Finite Group Databasebeta

← #13168599

Subgroups — #13168599

Order 1728.

1106 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
2C4×#6290C211yesmaximal, characteristic
3#11723450C211yesmaximal, characteristic, complemented
4#11723410C211yesmaximal, characteristic, complemented
5C3×#63900C211yesmaximal, characteristic, complemented
6C3×#63857C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic, complemented
8#11723022C212yesmaximal, complemented
9#11723014C212yesmaximal, complemented
10#11722992C212yesmaximal
11#11722915C212yesmaximal, complemented
12#10594970—31nomaximal
13#10594551—31nomaximal
14#10594550—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6290C2211yescharacteristic
19C2×C3×#624C2212yes—
20C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24#88815C2212yes—
25#88814C2212yes—
26#88807C2212yes—
27#88807C2212yes—
28#88806C2211yescharacteristic
29Dic3⋊(C3⋊Dic3)C2212yes—
30#88803C2211yescharacteristic
31(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
32Dic3×C3⋊Dic3C2212yes—
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×Dic32C2212yes—
38C4×#638—31no—
39#64099—31no—
40#64096—31no—
41C3×#926—31no—
42C3×#924—31no—
43C3×#897—31no—
44C3×#892—31no—
45C3×D3×C4⋊C4—31no—
46C3×D3×C4⋊C4—31no—
47#63975—32no—
48#63956—32no—
49#63905—32no—
50#63905—32no—
51C4×#625—31no—
52C4×#625—31no—
53C4×#625—61no—
54#63900D311yescharacteristic, complemented
55#63872—31no—
56#63872—31no—
57#63872—61no—
58#63871—31no—
59#63867—32no—
60#63867—32no—
61#63862—32no—
62#63861—32no—
63#63857—31no—
64#63857D311yescharacteristic, complemented
65#63856—31no—
66#63855—32no—
67#63847—32no—
68#63843—31no—
69#63843—31no—
70#63843—61no—
71#63841—32no—
72#63841D311yescharacteristic, complemented
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4×C3⋊D3—22no—
83C3×#634—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88#6290—22no—
89C3×#624—24no—
90#5639—91no—
91#5529—91no—
92#5513—91no—
93C22×C32×C4—31no—
94C2×#638—31no—
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×#634C2×D311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×C4×D3—61no—
103C2×C3×C4×D3C2×D311yescharacteristic
104C2×C3×C4×D3C2×D311yescharacteristic
105C2×C3×Dic6—31no—
106C2×C3×Dic6—31no—
107C2×C3×Dic6—61no—
108C2×#625—31no—
109C2×#625—31no—
110C2×#625—61no—
111C2×#624C2×D312yes—
112C32×C4⋊C4—31no—
113C32×C4⋊C4—31no—
114#3757—31no—
115#3752—31no—
116C4⋊(C3⋊Dic3)—32no—
117C4⋊(C3⋊Dic3)C2×D311yescharacteristic
118#3750—32no—
119#3750—32no—
120#3750—31no—
121C4×C3⋊Dic3—31no—
122C4×C3⋊Dic3—31no—
123C4×C3⋊Dic3—31no—
124C4×C3⋊Dic3—32no—
125C4×C3⋊Dic3—61no—
126C4×C3⋊Dic3—61no—
127C4×C3⋊Dic3—61no—
128C4×C3⋊Dic3—121no—
129C3×#217—32no—
130C3×#217—32no—
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—61no—
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D311yescharacteristic
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×C4×Dic3—32no—
147C3×C4×Dic3—32no—
148#3724—32no—
149#3724—31no—
150#3724—31no—
151#3724—61no—
152#3724C2×D312yes—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—62no—
162Dic3⋊Dic3—62no—
163Dic3⋊Dic3—62no—
164Dic3⋊Dic3C2×D312yes—
165#3722—32no—
166(C2×D3)⋊Dic3—31no—
167(C2×D3)⋊Dic3—31no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—61no—
173(C2×D3)⋊Dic3—61no—
174(C2×D3)⋊Dic3C2×D312yes—
175(C2×D3)⋊Dic3C2×D312yes—
176Dic32—32no—
177Dic32—32no—
178Dic32—62no—
179Dic32C2×D312yes—
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3#4112yes—
184C2×C32×D3—21no—
185C2×C32×D3—21no—
186C2×C32×D3—21no—
187C33×C4#4112yes—
188C3⋊(C3⋊Dic3)—21no—
189C3⋊(C3⋊Dic3)—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—22no—
193C32×Dic3—22no—
194C32×Dic3—22no—
195C32×Dic3—21no—
196C3×C22⋊Q8—91no—
197C3×#117—91no—
198C2×C3×C4⋊C4—91no—
199#946—91no—
200Q8×Dic3—91no—
201#929—92no—
202C4×#67—91no—
203C4×#67—91no—
204C4×#67—91no—
205C4×#67—181no—
206#926—31no—
207#926—92no—
208#924—31no—
209#924—91no—
210#898—92no—
211#897—31no—
212#897—91no—
213#892—31no—
214#892—92no—
215D3×C4⋊C4—31no—
216D3×C4⋊C4—31no—
217#890—91no—
218#890—91no—
219#890—91no—
220#890—181no—
221#889—92no—
222#889—92no—
223#887—91no—
224#887—91no—
225#887—181no—
226#883—92no—
227#883—92no—
228#879—92no—
229#879—92no—
230#872—92no—
231#870—92no—
