Finite Group Databasebeta

← #11870458

Subgroups — #11870458

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595139C211yesmaximal, characteristic, complemented
2#10594605C211yesmaximal, characteristic, complemented
3#10592473C211yesmaximal, characteristic, complemented
4C3×#4786C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591516C211yesmaximal, characteristic, complemented
7#10591428C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10590945C211yesmaximal, characteristic, complemented
10#10590762C211yesmaximal, characteristic, complemented
11Dic3×D24C211yesmaximal, characteristic, complemented
12#10590643C211yesmaximal, characteristic, complemented
13#10590555C211yesmaximal, characteristic, complemented
14#10590510C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#80312—31nomaximal
17#79590—31nomaximal
18C2×#3804—21no—
19C2×#3802C2211yescharacteristic
20C2×C4×D32—21no—
21#64147C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C3×#940C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28C3×#893C2211yescharacteristic
29C3×#893C2211yescharacteristic
30Dic3×#67—21no—
31#63959—21no—
32#63958—21no—
33#63921—21no—
34#63918C2211yescharacteristic, complemented
35#63916C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37Dic3×D12C2211yescharacteristic
38Dic3×D12C2211yescharacteristic, complemented
39C4×#624C2211yescharacteristic
40#63879—21no—
41#63879—21no—
42C2×#3713C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63645C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5716—31no—
62#5548—31no—
63C4×D3×D4—31no—
64C4×D3×D4—31no—
65C3×#459—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5156—31no—
69#5156—31no—
70#5150—31no—
71Dic3×D8—31no—
72Dic3×D8—31no—
73#5072—31no—
74C4×#213—31no—
75C4×#213—31no—
76#5007—31no—
77#4890—31no—
78#4882—31no—
79#4846—31no—
80#4833—31no—
81#4786D311yescharacteristic, complemented
82#4774—31no—
83#4774—31no—
84#4774—31no—
85#4774—61no—
86#4773—31no—
87#4759—31no—
88#4756—31no—
89#4756D311yescharacteristic, complemented
90C4×D24—31no—
91#4685—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×#627—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#624D411yescharacteristic
109C2×#624D411yescharacteristic
110#3804—44no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—22no—
116C4×D32—44no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3757—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#213—22no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—22no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32D411yescharacteristic
141Dic32D411yescharacteristic
142#3713—22no—
143#3100—91noSylow
144C2×#237—61no—
145C2×D3×D4—31no—
146C2×D3×D4—31no—
147C2×#235—61no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C2×C3×D8—31no—
151C2×C3×D8—31no—
152C2×C3×D8—31no—
153C3×#127—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157#940C2×D311yescharacteristic, complemented
158#938—31no—
159#938—31no—
160#938—31no—
161#938—61no—
162#938—61no—
163#936—61no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168D4×Dic3C2×D311yescharacteristic, complemented
169C2×#213—31no—
170C2×#213—31no—
171C2×#213C2×D311yescharacteristic
172C2×#213C2×D311yescharacteristic
173C4×#67—61no—
174C4×#67—61no—
175C4×#67—61no—
176C2×D24C2×D311yescharacteristic
177#895—31no—
178#893C2×D311yescharacteristic
179#893C2×D311yescharacteristic
180D3×C4⋊C4—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—61no—
183#888—31no—
184#885—61no—
185#884—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C42×D3—31no—
194C42×D3—31no—
195#869—31no—
196C3×#107—31no—
197C3×C4⋊C8—31no—
198C3×#102—21no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102C2×D311yescharacteristic, complemented
202C3×#102C2×D311yescharacteristic, complemented
203C3×C4×C8—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—61no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818—31no—
221#818—31no—
222#818—31no—
223#818—61no—
224Dic3⋊C8—31no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226C8×Dic3—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#809—31no—
229#809C2×D311yescharacteristic, complemented
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic, complemented
235C4⋊(C3⋊C8)—31no—
