Finite Group Databasebeta

← #11895683

Subgroups — #11895683

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595388C211yesmaximal, characteristic
2#10594317C211yesmaximal, characteristic, complemented
3#10592499C211yesmaximal, characteristic, complemented
4C3×#4798C211yesmaximal, characteristic, complemented
5C3×#4791C211yesmaximal, characteristic, complemented
6#10591614C211yesmaximal, characteristic, complemented
7#10591579C211yesmaximal, characteristic, complemented
8Dic3×#216C211yesmaximal, characteristic, complemented
9#10590799C211yesmaximal, characteristic
10#10590775C211yesmaximal, characteristic, complemented
11#10590769C211yesmaximal, characteristic, complemented
12#10590645C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic
14#10590474C211yesmaximal, characteristic, complemented
15#10590458C211yesmaximal, characteristic, complemented
16#81041—31nomaximal
17#80581—31nomaximal
18#64156C2211yescharacteristic
19#64099C2211yescharacteristic
20C3×#947C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63911C2211yescharacteristic
28#63898C2211yescharacteristic
29#63894C2211yescharacteristic
30#63890—21no—
31#63880—21no—
32#63869C2211yescharacteristic
33#63867—21no—
34#63854—21no—
35#63852—21no—
36#63845—21no—
37#63843C2211yescharacteristic
38Dic3×Dic6—21no—
39Dic3×Dic6C2211yescharacteristic
40#63839—21no—
41C2×#3717C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63662C2211yescharacteristic
44#63648C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63575C2211yescharacteristic
54#63572C2211yescharacteristic
55#63565C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5721—31no—
62#5681—31no—
63#5585—31no—
64#5569—31no—
65C3×#475—31no—
66C3×#464—31no—
67#5185—31no—
68Dic3×Q16—31no—
69#5163—31no—
70Dic3×SD16—31no—
71#5088—31no—
72#5056—31no—
73C4×#216—31no—
74C4×#215—31no—
75#4871—31no—
76#4871—31no—
77#4852—31no—
78#4852—31no—
79#4848—31no—
80#4847—31no—
81#4830—31no—
82#4830—31no—
83#4800—31no—
84#4800—31no—
85#4800—31no—
86#4800—61no—
87#4798—31no—
88#4798D311yescharacteristic, complemented
89#4791D311yescharacteristic, complemented
90#4766—31no—
91#4760—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×Dic6—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×#627D411yescharacteristic
98C2×#626—21no—
99C2×#626—21no—
100C2×#624—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×#204—22no—
126#3724—21no—
127#3724D411yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3D411yescharacteristic
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137#3717—22no—
138#3365—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×C4⋊Q8—31no—
142C3×#124—31no—
143C3×C4×Q8—31no—
144C3×C4×Q8—31no—
145#947—31no—
146#947—31no—
147#947—61no—
148#947C2×D311yescharacteristic
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—61no—
152Q8×Dic3C2×D311yescharacteristic
153#944—61no—
154C2×#216C2×D311yescharacteristic
155C2×#215—31no—
156#940—31no—
157D4×Dic3—31no—
158C2×#204—31no—
159C2×#204C2×D311yescharacteristic
160#894—61no—
161#894—61no—
162#893—31no—
163#893—31no—
164#890—31no—
165#890—31no—
166#890—31no—
167#890—61no—
168#890—61no—
169#889—61no—
170#889—61no—
171#888—61no—
172#888C2×D311yescharacteristic
173#887—31no—
174#887C2×D311yescharacteristic
175#886—61no—
176#885—61no—
177#883—61no—
178#67⋊C4—61no—
179#875—61no—
180#874—31no—
181C4×D12—31no—
182C4×D12—61no—
183#870—31no—
184#870—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#106—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×#103—21no—
194C3×#103—31no—
195C3×#103C2×D311yescharacteristic
196C3×#103C2×D311yescharacteristic
197C3×#102—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#818—31no—
211#817C2×D311yescharacteristic
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8C2×D311yescharacteristic
215Dic3⋊C8C2×D311yescharacteristic
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—61no—
221#810—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#809C2×D311yescharacteristic
228#808C2×D311yescharacteristic
229#807—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×Dic6—21no—
254C3×Dic6—42no—
255C3×Dic6#4112yes—
256#627—22no—
257#626—42no—
258#626—81no—
259#624—81no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—91no—
266#557—91no—
267#488—91no—
268#488—91no—
269#486—91no—
270#478—91no—
271#478—91no—
272#475—31no—
273#464—31no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×D4—31no—
286C2×#67—61no—
287C2×#67—61no—
288C22×Dic3—61no—
289C2×D12—31no—
290C2×D12—31no—
291C2×D12—61no—
292C2×D12—61no—
293C2×D12—61no—
294C2×D12C22×D311yescharacteristic
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×Dic6—21no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6C22×D311yescharacteristic
302C3×Q16—62no—
303C3×SD16—62no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C42—31no—
320C3×C42—31no—
321C3×C42—61no—
322C3×C42—61no—
323#217—61no—
324#216—22no—
325#215—62no—
326(C2×D3)⋊C4—21no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—121no—
336(C2×D3)⋊C4—121no—
337C4⋊Dic3—21no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—121no—
349C4⋊Dic3C22×D311yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—121no—
365C4×Dic3—21no—
366C4×Dic3—21no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381#204—22no—
382#204—62no—
383C22×C32C22×D411yescharacteristic
384C2×C3⋊D3—41no—