232C23×C32—31no—
233C22×C3⋊D3C22×D311yescharacteristic
234C22×C3×D3—21no—
235C22×C3×D3—31no—
236C22×C3×D3—31no—
237C22×C3×D3—61no—
238C22×C3×D3C22×D311yescharacteristic
239C22×C3×D3C22×D311yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—31no—
244C2×C32×C4—32no—
245C2×C32×C4—32no—
246C2×C32×C4—41no—
247C2×C32×C4—62no—
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251#638—62no—
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—61no—
259C2×C3⋊Dic3—61no—
260C2×C3⋊Dic3—61no—
261C2×C3⋊Dic3—61no—
262C2×C3⋊Dic3—61no—
263C2×C3⋊Dic3—61no—
264C2×C3⋊Dic3—121no—
265C2×C3⋊Dic3—121no—
266C2×C3⋊Dic3C22×D312yes—
267C2×C3⋊Dic3C22×D312yes—
268C2×C3⋊Dic3C22×D311yescharacteristic
269C4×C3⋊D3—22no—
270#634—22no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D312yes—
289C3×C4×D3—22no—
290C3×C4×D3—22no—
291C3×C4×D3—42no—
292C3×C4×D3—64no—
293C3×C4×D3—64no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—122no—
297C3×Dic6—64no—
298C3×Dic6—62no—
299C3×Dic6—62no—
300#625—62no—
301#625—62no—
302#625—64no—
303#624—24no—
304#552—271noSylow
305C2×C33C2×#4111yescharacteristic
306C2×C33C2×#4111yescharacteristic
307C2×C332−1+411yescharacteristic
308C3×C3⋊D3—22no—
309C32×D3—41no—
310C2×C3×Q8—91no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—92no—
315C22×C3×C4—91no—
316C2×#67—91no—
317C2×#67—91no—
318C2×#67—91no—
319C2×#67—181no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—32no—
323C2×C4×D3—32no—
324C2×C4×D3—61no—
325C2×C4×D3D3211yescharacteristic
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—92no—
336C3×C4⋊C4—92no—
337C3×C4⋊C4—91no—
338C3×C22⋊C4—92no—
339C3×C22⋊C4—92no—
340C3×C42—92no—
341#217—32no—
342#217—32no—
343#217—92no—
344#217—91no—
345#217—91no—
346#217—91no—
347#217—181no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352(C2×D3)⋊C4—91no—
353(C2×D3)⋊C4—91no—
354(C2×D3)⋊C4—91no—
355(C2×D3)⋊C4—181no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—32no—
359C4⋊Dic3—61no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362C4⋊Dic3—92no—
363C4⋊Dic3—92no—
364C4⋊Dic3—92no—
365C4⋊Dic3—182no—
366C4⋊Dic3D3211yescharacteristic
367C4⋊Dic3D3211yescharacteristic
368Dic3⋊C4—32no—
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—91no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—91no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—91no—
381Dic3⋊C4—182no—
382Dic3⋊C4—182no—
383Dic3⋊C4—181no—
384C4×Dic3—32no—
385C4×Dic3—32no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—92no—
392C4×Dic3—182no—
393C4×Dic3—181no—
394C4×Dic3—181no—
395C4×Dic3—181no—
396C4×Dic3—361no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—41no—
401C22×C32—61no—
402C22×C32—61no—
403C22×C32—61no—
404C22×C32C23×D311yescharacteristic
405C22×C32C23×D311yescharacteristic
406C22×C32C23×D311yescharacteristic
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3⋊D3#23712yes—
410C2×C3×D3—22no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—32no—
418C2×C3×D3—32no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—62no—
422C2×C3×D3—61no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—121no—
427C2×C3×D3—121no—
428C32×C4—22no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—42no—
432C32×C4—61no—
433C32×C4—62no—
434C32×C4—62no—
435C32×C4#23512yes—
436C32×C4#23512yes—
437C32×C4#23712yes—
438C3⋊Dic3—22no—
439C3⋊Dic3—21no—
440C3⋊Dic3—22no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3⋊Dic3—62no—
444C3⋊Dic3—62no—
445C3⋊Dic3—61no—
446C3⋊Dic3—61no—
447C3⋊Dic3—61no—
448C3⋊Dic3—61no—
449C3⋊Dic3—121no—
450C3⋊Dic3—121no—
451C3⋊Dic3—121no—
452C3⋊Dic3—121no—
453C3⋊Dic3—122no—
454C3⋊Dic3—122no—
455C3×Dic3—21no—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—21no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—41no—
462C3×Dic3—42no—
463C3×Dic3—42no—
464C3×Dic3—64no—
465C3×Dic3—62no—
466C3×Dic3—62no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—121no—
472C3×Dic3—122no—
473#126—272no—
474#125—272no—
475#125—271no—
476#123—272no—
477C22⋊Q8—91no—
478C22⋊Q8—271no—
479C4×Q8—271no—
480C4×D4—271no—
481#117—91no—
482#117—272no—
483C2×C4⋊C4—91no—
484C33#55211yescharacteristic, complemented, Sylow
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—61no—
488C23×C3—91no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—61no—
