Finite Group Databasebeta

← #11792730

Subgroups — #11792730

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic, complemented
4C2×C3×#833C211yesmaximal, characteristic, complemented
5C2×#63561C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#72097—31nomaximal
9#70091—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×#3754—22no—
14C2×#3754—22no—
15C2×#3754—22no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#214—21no—
18C3×#932—22no—
19C3×#932—22no—
20C2×C3×#213—21no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×#3719—21no—
25#63831—22no—
26#63831—22no—
27C2×#3716—21no—
28C3×#833—22no—
29#63561—22no—
30(C2×D3)⋊(C3⋊C8)—22no—
31C2×C3×AGL(1,ℤ/8)—31no—
32C2×#951—31no—
33C22×#214—31no—
34C22×#214—31no—
35C22×#214—61no—
36C2×#932D311yescharacteristic
37C2×#909—31no—
38C2×C3×#100—31no—
39#5234—31no—
40C2×#833D311yescharacteristic, complemented
41C2×#824—31no—
42C2×#824—31no—
43#5129—31no—
44#4558—31no—
45#4558—31no—
46C24×C32—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4D412yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634D412yes—
61C2×C3×#67—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C2×C3×D12D411yescharacteristic
67C2×C3×C4×D3—21no—
68C2×C3×Dic6D411yescharacteristic
69#3754—28no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)D412yes—
73C3×#214—24no—
74C3×#213—24no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208D412yes—
80C3×#208D412yes—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84#3719—24no—
85#3716—24no—
86#2019—91noSylow
87C2×C3×#41—31no—
88C22×C3×D4—21no—
89C22×C3×D4C2×D311yescharacteristic
90C22×C3×D4C2×D311yescharacteristic
91C2×#235C2×D311yescharacteristic
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C3×AGL(1,ℤ/8)—62no—
96C3×AGL(1,ℤ/8)—62no—
97C2×C3×SD16—61no—
98C2×C3×D8—61no—
99C2×C3×M16—31no—
100C2×C3×M16—31no—
101C2×C3×M16—31no—
102#951—62no—
103#951—62no—
104C2×#216—61no—
105C2×#214—21no—
106C2×#214—61no—
107C2×#214—62no—
108C2×#214—62no—
109C2×#214—62no—
110C2×#214—62no—
111C2×#214—64no—
112C2×#214—64no—
113C2×#214—64no—
114C2×#214—62no—
115C2×#214—62no—
116#932—22no—
117#932—22no—
118C2×#213—21no—
119C2×#208C2×D311yescharacteristic
120C2×#208C2×D311yescharacteristic
121C2×#208C2×D311yescharacteristic
122C22×C3⋊C8—31no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—61no—
125#909—62no—
126#909—62no—
127C2×Dic12—61no—
128C2×#204—61no—
129C3×#100—62no—
130#833—22no—
131#830—62no—
132#824—62no—
133#824—62no—
134(C2×D3)⋊C8—62no—
135C23×C32—22no—
136C23×C32—41no—
137C23×C32—41no—
138C23×C32—82no—
139C23×C32#4111yescharacteristic
140C22×C3×D3—21no—
141C32×D4—22no—
142C32×D4—22no—
143C32×D4—41no—
144C32×D4—41no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—41no—
153C2×C3⋊Dic3—41no—
154#634—22no—
155#634—22no—
156#634—41no—
157#634—41no—
158C3×#67—41no—
159C3×#67—41no—
160C2×C3×Dic3—21no—
161C3×D12—21no—
162C3×D12—21no—
163C3×C4×D3—41no—
164C3×C4×D3—41no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—41no—
171C2×#137—91no—
172C2×AGL(1,ℤ/8)—31no—
173C22×SD16—91no—
174C2×#101—91no—
175C2×#100—31no—
176#408—91no—
177#341—91no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—41no—
181C3×#41—61no—
182C3×#41—61no—
183C3×#41—61no—
184C3×#41—61no—
185C2×C3×Q8—31no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—22no—
