Finite Group Databasebeta

← #11878800

Subgroups — #11878800

Order 1152.

938 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5548C211yesmaximal, characteristic, complemented
2#10593969C211yesmaximal, characteristic, complemented
3#10592715C211yesmaximal, characteristic, complemented
4C3×#5016C211yesmaximal, characteristic, complemented
5#10591521C211yesmaximal, characteristic, complemented
6#10591519C211yesmaximal, characteristic, complemented
7#10591490C211yesmaximal, characteristic, complemented
8#10591482C211yesmaximal, characteristic, complemented
9#10590615C211yesmaximal, characteristic, complemented
10#10590613C211yesmaximal, characteristic, complemented
11#10590560C211yesmaximal, characteristic, complemented
12#10590548C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590248C211yesmaximal, characteristic, complemented
16#83304—31nomaximal
17#80540—31nomaximal
18C2×C3×#235—21no—
19C2×#3799C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24#64084C2211yescharacteristic
25C3×#940C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×C4×#67—21no—
30C3×#895C2211yescharacteristic
31C3×#888C2211yescharacteristic
32C3×#885—21no—
33C3×#884—21no—
34C3×#875C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36C3×C42×D3C2211yescharacteristic
37#63911C2211yescharacteristic
38#63906—21no—
39#63906—21no—
40#63880—21no—
41#63880—21no—
42#63866C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×#3714C2211yescharacteristic
46C2×#3713C2211yescharacteristic
47#63637C2211yescharacteristic
48#63636C2211yescharacteristic
49C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63565C2211yescharacteristic
55#63564C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#532—31no—
62#5668—31no—
63#5548D311yescharacteristic, complemented
64#5477—31no—
65C3×#463—31no—
66#5175—31no—
67#5172—31no—
68#5158—31no—
69#5151—31no—
70#5093—31no—
71#5088—31no—
72#5076—31no—
73#5073—31no—
74#5057—31no—
75#5037—31no—
76#5037—31no—
77#5037—31no—
78#5037—31no—
79#5016—31no—
80#5016—31no—
81#5016—31no—
82#5016—31no—
83#5016—61no—
84#5016D311yescharacteristic, complemented
85#4925—31no—
86#4844—31no—
87#4833—31no—
88#4810—31no—
89#4792—31no—
90#4781—31no—
91#4760—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×#235—44no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×#624—21no—
114C2×D3×Dic3—21no—
115#3799—41no—
116#3799—41no—
117#3795—41no—
118#3795—41no—
119C32×C4⋊C4C2311yescharacteristic
120C32×C22⋊C4—21no—
121C32×C42C2311yescharacteristic
122#3754—41no—
123#3753—41no—
124#3752—21no—
125#3752—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#214—41no—
130C3×#213—41no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144#3716—41no—
145#3715—41no—
146#3714—41no—
147#3713—41no—
148#3207—91noSylow
149C2×C3×#41—61no—
150C2×#239—31no—
151C2×#237—31no—
152C2×#235—21no—
153C2×#235—31no—
154C2×#235—31no—
155C2×C3×SD16—31no—
156C2×C3×D8—31no—
157C3×C4⋊Q8—31no—
158C3×#127—31no—
159C3×#124—31no—
160C3×#124—61no—
161C3×#121—31no—
162C3×#121—31no—
163C3×#121—61no—
164C3×C4×D4—21no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C3×C4×D4C2×D311yescharacteristic
168C3×C4×D4C2×D311yescharacteristic
169C2×C3×C42—31no—
170#944—31no—
171C2×#215—31no—
172#940—31no—
173#940C2×D311yescharacteristic
174#938C2×D311yescharacteristic
175C2×#214—31no—
176C2×#214—31no—
177C2×#214—31no—
178C2×#214—31no—
179C2×#214—61no—
180C2×#214C2×D311yescharacteristic
181C2×#213—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—61no—
187C2×#213C2×D311yescharacteristic
188#930—61no—
189#930—61no—
190C4×#67—21no—
191C2×D24—31no—
192C2×#204—31no—
193#895C2×D311yescharacteristic
194#888C2×D311yescharacteristic
195#885—21no—
196#884—21no—
197#884—61no—
198#884—61no—
199#67⋊C4—61no—
200#67⋊C4—61no—
201#875—31no—
202#875—31no—
203#875—61no—
204#875C2×D311yescharacteristic
205#874—31no—
206C4×D12—61no—
207C4×D12—61no—
208C4×D12C2×D311yescharacteristic
209C42×D3C2×D311yescharacteristic
210#869—31no—
211C3×C4⋊C8—31no—
212C3×#103—31no—
213C3×#102—31no—
214#835—31no—
215#832—31no—
216#830—31no—
217#830—31no—
218#821—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#816—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#810C2×D311yescharacteristic
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic
236C4⋊(C3⋊C8)—31no—
237C4⋊(C3⋊C8)—31no—
238C4⋊(C3⋊C8)—61no—
239C4⋊(C3⋊C8)C2×D311yescharacteristic
240C4×C3⋊C8—31no—
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—42no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257#634—21no—
