Finite Group Databasebeta

← #11872739

Subgroups — #11872739

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic, complemented
2#10593989C211yesmaximal, characteristic, complemented
3#10592714C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591448C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591404C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590589C211yesmaximal, characteristic, complemented
10#10590456C211yesmaximal, characteristic, complemented
11#10590425C211yesmaximal, characteristic, complemented
12#10590424C211yesmaximal, characteristic, complemented
13#10590349C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82542—31nomaximal
17#81146—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64083C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×#870C2211yescharacteristic, complemented
33#63910—21no—
34#63910—21no—
35#63909C2211yescharacteristic
36#63909C2211yescharacteristic
37#63897—21no—
38#63897—21no—
39#63894C2211yescharacteristic, complemented
40#63894C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63636C2211yescharacteristic, complemented
44#63636C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#808C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5697—31no—
63#5545D311yescharacteristic, complemented
64#5535—31no—
65C3×#478—31no—
66#5217—31no—
67#5217—31no—
68#5066—31no—
69#5015—31no—
70#5015—31no—
71#5015—31no—
72#5015—61no—
73#5014—31no—
74#5014—31no—
75C4×#213—31no—
76C4×#213—31no—
77#5009—31no—
78#5009D311yescharacteristic, complemented
79#5003—31no—
80#5003—31no—
81#5000—31no—
82#4885—31no—
83#4872—31no—
84#4869—31no—
85#4866—31no—
86#4843—31no—
87#4840—31no—
88#4785—31no—
89#4773—31no—
90#4773—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×#624—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114#3753—22no—
115#3753—22no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C3×#125—31no—
145C3×C4×D4—21no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×C4×D4C2×D311yescharacteristic
152C3×C4×D4C2×D311yescharacteristic
153C3×#117—31no—
154C3×#117—31no—
155C2×C3×C22⋊C4—61no—
156C2×C3×C22⋊C4—61no—
157D4×Dic3C2×D311yescharacteristic
158C2×#213—31no—
159C2×#213—31no—
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—61no—
165C2×#213—61no—
166#930—31no—
167#930—31no—
168C4×#67—21no—
169C2×(C2×D3)⋊C4—21no—
170C2×D24—31no—
171C2×D24—31no—
172#895—31no—
173#895—31no—
174#895—61no—
175#895—61no—
176#894—61no—
177#894—61no—
178#894—61no—
179#894—61no—
180#893—31no—
181#893—31no—
182#893C2×D311yescharacteristic
183#892C2×D311yescharacteristic
184#884—61no—
185#884—61no—
186#67⋊C4—21no—
187D3×C22⋊C4—21no—
188#874—31no—
189#874—31no—
190#874—61no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12C2×D311yescharacteristic
194#872C2×D311yescharacteristic
195#870C2×D311yescharacteristic, complemented
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#102—31no—
200C3×#102—31no—
201#832—31no—
202#832—31no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#830—31no—
206#830—31no—
207#821—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#815—31no—
212C8×Dic3—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—61no—
222#809—61no—
223#808—31no—
224#808—31no—
225#808C2×D311yescharacteristic, complemented
226#807—31no—
227#807—31no—
228#807C2×D311yescharacteristic, complemented
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—81no—
255C4⋊(C3⋊D3)—81no—
256C3×#67—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270#626—81no—
271#626—81no—
272#624—81no—
273#624—81no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—31no—
280#482—91no—
281#482—91no—
282#478—31no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—41no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C22×Dic3—21no—
313D3×D4—22no—
314D3×D4—22no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—121no—
328C2×D12—121no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—21no—
359C3×C42—31no—
360C3×C42—61no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#217—21no—
364#213—62no—
365#213—62no—
366#213—62no—
367#213—62no—
368#213—62no—
369#213—62no—
370#213—122no—
371#213—122no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4#6711yescharacteristic
384(C2×D3)⋊C4#6711yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4#6711yescharacteristic
391Dic3⋊C4#6711yescharacteristic
392C4×Dic3—21no—
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402D24—62no—
403D24—62no—
404C22×C32—22no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—84no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C22×D4—31no—
433C2×D8—91no—
434C2×D8—91no—
435C2×D8—91no—
436C2×D8—91no—
437#127—91no—
438#125—31no—
439#123—181no—
440#123—181no—
441#121—91no—
442#121—91no—
443#121—181no—
444#121—181no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4D3211yescharacteristic
453#117—31no—
454#117—31no—
455C2×C22⋊C4—61no—
456C2×C22⋊C4—61no—
457#107—31no—
458#107—91no—
459#106—31no—
460#106—91no—
461C4⋊C8—31no—
462C4⋊C8—91no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471C22⋊C8—91no—
472C22⋊C8—91no—
473#97—91no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—31no—
478C23×C3—41no—
479C23×C3—64no—
480C23×C3—61no—
481C23×C3—241no—
482C23×C3—241no—
483C22×D3—21no—
484C22×D3—24no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—81no—
490C22×D3—81no—
491C22×D3—121no—
492C22×D3—121no—
493C22×D3C2×#6711yescharacteristic
