Finite Group Databasebeta

← #13168634

Subgroups — #13168634

Order 1728.

1194 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6294C211yesmaximal, characteristic, complemented
2#11723431C211yesmaximal, characteristic, complemented
3#11723429C211yesmaximal, characteristic, complemented
4#11723406C211yesmaximal, characteristic, complemented
5C3×#63916C211yesmaximal, characteristic
6C3×#63898C211yesmaximal, characteristic, complemented
7C3×#63872C211yesmaximal, characteristic, complemented
8#11723026C212yesmaximal, complemented
9#11722994C212yesmaximal, complemented
10#11722927C212yesmaximal, complemented
11#11722914C212yesmaximal, complemented
12#10595172—31nomaximal
13#10594447—31nomaximal
14#10594427—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×#6294C2211yescharacteristic
19C2×#6294C2211yescharacteristic
20C2×C3×#626C2212yes—
21C2×C3×D3×Dic3C2212yes—
22C3×C4×C3⋊Dic3C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26#88813C2211yescharacteristic
27#88813C2211yescharacteristic
28#88806C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30#88803C2212yes—
31(C2×D3)⋊(C3⋊Dic3)C2212yes—
32(C2×D3)⋊(C3⋊Dic3)C2212yes—
33Dic3×C3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38#64145—31no—
39#64106—31no—
40#64096—31no—
41C3×#938—31no—
42C3×D4×Dic3—31no—
43C3×#895—31no—
44C3×#893—31no—
45C3×#890—31no—
46C3×#890—31no—
47Dic3×#67—32no—
48#63969—32no—
49#63956—32no—
50#63955—32no—
51#63916D311yescharacteristic
52#63904—32no—
53#63898—32no—
54#63898D311yescharacteristic, complemented
55#63884—32no—
56C4×#624—31no—
57#63878—32no—
58C4×D3×Dic3—31no—
59C4×D3×Dic3—31no—
60#63872D311yescharacteristic, complemented
61#63861—32no—
62#63860—31no—
63#63860—31no—
64#63860—61no—
65#63858—32no—
66#63857—31no—
67#63857—31no—
68#63857—61no—
69#63854—32no—
70#63844—31no—
71#63844—31no—
72#63844—61no—
73#63841—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78#6308—22no—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4×C3⋊D3—22no—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C32×D12—22no—
88#6294—22no—
89#6294—22no—
90C3×#626—24no—
91C3×D3×Dic3—24no—
92#5691—91no—
93#5600—91no—
94#5557—91no—
95C2×C32×D4—31no—
96C2×C4×C3⋊D3C2×D311yescharacteristic
97C2×#634—31no—
98C2×#634—31no—
99C2×#634—31no—
100C2×#634—61no—
101C2×#634—61no—
102C2×#634—61no—
103C2×#634—121no—
104C2×C3×#67—32no—
105C22×C3×Dic3—32no—
106C2×C3×D12—21no—
107C2×C3×D12—32no—
108C2×C3×D12C2×D311yescharacteristic
109C2×C3×D12C2×D311yescharacteristic
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—61no—
114C2×#626C2×D312yes—
115C2×#624—31no—
116C2×#624—31no—
117C2×D3×Dic3—31no—
118C2×D3×Dic3—31no—
119C2×D3×Dic3—31no—
120C2×D3×Dic3—31no—
121C2×D3×Dic3C2×D312yes—
122C32×C4⋊C4—31no—
123C32×C4⋊C4—31no—
124#3757—32no—
125#3757—32no—
126#3752—32no—
127C4⋊(C3⋊Dic3)—32no—
128#3750—32no—
129C4×C3⋊Dic3—32no—
130C4×C3⋊Dic3C2×D311yescharacteristic
131C4×C3⋊Dic3C2×D311yescharacteristic
132C3×#217—32no—
133C3×#217—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D311yescharacteristic
143C3×C4⋊Dic3C2×D311yescharacteristic
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—61no—
151C3×C4×Dic3—61no—
152#3724—32no—
153#3724—32no—
154#3724—62no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—62no—
158Dic3⋊Dic3C2×D312yes—
159Dic3⋊Dic3C2×D312yes—