258#634—21no—
259C3×#67—42no—
260C3×#67—42no—
261C3×#67—42no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—42no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—22no—
275C3×C4×D3—22no—
276C3×C4×D3—42no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6—42no—
280#626—42no—
281#626—42no—
282#626—42no—
283#625—42no—
284#624—42no—
285D3×Dic3—42no—
286C3⋊(C3⋊C8)—21no—
287C3⋊(C3⋊C8)—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8—21no—
290#532—31no—
291#532—91no—
292#493—91no—
293#492—91no—
294#487—91no—
295#486—91no—
296#463—31no—
297#463—91no—
298#463—91no—
299#463—91no—
300#449—91no—
301#449—91no—
302#449—91no—
303#449—91no—
304#431—91no—
305C3×#41—124no—
306C2×C3×Q8—31no—
307C2×C3×Q8—61no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—41no—
323C22×C3×C4—61no—
324C2×#67—21no—
325C2×#67—21no—
326C2×#67—21no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C22×Dic3—61no—
333#239—121no—
334#239—121no—
335#237—121no—
336#237—121no—
337#235—44no—
338#235—121no—
339#235—121no—
340#235—121no—
341#235—121no—
342C2×D12—21no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12C22×D311yescharacteristic
350C2×D12C22×D311yescharacteristic
351C2×C4×D3—21no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3#6711yescharacteristic
356C2×C4×D3#6711yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6—21no—
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—61no—
362C2×Dic6C22×D311yescharacteristic
363C3×SD16—121no—
364C3×D8—121no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—41no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C42—21no—
381C3×C42—31no—
382C3×C42—31no—
383C3×C42—31no—
384C3×C42C22×D311yescharacteristic
385C3×C42C22×D311yescharacteristic
386#217—21no—
387#215—121no—
388#214—41no—
389#214—121no—
390#214—121no—
391#214—121no—
392#214—121no—
393#214—122no—
394#213—41no—
395#213—121no—
396#213—121no—
397#213—121no—
398#213—121no—
399#213—121no—
400#213—122no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—121no—
410(C2×D3)⋊C4—121no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417C4×Dic3#6711yescharacteristic
418C4×Dic3#6711yescharacteristic
419C4×Dic3C22×D311yescharacteristic
420C2×C3⋊C8—31no—
421C2×C3⋊C8—31no—
422C2×C3⋊C8—31no—
423C2×C3⋊C8—31no—
424C2×C3⋊C8—61no—
425C2×C3⋊C8—61no—
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428D24—121no—
429#204—121no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32C22×D411yescharacteristic
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—41no—
449C32×C4H(5,𝔽2)11yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3⋊Dic3—41no—
452C3×Dic3—21no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3#13512yes—
456C3×Dic3AGL(1,ℤ/8)12yes—
457C2×#41—61no—
458C2×#41—91no—
459C2×#41—91no—
460C2×SD16—31no—
461C2×SD16—91no—
462C2×SD16—91no—
463C2×SD16—91no—
464C2×D8—31no—
465C2×D8—91no—
466C2×D8—91no—
467C2×D8—91no—
468C4⋊Q8—31no—
469C4⋊Q8—91no—
470#127—31no—
471#127—91no—
472#124—31no—
473#124—61no—
474#124—91no—
475#121—31no—
476#121—31no—
477#121—61no—
478#121—181no—
479#121—181no—
480C4×D4—31no—
481C4×D4—61no—
482C4×D4—181no—
483C4×D4—181no—
484C4×D4D3211yescharacteristic
485C2×C42—31no—
486C4⋊C8—31no—
487C4⋊C8—91no—
488#103—31no—
489#103—91no—
490#103—91no—
491#103—91no—
492#102—31no—
493#102—91no—
494#102—91no—
495#102—91no—
496C22⋊C8—91no—
497C22⋊C8—91no—
498C4×C8—91no—
499C4×C8—91no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—31no—
503C23×C3—41no—
504C23×C3—61no—
505C23×C3—61no—
506C22×D3—21no—
507C22×D3—21no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—121no—
511C22×D3C2×#6711yescharacteristic
512C3×Q8—61no—
513C3×Q8—61no—
514C3×Q8—122no—
515C3×D4—22no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—41no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—122no—
526C3×D4—122no—
527C3×D4—122no—
528C3×D4—122no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—41no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4—62no—
541C2×C3×C4—62no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—82no—
547C2×C3×C4—122no—
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554#67—42no—
555#67—42no—
556#67—42no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—121no—
567C2×Dic3—122no—
568C2×Dic3C2×#6711yescharacteristic
569C2×Dic3C2×#6711yescharacteristic
570C2×Dic3C2×#6711yescharacteristic
571D12—21no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—42no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—122no—
583D12—122no—
