Finite Group Databasebeta

← #11867813

Subgroups — #11867813

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595997C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic, complemented
4C2×#63817C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic, complemented
6C3×#4995C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590525C212yesmaximal, complemented
9#10590524C212yesmaximal, complemented
10#10590507C212yesmaximal, complemented
11#10590506C212yesmaximal, complemented
12#79214—31nomaximal
13#78841—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C32×#117C2211yescharacteristic
18#64106C2212yes—
19#64106C2212yes—
20#64095—22no—
21#64084—21no—
22#64078—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63978—22no—
27#63916C2212yes—
28#63909—21no—
29#63871C2212yes—
30#63857—21no—
31C2×#3719C2212yes—
32#63831—24no—
33C2×#3716C2212yes—
34C2×#3712C2212yes—
35#63817—24no—
36C2×#3710C2212yes—
37C3×#810C2211yescharacteristic
38C3×#810C2211yescharacteristic
39C3×#809C2211yescharacteristic
40C3×#809C2211yescharacteristic
41C3×#808C2212yes—
42C3×#807C2212yes—
43#63567C2212yes—
44#63567C2212yes—
45#5833—31no—
46C2×#951—31no—
47C2×#909—31no—
48C2×#907—31no—
49C2×#901—31no—
50#5526—31no—
51#5526—31no—
52#5526—61no—
53#5510—31no—
54C3×#428—31no—
55C3×#416—31no—
56C2×#816—31no—
57#5002D311yescharacteristic, complemented
58#4995D311yescharacteristic, complemented
59C2×#810—31no—
60#4887—32no—
61#4886—32no—
62#4867—32no—
63#4864—32no—
64#4816—32no—
65#4813—32no—
66#4780—32no—
67#4778—32no—
68C22×C32×C4C2311yescharacteristic
69C2×#638D412yes—
70C22×C3⋊Dic3—21no—
71#3828—22no—
72#3828—22no—
73C2×C4⋊(C3⋊D3)D411yescharacteristic
74C2×C4×C3⋊D3C2312yes—
75C2×#634—22no—
76C2×#634—22no—
77C2×#634—21no—
78C2×#634D411yescharacteristic
79C2×#634C2312yes—
80C2×C3×#67—21no—
81C22×C3×Dic3—21no—
82C3×#235—22no—
83C3×#235—22no—
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3—21no—
86C2×C3×Dic6C2311yescharacteristic
87C2×#626—22no—
88C32×C4⋊C4C2311yescharacteristic
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91C32×C42—21no—
92#3752—22no—
93#3752—22no—
94C4⋊(C3⋊Dic3)—22no—
95C4⋊(C3⋊Dic3)—22no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2312yes—
98C3×#208D414yescomplemented
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—22no—
104#3722—22no—
105(C2×D3)⋊Dic3—22no—
106#3719—24no—
107#3716—24no—
108#3712—24no—
109#3710—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C2×#235—31no—
113C2×#235—31no—
114C2×#235—61no—
115C2×#235C2×D311yescharacteristic
116C22×Dic6—31no—
117C22×Dic6—31no—
118C22×Dic6—61no—
119C2×C3×M16—31no—
120C22×C3×C8—31no—
121C3×#117—21no—
122C3×#117C2×D311yescharacteristic
123C3×#117C2×D311yescharacteristic
124C2×C3×C4⋊C4—31no—
125#951—64no—
126#946—32no—
127C2×#216—32no—
128#939—62no—
129#938—32no—
130C2×#214—32no—
131#930—61no—
132#930—62no—
133C2×C4⋊Dic3C2×D311yescharacteristic
134#924—61no—
135C2×#208C2×D311yescharacteristic
136C22×C3⋊C8C2×D311yescharacteristic
137#909—64no—
138#907—64no—
139C2×Dic12—32no—
140C2×#204—32no—
141#901—64no—
142C2×ΓL(1,𝔽25)—32no—
143C2×ΓL(1,𝔽25)—32no—
144C2×D3×C8—32no—
145C2×D3×C8—32no—
146#897—32no—
147#897—32no—
