Finite Group Databasebeta

← #11876994

Subgroups — #11876994

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5548C211yesmaximal, characteristic, complemented
2#10593968C211yesmaximal, characteristic, complemented
3#10592713C211yesmaximal, characteristic, complemented
4C3×#5014C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591482C211yesmaximal, characteristic, complemented
7#10591453C211yesmaximal, characteristic, complemented
8#10591451C211yesmaximal, characteristic, complemented
9#10590586C211yesmaximal, characteristic, complemented
10#10590548C211yesmaximal, characteristic, complemented
11#10590504C211yesmaximal, characteristic, complemented
12#10590412C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590334C211yesmaximal, characteristic, complemented
16#83295—31nomaximal
17#79877—31nomaximal
18C2×C3×#235—21no—
19C2×#3798—21no—
20C32×C4×D4C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#940C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×C4×#67—21no—
27C3×#895C2211yescharacteristic
28C3×#888C2211yescharacteristic
29C3×#885—21no—
30C3×#884—21no—
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C42×D3C2211yescharacteristic
34#63918C2211yescharacteristic
35#63911C2211yescharacteristic
36#63909C2211yescharacteristic
37#63908C2211yescharacteristic
38#63906—21no—
39C4×#626—21no—
40#63852—21no—
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45#63659C2211yescharacteristic
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic
48#63630C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#803C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#532—31no—
62#5548—31no—
63#5548D311yescharacteristic, complemented
64#5477—31no—
65C3×#442—31no—
66#5159—31no—
67#5151—31no—
68#5088—31no—
69#5080—31no—
70#5073—31no—
71#5070—31no—
72#5039—31no—
73#5039—31no—
74#5039—31no—
75#5039—31no—
76#5014—31no—
77#5014—31no—
78#5014—31no—
79#5014—31no—
80#5014—31no—
81#5014—61no—
82#5014D311yescharacteristic, complemented
83C4×#208—31no—
84#4865—31no—
85#4855—31no—
86#4782—31no—
87#4782—31no—
88#4760—31no—
89#4760—31no—
90#4711—31no—
91#4707—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
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×D3—21no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×#627—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114#3798—44no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C42C2311yescharacteristic
118#3753—22no—
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#213—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3D411yescharacteristic
132C3×C4×Dic3D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3714—22no—
140#3713—22no—
141#3711—22no—
142#3711—22no—
143#3184—91noSylow
144C2×C3×#41—61no—
145C2×#235—21no—
146C2×#235—61no—
147C2×#235—61no—
148C2×C3×D8—31no—
149C3×C4⋊Q8—31no—
150C3×#127—31no—
151C3×#124—61no—
152C3×#121—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×C4×D4—21no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C2×C3×C42—31no—
162#940—31no—
163#940C2×D311yescharacteristic
164#938—31no—
165#938C2×D311yescharacteristic
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172C2×#213C2×D311yescharacteristic
173#930—31no—
174#930—31no—
175#930—61no—
176C4×#67—21no—
177C4×#67—61no—
178C2×#208—31no—
179C2×#208—31no—
180C2×D24—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183#895—31no—
184#895C2×D311yescharacteristic
185#888—31no—
186#888C2×D311yescharacteristic
187#885—21no—
188#885—61no—
189#884—21no—
190#884—61no—
191#875—61no—
192#874—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—61no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198C4×D12C2×D311yescharacteristic
199C42×D3C2×D311yescharacteristic
200#869—31no—
201C3×#106—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#97—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—61no—
211#832C2×D311yescharacteristic
212#821—31no—
213#821—31no—
214#817—31no—
215C8×Dic3—31no—
216C8×Dic3—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#809C2×D311yescharacteristic
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic
231#803—31no—
232#803—31no—
233#803—61no—
234#803C2×D311yescharacteristic
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C23×C32—21no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—42no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4×C3⋊D3—42no—
253C3×#67—42no—
254C3×#67—42no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—22no—
269C3×C4×D3—22no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×Dic6—42no—
273#627—42no—
274#626—42no—
275#626—42no—
276#626—42no—
277#625—42no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)#4112yescomplemented
280C3×C3⋊C8—21no—
281C3×C3⋊C8#4112yescomplemented
282#532—31no—
283#532—91no—
284#498—91no—
285#493—91no—
286#486—91no—
287#486—91no—
288#469—91no—
289#469—91no—
290#469—91no—
291#469—91no—
292#442—31no—
293#442—91no—
294#442—91no—
295#442—91no—
296C4×M16—91no—
297C3×#41—124no—
298C2×C3×Q8—61no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—41no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—21no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324#235—44no—
325#235—124no—
326#235—124no—
327C2×D12—21no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12C22×D311yescharacteristic
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—121no—
341C2×C4×D3#6711yescharacteristic
342C2×C4×D3#6711yescharacteristic
343C2×C4×D3C22×D311yescharacteristic
344C2×Dic6—21no—
345C2×Dic6—61no—
346C2×Dic6—61no—
347C3×D8—62no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42C22×D311yescharacteristic
368C3×C42C22×D311yescharacteristic
369#217—21no—
370#217—61no—
371#213—22no—
372#213—62no—
373#213—62no—
374#213—62no—
375#213—62no—
376#213—64no—
377#213—62no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—121no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—61no—
395C4×Dic3#6711yescharacteristic
