Finite Group Databasebeta

← #11878853

Subgroups — #11878853

Order 1152.

1040 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#940C211yesmaximal, characteristic
2#10594387C211yesmaximal, characteristic, complemented
3#10592461C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591490C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591444C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590877C211yesmaximal, characteristic, complemented
11#10590876C211yesmaximal, characteristic, complemented
12#10590655C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590553C211yesmaximal, characteristic, complemented
15#10590548C211yesmaximal, characteristic, complemented
16#81568—31nomaximal
17#80138—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22#64149C2211yescharacteristic
23C2×#3754C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic, complemented
25#64096C2211yescharacteristic, complemented
26C3×#940C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#888C2211yescharacteristic, complemented
31#63979—21no—
32#63979—21no—
33#63914C2211yescharacteristic
34#63911C2211yescharacteristic
35#63887—21no—
36#63878—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63866C2211yescharacteristic, complemented
39#63857C2211yescharacteristic
40#63846—21no—
41#63843—21no—
42#63843C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic, complemented
44C2×#3716C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic, complemented
48#63641C2211yescharacteristic, complemented
49#63636C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C2×#940—31no—
62#5728—31no—
63D3×#127—31no—
64#5622—31no—
65C3×#486—31no—
66C3×#450—31no—
67#5218—31no—
68#5175—31no—
69#5175—31no—
70#5163—31no—
71#5163—31no—
72#5088—31no—
73#5076—31no—
74#5046—31no—
75#4776—31no—
76#4776—31no—
77#4776—31no—
78#4776D311yescharacteristic, complemented
79#4762—31no—
80#4762—31no—
81#4762—31no—
82#4762—31no—
83#4762—31no—
84#4762—31no—
85#4762—61no—
86#4760—31no—
87#4760D311yescharacteristic, complemented
88#4731—31no—
89#4718—31no—
90#4693—31no—
91#4685—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—41no—
103C3×D3×D4—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109D3×#67—44no—
110D3×#67—44no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#625—21no—
115C2×#625—21no—
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118D3×D12—41no—
119D3×D12—41no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3754—41no—
123#3750—21no—
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3744—41no—
128C3×#214—41no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—41no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143Dic32D411yescharacteristic
144Dic32D411yescharacteristic
145#3717—41no—
146#3716—41no—
147#3716—41no—
148#3715—41no—
149#3208—91noSylow
150C22×C3×D4—31no—
151C22×#67—61no—
152C22×#67—61no—
153C2×D3×D4—31no—
154C2×D3×D4—61no—
155C2×D3×D4—61no—
156C2×D3×D4C2×D311yescharacteristic
157C22×D12—31no—
158C2×C3×SD16—31no—
159C2×C3×SD16—31no—
160C3×C4⋊Q8—31no—
161C3×#127—31no—
162C3×C22⋊Q8—31no—
163#946—61no—
164Q8×Dic3—31no—
165Q8×Dic3—61no—
166#944—31no—
167C2×#215—31no—
168C2×#215—31no—
169#940—31no—
170#940—31no—
171#940—31no—
172#940—31no—
173#940—31no—
174#940—61no—
175#940—61no—
176#940—61no—
177#940—61no—
178#940—61no—
179#940C2×D311yescharacteristic
180C2×#214—31no—
181C2×#214—31no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186C2×#214C2×D311yescharacteristic, complemented
187#924—31no—
188C2×C4×Dic3—31no—
189C2×#204—31no—
190C2×#204—31no—
191C2×#204—31no—
192C2×#204—31no—
193C2×#204—31no—
194C2×#204—61no—
195C2×#204C2×D311yescharacteristic, complemented
196#897—31no—
197#897C2×D311yescharacteristic
198#892—61no—
199#890—61no—
200#889—61no—
201#888C2×D311yescharacteristic, complemented
202#887—31no—
203#887—31no—
204#887—31no—
205#887—61no—
206#887—61no—
207#878—61no—
208#877—61no—
209#874—31no—
210C42×D3—31no—
211#869—31no—
