Finite Group Databasebeta

← #11793859

Subgroups — #11793859

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5822C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic, complemented
3C3×#5237C211yesmaximal, characteristic, complemented
4#10591120C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10591076C211yesmaximal, characteristic, complemented
7#10589159C211yesmaximal, characteristic, complemented
8#72117—31nomaximal
9#70144—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#951—21no—
15C3×#950—22no—
16C3×#949—21no—
17C3×#942—21no—
18C3×#932—21no—
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63664—21no—
23#63664—21no—
24C3×#836—21no—
25C3×#833—21no—
26#63572—22no—
27#63568—21no—
28#63568—21no—
29#63560—21no—
30#63558—21no—
31C3×#575—31no—
32#5822D311yescharacteristic
33C3×#413—31no—
34#5237—31no—
35#5237D311yescharacteristic, complemented
36C2×#837—31no—
37C2×#837—31no—
38C2×#837—31no—
39C2×#837—61no—
40C2×#825—31no—
41#5132—31no—
42#5118—31no—
43#5118—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
55C22×C3⋊Dic3—21no—
56C2×C3×#67—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6D411yescharacteristic
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3D411yescharacteristic
66C4×C3⋊Dic3D411yescharacteristic
67#3748—21no—
68#3748—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#216—22no—
71C3×#215—22no—
72C3×#214—22no—
73C3×#213—22no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208—21no—
80C2×C3×C3⋊C8—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×M16—31no—
97#951—21no—
98#950—22no—
99#949—21no—
100#942—21no—
101#932—21no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—61no—
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C2×#208C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111C3×#101—61no—
112C3×#100—61no—
113#837—61no—
114#837—61no—
115#837—61no—
116#837—61no—
117#837—61no—
118#837—61no—
119#837—62no—
120#837—62no—
121#836—21no—
122#836—61no—
123#833—21no—
124#833—61no—
125#825—61no—
126#825—61no—
127#824—61no—
128#823—61no—
129Dic3⋊C8—62no—
130Dic3⋊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
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—42no—
152C3×#67—41no—
153C3×#67—41no—
154C2×C3×Dic3—21no—
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—22no—
163C3×C3⋊C8—41no—
164C3×C3⋊C8—41no—
165#575—31no—
166#423—91no—
167C2×#104—91no—
168C2×#104—91no—
169#413—31no—
170#413—91no—
171#338—91no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
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×Q8#6711yescharacteristic
191C2×C3×Q8#6711yescharacteristic
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—31no—
196C2×C3×D4—41no—
197C2×C3×D4—61no—
198C2×C3×D4#6711yescharacteristic
199C2×C3×D4#6711yescharacteristic
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—41no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—21no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—121no—
211#235—21no—
212#235—21no—
213#235—21no—
214#235—21no—
215C2×D12#6711yescharacteristic
216C2×C4×D3—21no—
217C2×Dic6#6711yescharacteristic
218C3×Q16—62no—
219C3×SD16—62no—
220C3×SD16—62no—
221C3×D8—62no—
222C3×M16—61no—
223C3×M16—61no—
224C3×M16—61no—
225C3×M16—61no—
226C3×M16—61no—
227C3×M16—61no—
228C2×C3×C8—32no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231#216—22no—
232#215—22no—
233#214—22no—
234#213—22no—
235C4×Dic3—31no—
236C4×Dic3—31no—
237C4×Dic3—31no—
238C4×Dic3—31no—
239C4×Dic3—61no—
240C4×Dic3—61no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—121no—
244#208—21no—
245#208—21no—
246#208—21no—
247#208—21no—
248#208—21no—
249#208—21no—
250#208—62no—
251#208—61no—
252#208—61no—
253#208—61no—
254#208—61no—
255#208—121no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—121no—
261C2×C3⋊C8#6712yes—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32—81no—
265C22×C32#12111yescharacteristic
266C22×C32#12311yescharacteristic
267C22×C32#12311yescharacteristic
268C2×C3×D3—41no—
269C2×C3×D3—81no—
270C32×C4—41no—
271C32×C4#12011yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12111yescharacteristic
274C32×C4#12411yescharacteristic
275C3⋊Dic3—22no—
276C3⋊Dic3—41no—
277C3×Dic3—41no—
278C2×#41—31no—
279C2×#41D3211yescharacteristic
280#137—61no—
281#137—61no—
282AGL(1,ℤ/8)—61no—
283AGL(1,ℤ/8)—61no—
284#135—62no—
285C2×M16—31no—
286C2×M16—31no—
287C2×M16—31no—
288C2×M16—91no—
289C2×C42—91no—
290C4⋊C8—182no—
291#104—181no—
292#104—181no—
293#104—181no—
294#104—181no—