396C4×Dic3#6711yescharacteristic
397C4×Dic3C22×D311yescharacteristic
398#208—62no—
399#208—62no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409ΓL(1,𝔽25)—62no—
410ΓL(1,𝔽25)—62no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3AGL(1,ℤ/8)12yes—
437C3×Dic3AGL(1,ℤ/8)12yes—
438C2×#41—61no—
439C2×#41—181no—
440C2×D8—31no—
441C2×D8—91no—
442C2×D8—91no—
443C2×D8—91no—
444C2×M16—91no—
445C2×M16—91no—
446C4⋊Q8—31no—
447C4⋊Q8—91no—
448#127—31no—
449#127—91no—
450#124—61no—
451#124—181no—
452#121—31no—
453#121—31no—
454#121—61no—
455#121—91no—
456#121—91no—
457#121—181no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4—61no—
461C4×D4—91no—
462C4×D4—181no—
463C4×D4D3211yescharacteristic
464C2×C42—31no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#102—31no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#97—31no—
478#97—91no—
479C4×C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3C2×#6711yescharacteristic
493C3×Q8—122no—
494C3×D4—22no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—41no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—122no—
505C3×D4—122no—
506C3×D4—122no—
507C3×D4—122no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—82no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—42no—
535#67—42no—
536#67—42no—
537#67—122no—
538#67—122no—
539#67—122no—
540#67—122no—
541#67—122no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550D12—21no—
551D12—21no—
552D12—21no—
553D12—21no—
554D12—42no—
555D12—62no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12—122no—
562D12—122no—
563D12—122no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—22no—
567C4×D3—22no—
568C4×D3—42no—
569C4×D3—42no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—242no—
573Dic6—42no—
574Dic6—122no—
575Dic6—122no—
576C3×C8—32no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—32no—
580C3⋊C8—32no—
581C3⋊C8—62no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—121no—
585C3⋊C8#23512yescomplemented
586C2×C32—81no—
587C2×C32#53211yescharacteristic
588C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
589C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
590C3⋊D3—81no—
591C3×D3—41no—
592C3×D3—81no—
593C3×D3—81no—
594#41—124no—
595#41—364no—
596C2×Q8—61no—
597C2×Q8—181no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—91no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4C2×D3211yescharacteristic
610C22×C4—21no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—181no—
617D8—62no—
618D8—182no—
619D8—182no—
620D8—182no—
621M16—182no—
622M16—182no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—91no—
626C2×C8—91no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—181no—
632C4⋊C4C2×D3211yescharacteristic
633C22⋊C4—21no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—31no—
643C42—31no—
644C42C2×D3211yescharacteristic
645C22×C3—21no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—122no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—241no—
683C2×D3—241no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—32no—
691C3×C4—32no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—81no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×#23511yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4D3×#4111yescharacteristic
704Dic3—21no—
705Dic3—41no—
706Dic3—41no—
707Dic3—121no—
708Dic3—121no—
709Dic3—241no—
710Dic3#93212yes—
711Dic3#94912yes—
712C32#318411yescharacteristic, complemented, Sylow
713C23—21no—
714C23—31no—
715C23—61no—
716C23—61no—
717C23—181no—
718Q8—122no—
719Q8—362no—
720D4—21no—
721D4—21no—
722D4—61no—
723D4—61no—
724D4—61no—
725D4—61no—
726D4—122no—
727D4—122no—
728D4—122no—
729D4—122no—
730D4—181no—
731D4—181no—
732D4—362no—
733D4—362no—
734D4—362no—
735D4—362no—
736C2×C4—21no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—42no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—181no—
750C2×C4—362no—
751C2×C4D3×#6711yescharacteristic
752C2×C4D3×#6711yescharacteristic
753C2×C4C22×D3211yescharacteristic
754C8—32no—
755C8—61no—
756C8—92no—
757C8—181no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—82no—
762C2×C3—81no—
763C2×C3—81no—
764C2×C3—121no—
765C2×C3—241no—
766C2×C3—241no—
767C2×C3#554811yescharacteristic
768C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
769C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
770C2×C3C2×#93211yescharacteristic
771C2×C3C2×#94911yescharacteristic
772C2×C3#583211yescharacteristic
773D3—41no—
774D3—81no—
775D3—81no—
776D3—242no—
777D3—241no—
778D3—241no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—361no—
792C22—361no—
793C22—361no—
794C22C2×D3×#6711yescharacteristic
795C4—21no—
796C4—21no—
797C4—32no—
798C4—32no—
799C4—41no—
800C4—61no—
801C4—121no—
802C4—121no—
803C4—361no—
804C4D3×#23511yescharacteristic
805C4#6430611yescharacteristic
806C3—21no—
807C3#7987711yescharacteristic, complemented
808C3#8329511yescharacteristic, complemented
809C2—81no—
810C2—121no—
811C2—241no—
812C2—241no—
813C2—721no—
814C2#1059500311yescharacteristic
815C2D3×#93211yescharacteristic
816C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3184
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. #10593968C2semidirect
3. #10592713C2semidirect
4. C3×#5014C2semidirect
5. #10591487C2semidirect
6. #10591482C2semidirect
7. #10591453C2semidirect
8. #10591451C2semidirect
9. #10590586C2semidirect
10. #10590548C2semidirect
11. #10590504C2semidirect
12. #10590412C2semidirect
13. #10590346C2semidirect
14. #10590344C2semidirect
15. #10590334C2semidirect
63. #5548D3semidirect
82. #5014D3semidirect
279. C3⋊(C3⋊C8)#41semidirect
281. C3×C3⋊C8#41semidirect
585. C3⋊C8#235semidirect
712. C32#3184semidirect
807. C3#79877semidirect
808. C3#83295semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
#105939682
#105927132
C3×#50142
#105914872
#105914822
#105914532
#105914512
#105905862
#105905482
#105905042
#105904122
#105903462
#105903442
#105903342
#832953
#798773