Finite Group Databasebeta

← #13168423

Subgroups — #13168423

Order 1728.

1182 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic, complemented
2#11723522C211yesmaximal, characteristic
3#11723454C211yesmaximal, characteristic, complemented
4Dic3×#634C211yesmaximal, characteristic, complemented
5C3×Dic3×D12C211yesmaximal, characteristic, complemented
6C3×C4×#624C211yesmaximal, characteristic, complemented
7C3×#63860C211yesmaximal, characteristic, complemented
8#11723020C212yesmaximal, complemented
9#11722992C212yesmaximal, complemented
10#11722930C212yesmaximal, complemented
11#11722913C212yesmaximal, complemented
12#10595191—31nomaximal
13#10593974—31nomaximal
14#10593921—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×#6290C2212yes—
19C2×C3×#624C2211yescharacteristic
20C2×C3×#624C2211yescharacteristic
21C2×C3×D3×Dic3C2212yes—
22C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25C32×C4×Dic3C2211yescharacteristic
26#88815C2212yes—
27#88814C2212yes—
28#88807C2212yes—
29#88807C2212yes—
30#88806C2212yes—
31(C2×D3)⋊(C3⋊Dic3)C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×(C2×D3)⋊Dic3C2212yes—
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38#64147—31no—
39#64079—31no—
40C4×#634—31no—
41C3×#936—31no—
42C3×D4×Dic3—31no—
43C3×#875—31no—
44C3×C4×D12—31no—
45C3×C42×D3—31no—
46C3×C42×D3—31no—
47#63975—32no—
48#63956—32no—
49#63955—32no—
50#63952—32no—
51#63908—31no—
52#63908—31no—
53#63908—61no—
54#63905—32no—
55#63905—32no—
56C4×#625—32no—
57Dic3×D12D311yescharacteristic, complemented
58C4×#624D311yescharacteristic, complemented
59#63879—32no—
60#63877—32no—
61#63871—31no—
62#63869—31no—
63#63869—31no—
64#63869—61no—
65#63860D311yescharacteristic, complemented
66#63859—32no—
67#63859—32no—
68#63857—31no—
69#63856—31no—
70#63855—32no—
71Dic3×Dic6—31no—
72Dic3×Dic6—31no—
73Dic3×Dic6—61no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C3×C4×C3⋊D3—22no—
82C3×#634—22no—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×D12—22no—
88#6290—24no—
89C3×#624—22no—
90C3×#624—22no—
91C3×D3×Dic3—24no—
92#5680—91no—
93#5557—91no—
94#5479—91no—
95C2×C32×D4—31no—
96C2×#638—32no—
97C2×C4×C3⋊D3C2×D311yescharacteristic
98C2×#634C2×D311yescharacteristic
99C22×C3×Dic3—32no—
100C2×C3×D12—21no—
101C2×C3×D12C2×D311yescharacteristic
102C2×C3×D12C2×D311yescharacteristic
103C2×C3×C4×D3—32no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—61no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—31no—
113C2×C3×Dic6—61no—
114C2×#625—32no—
115C2×#625—32no—
116C2×#625—62no—
117C2×#624C2×D311yescharacteristic
118C2×#624C2×D311yescharacteristic
119C2×D3×Dic3C2×D312yes—
120C32×C42—31no—
121C32×C42—31no—
122#3757—32no—
123C4⋊(C3⋊Dic3)—31no—
124C4⋊(C3⋊Dic3)—31no—
125C4⋊(C3⋊Dic3)—31no—
126C4⋊(C3⋊Dic3)—61no—
127C4⋊(C3⋊Dic3)—61no—
128C4⋊(C3⋊Dic3)—61no—
129C4⋊(C3⋊Dic3)—121no—
130C4⋊(C3⋊Dic3)C2×D311yescharacteristic
131#3750—32no—
132#3750—32no—
133#3750—32no—
134C4×C3⋊Dic3—32no—
135C3×#217—32no—
136C3×#217—32no—
137C3×#217—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—61no—
144C3×C4×Dic3—21no—
145C3×C4×Dic3—21no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152C3×C4×Dic3C2×D311yescharacteristic
153C3×C4×Dic3C2×D311yescharacteristic
154#3724—32no—
155#3724—32no—
156#3724—32no—
157#3724—62no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—62no—
165Dic3⋊Dic3—62no—
166#3722—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—62no—
172(C2×D3)⋊Dic3C2×D312yes—
