Finite Group Databasebeta

← #11792737

Subgroups — #11792737

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×#3744C211yesmaximal, characteristic, complemented
2C2×#63831C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic
4C3×#5110C211yesmaximal, characteristic, complemented
5C2×#63561C211yesmaximal, characteristic, complemented
6C2×#63559C211yesmaximal, characteristic, complemented
7C3×#4552C211yesmaximal, characteristic, complemented
8#70007—31nomaximal
9#68943—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×#3744—22no—
15C2×#3744—22no—
16C2×#3744—22no—
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×#3719—21no—
21C2×#3717—21no—
22#63831—22no—
23#63831—22no—
24C2×#3716—21no—
25#63825—22no—
26#63825—22no—
27C2×#3714—21no—
28C3×(C2×D3)⋊C8—22no—
29#63561—22no—
30#63559—22no—
31C2×#951—31no—
32C2×#949—31no—
33C2×#909—31no—
34C2×#908—31no—
35C22×#204—31no—
36C22×#204—31no—
37C22×#204—61no—
38C3×#408—31no—
39C2×#824—31no—
40C2×#824—31no—
41C2×#823—31no—
42C2×#823—31no—
43#5110D311yescharacteristic, complemented
44C3×#341—31no—
45#4552D311yescharacteristic, complemented
46C23×C3⋊D3—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)D412yes—
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
69C2×C32×C8—21no—
70C2×C32×C8—21no—
71C2×C32×C8D412yes—
72#3744—28no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208D412yes—
78C3×#208D412yes—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82#3719—24no—
83#3717—24no—
84#3716—24no—
85#3714—24no—
86#2019—91noSylow
87C2×C3×#41—31no—
88C2×#235C2×D311yescharacteristic
89C22×D12—31no—
90C22×D12—31no—
91C22×D12—61no—
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C2×C3×M16—31no—
96C2×C3×M16—31no—
97C2×C3×M16—31no—
98C22×C3×C8—21no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101#951—62no—
102#951—62no—
103#949—62no—
104#949—62no—
105C2×#216—61no—
106C2×#215—61no—
107C2×#214—61no—
108C2×#213—61no—
109C2×#208C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111C2×#208C2×D311yescharacteristic
112#909—62no—
113#909—62no—
114#908—62no—
115#908—62no—
116C2×Dic12—61no—
117C2×D24—61no—
118C2×#204—62no—
119C2×#204—62no—
120C2×#204—62no—
121C2×#204—62no—
122C2×#204—64no—
123C2×#204—64no—
124C2×#204—64no—
125C2×#204—61no—
126C2×#204—61no—
127C2×#204—62no—
128C2×#204—62no—
129C3×C22⋊C8—62no—
130#824—62no—
131#824—62no—
132#823—62no—
133#823—62no—
134(C2×D3)⋊C8—22no—
135C23×C32#4111yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—41no—
138C22×C3⋊D3—41no—
139C22×C3⋊D3—82no—
140C22×C3×D3—21no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—41no—
153C4⋊(C3⋊D3)—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—
167C32×C8—22no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—41no—
171C2×#137—91no—
172C2×AGL(1,ℤ/8)—91no—
173C22×SD16—91no—
174C2×#101—91no—
175C2×#100—91no—
176#408—31no—
177#341—31no—
178C23×D3—61no—
179C23×D3—61no—
180C23×D3—121no—
181C3×#41—61no—
182C3×#41—61no—
183C3×#41—61no—
184C3×#41—61no—
185C2×C3×Q8—31no—
186C2×C3×D4—31no—
187C2×C3×D4—61no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—21no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—121no—
196#235—21no—
197#235—21no—
198#235—21no—
199#235—21no—
200C2×D12—32no—
201C2×D12—32no—
202C2×D12—62no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—121no—
216C2×D12—121no—
217C2×D12—121no—
218C2×D12D1211yescharacteristic
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×Dic6D1211yescharacteristic
239C3×M16—32no—
240C3×M16—32no—
241C3×M16—61no—
242C3×M16—61no—
243C3×M16—61no—
244C3×M16—61no—
245C2×C3×C8—22no—
246C2×C3×C8—22no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—22no—
252C2×C3×C8—61no—
253C2×C3×C8—61no—
254C2×C3×C8—61no—
255C2×C3×C8D1212yes—
256C2×C3×C8#6712yes—
257#216—64no—
258#215—64no—
259#214—64no—
260#213—64no—
261#208—21no—
262#208—21no—
263#208—21no—
264#208—21no—
265#208D1212yes—
266#208D1212yes—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270Dic12—64no—
271D24—64no—
272#204—616no—
273#204—68no—
274#204—68no—
275#204—64no—
276#204—64no—
277C22×C32—22no—
278C22×C32#12111yescharacteristic
279C22×C32#12111yescharacteristic
280C22×C32#12111yescharacteristic
281C2×C3⋊D3—42no—
282C2×C3⋊D3—82no—
283C2×C3⋊D3—82no—
284C2×C3⋊D3—82no—
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×D4—91no—
296#137—182no—
297#137—182no—
298AGL(1,ℤ/8)—182no—
299AGL(1,ℤ/8)—182no—
300C2×Q16—181no—
301C2×SD16—182no—
302C2×SD16—182no—
303C2×SD16—181no—
304C2×SD16—181no—
305C2×SD16—182no—
306C2×D8—181no—
307C2×M16—31no—
308C2×M16—31no—
309C2×M16—31no—
310C22×C8D3211yescharacteristic
311#101—182no—
312#100—182no—
