Finite Group Databasebeta

← #11793858

Subgroups — #11793858

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5822C211yesmaximal, characteristic
2#10592936C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4#10591115C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6#10591076C211yesmaximal, characteristic, complemented
7#10589159C211yesmaximal, characteristic, complemented
8#72117—31nomaximal
9#70379—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#951—21no—
15C3×#950—22no—
16C3×#949—21no—
17C3×#942—21no—
18C3×#932—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63663—21no—
23#63660—21no—
24C3×#837—21no—
25C3×#837—21no—
26Dic3⋊(C3⋊C8)—22no—
27#63569—21no—
28#63569—21no—
29#63560—21no—
30#63558—21no—
31C3×#575—31no—
32#5822D311yescharacteristic
33C2×C3×#104—31no—
34#5237—31no—
35#5237—31no—
36#5237—31no—
37#5237—61no—
38C2×#837—31no—
39C2×#837D311yescharacteristic, complemented
40#5132—31no—
41#5118—31no—
42C2×#805—31no—
43#4924—31no—
44C3⋊#338—31no—
45C3⋊#338—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
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6D411yescharacteristic
64#3748—21no—
65#3748—21no—
66#3748—21no—
67#3748—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#216—22no—
71C3×#215—22no—
72C3×#214—22no—
73C3×#213—22no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3D411yescharacteristic
76C3×C4×Dic3D411yescharacteristic
77C3×#208—21no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D412yes—
83#2050—91noSylow
84C2×C3×#41—21no—
85C2×C3×#41—31no—
86C2×C3×#41C2×D311yescharacteristic
87C2×C3×#41C2×D311yescharacteristic
88C2×#235C2×D311yescharacteristic
89C3×#137—61no—
90C3×#137—61no—
91C3×AGL(1,ℤ/8)—61no—
92C3×AGL(1,ℤ/8)—61no—
93C3×#135—62no—
94C2×C3×M16—31no—
95C2×C3×M16—31no—
96C2×C3×C42—31no—
97#951—21no—
98#950—22no—
99#949—21no—
100#942—21no—
101#932—21no—
102C2×C4×Dic3C2×D311yescharacteristic
103C2×#208—31no—
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208—61no—
109C2×#208C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111C3×#104—61no—
112C3×#104—61no—
113#837—21no—
114#837—21no—
115#837—61no—
116#837—61no—
117#836—61no—
118#836—62no—
119#836—61no—
120#836—61no—
121#833—61no—
122#833—62no—
123#833—61no—
124#833—61no—
125#824—61no—
126#823—61no—
127Dic3⋊C8—62no—
128#805—61no—
129#805—61no—
130C4⋊(C3⋊C8)—62no—
131C23×C32—21no—
132C23×C32#4111yescharacteristic
133C22×C3×D3—21no—
134C32×Q8—21no—
135C32×Q8—21no—
136C32×D4—21no—
137C32×D4—21no—
138C32×D4—41no—
139C32×D4—41no—
140C2×C32×C4—21no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C3×#67—41no—
150C3×#67—41no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—42no—
155C3×D12—21no—
156C3×D12—21no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3×Dic6—21no—
160C3×Dic6—21no—
161C3⋊(C3⋊C8)—41no—
162C3⋊(C3⋊C8)—41no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—41no—
165#575—31no—
166#423—91no—
167C2×#104—31no—
168C2×#104—91no—
169#413—91no—
170#413—91no—
171#338—91no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—41no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—61no—
185C3×#41—61no—
186C3×#41—61no—
187C3×#41—61no—
188C2×C3×Q8—21no—
189C2×C3×Q8—31no—
190C2×C3×Q8D1211yescharacteristic
191C2×C3×Q8#6711yescharacteristic
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—31no—
197C2×C3×D4—61no—
198C2×C3×D4D1211yescharacteristic
199C2×C3×D4#6711yescharacteristic
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C2×#67—21no—
209C22×Dic3—21no—
210#235—21no—
211#235—21no—
212#235—21no—
213#235—21no—
214C2×D12#6711yescharacteristic
215C2×C4×D3—21no—
216C2×Dic6#6711yescharacteristic
217C3×Q16—62no—
218C3×SD16—62no—
219C3×SD16—62no—
220C3×D8—62no—
221C3×M16—61no—
222C3×M16—61no—
223C3×M16—61no—
224C3×M16—61no—
225C2×C3×C8—32no—
226C2×C3×C8—61no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—61no—
230#216—22no—
231#215—22no—
232#214—22no—
233#213—22no—
234C4×Dic3—21no—
235C4×Dic3#6711yescharacteristic
236C4×Dic3#6711yescharacteristic
237#208—21no—
238#208—21no—
239#208—21no—
240#208—21no—
241#208—62no—
242#208—62no—
243#208—61no—
244#208—61no—
245#208—61no—
246#208—61no—
247#208—61no—
248#208—61no—
249#208—61no—
250#208—61no—
251#208—121no—
252#208—121no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—121no—
259C2×C3⋊C8—121no—
260C2×C3⋊C8#6712yes—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—81no—
264C22×C32#12111yescharacteristic
265C22×C32#12311yescharacteristic
266C22×C32#12311yescharacteristic
267C2×C3×D3—41no—
268C2×C3×D3—81no—
269C32×C4—41no—
270C32×C4#12011yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12411yescharacteristic
274C3×Dic3—22no—
275C3×Dic3—41no—
276C3×Dic3—41no—
277C2×#41—31no—
