Finite Group Databasebeta

← #11792770

Subgroups — #11792770

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic
5C2×#63561C211yesmaximal, characteristic, complemented
6C2×#63560C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72109—31nomaximal
9#70008—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13#64160—22no—
14#64160—22no—
15C2×#3756—21no—
16C2×#3754—21no—
17C2×#3748C2211yescharacteristic
18C3×#951—22no—
19C3×#951—22no—
20C2×C3×#216—21no—
21C2×C3×#214—21no—
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3719—22no—
26C2×#3719—22no—
27C2×#3719—22no—
28C3×#830—22no—
29#63561—22no—
30#63560—22no—
31C2×C3×#137—31no—
32C2×#951—31no—
33C2×#951—31no—
34C2×#951—61no—
35C2×#951D311yescharacteristic
36C22×#216—31no—
37C22×Dic12—31no—
38C3×#408—31no—
39#5234D311yescharacteristic
40C2×#836—31no—
41C2×#824—31no—
42C2×#824—31no—
43C2×#824—31no—
44#4558—31no—
45#4552—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×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634D412yes—
62C22×C3×Dic3—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6D412yes—
69#3756—24no—
70#3754—24no—
71#3748—21no—
72#3748D412yes—
73C2×C3⋊(C3⋊C8)—21no—
74C3×#216—24no—
75C3×#214—24no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208D412yes—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84C2×C3×C3⋊C8D412yes—
85#3719—28no—
86#2020—91noSylow
87C2×C3×#41—21no—
88C2×C3×#41C2×D311yescharacteristic
89C2×C3×#41C2×D311yescharacteristic
90C22×C3×Q8—31no—
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C3×#137—62no—
96C3×#137—62no—
97C2×C3×Q16—61no—
98C2×C3×SD16—61no—
99C2×C3×M16—31no—
100C2×C3×M16—31no—
101C22×C3×C8—31no—
102#951—22no—
103#951—22no—
104#951—62no—
105#951—62no—
106#951—62no—
107#951—62no—
108#951—64no—
109#951—64no—
110C2×#216—21no—
111C2×#216—62no—
112C2×#216—62no—
113C2×#216—62no—
114C2×#216—61no—
115C2×#216—61no—
116C2×#216—62no—
117C2×#214—21no—
118C2×#214—62no—
119C2×#214—61no—
120C2×#214—61no—
121C2×#208—31no—
122C2×#208—31no—
123C2×#208—61no—
124C2×#208C2×D311yescharacteristic
125C2×#208C2×D311yescharacteristic
126C22×C3⋊C8C2×D311yescharacteristic
127C2×Dic12—62no—
128C2×Dic12—62no—
129C2×Dic12—62no—
130C3×C22⋊C8—62no—
131#836—62no—
132#830—22no—
133#824—62no—
134#824—62no—
135#824—62no—
136C23×C32—21no—
137C23×C32#4111yescharacteristic
138C32×Q8—21no—
139C32×Q8—21no—
140C32×D4—21no—
141C32×D4—21no—
142C32×D4—41no—
143C32×D4—41no—
144C2×C32×C4—21no—
145C2×C32×C4—41no—
146C2×C32×C4—41no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—41no—
155C2×C3⋊Dic3—41no—
156#634—22no—
157#634—22no—
158#634—41no—
159#634—41no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—41no—
162C2×C3×Dic3—41no—
163C3×Dic6—22no—
164C3×Dic6—22no—
165C3×Dic6—41no—
166C3×Dic6—41no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—41no—
171C2×#137—31no—
172C2×#137—91no—
173C22×Q16—91no—
174C2×#101—91no—
175C2×#101—91no—
176#408—31no—
177#341—91no—
178C3×#41—22no—
179C3×#41—22no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—21no—
186C3×#41—21no—
187C3×#41—21no—
188C3×#41—41no—
189C3×#41—41no—
190C2×C3×Q8—21no—
191C2×C3×Q8—32no—
192C2×C3×Q8—61no—
193C2×C3×Q8—61no—
194C2×C3×Q8—61no—
195C2×C3×Q8—61no—
196C2×C3×Q8—61no—