313C22⋊C8—62no—
314C23×C3—21no—
315C23×C3—61no—
316C23×C3#23511yescharacteristic
317C23×C3#23911yescharacteristic
318C22×D3—21no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—122no—
324C22×D3—121no—
325C22×D3—121no—
326C22×D3—121no—
327C22×D3—121no—
328C22×D3—244no—
329C22×D3—242no—
330C22×D3—242no—
331C3×Q8—61no—
332C3×Q8—61no—
333C3×D4—61no—
334C3×D4—61no—
335C3×D4—121no—
336C3×D4—121no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—61no—
344C2×C3×C4—121no—
345C2×C3×C4—121no—
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358#67—41no—
359#67—41no—
360C2×Dic3—21no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370D12—21no—
371D12—21no—
372D12—64no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—62no—
377D12—122no—
378D12—122no—
379D12—122no—
380D12—121no—
381D12—121no—
382D12—121no—
383D12—121no—
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—24no—
401C3×C8—22no—
402C3×C8—22no—
403C3×C8—62no—
404C3×C8—62no—
405C3×C8—121no—
406C3⋊C8—22no—
407C3⋊C8—22no—
408C3⋊C8—41no—
409C2×C32—21no—
410C2×C32—21no—
411C2×C32#39211yescharacteristic
412C2×C32#47112yes—
413C3⋊D3—82no—
414C3×D3—81no—
415C24—181no—
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—31no—
428C2×D4—61no—
429C2×D4—92no—
430C2×D4—181no—
431C2×D4—181no—
432C2×D4—181no—
433C2×D4—181no—
434C2×D4—181no—
435C22×C4—61no—
436C22×C4—181no—
437C22×C4C2×D3211yescharacteristic
438Q16—184no—
439SD16—188no—
440SD16—184no—
441SD16—184no—
442D8—184no—
443M16—32no—
444M16—32no—
445M16—61no—
446M16—61no—
447M16—61no—
448M16—61no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—61no—
452C2×C8—61no—
453C2×C8—61no—
454C2×C8#62612yes—
455C22×C3—24no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—122no—
462C22×C3—121no—
463C22×C3#88411yescharacteristic
464C22×C3#88411yescharacteristic
465C22×C3#89511yescharacteristic
466C22×C3#89511yescharacteristic
467C22×C3#89511yescharacteristic
468C22×C3#93011yescharacteristic
469C2×D3—42no—
470C2×D3—41no—
471C2×D3—124no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—244no—
475C2×D3—244no—
476C2×D3—242no—
477C2×D3—242no—
478C2×D3—244no—
479C2×D3—242no—
480C2×D3—242no—
481C2×D3—242no—
482C2×D3—242no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—121no—
488C3×C4#87411yescharacteristic
489C3×C4#88211yescharacteristic
490C3×C4#88211yescharacteristic
491C3×C4#88211yescharacteristic
492C3×C4#88211yescharacteristic
493C3×C4#88211yescharacteristic
494C3×C4#93711yescharacteristic
495C3×C4#94011yescharacteristic
496Dic3—41no—
497Dic3—124no—
498Dic3—122no—
499Dic3—122no—
500C32#201911yescharacteristic, complemented, Sylow
501C23—61no—
502C23—182no—
503C23—361no—
504C23—361no—
505C23—722no—
506C23#379911yescharacteristic
507Q8—61no—
508Q8—61no—
509Q8—182no—
510Q8—182no—
511Q8—361no—
512Q8—361no—
513D4—61no—
514D4—61no—
515D4—121no—
516D4—121no—
517D4—182no—
518D4—182no—
519D4—361no—
520D4—361no—
521C2×C4—61no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—182no—
525C2×C4—361no—
526C2×C4—361no—
527C2×C4D3×D1211yescharacteristic
528C2×C4D3×D1211yescharacteristic
529C2×C4D3×D1211yescharacteristic
530C2×C4C2×#62611yescharacteristic
531C2×C4#381111yescharacteristic
532C2×C4#381111yescharacteristic
533C8—22no—
534C8—62no—
535C8—62no—
536C8—121no—
537C2×C3—22no—
538C2×C3—22no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—22no—
545C2×C3—241no—
546C2×C3#467111yescharacteristic
547C2×C3#489812yes—
548C2×C3#496011yescharacteristic
549C2×C3#514112yes—
550D3—81no—
551D3—244no—
552D3—242no—
553D3—242no—
554C22—22no—
555C22—121no—
556C22—122no—
557C22—362no—
558C22—722no—
559C22—722no—
560C22—722no—
561C22#6390911yescharacteristic
562C22#6391011yescharacteristic
563C22#6391011yescharacteristic
564C4—121no—
565C4—362no—
566C4#6391111yescharacteristic
567C4#6392311yescharacteristic
568C4#6392311yescharacteristic
569C4#6398111yescharacteristic
570C3—21no—
571C3#6894311yescharacteristic, complemented
572C3#7000711yescharacteristic, complemented
573C2—21no—
574C2—21no—
575C2—241no—
576C2—722no—
577C2#1059093112yes—
578C2#1059139511yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC2×#63825C2
hypercenterC22×C8D32
hypocenterC32#2019
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3744C2semidirect
2. C2×#63831C2semidirect
4. C3×#5110C2semidirect
5. C2×#63561C2semidirect
6. C2×#63559C2semidirect
7. C3×#4552C2semidirect
43. #5110D3semidirect
45. #4552D3semidirect
500. C32#2019semidirect
571. C3#68943semidirect
572. C3#70007semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#638312
C2×#638252
C3×#51102
C2×#635612
C2×#635592
C3×#45522
#700073
#689433