Finite Group Databasebeta

← #11793944

Subgroups — #11793944

Order 1152.

653 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic
2C3×#5234C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63561C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70310—31nomaximal
9#70004—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×#634C2211yescharacteristic
12#64160—22no—
13#64160—22no—
14C2×#3756—21no—
15C2×#3754—21no—
16C2×#3748C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#835—21no—
22C3×#832—21no—
23C3×#830—22no—
24#63577—22no—
25#63567—22no—
26#63561—22no—
27C2×#951—31no—
28C2×#951—31no—
29C2×#951—61no—
30C3×#417—31no—
31C3×#408—31no—
32#5234D311yescharacteristic
33#5232D311yescharacteristic
34C2×#824—31no—
35C2×#824—31no—
36C2×#822—31no—
37C2×#819—31no—
38C2×#816—31no—
39C2×#810—31no—
40#4554—31no—
41#4530—31no—
42C32×#41—21no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C2×C32×Q8D411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634D412yes—
58C22×C3×Dic3—21no—
59#3756—24no—
60#3754—24no—
61#3748—21no—
62#3748D412yes—
63C2×C3⋊(C3⋊C8)—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
75#2052—91noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79C22×Dic6—31no—
80C22×Dic6—31no—
81C22×Dic6—61no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—31no—
86#951—62no—
87#951—62no—
88#951—62no—
89#951—62no—
90#951—64no—
91#951—64no—
92C2×#216—62no—
93C2×#216—61no—
94C2×#216—61no—
95C2×#214—62no—
96C2×#214—61no—
97C2×#214—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105C3×#103—61no—
106C3×#102—61no—
107C3×C22⋊C8—62no—
108#835—21no—
109#832—21no—
110#830—22no—
111#824—62no—
112#824—62no—
113#822—62no—
114#819—62no—
115#816—62no—
116#810—62no—
117C23×C32—21no—
118C23×C32#4111yescharacteristic
119C32×Q8—21no—
120C32×Q8—21no—
121C32×D4—21no—
122C32×D4—21no—
123C32×D4—41no—
124C32×D4—41no—
125C2×C32×C4—21no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137#634—22no—
138#634—22no—
139#634—41no—
140#634—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—81no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C3×C3⋊C8—41no—
147C2×#137—91no—
148C2×#108—91no—
149#417—31no—
150C2×#103—91no—
151C2×#101—91no—
152#408—31no—
153#343—91no—
154C3×#41—22no—
155C3×#41—22no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41—21no—
164C3×#41—41no—
165C3×#41—41no—
166C2×C3×Q8—21no—
167C2×C3×Q8D1211yescharacteristic
168C2×C3×Q8#6711yescharacteristic
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—41no—
173C2×C3×D4D1211yescharacteristic
174C2×C3×D4#6711yescharacteristic
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—41no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×Dic3—21no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—121no—
186C2×Dic6—32no—
187C2×Dic6—32no—
188C2×Dic6—62no—
189C2×Dic6—62no—
190C2×Dic6—62no—
191C2×Dic6—61no—
192C2×Dic6—61no—
193C2×Dic6—61no—
194C2×Dic6—61no—
195C2×Dic6—61no—
196C2×Dic6—61no—
197C2×Dic6—61no—
198C2×Dic6—61no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—121no—
202C2×Dic6—121no—
203C2×Dic6—121no—
204C3×M16—61no—
205C3×M16—61no—
206C3×M16—61no—
207C3×M16—61no—
208C2×C3×C8—32no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215#216—68no—
216#216—64no—
217#216—64no—
218#214—68no—
219#214—64no—
220#214—64no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223#208—21no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208—32no—
228#208—32no—
229#208—62no—
230#208—62no—
231#208—61no—
232#208—61no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8#6712yes—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32#12111yescharacteristic
247C22×C32#12311yescharacteristic
248C22×C32#12411yescharacteristic
249C32×C4—41no—
250C32×C4#12011yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12111yescharacteristic
253C32×C4#12311yescharacteristic
254C3⋊Dic3—42no—
255C3×Dic3—81no—
256C2×#41D3211yescharacteristic
257C22×Q8—91no—
258#137—182no—
259#137—182no—
260C2×Q16—181no—
261C2×SD16—181no—
262C2×M16—31no—
263C2×M16—31no—
264C2×M16—91no—
265C22×C8—31no—
266C2×C4⋊C4—31no—
267#108—182no—
268#103—61no—
269#103—182no—
270#102—61no—
271#101—182no—
272C22⋊C8—62no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—41no—
277C23×C3#23511yescharacteristic
278C23×C3#23711yescharacteristic
