Finite Group Databasebeta

← #11867819

Subgroups — #11867819

Order 1152.

1091 conjugacy classes of subgroups.

The subgroup lattice has 651 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595981C211yesmaximal, characteristic
2#10594866C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C2×#63817C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C3×#4964C211yesmaximal, characteristic, complemented
7#10591105C211yesmaximal, characteristic, complemented
8#10590525C212yesmaximal, complemented
9#10590524C212yesmaximal, complemented
10#10590523C212yesmaximal, complemented
11#10590522C212yesmaximal, complemented
12#79214—31nomaximal
13#78800—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18#64139—22no—
19#64106—21no—
20#64106C2212yes—
21#64104—21no—
22#64104C2212yes—
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63966—22no—
27#63871C2212yes—
28#63871C2212yes—
29#63866—21no—
30#63864—21no—
31C2×#3719C2212yes—
32#63833—24no—
33C2×#3717C2212yes—
34C2×#3712C2212yes—
35#63817—24no—
36C2×#3710C2212yes—
37C3×#810C2212yes—
38C3×#810C2212yes—
39C3×#808C2212yes—
40C3×#807C2212yes—
41#63567C2211yescharacteristic
42#63567C2211yescharacteristic
43#63564C2211yescharacteristic
44#63564C2211yescharacteristic
45#5816—31no—
46C2×#942—31no—
47C2×#909—31no—
48C2×#907—31no—
49C2×#901—31no—
50#5526—31no—
51#5510—31no—
52#5510—31no—
53#5510—61no—
54C3×#428—31no—
55C2×C3×#103—31no—
56#5113—31no—
57#5002—31no—
58C2×#810D311yescharacteristic, complemented
59#4964D311yescharacteristic, complemented
60#4887—32no—
61#4886—32no—
62#4867—32no—
63#4864—32no—
64#4816—32no—
65#4813—32no—
66#4812—32no—
67#4807—32no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C2×#638D412yes—
72#3828—22no—
73#3828—22no—
74#3828—22no—
75#3828—22no—
76C2×C4⋊(C3⋊D3)—22no—
77C2×C4⋊(C3⋊D3)D411yescharacteristic
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—21no—
80C2×C4×C3⋊D3C2312yes—
81C2×#634D411yescharacteristic
82C2×#634C2311yescharacteristic
83C22×C3×Dic3—21no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6—21no—
87C2×C3×Dic6C2312yes—
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2312yes—
90#3752—22no—
91#3752—22no—
92C4⋊(C3⋊Dic3)—22no—
93C3×#217—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4×Dic3—21no—
97C3×#208D414yescomplemented
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104#3722—22no—
105#3722—22no—
106#3719—24no—
107#3717—24no—
108#3712—24no—
109#3710—24no—
110#3063—91noSylow
111C22×C3×Q8—31no—
112C2×#235—31no—
113C2×#235—31no—
114C2×#235—31no—
115C2×#235—31no—
116C2×#235—61no—
117C2×#235—61no—
118C22×Dic6C2×D311yescharacteristic
119C2×C3×M16—31no—
120C22×C3×C8—31no—
121C3×#117—31no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4C2×D311yescharacteristic
124C2×C3×C4⋊C4C2×D311yescharacteristic
125#947—61no—
126#946—32no—
127#946—32no—
128#944—61no—
129C2×#216—32no—
130#942—64no—
131C2×#215—32no—
132#930—62no—
133#930—62no—
134#930—64no—
135#929—62no—
136#926C2×D311yescharacteristic
137C2×#208C2×D311yescharacteristic
138C22×C3⋊C8C2×D311yescharacteristic
139#909—64no—
140#907—64no—
141C2×Dic12—32no—
142C2×#204—32no—
143#901—64no—
144C2×ΓL(1,𝔽25)—32no—
145C2×ΓL(1,𝔽25)—32no—
146C2×D3×C8—32no—
147C2×D3×C8—32no—
148#897—32no—
149#897—32no—
150#897—32no—
151#897—32no—
152#897—62no—
153#897—61no—
154#897—61no—
155#897—62no—
156#895—32no—
157#895—32no—
158#895—62no—
159#895—61no—
160#895—61no—
161#895—62no—
162#886—62no—
163#875—61no—
164#869—61no—
165C3×#107—32no—
166C3×#106—32no—
167C3×#103—32no—
168C3×#103—32no—
169#821—31no—
170#821—31no—
171#816—31no—
172#816—31no—
173#810—31no—
174#810—31no—
175#810C2×D312yes—
176#810C2×D312yes—
177#809—31no—
178#809—31no—
179#808C2×D312yes—
180#807C2×D312yes—
181C23×C32C2×D411yescharacteristic
182C22×C3⋊D3—21no—
183C22×C3⋊D3C2×D412yes—
184C2×C32×C4—22no—
185C2×C32×C4—81no—
186C2×C32×C4C2×D412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190#638—24no—