295#101—61no—
296#101—181no—
297#100—61no—
298#100—181no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—41no—
303C23×C3—61no—
304C23×C3#23511yescharacteristic
305C23×C3#23711yescharacteristic
306C22×D3—21no—
307C3×Q8—22no—
308C3×Q8—21no—
309C3×Q8—21no—
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—41no—
313C3×Q8—61no—
314C3×Q8—61no—
315C3×D4—22no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—21no—
319C3×D4—21no—
320C3×D4—41no—
321C3×D4—42no—
322C3×D4—42no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—41no—
327C3×D4—61no—
328C3×D4—61no—
329C3×D4—121no—
330C3×D4—121no—
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—41no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—61no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4#23711yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361#67—41no—
362#67—41no—
363C2×Dic3—21no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—124no—
373D12—21no—
374D12—21no—
375C4×D3—41no—
376C4×D3—41no—
377Dic6—21no—
378Dic6—21no—
379C3×C8—62no—
380C3×C8—121no—
381C3×C8—121no—
382C3⋊C8—22no—
383C3⋊C8—41no—
384C3⋊C8—41no—
385C3⋊C8—122no—
386C3⋊C8—121no—
387C3⋊C8—121no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32—21no—
391C2×C32—81no—
392C2×C32#39411yescharacteristic
393C3×D3—81no—
394#41—21no—
395#41—21no—
396#41—21no—
397#41—21no—
398#41—61no—
399#41—61no—
400#41—61no—
401#41—61no—
402C2×Q8—31no—
403C2×Q8#62511yescharacteristic
404C2×D4—21no—
405C2×D4—31no—
406C2×D4—61no—
407C2×D4#62511yescharacteristic
408C22×C4—21no—
409C22×C4—61no—
410C22×C4—181no—
411C22×C4C2×D3211yescharacteristic
412Q16—62no—
413SD16—62no—
414SD16—62no—
415D8—62no—
416M16—61no—
417M16—61no—
418M16—61no—
419M16—61no—
420M16—61no—
421M16—61no—
422M16—181no—
423M16—181no—
424C2×C8—32no—
425C2×C8—61no—
426C2×C8—61no—
427C2×C8—181no—
428C42—91no—
429C42—91no—
430C42—181no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—81no—
441C22×C3—81no—
442C22×C3—82no—
443C22×C3—121no—
444C22×C3—241no—
445C22×C3#88311yescharacteristic
446C22×C3#88411yescharacteristic
447C22×C3#92911yescharacteristic
448C22×C3#93511yescharacteristic
449C22×C3#93511yescharacteristic
450C22×C3#93811yescharacteristic
451C2×D3—41no—
452C2×D3—81no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—121no—
461C3×C4#88411yescharacteristic
462C3×C4#88511yescharacteristic
463C3×C4#93611yescharacteristic
464C3×C4#93711yescharacteristic
465C3×C4#93911yescharacteristic
466C3×C4#93911yescharacteristic
467C3×C4#93911yescharacteristic
468C3×C4#95311yescharacteristic
469Dic3—41no—
470Dic3—62no—
471Dic3—62no—
472Dic3—122no—
473Dic3—121no—
474Dic3—121no—
475Dic3—122no—
476C32#205011yescharacteristic, complemented, Sylow
477C23—21no—
478C23—61no—
479C23#380411yescharacteristic
480Q8—21no—
481Q8—21no—
482Q8—61no—
483Q8—61no—
484D4—21no—
485D4—21no—
486D4—41no—
487D4—41no—
488D4—61no—
489D4—61no—
490D4—121no—
491D4—121no—
492C2×C4—21no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—61no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—362no—
501C2×C4#380411yescharacteristic
502C2×C4#380511yescharacteristic
503C2×C4C2×#62511yescharacteristic
504C2×C4D3×#6711yescharacteristic
505C2×C4D3×#6711yescharacteristic
506C2×C4#381111yescharacteristic
507C8—62no—
508C8—121no—
509C8—121no—
510C8—361no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—41no—
520C2×C3—41no—
521C2×C3—82no—
522C2×C3—81no—
523C2×C3—81no—
524C2×C3—241no—
525C2×C3#495911yescharacteristic
526C2×C3#522211yescharacteristic
527D3—81no—
528C22—41no—
529C22—41no—
530C22—81no—
531C22—121no—
532C22—241no—
533C22#6395811yescharacteristic
534C22#6396111yescharacteristic
535C22#6396911yescharacteristic
536C4—41no—
537C4—121no—
538C4—182no—
539C4—361no—
540C4#6395911yescharacteristic
541C4#6397111yescharacteristic
542C4#6397611yescharacteristic
543C4#6398011yescharacteristic
544C3—21no—
545C3#7014411yescharacteristic, complemented
546C3#7211711yescharacteristic, complemented
547C2—21no—
548C2—21no—
549C2—21no—
550C2—81no—
551C2—241no—
552C2#1059170811yescharacteristic
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. C2×#63664C2semidirect
3. C3×#5237C2semidirect
4. #10591120C2semidirect
5. C2×#63568C2semidirect
6. #10591076C2semidirect
7. #10589159C2semidirect
35. #5237D3semidirect
476. C32#2050semidirect
545. C3#70144semidirect
546. C3#72117semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
C2×#636642
C3×#52372
#105911202
C2×#635682
#105910762
#105891592
#721173
#701443