199C2×C3×D4—31no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—61no—
204C2×C3×D4D1212yes—
205C2×C3×D4#6712yes—
206C22×C3×C4—21no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—21no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—121no—
214#235—21no—
215#235—21no—
216#235—21no—
217#235—21no—
218C2×D12#6711yescharacteristic
219C2×C4×D3—21no—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C2×Dic6—61no—
231C2×Dic6—61no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C2×Dic6—61no—
235C2×Dic6—121no—
236C2×Dic6—121no—
237C2×Dic6—121no—
238C2×Dic6#6711yescharacteristic
239C3×SD16—64no—
240C3×D8—64no—
241C3×M16—32no—
242C3×M16—32no—
243C3×M16—61no—
244C3×M16—61no—
245C3×M16—61no—
246C3×M16—61no—
247C2×C3×C8—61no—
248C2×C3×C8—61no—
249C2×C3×C8—61no—
250#216—64no—
251#214—24no—
252#214—64no—
253#214—616no—
254#214—68no—
255#214—68no—
256#213—24no—
257#208—21no—
258#208—21no—
259#208—21no—
260#208—21no—
261#208#6712yes—
262#208#6712yes—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8—62no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—61no—
275Dic12—64no—
276#204—64no—
277C22×C32—22no—
278C22×C32—42no—
279C22×C32—82no—
280C22×C32—82no—
281C22×C32—82no—
282C22×C32#12111yescharacteristic
283C22×C32#12111yescharacteristic
284C22×C32#12111yescharacteristic
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C32×C4#12011yescharacteristic
288C32×C4#12011yescharacteristic
289C32×C4#12011yescharacteristic
290C32×C4#12711yescharacteristic
291C3⋊Dic3—42no—
292C3×Dic3—41no—
293C2×#41—31no—
294C22×Q8—91no—
295C22×D4D3211yescharacteristic
296#137—182no—
297#137—182no—
298AGL(1,ℤ/8)—62no—
299AGL(1,ℤ/8)—62no—
300C2×Q16—181no—
301C2×SD16—61no—
302C2×SD16—181no—
303C2×SD16—182no—
304C2×SD16—182no—
305C2×SD16—182no—
306C2×D8—61no—
307C2×M16—31no—
308C2×M16—31no—
309C2×M16—31no—
310C22×C8—91no—
311#101—182no—
312#100—62no—
313C22⋊C8—182no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—61no—
325C23×C3—82no—
326C23×C3—82no—
327C23×C3—84no—
328C23×C3#23511yescharacteristic
329C23×C3#23711yescharacteristic
330C22×D3—21no—
331C3×Q8—61no—
332C3×Q8—61no—
333C3×D4—24no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—42no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—41no—
344C3×D4—41no—
345C3×D4—61no—
346C3×D4—61no—
347C3×D4—121no—
348C3×D4—121no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—61no—
356C2×C3×C4—121no—
357C2×C3×C4—121no—
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370#67—41no—
371#67—41no—
372C2×Dic3—21no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382D12—21no—
383D12—21no—
384C4×D3—41no—
385C4×D3—41no—
386Dic6—21no—
387Dic6—21no—
388Dic6—64no—
389Dic6—62no—
390Dic6—62no—
391Dic6—62no—
392Dic6—62no—
393Dic6—122no—
394Dic6—122no—
395Dic6—122no—
396Dic6—121no—
397Dic6—121no—
398Dic6—121no—
399Dic6—121no—
400C3×C8—62no—
401C3×C8—62no—
402C3×C8—121no—
403C3⋊C8—22no—
404C3⋊C8—22no—
405C3⋊C8—41no—
406C3⋊C8—64no—
407C3⋊C8—62no—
408C3⋊C8—62no—
409C2×C32—21no—
410C2×C32—21no—
411C2×C32—82no—
412C2×C32#39211yescharacteristic
413C2×C32#47112yes—
414C3×D3—81no—
415C24—21no—
416#41—61no—
417#41—61no—
418#41—61no—
419#41—61no—
420C2×Q8—31no—
421C2×Q8—92no—
422C2×Q8—181no—
423C2×Q8—181no—
424C2×Q8—181no—
425C2×Q8—181no—