160(C2×D3)⋊Dic3—32no—
161(C2×D3)⋊Dic3—32no—
162(C2×D3)⋊Dic3—32no—
163(C2×D3)⋊Dic3—32no—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—62no—
167(C2×D3)⋊Dic3—62no—
168(C2×D3)⋊Dic3—62no—
169(C2×D3)⋊Dic3C2×D312yes—
170(C2×D3)⋊Dic3C2×D312yes—
171Dic32—31no—
172Dic32—31no—
173Dic32—31no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—32no—
178Dic32—32no—
179Dic32—62no—
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—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3#4112yes—
194C32×Dic3—22no—
195C32×Dic3—22no—
196C3×#125—91no—
197C3×#121—91no—
198C3×C4×D4—91no—
199#938—31no—
200#936—91no—
201#936—91no—
202#936—181no—
203#935—92no—
204D4×Dic3—31no—
205D4×Dic3—92no—
206C4×#67—92no—
207#926—92no—
208#924—91no—
209C2×C4×Dic3—91no—
210#898—92no—
211#897—91no—
212#897—91no—
213#897—181no—
214#895—31no—
215#894—92no—
216#893—31no—
217#893—92no—
218#892—92no—
219#890—31no—
220#890—31no—
221#887—91no—
222#887—91no—
223#887—181no—
224#883—92no—
225#879—92no—
226#879—92no—
227#877—92no—
228#875—91no—
229C42×D3—91no—
230C42×D3—91no—
231C4×Dic6—91no—
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—32no—
245C2×C32×C4—32no—
246C2×C32×C4—41no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C3⋊Dic3—32no—
251C2×C3⋊Dic3—32no—
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—62no—
254C2×C3⋊Dic3—62no—
255C2×C3⋊Dic3—62no—
256C2×C3⋊Dic3—122no—
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C4×C3⋊D3—22no—
263#634—62no—
264#634—64no—
265#634—62no—
266#634—62no—
267#634—122no—
268#634—122no—
269#634—124no—
270C3×#67—64no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—64no—
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C3×D12—22no—
294C3×D12—22no—
295C3×D12—42no—
296C3×D12—64no—
297C3×C4×D3—64no—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×C4×D3—122no—
301#626—24no—
302#624—62no—
303#624—62no—
304D3×Dic3—24no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307D3×Dic3—62no—
308D3×Dic3—62no—
309#529—271noSylow
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C3×C3⋊D3—22no—
314C32×D3—42no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—61no—
318C2×C3×D4—92no—
319C22×C3×C4—92no—
320C22×C3×C4—91no—
321C2×#67—32no—
322C22×Dic3—32no—
323C22×Dic3—91no—
324C22×Dic3—91no—
325C2×D12—32no—
326C2×D12D3211yescharacteristic
327C2×C4×D3—32no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×Dic6—91no—
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—181no—
339C2×Dic6—181no—
340C2×Dic6—181no—
341C2×Dic6—361no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—92no—
349C3×C4⋊C4—92no—
350C3×C22⋊C4—92no—
351C3×C22⋊C4—92no—
352C3×C42—91no—
353C3×C42—91no—
354#217—32no—
355#217—32no—
356#217—92no—
357#217—92no—
358#217—92no—
359#217—92no—
360#217—92no—
361#217—182no—
362#217—182no—
363(C2×D3)⋊C4—32no—
364(C2×D3)⋊C4—32no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—92no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—182no—
370C4⋊Dic3—32no—
371C4⋊Dic3—32no—
372C4⋊Dic3—92no—
373C4⋊Dic3—92no—
374C4⋊Dic3—182no—
375C4⋊Dic3D3211yescharacteristic
376C4⋊Dic3D3211yescharacteristic
377Dic3⋊C4—32no—
378Dic3⋊C4—32no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—92no—
382Dic3⋊C4—92no—
383Dic3⋊C4—182no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—92no—