197C2×C3×Q8D1211yescharacteristic
198C2×C3×Q8#6711yescharacteristic
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—41no—
203C2×C3×D4D1211yescharacteristic
204C2×C3×D4#6711yescharacteristic
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—41no—
209C22×C3×C4—61no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×Dic3—21no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215C22×Dic3—121no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—32no—
222C2×Dic6—32no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
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—61no—
236C2×Dic6—121no—
237C2×Dic6—121no—
238C2×Dic6—121no—
239C2×Dic6#6712yes—
240C3×Q16—64no—
241C3×SD16—64no—
242C3×M16—32no—
243C3×M16—61no—
244C3×M16—61no—
245C3×M16—61no—
246C2×C3×C8—32no—
247C2×C3×C8—61no—
248C2×C3×C8—61no—
249C2×C3×C8—61no—
250C2×C3×C8—61no—
251#216—24no—
252#216—68no—
253#216—68no—
254#216—64no—
255#216—64no—
256#214—24no—
257#214—68no—
258#214—64no—
259#214—64no—
260#208—21no—
261#208—21no—
262#208—21no—
263#208—32no—
264#208—32no—
265#208—62no—
266#208—62no—
267#208—61no—
268#208—61no—
269#208#6712yes—
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8#6712yes—
278Dic12—68no—
279C22×C32—22no—
280C22×C32—41no—
281C22×C32—42no—
282C22×C32#12111yescharacteristic
283C22×C32#12111yescharacteristic
284C22×C32#12111yescharacteristic
285C32×C4—41no—
286C32×C4#12011yescharacteristic
287C32×C4#12011yescharacteristic
288C32×C4#12011yescharacteristic
289C32×C4#12711yescharacteristic
290C3⋊Dic3—42no—
291C3×Dic3—42no—
292C2×#41D3211yescharacteristic
293C22×Q8—31no—
294C22×Q8—91no—
295#137—62no—
296#137—62no—
297#137—182no—
298#137—182no—
299C2×Q16—61no—
300C2×Q16—182no—
301C2×Q16—182no—
302C2×Q16—182no—
303C2×Q16—181no—
304C2×SD16—61no—
305C2×SD16—181no—
306C2×M16—31no—
307C2×M16—31no—
308C2×M16—91no—
309C22×C8—31no—
310#101—182no—
311#101—182no—
312C22⋊C8—62no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—41no—
317C23×C3#23511yescharacteristic
318C23×C3#23711yescharacteristic
319C3×Q8—22no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—41no—
325C3×Q8—62no—
326C3×Q8—62no—
327C3×Q8—121no—
328C3×Q8—121no—
329C3×D4—22no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—41no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—41no—
338C3×D4—41no—
339C3×D4—41no—
340C3×D4—41no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—41no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—62no—
357C2×C3×C4—121no—
358C2×C3×C4—121no—
359C2×C3×C4C2×D1211yescharacteristic
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×C4D3×D411yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×Dic3—22no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383Dic6—22no—
384Dic6—22no—
385Dic6—41no—
386Dic6—41no—
387Dic6—64no—
388Dic6—62no—
389Dic6—62no—
390Dic6—62no—
391Dic6—62no—
392Dic6—122no—
393Dic6—122no—
394Dic6—122no—
395Dic6—121no—
396Dic6—121no—
397Dic6—121no—
398Dic6—121no—
399C3×C8—62no—
400C3×C8—62no—
401C3×C8—121no—
402C3⋊C8—22no—
403C3⋊C8—22no—
404C3⋊C8—41no—
405C3⋊C8—64no—
406C3⋊C8—62no—
407C3⋊C8—62no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32—81no—
411C2×C32#39211yescharacteristic
412C2×C32#47312yes—