173(C2×D3)⋊Dic3C2×D312yes—
174(C2×D3)⋊Dic3C2×D312yes—
175Dic32—32no—
176Dic32—32no—
177Dic32—62no—
178Dic32C2×D311yescharacteristic
179Dic32C2×D311yescharacteristic
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3#4112yes—
184C2×C32×D3—22no—
185C2×C32×D3—22no—
186C2×C32×D3—22no—
187C33×C4#4112yes—
188C3⋊(C3⋊Dic3)—22no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—21no—
192C32×Dic3—21no—
193C32×Dic3—21no—
194C32×Dic3—21no—
195C32×Dic3#4112yes—
196C3×#124—91no—
197C3×C4×D4—91no—
198C2×C3×C42—91no—
199#946—91no—
200Q8×Dic3—91no—
201#938—91no—
202#938—91no—
203#938—181no—
204#936—31no—
205D4×Dic3—31no—
206#930—91no—
207#929—92no—
208C4×#67—92no—
209C4×#67—92no—
210#926—92no—
211#924—91no—
212#897—91no—
213#890—91no—
214#883—92no—
215#883—92no—
216#67⋊C4—92no—
217#879—92no—
218#879—92no—
219#877—92no—
220#876—92no—
221#875—31no—
222C4×D12—31no—
223#872—92no—
224C42×D3—31no—
225C42×D3—31no—
226#870—91no—
227#870—91no—
228#870—181no—
229C4×Dic6—91no—
230C4×Dic6—91no—
231C4×Dic6—181no—
232C23×C32—32no—
233C22×C3⋊D3C22×D311yescharacteristic
234C22×C3×D3—22no—
235C22×C3×D3—31no—
236C22×C3×D3—31no—
237C22×C3×D3—61no—
238C22×C3×D3C22×D312yes—
239C22×C3×D3C22×D312yes—
240C32×D4—62no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—31no—
245C2×C32×C4—31no—
246C2×C32×C4—31no—
247C2×C32×C4—31no—
248C2×C32×C4—41no—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252#638—64no—
253C2×C3⋊Dic3—32no—
254C2×C3⋊Dic3—32no—
255C2×C3⋊Dic3—32no—
256C2×C3⋊Dic3—62no—
257C2×C3⋊Dic3—62no—
258C2×C3⋊Dic3—62no—
259C2×C3⋊Dic3—122no—
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D312yes—
263C4×C3⋊D3—22no—
264#634—22no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—62no—
278C2×C3×Dic3—64no—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C3×D12—22no—
288C3×D12—22no—
289C3×D12—42no—
290C3×C4×D3—62no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293C3×C4×D3—64no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—62no—
297C3×C4×D3—122no—
298C3×Dic6—64no—
299C3×Dic6—62no—
300C3×Dic6—62no—
301#625—64no—
302#625—64no—
303#625—124no—
304#624—22no—
305#624—22no—
306D3×Dic3—24no—
307#529—271noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—22no—
312C32×D3—42no—
313C2×C3×Q8—91no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—61no—
317C22×C3×C4—91no—
318C22×C3×C4—91no—
319C22×C3×C4—92no—
320C22×C3×C4—91no—
321C2×#67—92no—
322C2×#67—92no—
323C2×#67—92no—
324C2×#67—182no—
325C22×Dic3—32no—
326C2×D12D3211yescharacteristic
327C2×C4×D3—32no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—61no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C3×C4⋊C4—91no—
339C3×C22⋊C4—92no—
340C3×C22⋊C4—92no—
341C3×C22⋊C4—92no—
342C3×C42—31no—
343C3×C42—31no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—61no—
347C3×C42—61no—
348C3×C42—91no—
349C3×C42—91no—
350#217—32no—
351#217—32no—
352#217—32no—
353#217—92no—
354#217—92no—
355#217—92no—
356#217—182no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—32no—
360(C2×D3)⋊C4—92no—
361(C2×D3)⋊C4—92no—
362(C2×D3)⋊C4—92no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—61no—
366C4⋊Dic3—92no—
367C4⋊Dic3—91no—
368C4⋊Dic3—91no—
369C4⋊Dic3—91no—
370C4⋊Dic3—92no—
371C4⋊Dic3—92no—
372C4⋊Dic3—181no—
373C4⋊Dic3—181no—
374C4⋊Dic3—181no—
375C4⋊Dic3—361no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—92no—
382Dic3⋊C4—92no—
383Dic3⋊C4—92no—
384Dic3⋊C4—92no—
385Dic3⋊C4—182no—
386Dic3⋊C4—182no—