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—41no—
391C32×C4—41no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3⋊Dic3—21no—
395C3⋊Dic3—21no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3#13512yes—
404C2×Q16—31no—
405C2×SD16—31no—
406C2×SD16—91no—
407C4⋊Q8—31no—
408C4⋊Q8—181no—
409#127—91no—
410#125—91no—
411#125—91no—
412#125—181no—
413#125—181no—
414#124—31no—
415#124—91no—
416#124—181no—
417#123—181no—
418#123—181no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—181no—
425C4×D4—91no—
426C4×D4—91no—
427C4×D4—181no—
428#107—91no—
429#106—31no—
430#106—31no—
431C4⋊C8—31no—
432C4⋊C8—31no—
433C4⋊C8—91no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103D3211yescharacteristic
438#102—31no—
439#102—91no—
440#102—91no—
441#102—91no—
442#102—91no—
443#102—91no—
444C4×C8—91no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—61no—
448C22×D3—21no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—121no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—32no—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—61no—
460C3×Q8—122no—
461C3×D4—61no—
462C3×D4—61no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4C23×D311yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479#67—122no—
480#67—241no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3—241no—
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498D12—21no—
499D12—21no—
500D12—61no—
501D12—61no—
502D12—61no—
503D12—61no—
504D12—121no—
505D12—121no—
506D12—122no—
507D12—241no—
508C4×D3—241no—
509C4×D3—241no—
510C4×D3—241no—
511Dic6—21no—
512Dic6—42no—
513Dic6—62no—
514Dic6—62no—
515Dic6#23712yes—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—41no—
519C3×C8—61no—
520C3×C8—61no—
521C3⋊C8—21no—
522C3⋊C8—21no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—121no—
526C2×C32#54811yescharacteristic
527C2×C32C2×#13511yescharacteristic
528C2×C32#57711yescharacteristic
529C3⋊D3—81no—
530C3×D3—81no—
531C2×Q8—31no—
532C2×Q8—61no—
533C2×Q8—91no—
534C2×Q8C2×D3211yescharacteristic
535C2×D4—31no—
536C2×D4—91no—
537C2×D4—181no—
538C2×D4—181no—
539C22×C4—181no—
540C22×C4—181no—
541Q16—62no—
542SD16—62no—
543SD16—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8C2×D3211yescharacteristic
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4C2×D3211yescharacteristic
564C22⋊C4—61no—
565C22⋊C4—61no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C42—31no—
571C42—31no—
572C42—61no—
573C42—61no—
574C42—91no—
575C42—181no—
576C42—181no—
577C22×C3—21no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C2×D3×D411yescharacteristic
583C2×D3—41no—
584C2×D3—41no—
585C2×D3—41no—
586C2×D3—121no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—241no—
593C2×D3—241no—
594C2×D3—241no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—32no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—62no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—81no—
607C3×C4—81no—
608C3×C4—121no—
609C3×C4—121no—
610C3×C4C2×#23711yescharacteristic
611C3×C4#100711yescharacteristic
612C3×C4D3×#4111yescharacteristic
613C3×C4#101011yescharacteristic
614Dic3—21no—
615Dic3—21no—
616Dic3—21no—
617Dic3—22no—
618Dic3—41no—
619Dic3—41no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—61no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—241no—
629Dic3#91612yes—
630C32#336511yescharacteristic, complemented, Sylow
631C23—61no—
632C23—181no—
633Q8—21no—
634Q8—21no—
635Q8—32no—
636Q8—61no—
637Q8—122no—
638Q8—182no—
639D4—61no—
640D4—61no—
641D4—181no—
642D4—181no—
643D4—362no—
644D4—721no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—181no—
657C2×C4—721no—
658C2×C4—721no—
659C2×C4C22×D3211yescharacteristic
660C8—21no—
661C8—61no—
662C8—61no—
663C8—181no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—241no—
668C2×C3#559811yescharacteristic
669C2×C3#563311yescharacteristic
670C2×C3C2×#91611yescharacteristic
671C2×C3D3×#13511yescharacteristic
672C2×C3#577811yescharacteristic
673C2×C3#577811yescharacteristic
674D3—81no—
675D3—241no—
676D3—241no—
677D3—481no—
678C22—121no—
679C22—121no—
680C22—121no—
681C22—361no—
682C22—361no—
683C22—361no—
684C22D32×D411yescharacteristic
685C4—32no—
686C4—41no—
687C4—41no—
688C4—62no—
689C4—61no—
690C4—61no—
691C4—61no—
692C4—121no—
693C4—121no—
694C4—181no—
695C4—181no—
696C4—361no—
697C4#6429711yescharacteristic
698C4D3×#23711yescharacteristic
699C3—21no—
700C3#8058111yescharacteristic, complemented
701C3#8104111yescharacteristic, complemented
702C2—241no—
703C2—721no—
704C2#1059407411yescharacteristic
705C2D3×#91611yescharacteristic
706C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenter#103D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594317C2semidirect
3. #10592499C2semidirect
4. C3×#4798C2semidirect
5. C3×#4791C2semidirect
6. #10591614C2semidirect
7. #10591579C2semidirect
8. Dic3×#216C2semidirect
10. #10590775C2semidirect
11. #10590769C2semidirect
12. #10590645C2semidirect
14. #10590474C2semidirect
15. #10590458C2semidirect
88. #4798D3semidirect
89. #4791D3semidirect
630. C32#3365semidirect
700. C3#80581semidirect
701. C3#81041semidirect

Maximal subgroups

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

subgroupindex
#105953882
#105943172
#105924992
C3×#47982
C3×#47912
#105916142
#105915792
Dic3×#2162
#105907992
#105907752
#105907692
#105906452
#105905482
#105904742
#105904582
#810413
#805813