413#41—21no—
414#41—21no—
415#41—21no—
416#41—21no—
417C2×Q8—32no—
418C2×Q8—61no—
419C2×Q8—61no—
420C2×Q8—61no—
421C2×Q8—61no—
422C2×Q8—61no—
423C2×Q8—92no—
424C2×Q8—181no—
425C2×Q8—181no—
426C2×Q8—181no—
427C2×Q8—181no—
428C2×Q8—181no—
429C2×Q8#62611yescharacteristic
430C2×D4—21no—
431C2×D4#62611yescharacteristic
432C22×C4—21no—
433C22×C4—61no—
434C22×C4—181no—
435C22×C4C2×D3211yescharacteristic
436Q16—64no—
437Q16—188no—
438Q16—184no—
439SD16—64no—
440SD16—184no—
441M16—32no—
442M16—61no—
443M16—61no—
444M16—61no—
445M16—92no—
446M16—181no—
447C2×C8—32no—
448C2×C8—61no—
449C2×C8—61no—
450C2×C8—61no—
451C2×C8—61no—
452C2×C8—181no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—82no—
465C22×C3#88411yescharacteristic
466C22×C3#88411yescharacteristic
467C22×C3#93011yescharacteristic
468C22×C3#93811yescharacteristic
469C22×C3#93911yescharacteristic
470C22×C3#93911yescharacteristic
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—42no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—122no—
479C3×C4#88211yescharacteristic
480C3×C4#88211yescharacteristic
481C3×C4#93711yescharacteristic
482C3×C4#93711yescharacteristic
483C3×C4#93711yescharacteristic
484C3×C4#94011yescharacteristic
485C3×C4#94011yescharacteristic
486C3×C4#95311yescharacteristic
487Dic3—42no—
488Dic3—124no—
489Dic3—122no—
490Dic3—122no—
491C32#202011yescharacteristic, complemented, Sylow
492C23—21no—
493C23#380411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—62no—
497Q8—62no—
498Q8—121no—
499Q8—121no—
500Q8—182no—
501Q8—182no—
502Q8—361no—
503Q8—361no—
504D4—21no—
505D4—21no—
506D4—41no—
507D4—41no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—62no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—182no—
515C2×C4—361no—
516C2×C4—361no—
517C2×C4C2×#62611yescharacteristic
518C2×C4D3×#6711yescharacteristic
519C2×C4D3×#6711yescharacteristic
520C2×C4D3×#6711yescharacteristic
521C2×C4#381111yescharacteristic
522C2×C4#381111yescharacteristic
523C8—62no—
524C8—62no—
525C8—121no—
526C8—182no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—22no—
532C2×C3—21no—
533C2×C3—41no—
534C2×C3—41no—
535C2×C3—82no—
536C2×C3—81no—
537C2×C3—81no—
538C2×C3#496011yescharacteristic
539C2×C3#514312yes—
540C2×C3#520412yes—
541C2×C3#522311yescharacteristic
542C22—22no—
543C22—42no—
544C22—41no—
545C22#6395811yescharacteristic
546C22#6397111yescharacteristic
547C22#6397811yescharacteristic
548C4—41no—
549C4—122no—
550C4—362no—
551C4#6397711yescharacteristic
552C4#6397911yescharacteristic
553C4#6398111yescharacteristic
554C4#6398311yescharacteristic
555C3—21no—
556C3#7000811yescharacteristic, complemented
557C3#7210911yescharacteristic, complemented
558C2—21no—
559C2—21no—
560C2—81no—
561C2#1059168212yes—
562C2#1059172411yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#121
hypercenterC2×#41D32
hypocenterC32#2020
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
3. C22×#3719C2semidirect
5. C2×#63561C2semidirect
6. C2×#63560C2semidirect
7. #10589166C2semidirect
491. C32#2020semidirect
556. C3#70008semidirect
557. C3#72109semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C2×C3×#9512
C22×#37192
C3×#52342
C2×#635612
C2×#635602
#105891662
#721093
#700083