278C2×#41D3211yescharacteristic
279#137—61no—
280#137—61no—
281AGL(1,ℤ/8)—61no—
282AGL(1,ℤ/8)—61no—
283#135—62no—
284C2×M16—31no—
285C2×M16—31no—
286C2×M16—91no—
287C2×M16—91no—
288C2×C42—31no—
289C4⋊C8—182no—
290#104—61no—
291#104—61no—
292#104—181no—
293#104—181no—
294#101—181no—
295#101—181no—
296#100—181no—
297#100—181no—
298C23×C3—22no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—61no—
303C23×C3#23711yescharacteristic
304C23×C3#23711yescharacteristic
305C22×D3—21no—
306C3×Q8—21no—
307C3×Q8—21no—
308C3×Q8—21no—
309C3×Q8—21no—
310C3×Q8—41no—
311C3×Q8—41no—
312C3×Q8—61no—
313C3×Q8—61no—
314C3×D4—21no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—61no—
327C3×D4—61no—
328C3×D4—121no—
329C3×D4—121no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—122no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4#23711yescharacteristic
358C2×C3×C4#23711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363#67—41no—
364#67—41no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—42no—
369D12—21no—
370D12—21no—
371C4×D3—41no—
372C4×D3—41no—
373Dic6—21no—
374Dic6—21no—
375C3×C8—62no—
376C3×C8—121no—
377C3⋊C8—22no—
378C3⋊C8—41no—
379C3⋊C8—122no—
380C3⋊C8—122no—
381C3⋊C8—121no—
382C3⋊C8—121no—
383C3⋊C8—121no—
384C3⋊C8—121no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32—21no—
388C2×C32—81no—
389C2×C32#39411yescharacteristic
390C3×D3—81no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—61no—
396#41—61no—
397#41—61no—
398#41—61no—
399C2×Q8—31no—
400C2×Q8#62611yescharacteristic
401C2×D4—21no—
402C2×D4—31no—
403C2×D4—61no—
404C2×D4#62611yescharacteristic
405C22×C4—21no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4C2×D3211yescharacteristic
409Q16—62no—
410SD16—62no—
411SD16—62no—
412D8—62no—
413M16—61no—
414M16—61no—
415M16—61no—
416M16—61no—
417M16—181no—
418M16—181no—
419M16—181no—
420M16—181no—
421C2×C8—32no—
422C2×C8—61no—
423C2×C8—181no—
424C2×C8—181no—
425C42—31no—
426C42—31no—
427C42—61no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3—81no—
439C22×C3—82no—
440C22×C3—121no—
441C22×C3—241no—
442C22×C3#88311yescharacteristic
443C22×C3#88611yescharacteristic
444C22×C3#93511yescharacteristic
445C22×C3#93511yescharacteristic
446C22×C3#93811yescharacteristic
447C22×C3#93911yescharacteristic
448C2×D3—41no—
449C2×D3—81no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—42no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—62no—
458C3×C4—121no—
459C3×C4—121no—
460C3×C4#88211yescharacteristic
461C3×C4#88511yescharacteristic
462C3×C4#93011yescharacteristic
463C3×C4#93611yescharacteristic
464C3×C4#93811yescharacteristic
465C3×C4#93911yescharacteristic
466C3×C4#93911yescharacteristic
467C3×C4#95311yescharacteristic
468Dic3—22no—
469Dic3—41no—
470Dic3—41no—
471C32#205011yescharacteristic, complemented, Sylow
472C23—21no—
473C23—61no—
474C23#380511yescharacteristic
475Q8—21no—
476Q8—21no—
477Q8—61no—
478Q8—61no—
479D4—21no—
480D4—21no—
481D4—41no—
482D4—41no—
483D4—61no—
484D4—61no—
485D4—121no—
486D4—121no—
487C2×C4—21no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—122no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4#380411yescharacteristic
497C2×C4#380511yescharacteristic
498C2×C4C2×#62611yescharacteristic
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4D3×#6711yescharacteristic
502C8—62no—
503C8—121no—
504C8—361no—
505C8—361no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—41no—
514C2×C3—41no—
515C2×C3—41no—
516C2×C3—82no—
517C2×C3—81no—
518C2×C3—81no—
519C2×C3—241no—
520C2×C3#496111yescharacteristic
521C2×C3#522211yescharacteristic
522D3—81no—
523C22—41no—
524C22—41no—
525C22—81no—
526C22—121no—
527C22—241no—
528C22#6396211yescharacteristic
529C22#6396911yescharacteristic
530C22#6397011yescharacteristic
531C4—41no—
532C4—62no—
533C4—121no—
534C4—121no—
535C4#6395911yescharacteristic
536C4#6397011yescharacteristic
537C4#6397711yescharacteristic
538C4#6397811yescharacteristic
539C3—21no—
540C3#7037911yescharacteristic, complemented
541C3#7211711yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—21no—
545C2—81no—
546C2—241no—
547C2#1059170911yescharacteristic
subgroupG/H
centerC4#63959
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#394
prime radicalC3×#5822C2
hypercenterC2×#41D32
hypocenterC32#2050
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10592936C2semidirect
3. C2×C3×#837C2semidirect
4. #10591115C2semidirect
5. C2×#63569C2semidirect
6. #10591076C2semidirect
7. #10589159C2semidirect
39. C2×#837D3semidirect
471. C32#2050semidirect
540. C3#70379semidirect
541. C3#72117semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
#105929362
C2×C3×#8372
#105911152
C2×#635692
#105910762
#105891592
#721173
#703793