584D12—122no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—22no—
588C4×D3—22no—
589C4×D3—42no—
590C4×D3—122no—
591C4×D3—122no—
592C4×D3—122no—
593Dic6—21no—
594Dic6—21no—
595Dic6—42no—
596Dic6—61no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—121no—
601Dic6—121no—
602C3×C8—61no—
603C3×C8—61no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—61no—
610C3⋊C8—121no—
611C3⋊C8—121no—
612C2×C32—81no—
613C2×C32#53511yescharacteristic
614C2×C32C2×#13511yescharacteristic
615C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
616C3⋊D3—81no—
617C3×D3—41no—
618C3×D3—81no—
619C3×D3—81no—
620#41—124no—
621#41—361no—
622#41—361no—
623#41—361no—
624#41—361no—
625C2×Q8—31no—
626C2×Q8—61no—
627C2×Q8—91no—
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—61no—
634C2×D4—91no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4C2×D3211yescharacteristic
640C22×C4—21no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—61no—
645C22×C4—181no—
646C22×C4—181no—
647SD16—121no—
648SD16—361no—
649SD16—361no—
650SD16—361no—
651D8—121no—
652D8—361no—
653D8—361no—
654D8—361no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—91no—
658C2×C8—91no—
659C4⋊C4—31no—
660C4⋊C4—61no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4C2×D3211yescharacteristic
664C22⋊C4—21no—
665C22⋊C4—61no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C42—31no—
673C42—31no—
674C42—31no—
675C42C2×D3211yescharacteristic
676C22×C3—21no—
677C22×C3—42no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C22×#6711yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—241no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—32no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—61no—
728C3×C4—81no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4#100411yescharacteristic
732C3×C4#100911yescharacteristic
733C3×C4#100911yescharacteristic
734C3×C4#100911yescharacteristic
735Dic3—21no—
736Dic3—41no—
737Dic3—41no—
738Dic3—121no—
739Dic3—121no—
740Dic3—241no—
741Dic3#93212yes—
742Dic3#95012yes—
743C32#320711yescharacteristic, complemented, Sylow
744C23—21no—
745C23—31no—
746C23—61no—
747C23—61no—
748C23—181no—
749Q8—61no—
750Q8—61no—
751Q8—122no—
752Q8—181no—
753Q8—181no—
754D4—21no—
755D4—21no—
756D4—61no—
757D4—61no—
758D4—61no—
759D4—61no—
760D4—122no—
761D4—122no—
762D4—122no—
763D4—122no—
764D4—181no—
765D4—181no—
766D4—362no—
767D4—362no—
768D4—362no—
769D4—362no—
770C2×C4—21no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—42no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—122no—
782C2×C4—181no—
783C2×C4—362no—
784C2×C4—362no—
785C2×C4D3×#6711yescharacteristic
786C2×C4D3×#6711yescharacteristic
787C2×C4C22×D3211yescharacteristic
788C8—61no—
789C8—61no—
790C8—181no—
791C8—181no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—82no—
796C2×C3—81no—
797C2×C3—81no—
798C2×C3—121no—
799C2×C3—241no—
800C2×C3—241no—
801C2×C3#560711yescharacteristic
802C2×C3D3×#13511yescharacteristic
803C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
804C2×C3C2×#93211yescharacteristic
805C2×C3C2×#95011yescharacteristic
806C2×C3#583011yescharacteristic
807D3—41no—
808D3—81no—
809D3—81no—
810D3—241no—
811D3—241no—
812D3—481no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—361no—
826C22—361no—
827C22—361no—
828C22C2×D3×#6711yescharacteristic
829C4—21no—
830C4—21no—
831C4—32no—
832C4—32no—
833C4—41no—
834C4—61no—
835C4—121no—
836C4—121no—
837C4—361no—
838C4#6430711yescharacteristic
839C4#6430811yescharacteristic
840C3—21no—
841C3#8054011yescharacteristic, complemented
842C3#8330411yescharacteristic, complemented
843C2—81no—
844C2—121no—
845C2—241no—
846C2—241no—
847C2—721no—
848C2#1059506411yescharacteristic
849C2D3×#93211yescharacteristic
850C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3207
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5548C2semidirect
2. #10593969C2semidirect
3. #10592715C2semidirect
4. C3×#5016C2semidirect
5. #10591521C2semidirect
6. #10591519C2semidirect
7. #10591490C2semidirect
8. #10591482C2semidirect
9. #10590615C2semidirect
10. #10590613C2semidirect
11. #10590560C2semidirect
12. #10590548C2semidirect
13. #10590366C2semidirect
14. #10590348C2semidirect
15. #10590248C2semidirect
63. #5548D3semidirect
84. #5016D3semidirect
743. C32#3207semidirect
841. C3#80540semidirect
842. C3#83304semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
#105939692
#105927152
C3×#50162
#105915212
#105915192
#105914902
#105914822
#105906152
#105906132
#105905602
#105905482
#105903662
#105903482
#105902482
#833043
#805403