148#897—32no—
149#897—32no—
150#897—32no—
151#897—62no—
152#897—62no—
153#897—61no—
154#895—32no—
155#895—61no—
156#886—62no—
157#886—62no—
158#886—64no—
159#875—61no—
160#875—61no—
161#875—62no—
162#869—61no—
163#869—61no—
164#869—62no—
165C3×#107—32no—
166C3×#106—32no—
167C3×#103—31no—
168C3×#103—31no—
169C3×#102—31no—
170C3×#102—31no—
171#816—32no—
172#816—32no—
173#810—32no—
174#810—32no—
175#810C2×D311yescharacteristic
176#810C2×D311yescharacteristic
177#809C2×D311yescharacteristic
178#809C2×D311yescharacteristic
179#808C2×D312yes—
180#807C2×D312yes—
181C23×C32C2×D411yescharacteristic
182C22×C3⋊D3C2×D412yes—
183C22×C3×D3—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4C2×D412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190#638—24no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—42no—
193C2×C3⋊Dic3C2×D412yes—
194C4⋊(C3⋊D3)—22no—
195C4×C3⋊D3—22no—
196C4×C3⋊D3—22no—
197#634—22no—
198#634—22no—
199#634—22no—
200#634—42no—
201C3×#67—42no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—81no—
205C3×D12—21no—
206C3×D12—21no—
207C3×C4×D3—42no—
208C3×Dic6—21no—
209C3×Dic6—21no—
210#626—82no—
211C3×C3⋊C8—21no—
212C3×C3⋊C8—21no—
213C3×C3⋊C8C2×D414yes—
214C2×#137—91no—
215C2×#131—91no—
216#537—91no—
217#536—91no—
218#470—92no—
219#468—92no—
220#467—92no—
221#465—92no—
222#428—31no—
223#416—31no—
224C2×#103—91no—
225C3×#41—62no—
226C3×#41—62no—
227C2×C3×Q8—31no—
228C2×C3×D4—31no—
229C2×C3×D4—61no—
230C22×C3×C4—21no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—21no—
236C2×#67—32no—
237C2×#67—32no—
238C2×#67—62no—
239C2×#67—62no—
240C22×Dic3—21no—
241C22×Dic3—62no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244#235—22no—
245#235—22no—
246#235—62no—
247#235—62no—
248#235—62no—
249#235—62no—
250#235—122no—
251#235—122no—
252C2×D12—31no—
253C2×D12—31no—
254C2×D12—61no—
255C2×D12—62no—
256C2×D12C22×D311yescharacteristic
257C2×C4×D3—21no—
258C2×C4×D3—32no—
259C2×C4×D3—32no—
260C2×C4×D3—62no—
261C2×Dic6—31no—
262C2×Dic6—31no—
263C2×Dic6—32no—
264C2×Dic6—32no—
265C2×Dic6—61no—
266C2×Dic6—62no—
267C2×Dic6—62no—
268C2×Dic6—62no—
269C2×Dic6—62no—
270C2×Dic6—62no—
271C2×Dic6—62no—
272C2×Dic6—61no—
273C2×Dic6—61no—
274C2×Dic6—122no—
275C2×Dic6—122no—
276C2×Dic6C22×D311yescharacteristic
277C3×M16—34no—
278C2×C3×C8—32no—
279C2×C3×C8—31no—
280C2×C3×C8—31no—
281C2×C3×C8—62no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—32no—
285C3×C4⋊C4—61no—
286C3×C4⋊C4C22×D311yescharacteristic
287C3×C4⋊C4C22×D311yescharacteristic
288C3×C4⋊C4C22×D311yescharacteristic
289C3×C4⋊C4C22×D311yescharacteristic
290C3×C22⋊C4—22no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C42—22no—
294C3×C42—21no—
295C3×C42—21no—
296#217—62no—
297#216—64no—
298#214—64no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—62no—
305(C2×D3)⋊C4—62no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—64no—
308C4⋊Dic3—21no—
309C4⋊Dic3—62no—
310C4⋊Dic3—62no—
311C4⋊Dic3—62no—
312C4⋊Dic3—62no—
313C4⋊Dic3—62no—
314C4⋊Dic3—64no—
315C4⋊Dic3—64no—
316C4⋊Dic3C22×D312yes—
317Dic3⋊C4—62no—
318#208D1214yescomplemented
319C2×C3⋊C8—22no—
320C2×C3⋊C8C22×D311yescharacteristic
321C2×C3⋊C8C22×D311yescharacteristic