212C3×#102—21no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102C2×D311yescharacteristic, complemented
218C3×#102C2×D311yescharacteristic, complemented
219C3×C22⋊C8—31no—
220C3×C4×C8—31no—
221#832—31no—
222#832C2×D311yescharacteristic, complemented
223#830—31no—
224#821—31no—
225#821C2×D311yescharacteristic, complemented
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8C2×D311yescharacteristic
228Dic3⋊C8—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—61no—
233C8×Dic3—31no—
234C8×Dic3C2×D311yescharacteristic, complemented
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#809—61no—
240#809C2×D311yescharacteristic, complemented
241#809C2×D311yescharacteristic, complemented
242C4×C3⋊C8—31no—
243C23×C32—21no—
244C22×C3⋊D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3C2×D411yescharacteristic
251C2×D32—42no—
252C2×D32—42no—
253C2×D32—42no—
254C32×D4—21no—
255C32×D4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2411yescharacteristic
258#638—42no—
259#638—42no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265#634—21no—
266#634—21no—
267C3×#67—42no—
268C3×#67—42no—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—42no—
284#626—42no—
285#626—42no—
286#626—42no—
287#625—42no—
288#625—42no—
289D3×Dic3—22no—
290D3×Dic3SD1614yescomplemented
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295#533—91no—
296C2×#127—91no—
297#492—91no—
298#492—91no—
299#486—31no—
300#486—91no—
301#460—91no—
302#460—91no—
303#460—91no—
304#460—91no—
305#450—31no—
306#450—91no—
307#450—91no—
308#450—91no—
309#431—91no—
310C24×C3—61no—
311C23×D3—21no—
312C23×D3—61no—
313C23×D3—61no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×D4—21no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—121no—
323C2×C3×D4—121no—
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C22×D311yescharacteristic
326C22×C3×C4—31no—
327C2×#67—21no—
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—121no—
342C2×#67—121no—
343C2×#67—124no—
344C2×#67—124no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347D3×D4—41no—
348D3×D4—41no—
349D3×D4—121no—
350D3×D4—121no—
351D3×D4—124no—
352D3×D4—124no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—121no—
360C2×D12—121no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—21no—
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—61no—
370C2×Dic6C22×D311yescharacteristic
371C3×SD16—121no—
372C3×SD16—121no—
373C2×C3×C8—21no—
374C2×C3×C8—31no—
375C2×C3×C8—31no—
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C22×D311yescharacteristic
378C3×C4⋊C4—21no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4C22×D311yescharacteristic
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C22⋊C4—61no—
385C3×C42—31no—
386#217—61no—
387#215—121no—
388#215—121no—
389#214—41no—
390#214—121no—
391#214—121no—
392#214—121no—
393#214—121no—
394#214—121no—
395#214—122no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—61no—
398C4⋊Dic3—21no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3C22×D311yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—121no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—121no—
424C4×Dic3C22×D311yescharacteristic
425C2×C3⋊C8—31no—
426C2×C3⋊C8—31no—
427C2×C3⋊C8—61no—
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430#204—41no—
431#204—121no—
432#204—121no—
433#204—122no—
434#204—121no—
435#204—121no—
436#204—121no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32C22×D411yescharacteristic
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3×D3—21no—
445C2×C3×D3—21no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—84no—
453C2×C3×D3C2×SD1612yes—
454D32—84no—
455C32×C4—41no—
456C32×C4H(5,𝔽2)11yescharacteristic
457C32×C4H(5,𝔽2)11yescharacteristic
458C3⋊Dic3—21no—
459C3⋊Dic3—41no—
460C3⋊Dic3C2×SD1612yes—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3C2×SD1612yes—
465C3×Dic3AGL(1,ℤ/8)12yes—
466C22×D4—31no—
467C22×D4—91no—
468C22×D4—181no—
469C22×D4—181no—
470C2×SD16—31no—
471C2×SD16—31no—
472C2×SD16—91no—