279C3×Q8—22no—
280C3×Q8—21no—
281C3×Q8—21no—
282C3×Q8—21no—
283C3×Q8—21no—
284C3×Q8—41no—
285C3×D4—22no—
286C3×D4—21no—
287C3×D4—21no—
288C3×D4—21no—
289C3×D4—21no—
290C3×D4—41no—
291C3×D4—42no—
292C3×D4—42no—
293C3×D4—41no—
294C3×D4—41no—
295C3×D4—41no—
296C3×D4—41no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—41no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—121no—
313C2×C3×C4—241no—
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×Dic3—41no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—81no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337Dic6—64no—
338Dic6—62no—
339Dic6—62no—
340Dic6—62no—
341Dic6—62no—
342Dic6—122no—
343Dic6—122no—
344Dic6—122no—
345Dic6—121no—
346Dic6—121no—
347Dic6—121no—
348Dic6—121no—
349C3×C8—62no—
350C3×C8—121no—
351C3×C8—121no—
352C3⋊C8—22no—
353C3⋊C8—41no—
354C3⋊C8—41no—
355C3⋊C8—64no—
356C3⋊C8—62no—
357C3⋊C8—62no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—81no—
361C2×C32#39411yescharacteristic
362C2×C32#47111yescharacteristic
363C2×C32#47311yescharacteristic
364#41—21no—
365#41—21no—
366#41—21no—
367#41—21no—
368C2×Q8—92no—
369C2×Q8—181no—
370C2×Q8—181no—
371C2×Q8—181no—
372C2×Q8—181no—
373C2×Q8—181no—
374C2×Q8#62611yescharacteristic
375C2×D4—21no—
376C2×D4#62611yescharacteristic
377C22×C4—21no—
378C22×C4—61no—
379C22×C4—181no—
380C22×C4C2×D3211yescharacteristic
381Q16—184no—
382SD16—184no—
383M16—61no—
384M16—61no—
385M16—61no—
386M16—61no—
387M16—92no—
388M16—181no—
389C2×C8—32no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—61no—
393C2×C8—61no—
394C2×C8—181no—
395C4⋊C4—61no—
396C4⋊C4—61no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—42no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3#88311yescharacteristic
416C22×C3#88311yescharacteristic
417C22×C3#88511yescharacteristic
418C22×C3#88511yescharacteristic
419C22×C3#93011yescharacteristic
420C22×C3#93911yescharacteristic
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—42no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—241no—
429C3×C4#88211yescharacteristic
430C3×C4#88411yescharacteristic
431C3×C4#88411yescharacteristic
432C3×C4#88611yescharacteristic
433C3×C4#92911yescharacteristic
434C3×C4#93711yescharacteristic
435C3×C4#93811yescharacteristic
436C3×C4#93911yescharacteristic
437Dic3—81no—
438Dic3—124no—
439Dic3—122no—
440Dic3—122no—
441C32#205211yescharacteristic, complemented, Sylow
442C23—21no—
443C23#380411yescharacteristic
444Q8—21no—
445Q8—21no—
446Q8—182no—
447Q8—182no—
448Q8—361no—
449Q8—361no—
450D4—21no—
451D4—21no—
452D4—41no—
453D4—41no—
454C2×C4—21no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—121no—
458C2×C4—182no—
459C2×C4—241no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4#380411yescharacteristic
463C2×C4#380411yescharacteristic
464C2×C4C2×#62611yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C2×C4#381111yescharacteristic
467C2×C4#381111yescharacteristic
468C8—62no—
469C8—121no—
470C8—121no—
471C8—182no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—41no—
480C2×C3—41no—
481C2×C3—82no—
482C2×C3—81no—
483C2×C3—81no—
484C2×C3#495911yescharacteristic
485C2×C3#496111yescharacteristic
486C2×C3#514111yescharacteristic
487C2×C3#514311yescharacteristic
488C2×C3#520011yescharacteristic
489C2×C3#520411yescharacteristic
490C22—21no—
491C22—21no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22#6395311yescharacteristic
496C22#6397511yescharacteristic
497C22#6397811yescharacteristic
498C4—41no—
499C4—241no—
500C4—362no—
501C4#6395811yescharacteristic
502C4#6396611yescharacteristic
503C4#6397111yescharacteristic
504C4#6398111yescharacteristic
505C3—21no—
506C3#7000411yescharacteristic, complemented
507C3#7031011yescharacteristic, complemented
508C2—21no—
509C2—21no—
510C2—81no—
511C2#1059167911yescharacteristic
512C2#1059168211yescharacteristic
513C2#1059171211yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#121
hypercenterC2×#41D32
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. C2×#63567C2semidirect
6. C2×#63561C2semidirect
7. #10589167C2semidirect
441. C32#2052semidirect
506. C3#70004semidirect
507. C3#70310semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C3×#52342
C3×#52322
C2×#635772
C2×#635672
C2×#635612
#105891672
#703103
#700043