397C4×Dic3—92no—
398C4×Dic3—92no—
399C4×Dic3—182no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—41no—
404C22×C32—62no—
405C22×C32—62no—
406C22×C32—62no—
407C22×C32C23×D311yescharacteristic
408C22×C32C23×D311yescharacteristic
409C22×C32C23×D311yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3#23712yes—
413C2×C3×D3—22no—
414C2×C3×D3—22no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—32no—
420C2×C3×D3—32no—
421C2×C3×D3—42no—
422C2×C3×D3—42no—
423C2×C3×D3—42no—
424C2×C3×D3—62no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3—61no—
429C2×C3×D3—121no—
430C2×C3×D3—121no—
431C32×C4—22no—
432C32×C4—22no—
433C32×C4—22no—
434C32×C4—42no—
435C32×C4—62no—
436C32×C4—62no—
437C32×C4#23512yes—
438C32×C4#23712yes—
439C32×C4#23912yes—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—62no—
445C3⋊Dic3—64no—
446C3⋊Dic3—62no—
447C3⋊Dic3—62no—
448C3⋊Dic3—122no—
449C3⋊Dic3—122no—
450C3⋊Dic3—124no—
451C3⋊Dic3#23712yes—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—32no—
457C3×Dic3—32no—
458C3×Dic3—42no—
459C3×Dic3—42no—
460C3×Dic3—62no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—121no—
470C3×Dic3—121no—
471C3×Dic3—121no—
472C3×Dic3—121no—
473#126—272no—
474#125—91no—
475#124—271no—
476#123—272no—
477C22⋊Q8—271no—
478#121—91no—
479C4×Q8—271no—
480C4×D4—91no—
481C4×D4—272no—
482#117—272no—
483C2×C42—271no—
484C33#52911yescharacteristic, complemented, Sylow
485C23×C3—32no—
486C23×C3—32no—
487C23×C3—62no—
488C23×C3—91no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—61no—
492C22×D3C2×D3212yes—
493C3×D4—62no—
494C3×D4—62no—
495C3×D4—122no—
496C3×D4—184no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—41no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—184no—
513C2×C3×C4—182no—
514C2×C3×C4C2×D3211yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517#67—64no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—64no—
534C2×Dic3—92no—
535C2×Dic3—92no—
536C2×Dic3—92no—
537C2×Dic3—182no—
538C2×Dic3—182no—
539C2×Dic3—182no—
540C2×Dic3—182no—
541C2×Dic3—182no—
542C2×Dic3—362no—
543C2×Dic3C2×D3212yes—
544C2×Dic3C2×D3212yes—
545D12—22no—
546D12—64no—
547C4×D3—64no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—122no—
551C4×D3—182no—
552C4×D3—182no—
553C4×D3—182no—
554C4×D3—182no—
555Dic6—184no—
556Dic6—182no—
557Dic6—182no—
558Dic6—182no—
559Dic6—362no—
560Dic6—362no—
561Dic6—364no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32—41no—
574C2×C32—122no—
575C2×C32C2×#23511yescharacteristic
576C2×C32C2×#23711yescharacteristic
577C2×C32C2×#23711yescharacteristic
578C2×C32C2×#23711yescharacteristic
579C2×C32C2×#23911yescharacteristic
580C2×C32D3×#4111yescharacteristic
581C2×C32D3×#4111yescharacteristic
582C2×C32D3×#4111yescharacteristic
583C2×C32D3×#4111yescharacteristic
584C3⋊D3—22no—
585C3×D3—42no—
586C3×D3—42no—
587C3×D3—62no—
588C3×D3—62no—
589C3×D3—82no—
590C3×D3—122no—
591C2×Q8—271no—
592C2×D4—31no—
593C2×D4—92no—
594C22×C4—92no—
595C22×C4—91no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—92no—
601C4⋊C4—92no—
602C4⋊C4—272no—
603C4⋊C4—272no—
604C22⋊C4—92no—
605C22⋊C4—92no—
606C22⋊C4—272no—
607C22⋊C4—272no—
608C22⋊C4—272no—
609C42—91no—
610C42—91no—
611C42—272no—
612C42—271no—
613C42—271no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—41no—