322C2×C3⋊C8C22×D312yes—
323Dic12—64no—
324#204—64no—
325ΓL(1,𝔽25)—64no—
326ΓL(1,𝔽25)—64no—
327D3×C8—64no—
328D3×C8—64no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32#12112yes—
332C22×C32C22×D411yescharacteristic
333C2×C3⋊D3—22no—
334C2×C3⋊D3—22no—
335C2×C3⋊D3—22no—
336C2×C3×D3—41no—
337C2×C3×D3—41no—
338C2×C3×D3—41no—
339C32×C4—41no—
340C32×C4—41no—
341C32×C4#12112yes—
342C32×C4C22×D411yescharacteristic
343C32×C4C2×#4111yescharacteristic
344C3⋊Dic3—22no—
345C3⋊Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3—42no—
348C2×#41—31no—
349C2×#41—91no—
350C22×Q8—91no—
351#137—184no—
352C2×Q16—92no—
353C2×SD16—92no—
354#131—184no—
355C2×M16—31no—
356C2×M16—92no—
357C22×C8—31no—
358C22×C8—92no—
359C4⋊Q8—181no—
360#124—181no—
361#123—182no—
362C22⋊Q8—92no—
363C22⋊Q8—92no—
364C22⋊Q8—92no—
365C22⋊Q8—181no—
366#121—92no—
367#121—181no—
368#121—182no—
369#117D3211yescharacteristic
370C2×C4⋊C4—31no—
371#107—32no—
372#106—32no—
373#103—31no—
374#103—31no—
375#103—92no—
376#103—92no—
377#102—31no—
378#102—31no—
379C23×C3—21no—
380C23×C3—61no—
381C23×C3D3×D411yescharacteristic
382C23×C3D3×D411yescharacteristic
383C22×D3—21no—
384C22×D3—32no—
385C22×D3—32no—
386C22×D3—62no—
387C3×Q8—61no—
388C3×Q8—61no—
389C3×D4—61no—
390C3×D4—61no—
391C3×D4—122no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—122no—
405C2×C3×C4—241no—
406C2×C3×C4C2×D1212yes—
407C2×C3×C4#23512yes—
408C2×C3×C4D3×D412yes—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4#23912yes—
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414#67—42no—
415#67—64no—
416#67—64no—
417#67—124no—
418#67—242no—
419C2×Dic3—22no—
420C2×Dic3—21no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—62no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—81no—
428C2×Dic3—124no—
429C2×Dic3—122no—
430C2×Dic3—122no—
431D12—21no—
432D12—21no—
433D12—62no—
434D12—62no—
435D12—122no—
436D12—242no—
437C4×D3—42no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—62no—
442C4×D3—122no—
443C4×D3—122no—
444Dic6—21no—
445Dic6—21no—
446Dic6—62no—
447Dic6—62no—
448Dic6—62no—
449Dic6—62no—
450Dic6—62no—
451Dic6—62no—
452Dic6—122no—
453Dic6—122no—
454Dic6—122no—
455Dic6—124no—
456Dic6—122no—
457Dic6—122no—
458C3×C8—34no—
459C3×C8—61no—
460C3×C8—61no—
461C3⋊C8—21no—
462C3⋊C8—21no—
463C3⋊C8C2×D1214yes—
464C2×C32—22no—
465C2×C32C2×#12111yescharacteristic
466C2×C32#57711yescharacteristic
467C2×C32#57811yescharacteristic
468C3⋊D3—42no—
469C3×D3—81no—
470#41—62no—
471#41—62no—
472#41—182no—
473#41—182no—
474C2×Q8—31no—
475C2×Q8—91no—
476C2×Q8—92no—
477C2×Q8—181no—
478C2×Q8—182no—
479C2×Q8—182no—
480C2×D4—31no—
481C2×D4—61no—
482C2×D4—92no—
483C2×D4—91no—
484C2×D4—182no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—92no—
488C22×C4—181no—
489C22×C4C2×D3211yescharacteristic
490Q16—184no—
491SD16—184no—
492M16—34no—
493M16—184no—
494C2×C8—32no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—62no—
498C2×C8—184no—
499C4⋊C4—32no—
500C4⋊C4—61no—
501C4⋊C4—182no—
502C4⋊C4—182no—
503C4⋊C4—182no—
504C4⋊C4C2×D3211yescharacteristic
505C4⋊C4C2×D3211yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—182no—
508C22⋊C4—182no—
509C22⋊C4—182no—
