Finite Group Databasebeta

← #11876980

Subgroups — #11876980

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic, complemented
3#10592738C211yesmaximal, characteristic, complemented
4C3×#5039C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591482C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10591167C211yesmaximal, characteristic, complemented
10#10591165C211yesmaximal, characteristic, complemented
11Dic3×#208C211yesmaximal, characteristic, complemented
12#10590589C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590412C211yesmaximal, characteristic, complemented
16#83295—31nomaximal
17#80853—31nomaximal
18C2×C3×#237—21no—
19C2×#3804—21no—
20C32×#121C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64139C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C3×#940C2211yescharacteristic
25C3×#939—21no—
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×#930C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×#208C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#885—21no—
35C3×#67⋊C4—21no—
36#63978—21no—
37#63918C2211yescharacteristic
38#63911C2211yescharacteristic
39#63894C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41#63880—21no—
42#63852—21no—
43C2×#3714C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45#63659C2211yescharacteristic
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63564C2211yescharacteristic
54#63563C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63554C2211yescharacteristic
58#63554C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#532—31no—
62#5596—31no—
63#5596D311yescharacteristic, complemented
64#5477—31no—
65C3×#469—31no—
66#5152—31no—
67#5151—31no—
68#5135—31no—
69Dic3×M16—31no—
70#5088—31no—
71#5080—31no—
72#5073—31no—
73#5070—31no—
74#5039—31no—
75#5039—31no—
76#5039—31no—
77#5039—31no—
78#5039—31no—
79#5039—61no—
80#5039D311yescharacteristic, complemented
81#5014—31no—
82#5014—31no—
83#5014—31no—
84#5014—31no—
85C4×#208—31no—
86#4869—31no—
87#4855—31no—
88#4785—31no—
89#4785—31no—
90#4760—31no—
91#4760—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3D411yescharacteristic
103C22×C3×Dic3D411yescharacteristic
104C3×#237—44no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×Dic6—21no—
109C2×#627—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113#3804—44no—
114C2×D3×Dic3—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117#3753—22no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3748—22no—
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
134C3×C4×Dic3C2311yescharacteristic
135C3×#208—22no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141#3714—22no—
142#3713—22no—
143#3184—91noSylow
144C2×C3×#41—61no—
145C2×#237—21no—
146C2×#237—61no—
147C2×#235—61no—
148C2×C3×D8—31no—
149C2×C3×M16—31no—
150C3×C4⋊Q8—31no—
151C3×#127—31no—
152C3×#124—61no—
153C3×#121—21no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#121C2×D311yescharacteristic
158C3×#121C2×D311yescharacteristic
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C2×C3×C42—31no—
163#940—31no—
164#940C2×D311yescharacteristic
165#939—21no—
166#939—61no—
167D4×Dic3—31no—
168D4×Dic3C2×D311yescharacteristic
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—61no—
175C2×#213C2×D311yescharacteristic
176#930—31no—
177#930—31no—
178#930—61no—
179#930—61no—
180#930C2×D311yescharacteristic
181#930C2×D311yescharacteristic
182C2×C4×Dic3C2×D311yescharacteristic
183C2×#208—31no—
184C2×#208—31no—
185C2×#208—61no—
186C2×#208C2×D311yescharacteristic
187C2×D24—31no—
188#893—31no—
189#893C2×D311yescharacteristic
190#888—31no—
191#888C2×D311yescharacteristic
192#885—21no—
193#885—61no—
194#67⋊C4—21no—
195#67⋊C4—61no—
196#875—61no—
197#874—31no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—61no—
201#869—31no—
202C3×#106—31no—
203C3×#102—31no—
204C3×#102—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—
215#815—31no—
216#815—31no—
217C8×Dic3—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—61no—
225#809C2×D311yescharacteristic
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic
233#803—31no—
234#803—31no—
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C23×C32—21no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C3×#67—42no—
255C3×#67—42no—
256C3×#67—42no—
257C3×#67—42no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
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×C4×D3—42no—
272C3×Dic6—42no—
273#627—42no—
274#626—42no—
275#626—42no—
276#624—42no—
277D3×Dic3—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—31no—
289#469—91no—
290#469—91no—
291#469—91no—
292#442—91no—
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—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—41no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—121no—
327C22×Dic3—21no—
328C22×Dic3—61no—
329C22×Dic3#6711yescharacteristic
330C22×Dic3#6711yescharacteristic
331#237—44no—
332#237—124no—
333#235—124no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12C22×D311yescharacteristic
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×Dic6—21no—
346C2×Dic6—61no—
347C2×Dic6—61no—
348C3×D8—62no—
349C3×M16—62no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—31no—
369#217—21no—
370#217—61no—
371#213—22no—
372#213—62no—
373#213—62no—
374#213—62no—
375#213—62no—
376#213—62no—
377#213—122no—
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
398C4×Dic3C22×D311yescharacteristic
399#208—22no—
400#208—62no—
401#208—62no—
402#208—122no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—62no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3AGL(1,ℤ/8)12yes—
438C3×Dic3AGL(1,ℤ/8)12yes—
439C2×#41—61no—
440C2×#41—181no—
441C2×D8—31no—
442C2×D8—91no—
443C2×D8—91no—
444C2×D8—91no—
445C2×M16—31no—
446C2×M16—91no—
447C4⋊Q8—31no—