191#638—42no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3C2×D412yes—
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—21no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)—82no—
198C4×C3⋊D3—22no—
199C4×C3⋊D3—22no—
200C4×C3⋊D3—42no—
201#634—22no—
202#634—21no—
203#634—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—42no—
208C3×Dic6—22no—
209C3×Dic6—22no—
210C3×Dic6—42no—
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—91no—
224C2×#103—31no—
225C2×C3×Q8—32no—
226C2×C3×Q8—61no—
227C2×C3×Q8—62no—
228C2×C3×Q8—62no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—61no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—32no—
237C2×#67—32no—
238C2×#67—62no—
239C2×#67—62no—
240C2×#67—61no—
241C2×#67—61no—
242C22×Dic3—21no—
243#235—62no—
244#235—62no—
245#235—62no—
246#235—62no—
247#235—62no—
248#235—62no—
249#235—62no—
250#235—62no—
251#235—122no—
252#235—122no—
253#235—122no—
254#235—122no—
255C2×D12—31no—
256C2×D12—31no—
257C2×D12—31no—
258C2×D12—31no—
259C2×D12—61no—
260C2×D12—61no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12—64no—
264C2×C4×D3—32no—
265C2×C4×D3—32no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×Dic6—22no—
271C2×Dic6—22no—
272C2×Dic6—21no—
273C2×Dic6—31no—
274C2×Dic6—31no—
275C2×Dic6—31no—
276C2×Dic6—31no—
277C2×Dic6—61no—
278C2×Dic6—61no—
279C2×Dic6C22×D312yes—
280C3×M16—34no—
281C2×C3×C8—32no—
282C2×C3×C8—31no—
283C2×C3×C8—31no—
284C2×C3×C8—62no—
285C3×C4⋊C4—22no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—22no—
289C3×C4⋊C4—31no—
290C3×C4⋊C4—31no—
291C3×C4⋊C4C22×D312yes—
292C3×C4⋊C4C22×D312yes—
293C3×C22⋊C4—61no—
294C3×C42—61no—
295#217—21no—
296#216—64no—
297#215—64no—
298(C2×D3)⋊C4—62no—
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—62no—
309C4⋊Dic3—62no—
310C4⋊Dic3—62no—
311C4⋊Dic3—62no—
312C4⋊Dic3—64no—
313C4⋊Dic3C22×D311yescharacteristic
314C4⋊Dic3C22×D311yescharacteristic
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317C4×Dic3—21no—
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—42no—
340C32×C4#12112yes—
341C32×C4C22×D411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3⋊Dic3—22no—
344C3⋊Dic3—41no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3—41no—
348C2×#41—91no—
349C2×#41—91no—
350C22×Q8—31no—
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#117—31no—
370C2×C4⋊C4D3211yescharacteristic
371#107—32no—
372#106—32no—
373#103—32no—
374#103—32no—
375#103—91no—
376#103—91no—
377#102—91no—
378#102—91no—
379C23×C3—21no—
380C23×C3D3×D411yescharacteristic
381C23×C3D3×D411yescharacteristic
382C22×D3—32no—
383C22×D3—32no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—61no—
387C22×D3—61no—
388C3×Q8—62no—
389C3×Q8—62no—
390C3×Q8—122no—
391C2×C3×C4—24no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—81no—
402C2×C3×C4—81no—
403C2×C3×C4—82no—
404C2×C3×C4—122no—
405C2×C3×C4C2×D1212yes—
406C2×C3×C4#23512yes—
407C2×C3×C4D3×D412yes—
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4#23912yes—
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413#67—64no—
414#67—64no—
415#67—124no—
416#67—124no—
417#67—122no—
418#67—122no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—22no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—42no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429D12—62no—
430D12—62no—
431D12—61no—
432D12—61no—
433D12—61no—
434D12—61no—
435D12—121no—
436D12—121no—
437D12—122no—
438D12—242no—
439D12—242no—
440D12—244no—
441C4×D3—62no—
442C4×D3—62no—
443C4×D3—62no—
444C4×D3—62no—
445C4×D3—122no—
446C4×D3—122no—
447C4×D3—124no—
448C4×D3—122no—
449C4×D3—122no—
450Dic6—22no—
451Dic6—22no—
452Dic6—42no—
453Dic6—62no—
454Dic6—62no—
455Dic6—61no—
456Dic6—61no—
457Dic6—61no—
458Dic6—61no—
459Dic6—122no—
460Dic6—121no—
461Dic6—121no—
462C3×C8—34no—
463C3×C8—61no—
464C3×C8—61no—
465C3⋊C8—21no—
466C3⋊C8—21no—
467C3⋊C8C2×D1214yes—
468C2×C32—22no—
469C2×C32C2×#12111yescharacteristic