426C2×Q8—181no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—31no—
433C2×D4—61no—
434C2×D4#62612yes—
435C22×C4—61no—
436C22×C4—181no—
437C22×C4C2×D3211yescharacteristic
438Q16—184no—
439SD16—64no—
440SD16—184no—
441SD16—188no—
442D8—64no—
443M16—32no—
444M16—32no—
445M16—61no—
446M16—61no—
447M16—61no—
448M16—61no—
449C2×C8—61no—
450C2×C8—61no—
451C2×C8—61no—
452C2×C8—92no—
453C2×C8—181no—
454C2×C8—181no—
455C22×C3—24no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—44no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—82no—
465C22×C3—82no—
466C22×C3—84no—
467C22×C3—84no—
468C22×C3—82no—
469C22×C3—82no—
470C22×C3—84no—
471C22×C3—82no—
472C22×C3—82no—
473C22×C3—121no—
474C22×C3—122no—
475C22×C3#88411yescharacteristic
476C22×C3#88411yescharacteristic
477C22×C3#93011yescharacteristic
478C22×C3#93811yescharacteristic
479C22×C3#93911yescharacteristic
480C22×C3#93911yescharacteristic
481C2×D3—42no—
482C2×D3—41no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—121no—
488C3×C4#88211yescharacteristic
489C3×C4#88211yescharacteristic
490C3×C4#93711yescharacteristic
491C3×C4#93711yescharacteristic
492C3×C4#93711yescharacteristic
493C3×C4#94011yescharacteristic
494C3×C4#94011yescharacteristic
495C3×C4#95311yescharacteristic
496Dic3—41no—
497Dic3—124no—
498Dic3—122no—
499Dic3—122no—
500C32#201911yescharacteristic, complemented, Sylow
501C23—22no—
502C23—41no—
503C23—41no—
504C23—61no—
505C23—82no—
506C23#380411yescharacteristic
507Q8—61no—
508Q8—61no—
509Q8—182no—
510Q8—182no—
511Q8—361no—
512Q8—361no—
513D4—22no—
514D4—22no—
515D4—41no—
516D4—41no—
517D4—61no—
518D4—61no—
519D4—121no—
520D4—121no—
521C2×C4—61no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—182no—
525C2×C4—361no—
526C2×C4—361no—
527C2×C4C2×#62611yescharacteristic
528C2×C4D3×#6711yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4D3×#6711yescharacteristic
531C2×C4#381111yescharacteristic
532C2×C4#381111yescharacteristic
533C8—62no—
534C8—62no—
535C8—121no—
536C8—182no—
537C2×C3—22no—
538C2×C3—22no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—84no—
546C2×C3—82no—
547C2×C3—82no—
548C2×C3—241no—
549C2×C3#474812yes—
550C2×C3#496011yescharacteristic
551C2×C3#520012yes—
552C2×C3#522311yescharacteristic
553D3—81no—
554C22—22no—
555C22—42no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—122no—
560C22—121no—
561C22#6395811yescharacteristic
562C22#6397111yescharacteristic
563C22#6397811yescharacteristic
564C4—121no—
565C4—362no—
566C4#6397711yescharacteristic
567C4#6397911yescharacteristic
568C4#6398111yescharacteristic
569C4#6398311yescharacteristic
570C3—21no—
571C3#7009111yescharacteristic, complemented
572C3#7209711yescharacteristic, complemented
573C2—21no—
574C2—21no—
575C2—82no—
576C2—241no—
577C2#1059150712yes—
578C2#1059172411yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×C3×#932C2
hypercenterC22×D4D32
hypocenterC32#2019
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3754C2semidirect
3. C2×#63831C2semidirect
4. C2×C3×#833C2semidirect
5. C2×#63561C2semidirect
6. #10591071C2semidirect
7. #10589165C2semidirect
40. C2×#833D3semidirect
500. C32#2019semidirect
571. C3#70091semidirect
572. C3#72097semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×#9322
C2×#638312
C2×C3×#8332
C2×#635612
#105910712
#105891652
#720973
#700913