236C4×C3⋊C8—31no—
237C23×C32—21no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C2×D32—24no—
243C2×D32—42no—
244C2×D32—42no—
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—42no—
256C3×#67—42no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12#4112yescomplemented
269C3×D12#4112yescomplemented
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272#627—42no—
273#626—42no—
274#625—24no—
275#624—41no—
276#624D814yescomplemented
277D3×Dic3—42no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—91no—
286#480—91no—
287#480—91no—
288#474—91no—
289#474—91no—
290#459—31no—
291#459—91no—
292#447—91no—
293#447—91no—
294C4×D8—31no—
295C4×D8—91no—
296C4×D8—91no—
297C4×D8—91no—
298#431—91no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—121no—
320C22×Dic3—21no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324#237—124no—
325D3×D4—62no—
326D3×D4—62no—
327D3×D4—62no—
328D3×D4—62no—
329#235—124no—
330C2×D12—61no—
331C2×D12C22×D311yescharacteristic
332C2×D12C22×D311yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—121no—
349C2×C4×D3—124no—
350C2×C4×D3—124no—
351C2×Dic6—61no—
352C2×Dic6—61no—
353C3×D8—62no—
354C3×D8—62no—
355C3×D8—62no—
356C2×C3×C8—21no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—31no—
369C3×C42—31no—
370#217—21no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—121no—
378#213—22no—
379#213—22no—
380#213—62no—
381#213—62no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—121no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3C22×D311yescharacteristic
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—22no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3C2×D812yes—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
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—
428D32—48no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3C2×D812yes—
439C3×Dic3C2×D812yes—
440C2×#41—181no—
441C22×D4—91no—
442C23×C4—181no—
443C2×D8—31no—
444C2×D8—31no—
445C2×D8—31no—
446C2×D8—91no—
447C4⋊Q8—91no—
448#127—31no—
449#124—181no—
450#121—91no—
451#121—91no—
452#121—181no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C4×D4—181no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—181no—
464C2×C42—91no—
465#107—31no—
466#107—91no—
467#107—91no—
468#107—91no—
469C4⋊C8—31no—
470C4⋊C8—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102D3211yescharacteristic, complemented
479C22⋊C8—91no—
480C22⋊C8—91no—
481C4×C8—31no—
482C4×C8—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—61no—
495C22×D3—64no—
496C22×D3—64no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—32no—
506C3×D4—32no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—122no—
514C3×D4—122no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—42no—
530#67—42no—
531#67—64no—
532#67—64no—
533#67—122no—
534#67—122no—
535#67—122no—
536#67—242no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—42no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—122no—
549C2×Dic3—122no—
550C2×Dic3—122no—
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555D12—21no—
556D12—21no—
557D12—21no—
558D12—21no—
559D12—122no—
560D12#23512yescomplemented
561D12#23712yescomplemented
562C4×D3—34no—
563C4×D3—34no—
564C4×D3—42no—
565C4×D3—42no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—61no—
569C4×D3—61no—
570C4×D3—121no—
571C4×D3—121no—
572C4×D3—121no—
573C4×D3—121no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—242no—
580Dic6—122no—
581Dic6—122no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—41no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—121no—
592C2×C32—81no—
593C2×C32#52511yescharacteristic
594C2×C32C22×D811yescharacteristic
595C2×C32#57511yescharacteristic
596C3⋊D3—22no—
597C3×D3—42no—
598C3×D3—42no—
599C3×D3—81no—
600C24—181no—
601#41—364no—
602C2×Q8—181no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—182no—
611C2×D4—182no—
612C2×D4—181no—
613C2×D4C2×D3211yescharacteristic
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—91no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—364no—
625D8—62no—
626D8—62no—
627D8—62no—
628D8—182no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8C2×D3211yescharacteristic
633C4⋊C4—31no—
634C4⋊C4—91no—