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—22no—
497C3×D4—32no—
498C3×D4—41no—
499C3×D4—64no—
500C3×D4—61no—
501C3×D4#23512yes—
502C3×D4#23912yes—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—81no—
518C2×C3×C4—81no—
519C2×C3×C4—82no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4—241no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—24no—
530#67—241no—
531#67—241no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—81no—
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—21no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—61no—
548D12—121no—
549D12—121no—
550D12—121no—
551D12—121no—
552D12—241no—
553D12—241no—
554D12—241no—
555D12—241no—
556D12—242no—
557D12—242no—
558D12—241no—
559D12—241no—
560D12#23512yes—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—81no—
564C4×D3—81no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C3⋊C8—121no—
579C2×C32—42no—
580C2×C32#52511yescharacteristic
581C2×C32#57611yescharacteristic
582C2×C32#57611yescharacteristic
583C3⋊D3—81no—
584C3⋊D3—81no—
585C3×D3—41no—
586C3×D3—42no—
587C24—61no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—62no—
591C2×D4—62no—
592C2×D4—91no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4—181no—
597C2×D4—181no—
598C2×D4C2×D3211yescharacteristic
599C22×C4—21no—
600C22×C4—31no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—181no—
605C22×C4—181no—
606D8—182no—
607D8—182no—
608D8—182no—
609D8—182no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—91no—
613C2×C8—91no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4C2×D3211yescharacteristic
622C22⋊C4—21no—
623C22⋊C4—31no—
624C22⋊C4—31no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—31no—
634C42—61no—
635C42C2×D3211yescharacteristic
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—62no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—244no—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C22×#6711yescharacteristic
655C2×D3—21no—
656C2×D3—22no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—84no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—241no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—241no—
679C2×D3—241no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4C2×#23511yescharacteristic
698C3×C4C2×#23511yescharacteristic
699C3×C4C2×#23911yescharacteristic
700C3×C4D3×#4111yescharacteristic
701Dic3—21no—
702Dic3—21no—
703Dic3—21no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707C32#312211yescharacteristic, complemented, Sylow
708C23—21no—
709C23—31no—
710C23—64no—
711C23—61no—
712C23—181no—
713C23—181no—
714C23—241no—
715C23—241no—
716D4—21no—
717D4—32no—
718D4—64no—
719D4—61no—
720D4—181no—
721D4—181no—
722D4—181no—
723D4—181no—
724D4—721no—
725D4—721no—
726D4—721no—
727D4—721no—
728D4#379912yes—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—81no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4D3×#6711yescharacteristic
745C2×C4D3×#6711yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—61no—
748C8—61no—
749C8—181no—
750C8—181no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—42no—
756C2×C3—82no—
757C2×C3—121no—
758C2×C3—122no—
759C2×C3#562711yescharacteristic
760C2×C3#576911yescharacteristic
761C2×C3#577411yescharacteristic
762C2×C3#579111yescharacteristic
763C2×C3#583511yescharacteristic
764C2×C3#583511yescharacteristic
765D3—41no—
766D3—42no—
767D3—241no—
768D3—241no—
769D3—241no—
770D3—241no—
771D3—481no—
772D3—481no—
773C22—22no—
774C22—41no—
775C22—41no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—62no—
780C22—121no—
781C22—121no—
782C22—244no—
783C22—361no—
784C22—361no—
785C22—361no—
786C22—361no—
787C22—361no—
788C22—361no—
789C22C2×D3×#6711yescharacteristic
790C4—21no—
791C4—21no—
792C4—41no—
793C4—61no—
794C4—61no—
795C4—61no—
796C4—121no—
797C4—121no—
798C4—121no—
799C4C2×#379911yescharacteristic
800C4D3×#23511yescharacteristic
801C3—21no—
802C3#8114611yescharacteristic, complemented
803C3#8254211yescharacteristic, complemented
804C2—42no—
805C2—121no—
806C2—122no—
807C2—721no—
808C2—721no—
809C2#1059500511yescharacteristic
810C2#1059509711yescharacteristic
811C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3122
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×#5545C2semidirect
2. #10593989C2semidirect
3. #10592714C2semidirect
4. C3×#5009C2semidirect
5. #10591448C2semidirect
6. #10591448C2semidirect
7. #10591404C2semidirect
8. #10591400C2semidirect
9. #10590589C2semidirect
10. #10590456C2semidirect
11. #10590425C2semidirect
12. #10590424C2semidirect
13. #10590349C2semidirect
14. #10590270C2semidirect
15. #10590253C2semidirect
22. #64083C22semidirect
32. C3×#870C22semidirect
39. #63894C22semidirect
40. #63894C22semidirect
43. #63636C22semidirect
44. #63636C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#808C22semidirect
49. C3×#807C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63576C22semidirect
52. #63574C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5545D3semidirect
78. #5009D3semidirect
195. #870C2×D3semidirect
225. #808C2×D3semidirect
228. #807C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
707. C32#3122semidirect
802. C3#81146semidirect
803. C3#82542semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105939892
#105927142
C3×#50092
#105914482
#105914042
#105914002
#105905892
#105904562
#105904252
#105904242
#105903492
#105902702
#105902532
#825423
#811463