510C22⋊C4—182no—
511C42—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—22no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—121no—
521C22×C3—121no—
522C22×C3—121no—
523C22×C3#88412yes—
524C22×C3#89512yes—
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C2×D3×D411yescharacteristic
527C2×D3—41no—
528C2×D3—41no—
529C2×D3—41no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—62no—
534C2×D3—62no—
535C2×D3—62no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—22no—
542C3×C4—42no—
543C3×C4—42no—
544C3×C4—41no—
545C3×C4—41no—
546C3×C4—41no—
547C3×C4—41no—
548C3×C4—121no—
549C3×C4—122no—
550C3×C4#88412yes—
551C3×C4#89512yes—
552C3×C4C22×D1211yescharacteristic
553C3×C4C2×#23511yescharacteristic
554C3×C4C2×D3×D411yescharacteristic
555C3×C4C2×#23911yescharacteristic
556Dic3—41no—
557Dic3—42no—
558Dic3—62no—
559Dic3—62no—
560Dic3—122no—
561Dic3—124no—
562Dic3—122no—
563Dic3—122no—
564C32#306311yescharacteristic, complemented, Sylow
565C23—61no—
566C23—92no—
567C23#381111yescharacteristic
568Q8—61no—
569Q8—61no—
570Q8—182no—
571Q8—182no—
572Q8—182no—
573Q8—362no—
574D4—61no—
575D4—61no—
576D4—122no—
577D4—184no—
578D4—182no—
579D4—722no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—62no—
583C2×C4—61no—
584C2×C4—92no—
585C2×C4—122no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—241no—
590C2×C4—362no—
591C2×C4#379912yes—
592C2×C4D3×D1212yes—
593C2×C4#381111yescharacteristic
594C2×C4C22×D3211yescharacteristic
595C8—34no—
596C8—61no—
597C8—61no—
598C2×C3—22no—
599C2×C3—22no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—42no—
604C2×C3—241no—
605C2×C3C2×#88411yescharacteristic
606C2×C3C2×#89511yescharacteristic
607C2×C3#577011yescharacteristic
608C2×C3#577111yescharacteristic
609C2×C3#577511yescharacteristic
610C2×C3#577911yescharacteristic
611D3—81no—
612D3—122no—
613D3—122no—
614D3—242no—
615C22—21no—
616C22—21no—
617C22—121no—
618C22—121no—
619C22—121no—
620C22—182no—
621C22—182no—
622C22—182no—
623C22#6391012yes—
624C22C2×#381111yescharacteristic
625C4—41no—
626C4—41no—
627C4—122no—
628C4—121no—
629C4—182no—
630C4—362no—
631C4#6391012yes—
632C4C2×#379911yescharacteristic
633C4C2×D3×D1211yescharacteristic
634C3—21no—
635C3#7884111yescharacteristic, complemented
636C3#7921411yescharacteristic, complemented
637C2—22no—
638C2—241no—
639C2—362no—
640C2C2×#6391011yescharacteristic
641C2#1059546211yescharacteristic
642C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenter#117D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595997C2semidirect
3. C2×#63831C2semidirect
4. C2×#63817C2semidirect
5. C3×#5002C2semidirect
6. C3×#4995C2semidirect
7. C2×#63567C2semidirect
8. #10590525C2semidirect
9. #10590524C2semidirect
10. #10590507C2semidirect
11. #10590506C2semidirect
57. #5002D3semidirect
58. #4995D3semidirect
98. C3×#208D4semidirect
318. #208D12semidirect
564. C32#3063semidirect
635. C3#78841semidirect
636. C3#79214semidirect

Maximal subgroups

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

subgroupindex
#105959972
#105950432
C2×#638312
C2×#638172
C3×#50022
C3×#49952
C2×#635672
#105905252
#105905242
#105905072
#105905062
#792143
#788413