635C4⋊C4—91no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4C2×D3211yescharacteristic
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—31no—
648C42—31no—
649C42—91no—
650C42—91no—
651C22×C3—21no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—62no—
659C22×C3—62no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—22no—
673C2×D3—22no—
674C2×D3—32no—
675C2×D3—32no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—62no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—128no—
691C2×D3—128no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—32no—
695C3×C4—32no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4C2×#23511yescharacteristic
703C3×C4C2×#23711yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4D3×#4111yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—41no—
709Dic3—61no—
710Dic3—61no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—241no—
717Dic3—241no—
718Dic3D3×D812yes—
719Dic3D3×D812yes—
720C32#310011yescharacteristic, complemented, Sylow
721C23—21no—
722C23—61no—
723C23—61no—
724C23—61no—
725C23—91no—
726C23—184no—
727C23—362no—
728C23—362no—
729Q8—362no—
730D4—21no—
731D4—21no—
732D4—32no—
733D4—32no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—61no—
738D4—122no—
739D4—122no—
740D4—184no—
741D4—362no—
742D4—362no—
743C2×C4—21no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—61no—
749C2×C4—94no—
750C2×C4—91no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—362no—
759C2×C4—362no—
760C2×C4—362no—
761C2×C4—362no—
762C2×C4—361no—
763C2×C4C22×D3211yescharacteristic
764C8—21no—
765C8—61no—
766C8—61no—
767C8—181no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—81no—
772C2×C3—81no—
773C2×C3—122no—
774C2×C3—122no—
775C2×C3—161no—
776C2×C3—241no—
777C2×C3#554711yescharacteristic
778C2×C3#560611yescharacteristic
779C2×C3C2×D3×D811yescharacteristic
780C2×C3C2×D3×D811yescharacteristic
781C2×C3#576811yescharacteristic
782C2×C3#577311yescharacteristic
783D3—42no—
784D3—42no—
785D3—62no—
786D3—62no—
787D3—81no—
788D3—122no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—62no—
793C22—62no—
794C22—92no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—181no—
803C22—181no—
804C22—368no—
805C22D32×D411yescharacteristic
806C4—32no—
807C4—32no—
808C4—41no—
809C4—61no—
810C4—61no—
811C4—121no—
812C4—181no—
813C4—361no—
814C4—361no—
815C4D3×#23511yescharacteristic
816C4D3×#23711yescharacteristic
817C3—21no—
818C3#7959011yescharacteristic, complemented
819C3#8031211yescharacteristic, complemented
820C2—81no—
821C2—122no—
822C2—122no—
823C2—182no—
824C2—241no—
825C2#1059428611yescharacteristic
826C2D32×D811yescharacteristic
827C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3100
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
1. #10595139C2semidirect
2. #10594605C2semidirect
3. #10592473C2semidirect
4. C3×#4786C2semidirect
5. C3×#4756C2semidirect
6. #10591516C2semidirect
7. #10591428C2semidirect
8. Dic3×#213C2semidirect
9. #10590945C2semidirect
10. #10590762C2semidirect
11. Dic3×D24C2semidirect
12. #10590643C2semidirect
13. #10590555C2semidirect
14. #10590510C2semidirect
15. #10590452C2semidirect
23. C3×#940C22semidirect
24. C3×D4×Dic3C22semidirect
34. #63918C22semidirect
38. Dic3×D12C22semidirect
43. C32×#102C22semidirect
44. #63659C22semidirect
46. #63645C22semidirect
47. #63634C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#809C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
57. #63563C22semidirect
60. Dic3×C3⋊C8C22semidirect
81. #4786D3semidirect
89. #4756D3semidirect
157. #940C2×D3semidirect
168. D4×Dic3C2×D3semidirect
201. C3×#102C2×D3semidirect
202. C3×#102C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
227. C8×Dic3C2×D3semidirect
229. #809C2×D3semidirect
234. #807C2×D3semidirect
268. C3×D12#41semidirect
269. C3×D12#41semidirect
276. #624D8semidirect
478. #102D32semidirect
560. D12#235semidirect
561. D12#237semidirect
720. C32#3100semidirect
818. C3#79590semidirect
819. C3#80312semidirect

Maximal subgroups

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

subgroupindex
#105951392
#105946052
#105924732
C3×#47862
C3×#47562
#105915162
#105914282
Dic3×#2132
#105909452
#105907622
Dic3×D242
#105906432
#105905552
#105905102
#105904522
#803123
#795903