2#1059170811yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591221C2semidirect
5. C2×#63572C2semidirect
6. C2×#63566C2semidirect
7. #10589164C2semidirect
142. C2×C3⋊Dic3SD16semidirect
501. C32#2055semidirect
589. C3#70217semidirect
590. C3#72051semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2142
#105929202
C2×C3×#8322
#105912212
C2×#635722
C2×#635662
#105891642
#720513
#702173