470C2×C32#57711yescharacteristic
471C2×C32#57811yescharacteristic
472C3⋊D3—42no—
473C3⋊D3—81no—
474#41—182no—
475#41—182no—
476#41—182no—
477#41—182no—
478C2×Q8—32no—
479C2×Q8—61no—
480C2×Q8—62no—
481C2×Q8—62no—
482C2×Q8—91no—
483C2×Q8—91no—
484C2×D4—92no—
485C2×D4—91no—
486C2×D4—91no—
487C2×D4—182no—
488C2×D4—181no—
489C22×C4—21no—
490C22×C4—61no—
491C22×C4—92no—
492C22×C4—181no—
493C22×C4C2×D3211yescharacteristic
494Q16—184no—
495SD16—184no—
496M16—34no—
497M16—184no—
498C2×C8—32no—
499C2×C8—31no—
500C2×C8—31no—
501C2×C8—62no—
502C2×C8—184no—
503C4⋊C4—21no—
504C4⋊C4—31no—
505C4⋊C4—31no—
506C4⋊C4—182no—
507C4⋊C4—182no—
508C4⋊C4—182no—
509C4⋊C4C2×D3212yes—
510C22⋊C4—61no—
511C22⋊C4—182no—
512C22⋊C4—182no—
513C22⋊C4—182no—
514C22⋊C4—182no—
515C42—61no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—22no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3#88412yes—
525C22×C3#89512yes—
526C22×C3C2×D3×D411yescharacteristic
527C22×C3C2×D3×D411yescharacteristic
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—62no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—121no—
541C2×D3—121no—
542C2×D3—121no—
543C2×D3—121no—
544C2×D3—121no—
545C2×D3—121no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—22no—
549C3×C4—44no—
550C3×C4—42no—
551C3×C4—42no—
552C3×C4—122no—
553C3×C4—121no—
554C3×C4—121no—
555C3×C4#88412yes—
556C3×C4#89512yes—
557C3×C4C22×D1211yescharacteristic
558C3×C4C2×#23511yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560C3×C4C2×#23911yescharacteristic
561Dic3—42no—
562Dic3—41no—
563Dic3—41no—
564Dic3—62no—
565Dic3—62no—
566Dic3—122no—
567Dic3—122no—
568Dic3—121no—
569Dic3—121no—
570C32#306311yescharacteristic, complemented, Sylow
571C23—92no—
572C23—181no—
573C23#381111yescharacteristic
574Q8—62no—
575Q8—62no—
576Q8—122no—
577Q8—182no—
578Q8—181no—
579Q8—181no—
580D4—184no—
581D4—181no—
582D4—181no—
583D4—182no—
584D4—362no—
585D4—722no—
586C2×C4—22no—
587C2×C4—61no—
588C2×C4—61no—
589C2×C4—62no—
590C2×C4—81no—
591C2×C4—92no—
592C2×C4—122no—
593C2×C4—182no—
594C2×C4—182no—
595C2×C4—181no—
596C2×C4—362no—
597C2×C4#379912yes—
598C2×C4D3×D1212yes—
599C2×C4#381111yescharacteristic
600C2×C4C22×D3211yescharacteristic
601C8—34no—
602C8—61no—
603C8—61no—
604C2×C3—22no—
605C2×C3—22no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—42no—
610C2×C3C2×#88411yescharacteristic
611C2×C3C2×#89511yescharacteristic
612C2×C3#576211yescharacteristic
613C2×C3#576611yescharacteristic
614C2×C3#577511yescharacteristic
615C2×C3#577911yescharacteristic
616D3—122no—
617D3—122no—
618D3—242no—
619D3—242no—
620D3—241no—
621D3—241no—
622C22—21no—
623C22—21no—
624C22—182no—
625C22—182no—
626C22—182no—
627C22—361no—
628C22—361no—
629C22—361no—
630C22#6391012yes—
631C22C2×#381111yescharacteristic
632C4—42no—
633C4—121no—
634C4—121no—
635C4—122no—
636C4—182no—
637C4—361no—
638C4#6391012yes—
639C4C2×#379911yescharacteristic
640C4C2×D3×D1211yescharacteristic
641C3—21no—
642C3#7880011yescharacteristic, complemented
643C3#7921411yescharacteristic, complemented
644C2—22no—
645C2—362no—
646C2—721no—
647C2C2×#6391011yescharacteristic
648C2#1059511511yescharacteristic
649C2#1059533711yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10595981C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594866C2semidirect
3. C2×#63833C2semidirect
4. C2×#63817C2semidirect
5. C2×C3×#810C2semidirect
6. C3×#4964C2semidirect
7. #10591105C2semidirect
8. #10590525C2semidirect
9. #10590524C2semidirect
10. #10590523C2semidirect
11. #10590522C2semidirect
58. C2×#810D3semidirect
59. #4964D3semidirect
97. C3×#208D4semidirect
318. #208D12semidirect
570. C32#3063semidirect
642. C3#78800semidirect
643. C3#79214semidirect

Maximal subgroups

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

subgroupindex
#105959812
#105948662
C2×#638332
C2×#638172
C2×C3×#8102
C3×#49642
#105911052
#105905252
#105905242
#105905232
#105905222
#792143
#788003