448C4⋊Q8—91no—
449#127—31no—
450#127—91no—
451#124—61no—
452#124—181no—
453#121—31no—
454#121—31no—
455#121—61no—
456#121—91no—
457#121—181no—
458#121D3211yescharacteristic
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—61no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—181no—
465C2×C42—31no—
466#106—31no—
467#106—91no—
468#106—91no—
469#106—91no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#97—91no—
479#97—91no—
480C4×C8—91no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3D3×D411yescharacteristic
489C23×C3C2×#6711yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—121no—
495C3×Q8—122no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—42no—
503C3×D4—42no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—82no—
509C3×D4—122no—
510C3×D4—122no—
511C3×D4—122no—
512C3×D4—122no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—62no—
529C2×C3×C4—62no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4—122no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—42no—
539#67—42no—
540#67—42no—
541#67—42no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—242no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—42no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—121no—
555C2×Dic3—122no—
556C2×Dic3C2×#6711yescharacteristic
557C2×Dic3C2×#6711yescharacteristic
558C2×Dic3C2×#6711yescharacteristic
559C2×Dic3C2×#6711yescharacteristic
560D12—21no—
561D12—21no—
562D12—21no—
563D12—21no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—61no—
568D12—121no—
569D12—121no—
570D12—122no—
571D12—122no—
572C4×D3—42no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576Dic6—42no—
577Dic6—122no—
578Dic6—122no—
579C3×C8—32no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—32no—
583C3⋊C8—32no—
584C3⋊C8—62no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8#23712yescomplemented
589C2×C32—41no—
590C2×C32—81no—
591C2×C32#53211yescharacteristic
592C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
593C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
594C3⋊D3—81no—
595C3×D3—81no—
596C3×D3—81no—
597#41—124no—
598#41—364no—
599C2×Q8—61no—
600C2×Q8—181no—
601C2×D4—21no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—91no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4C2×D3211yescharacteristic
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4C2×D3211yescharacteristic
620D8—62no—
621D8—182no—
622D8—182no—
623D8—182no—
624M16—62no—
625M16—182no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—91no—
629C2×C8—91no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4C2×D3211yescharacteristic
636C22⋊C4—21no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C42—31no—
645C42—31no—
646C42—31no—
647C42—31no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3C2×D3×D411yescharacteristic
674C22×C3C22×#6711yescharacteristic
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—241no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—32no—
695C3×C4—32no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—81no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4C2×#23711yescharacteristic
705C3×C4D3×#4111yescharacteristic
706C3×C4D3×#4111yescharacteristic
707C3×C4D3×#4111yescharacteristic
708Dic3—21no—
709Dic3—21no—
710Dic3—41no—
711Dic3—41no—
712Dic3—121no—
713Dic3—121no—
714Dic3—241no—
715Dic3#93212yes—
716Dic3#94912yes—
717C32#318411yescharacteristic, complemented, Sylow
718C23—21no—
719C23—61no—
720C23—61no—
721C23—181no—
722C23D3×#6711yescharacteristic
723Q8—122no—
724Q8—362no—
725D4—21no—
726D4—21no—
727D4—42no—
728D4—61no—
729D4—61no—
730D4—61no—
731D4—61no—
732D4—122no—
733D4—122no—
734D4—122no—
735D4—122no—
736D4—181no—
737D4—181no—
738D4—362no—
739D4—362no—
740D4—362no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—181no—
755C2×C4—362no—
756C2×C4—362no—
757C2×C4D3×#6711yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—32no—
760C8—61no—
761C8—92no—
762C8—181no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3—81no—
769C2×C3—81no—
770C2×C3—81no—
771C2×C3—161no—
772C2×C3—241no—
773C2×C3—241no—
774C2×C3#559611yescharacteristic
775C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
776C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
777C2×C3C2×#93211yescharacteristic
778C2×C3C2×#94911yescharacteristic
779C2×C3#583211yescharacteristic
780D3—81no—
781D3—81no—
782D3—241no—
783D3—241no—
784D3—481no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—361no—
798C22—361no—
799C22—361no—
800C22C2×D3×#6711yescharacteristic
801C4—21no—
802C4—32no—
803C4—32no—
804C4—41no—
805C4—61no—
806C4—61no—
807C4—121no—
808C4—121no—
809C4—361no—
810C4D3×#23711yescharacteristic
811C4#6431211yescharacteristic
812C3—21no—
813C3#8085311yescharacteristic, complemented
814C3#8329511yescharacteristic, complemented
815C2—41no—
816C2—81no—
817C2—241no—
818C2—241no—
819C2—721no—
820C2D3×#93211yescharacteristic
821C2#1059515511yescharacteristic
822C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5596C2semidirect
2. #10594910C2semidirect
3. #10592738C2semidirect
4. C3×#5039C2semidirect
5. #10591487C2semidirect
6. #10591482C2semidirect
7. #10591430C2semidirect
8. #10591404C2semidirect
9. #10591167C2semidirect
10. #10591165C2semidirect
11. Dic3×#208C2semidirect
12. #10590589C2semidirect
13. #10590548C2semidirect
14. #10590455C2semidirect
15. #10590412C2semidirect
63. #5596D3semidirect
80. #5039D3semidirect
279. C3⋊(C3⋊C8)#41semidirect
281. C3×C3⋊C8#41semidirect
588. C3⋊C8#237semidirect
717. C32#3184semidirect
813. C3#80853semidirect
814. C3#83295semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
#105949102
#105927382
C3×#50392
#105914872
#105914822
#105914302
#105914042
#105911672
#105911652
Dic3×#2082
#105905892
#105905482
#105904552
#105904122
#832953
#808533