618C22×C3—62no—
619C22×C3—62no—
620C22×C3—62no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—62no—
624C22×C3—92no—
625C22×C3—122no—
626C22×C3—122no—
627C22×C3—122no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3C22×D3211yescharacteristic
631C22×C3C22×D3211yescharacteristic
632C22×C3C22×D3211yescharacteristic
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—32no—
637C2×D3—32no—
638C2×D3—62no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—121no—
644C2×D3—121no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—42no—
649C3×C4—62no—
650C3×C4—62no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—92no—
654C3×C4—122no—
655C3×C4—122no—
656C3×C4—181no—
657C3×C4—181no—
658C3×C4—181no—
659C3×C4—181no—
660C3×C4#379612yes—
661C3×C4#379912yes—
662C3×C4#380412yes—
663Dic3—22no—
664Dic3—22no—
665Dic3—32no—
666Dic3—32no—
667Dic3—62no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—184no—
681Dic3—182no—
682Dic3—182no—
683Dic3—182no—
684Dic3—362no—
685Dic3—362no—
686Dic3—364no—
687C32—21no—
688C32—21no—
689C32—21no—
690C32—41no—
691C32#555711yescharacteristic, complemented
692C32#560011yescharacteristic, complemented
693C32#569111yescharacteristic, complemented
694C23—32no—
695C23—91no—
696Q8—542no—
697D4—62no—
698D4—184no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—184no—
707C2×C4—182no—
708C2×C4—272no—
709C2×C4—542no—
710C2×C4—542no—
711C2×C4D3311yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—41no—
722C2×C3—41no—
723C2×C3—41no—
724C2×C3—122no—
725C2×C3—122no—
726C2×C3—182no—
727C2×C3—242no—
728C2×C3C2×#379611yescharacteristic
729C2×C3C2×#379911yescharacteristic
730C2×C3D3×#23711yescharacteristic
731C2×C3D3×#23711yescharacteristic
732C2×C3D3×#23711yescharacteristic
733C2×C3D3×#23711yescharacteristic
734C2×C3#6431911yescharacteristic
735C2×C3#6431911yescharacteristic
736C2×C3C2×#380411yescharacteristic
737D3—42no—
738D3—62no—
739D3—62no—
740D3—122no—
741C22—62no—
742C22—62no—
743C22—62no—
744C22—92no—
745C22—181no—
746C22—181no—
747C22C2×D3311yescharacteristic
748C4—62no—
749C4—62no—
750C4—92no—
751C4—181no—
752C4—181no—
753C4—181no—
754C4—181no—
755C4—542no—
756C4#8896212yes—
757C3—21no—
758C3—21no—
759C3—21no—
760C3—41no—
761C3#1059442711yescharacteristic, complemented
762C3#1059444711yescharacteristic, complemented
763C3#1059517211yescharacteristic, complemented
764C2—122no—
765C2—182no—
766C2#1172437411yescharacteristic
767C2#1172437411yescharacteristic
768C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC3×#63916C2
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. C4×#6294C2semidirect
2. #11723431C2semidirect
3. #11723429C2semidirect
4. #11723406C2semidirect
6. C3×#63898C2semidirect
7. C3×#63872C2semidirect
8. #11723026C2semidirect
9. #11722994C2semidirect
10. #11722927C2semidirect
11. #11722914C2semidirect
54. #63898D3semidirect
60. #63872D3semidirect
484. C33#529semidirect
691. C32#5557semidirect
692. C32#5600semidirect
693. C32#5691semidirect
761. C3#10594427semidirect
762. C3#10594447semidirect
763. C3#10595172semidirect

Maximal subgroups

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

subgroupindex
C4×#62942
#117234312
#117234292
#117234062
C3×#639162
C3×#638982
C3×#638722
#117230262
#117229942
#117229272
#117229142
#105951723
#105944473
#105944273