473C2×SD16—91no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C4⋊Q8—31no—
479C4⋊Q8—91no—
480#127—31no—
481#127—91no—
482#127—91no—
483#127—91no—
484#127—181no—
485#127—181no—
486#125—181no—
487C22⋊Q8—31no—
488C22⋊Q8—91no—
489C22⋊Q8—181no—
490C4×Q8—91no—
491C4×Q8—91no—
492C4×Q8—181no—
493#117—181no—
494C2×C42—91no—
495C4⋊C8—91no—
496C4⋊C8—91no—
497#102—31no—
498#102—31no—
499#102—31no—
500#102—31no—
501#102—91no—
502#102—91no—
503#102—91no—
504#102D3211yescharacteristic, complemented
505C22⋊C8—31no—
506C22⋊C8—91no—
507C4×C8—31no—
508C4×C8—91no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—31no—
512C23×C3—41no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—122no—
516C23×C3—122no—
517C23×C3—122no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3—42no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—121no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3—122no—
530C22×D3—122no—
531C22×D3—122no—
532C22×D3D3×D411yescharacteristic
533C3×Q8—61no—
534C3×Q8—61no—
535C3×Q8—122no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—21no—
540C3×D4—41no—
541C3×D4—41no—
542C3×D4—61no—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—122no—
547C3×D4—122no—
548C3×D4—122no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—41no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—42no—
563#67—42no—
564#67—42no—
565#67—122no—
566#67—122no—
567#67—122no—
568#67—122no—
569#67—122no—
570#67—122no—
571#67—122no—
572#67—122no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—242no—
577#67—242no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—34no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—62no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—121no—
591C2×Dic3D3×D411yescharacteristic
592C2×Dic3D3×D411yescharacteristic
593C2×Dic3D3×D411yescharacteristic
594D12—21no—
595D12—21no—
596D12—21no—
597D12—21no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—121no—
603D12—121no—
604D12—122no—
605D12—122no—
606D12—122no—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—34no—
610C4×D3—62no—
611Dic6—21no—
612Dic6—21no—
613Dic6—42no—
614Dic6—62no—
615Dic6—61no—
616Dic6—61no—
617Dic6—61no—
618Dic6—61no—
619Dic6—121no—
620C3×C8—21no—
621C3×C8—21no—
622C3×C8—41no—
623C3×C8—61no—
624C3×C8—61no—
625C3⋊C8—21no—
626C3⋊C8—21no—
627C3⋊C8—61no—
628C3⋊C8—61no—
629C3⋊C8—121no—
630C2×C32—81no—
631C2×C32#53511yescharacteristic
632C2×C32C22×SD1611yescharacteristic
633C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
634C3⋊D3—81no—
635C3×D3—22no—
636C3×D3—81no—
637C3×D3—81no—
638C24—61no—
639C24—181no—
640C2×Q8—31no—
641C2×Q8—61no—
642C2×Q8—91no—
643C2×D4—31no—
644C2×D4—31no—
645C2×D4—61no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—91no—
649C2×D4—121no—
650C2×D4—121no—
651C2×D4—181no—
652C2×D4—181no—
653C2×D4—181no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4—181no—
657C2×D4—181no—
658C2×D4—361no—
659C2×D4—361no—
660C2×D4—364no—
661C2×D4—364no—
662C2×D4C2×D3211yescharacteristic
663C22×C4—31no—
664C22×C4—91no—
665C22×C4—91no—
666SD16—121no—
667SD16—121no—
668SD16—361no—
669SD16—361no—
670SD16—361no—
671SD16—361no—
672SD16—361no—
673SD16—361no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8—91no—
677C2×C8C2×D3211yescharacteristic
678C4⋊C4—31no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—181no—
682C4⋊C4—181no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C4⋊C4—181no—
686C4⋊C4C2×D3211yescharacteristic
687C22⋊C4—61no—
688C22⋊C4—181no—
689C42—31no—
690C42—91no—
691C42—91no—
692C42—91no—
693C42—181no—
694C42—181no—
695C22×C3—21no—
696C22×C3—32no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—244no—
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C2×D3×D411yescharacteristic
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—84no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—241no—
733C2×D3—241no—
734C2×D3—241no—
735C2×D3—244no—
736C2×D3—244no—
737C2×D3D3×SD1612yes—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—32no—