387Dic3⋊C4—182no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—92no—
393C4×Dic3—92no—
394C4×Dic3—92no—
395C4×Dic3—182no—
396C4×Dic3D3211yescharacteristic
397C4×Dic3D3211yescharacteristic
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—41no—
402C22×C32—62no—
403C22×C32—62no—
404C22×C32—62no—
405C22×C32C23×D311yescharacteristic
406C22×C32C23×D311yescharacteristic
407C22×C32C23×D311yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3#23512yes—
411C2×C3×D3—22no—
412C2×C3×D3—22no—
413C2×C3×D3—22no—
414C2×C3×D3—22no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—32no—
418C2×C3×D3—32no—
419C2×C3×D3—42no—
420C2×C3×D3—42no—
421C2×C3×D3—42no—
422C2×C3×D3—62no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—121no—
428C2×C3×D3—121no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—32no—
433C32×C4—42no—
434C32×C4—61no—
435C32×C4—61no—
436C32×C4—61no—
437C32×C4#23512yes—
438C32×C4#23512yes—
439C32×C4#23712yes—
440C3⋊Dic3—22no—
441C3⋊Dic3—21no—
442C3⋊Dic3—22no—
443C3⋊Dic3—62no—
444C3⋊Dic3—62no—
445C3⋊Dic3—62no—
446C3⋊Dic3—122no—
447C3⋊Dic3—122no—
448C3⋊Dic3—122no—
449C3⋊Dic3—242no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—22no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C3×Dic3—64no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C3×Dic3—61no—
464C3×Dic3—62no—
465C3×Dic3—61no—
466C3×Dic3—62no—
467C3×Dic3—121no—
468C3×Dic3—122no—
469C3×Dic3#23512yes—
470C3×Dic3#23712yes—
471#126—272no—
472#125—271no—
473#124—91no—
474#123—272no—
475C22⋊Q8—271no—
476#121—271no—
477C4×Q8—271no—
478C4×D4—91no—
479C4×D4—272no—
480#117—272no—
481C2×C42—91no—
482C33#52911yescharacteristic, complemented, Sylow
483C23×C3—32no—
484C23×C3—32no—
485C23×C3—62no—
486C23×C3—91no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3C2×D3212yes—
491C3×Q8—182no—
492C3×D4—62no—
493C3×D4—62no—
494C3×D4—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—92no—
512C2×C3×C4—91no—
513C2×C3×C4—92no—
514C2×C3×C4—182no—
515C2×C3×C4—184no—
516C2×C3×C4—182no—
517C2×C3×C4—182no—
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521#67—184no—
522#67—184no—
523#67—184no—
524#67—364no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—61no—
534C2×Dic3—64no—
535C2×Dic3—92no—
536C2×Dic3—92no—
537C2×Dic3—92no—
538C2×Dic3—182no—
539C2×Dic3—182no—
540C2×Dic3—182no—
541C2×Dic3—362no—
542C2×Dic3C2×D3211yescharacteristic
543C2×Dic3C2×D3211yescharacteristic
544C2×Dic3C2×D3211yescharacteristic
545C2×Dic3C2×D3211yescharacteristic
546D12—22no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—64no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—62no—
554C4×D3—122no—
555Dic6—64no—
556Dic6—62no—
557Dic6—62no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32—41no—
570C2×C32—122no—
571C2×C32C2×#23511yescharacteristic
572C2×C32C2×#23511yescharacteristic
573C2×C32C2×#23511yescharacteristic
574C2×C32C2×#23511yescharacteristic
575C2×C32C2×#23711yescharacteristic
576C2×C32C2×#23711yescharacteristic
577C2×C32D3×#4111yescharacteristic
578C2×C32D3×#4111yescharacteristic
579C2×C32D3×#4111yescharacteristic
580C3⋊D3—22no—
581C3×D3—42no—
582C3×D3—42no—
583C3×D3—62no—
584C3×D3—62no—
585C3×D3—82no—
586C3×D3—122no—
587C2×Q8—91no—
588C2×D4—31no—
589C2×D4—272no—
590C22×C4—91no—
591C22×C4—91no—
592C22×C4—92no—
593C22×C4—91no—
594C4⋊C4—91no—
595C4⋊C4—272no—
596C4⋊C4—272no—
597C4⋊C4—272no—
598C4⋊C4—272no—
599C4⋊C4—271no—
600C22⋊C4—92no—
601C22⋊C4—92no—
602C22⋊C4—92no—
603C22⋊C4—272no—
604C22⋊C4—272no—
605C42—31no—
606C42—31no—