741C3×C4—32no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—61no—
745C3×C4—81no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4#100411yescharacteristic
749C3×C4#100411yescharacteristic
750C3×C4#100911yescharacteristic
751C3×C4#100911yescharacteristic
752Dic3—21no—
753Dic3—32no—
754Dic3—32no—
755Dic3—41no—
756Dic3—41no—
757Dic3—62no—
758Dic3—61no—
759Dic3—61no—
760Dic3—121no—
761Dic3—122no—
762Dic3—121no—
763Dic3—121no—
764Dic3#91112yes—
765Dic3D3×SD1612yes—
766C32#320811yescharacteristic, complemented, Sylow
767C23—21no—
768C23—31no—
769C23—61no—
770C23—61no—
771C23—122no—
772C23—122no—
773C23—122no—
774C23—181no—
775C23—362no—
776C23—362no—
777C23—362no—
778Q8—61no—
779Q8—61no—
780Q8—122no—
781Q8—181no—
782Q8—181no—
783D4—21no—
784D4—21no—
785D4—61no—
786D4—61no—
787D4—61no—
788D4—61no—
789D4—122no—
790D4—122no—
791D4—122no—
792D4—181no—
793D4—181no—
794D4—362no—
795D4—362no—
796D4—362no—
797D4—362no—
798D4—362no—
799D4—362no—
800D4—362no—
801C2×C4—21no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—94no—
810C2×C4—91no—
811C2×C4—91no—
812C2×C4—182no—
813C2×C4—181no—
814C2×C4C22×D3211yescharacteristic
815C8—21no—
816C8—61no—
817C8—61no—
818C8—181no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—62no—
823C2×C3—81no—
824C2×C3—81no—
825C2×C3—161no—
826C2×C3—241no—
827C2×C3—241no—
828C2×C3#559211yescharacteristic
829C2×C3#567411yescharacteristic
830C2×C3C2×#91111yescharacteristic
831C2×C3C2×D3×SD1611yescharacteristic
832C2×C3C2×D3×SD1611yescharacteristic
833C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
834D3—22no—
835D3—81no—
836D3—81no—
837D3—241no—
838D3—241no—
839D3—481no—
840C22—32no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—61no—
845C22—61no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—244no—
853C22—361no—
854C22—361no—
855C22—361no—
856C22—724no—
857C22D32×D411yescharacteristic
858C4—32no—
859C4—32no—
860C4—41no—
861C4—61no—
862C4—92no—
863C4—121no—
864C4—121no—
865C4—181no—
866C4—361no—
867C4#6430711yescharacteristic
868C4#6431411yescharacteristic
869C3—21no—
870C3#8013811yescharacteristic, complemented
871C3#8156811yescharacteristic, complemented
872C2—62no—
873C2—81no—
874C2—241no—
875C2—241no—
876C2—721no—
877C2#1059427011yescharacteristic
878C2D3×#91111yescharacteristic
879C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD3×#940C2
hypercenter#102D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594387C2semidirect
3. #10592461C2semidirect
4. C3×#4776C2semidirect
5. C3×#4760C2semidirect
6. #10591490C2semidirect
7. #10591459C2semidirect
8. #10591444C2semidirect
9. #10590946C2semidirect
10. #10590877C2semidirect
11. #10590876C2semidirect
12. #10590655C2semidirect
13. #10590596C2semidirect
14. #10590553C2semidirect
15. #10590548C2semidirect
23. C2×#3754C22semidirect
24. C2×#3744C22semidirect
25. #64096C22semidirect
27. C2×C3×#214C22semidirect
28. C2×C3×#204C22semidirect
30. C3×#888C22semidirect
38. #63866C22semidirect
42. #63843C22semidirect
43. C2×#3717C22semidirect
44. C2×#3716C22semidirect
45. C2×#3716C22semidirect
46. C2×#3715C22semidirect
47. C32×#102C22semidirect
48. #63641C22semidirect
49. #63636C22semidirect
50. C3×#832C22semidirect
51. C3×#821C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#809C22semidirect
55. C3×#809C22semidirect
56. #63572C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
78. #4776D3semidirect
87. #4760D3semidirect
186. C2×#214C2×D3semidirect
195. C2×#204C2×D3semidirect
201. #888C2×D3semidirect
217. C3×#102C2×D3semidirect
218. C3×#102C2×D3semidirect
222. #832C2×D3semidirect
225. #821C2×D3semidirect
234. C8×Dic3C2×D3semidirect
240. #809C2×D3semidirect
241. #809C2×D3semidirect
290. D3×Dic3SD16semidirect
504. #102D32semidirect
766. C32#3208semidirect
870. C3#80138semidirect
871. C3#81568semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
#105943872
#105924612
C3×#47762
C3×#47602
#105914902
#105914592
#105914442
#105909462
#105908772
#105908762
#105906552
#105905962
#105905532
#105905482
#815683
#801383