607C42—91no—
608C42—91no—
609C42—272no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—41no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—62no—
620C22×C3—92no—
621C22×C3—122no—
622C22×C3—122no—
623C22×C3—122no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3C22×D3211yescharacteristic
627C22×C3C22×D3211yescharacteristic
628C22×C3C22×D3211yescharacteristic
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—22no—
632C2×D3—32no—
633C2×D3—32no—
634C2×D3—62no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—121no—
640C2×D3—121no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—32no—
645C3×C4—32no—
646C3×C4—42no—
647C3×C4—62no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—182no—
658C3×C4—182no—
659C3×C4—181no—
660C3×C4#379512yes—
661C3×C4#379812yes—
662C3×C4#380412yes—
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—64no—
667Dic3—62no—
668Dic3—61no—
669Dic3—62no—
670Dic3—61no—
671Dic3—62no—
672Dic3—62no—
673Dic3—121no—
674Dic3—122no—
675Dic3—182no—
676Dic3—182no—
677Dic3—182no—
678Dic3—362no—
679Dic3—362no—
680Dic3—362no—
681Dic3—722no—
682Dic3#379512yes—
683C32—21no—
684C32—21no—
685C32—21no—
686C32—41no—
687C32#547911yescharacteristic, complemented
688C32#555711yescharacteristic, complemented
689C32#568011yescharacteristic, complemented
690C23—32no—
691C23—91no—
692Q8—182no—
693D4—62no—
694D4—544no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—91no—
700C2×C4—92no—
701C2×C4—92no—
702C2×C4—182no—
703C2×C4—184no—
704C2×C4—182no—
705C2×C4—182no—
706C2×C4—272no—
707C2×C4D3311yescharacteristic
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—122no—
721C2×C3—122no—
722C2×C3—182no—
723C2×C3—242no—
724C2×C3C2×#379511yescharacteristic
725C2×C3C2×#379511yescharacteristic
726C2×C3C2×#379811yescharacteristic
727C2×C3D3×#23511yescharacteristic
728C2×C3D3×#23511yescharacteristic
729C2×C3D3×#23511yescharacteristic
730C2×C3D3×#23711yescharacteristic
731C2×C3#6431211yescharacteristic
732C2×C3C2×#380411yescharacteristic
733D3—42no—
734D3—62no—
735D3—62no—
736D3—122no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—92no—
741C22—181no—
742C22—181no—
743C22C2×D3311yescharacteristic
744C4—32no—
745C4—61no—
746C4—61no—
747C4—61no—
748C4—182no—
749C4—181no—
750C4—182no—
751C4—542no—
752C4#8896012yes—
753C3—21no—
754C3—21no—
755C3—21no—
756C3—41no—
757C3#1059392111yescharacteristic, complemented
758C3#1059397411yescharacteristic, complemented
759C3#1059519111yescharacteristic, complemented
760C2—122no—
761C2—182no—
762C2D3×#379511yescharacteristic
763C2#1172438811yescharacteristic
764C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723522C2
hypercenterC2×C4D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723674C2semidirect
3. #11723454C2semidirect
4. Dic3×#634C2semidirect
5. C3×Dic3×D12C2semidirect
6. C3×C4×#624C2semidirect
7. C3×#63860C2semidirect
8. #11723020C2semidirect
9. #11722992C2semidirect
10. #11722930C2semidirect
11. #11722913C2semidirect
57. Dic3×D12D3semidirect
58. C4×#624D3semidirect
65. #63860D3semidirect
482. C33#529semidirect
687. C32#5479semidirect
688. C32#5557semidirect
689. C32#5680semidirect
757. C3#10593921semidirect
758. C3#10593974semidirect
759. C3#10595191semidirect

Maximal subgroups

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

subgroupindex
#117236742
#117235222
#117234542
Dic3×#6342
C3×Dic3×D122
C3×C4×#6242
C3×#638602
#117230202
#117229922
#117229302
#117229132
#105951913
#105939743
#105939213