492C22×D3C2×D3211yescharacteristic
493C3×Q8—182no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—31no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—41no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—61no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—92no—
510C2×C3×C4—91no—
511C2×C3×C4—92no—
512C2×C3×C4—122no—
513C2×C3×C4—184no—
514C2×C3×C4—182no—
515C2×C3×C4C2×D3211yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518#67—182no—
519#67—182no—
520#67—182no—
521#67—184no—
522C2×Dic3—32no—
523C2×Dic3—32no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—62no—
529C2×Dic3—62no—
530C2×Dic3—61no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—181no—
538C2×Dic3—181no—
539C2×Dic3—181no—
540C2×Dic3—181no—
541C2×Dic3—181no—
542C2×Dic3—181no—
543C2×Dic3—361no—
544C2×Dic3—361no—
545C2×Dic3C2×D3211yescharacteristic
546C2×Dic3C2×D3212yes—
547C2×Dic3C2×D3212yes—
548C4×D3—22no—
549C4×D3—64no—
550C4×D3—64no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—122no—
554Dic6—64no—
555Dic6—62no—
556Dic6—62no—
557C2×C32—21no—
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—41no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32—121no—
570C2×C32C2×#23511yescharacteristic
571C2×C32C2×#23511yescharacteristic
572C2×C32C2×#23711yescharacteristic
573C2×C32C2×#23711yescharacteristic
574C2×C32#100711yescharacteristic
575C2×C32#100711yescharacteristic
576C2×C32D3×#4111yescharacteristic
577C2×C32D3×#4111yescharacteristic
578C2×C32#101011yescharacteristic
579C3⋊D3—22no—
580C3×D3—42no—
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—62no—
584C3×D3—62no—
585C3×D3—122no—
586C2×Q8—91no—
587C2×D4—271no—
588C22×C4—31no—
589C22×C4—92no—
590C22×C4—91no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—92no—
594C4⋊C4—92no—
595C4⋊C4—91no—
596C4⋊C4—272no—
597C4⋊C4—271no—
598C4⋊C4—272no—
599C4⋊C4—272no—
600C4⋊C4—272no—
601C22⋊C4—92no—
602C22⋊C4—92no—
603C22⋊C4—271no—
604C22⋊C4—272no—
605C22⋊C4—271no—
606C42—92no—
607C42—272no—
608C42—271no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—41no—
613C22×C3—62no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—92no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3C22×D3211yescharacteristic
626C22×C3C22×D3211yescharacteristic
627C22×C3C22×D3211yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—32no—
632C2×D3—32no—
633C2×D3—62no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—121no—
639C2×D3—121no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—42no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—62no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—62no—
650C3×C4—121no—
651C3×C4—122no—
652C3×C4—122no—
653C3×C4—182no—
654C3×C4—182no—
655C3×C4—181no—
656C3×C4#379512yes—
657C3×C4#379812yes—
658C3×C4#380412yes—
659Dic3—22no—
660Dic3—22no—
661Dic3—21no—
662Dic3—64no—
663Dic3—62no—
664Dic3—61no—
665Dic3—62no—
666Dic3—61no—
667Dic3—62no—
668Dic3—62no—
669Dic3—121no—
670Dic3—122no—
671Dic3—182no—
672Dic3—182no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—361no—
680Dic3—361no—
681Dic3—361no—
682Dic3—361no—
683Dic3—362no—
684Dic3—362no—
685C32—21no—
686C32—21no—
687C32—21no—
688C32—41no—
689C32#551311yescharacteristic, complemented
690C32#552911yescharacteristic, complemented
691C32#563911yescharacteristic, complemented
692C23—31no—
693C23—91no—
694Q8—182no—
695D4—542no—
696C2×C4—31no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—62no—
700C2×C4—92no—
701C2×C4—92no—
702C2×C4—91no—
703C2×C4—184no—
704C2×C4—182no—
705C2×C4—271no—
706C2×C4—271no—
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—121no—
722C2×C3—121no—
723C2×C3—182no—
724C2×C3C2×#379511yescharacteristic
725C2×C3#6429711yescharacteristic
726C2×C3C2×#379811yescharacteristic
727C2×C3#6430611yescharacteristic
728C2×C3D3×#23711yescharacteristic
729C2×C3D3×#23711yescharacteristic
730C2×C3#6431511yescharacteristic
731C2×C3#6431611yescharacteristic
732C2×C3C2×#380411yescharacteristic
733D3—41no—
734D3—62no—
735D3—62no—
736D3—122no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—92no—
741C22—181no—
742C22—181no—
743C22C2×D3311yescharacteristic
744C4—62no—
745C4—62no—
746C4—61no—
747C4—182no—
748C4—181no—
749C4—182no—
750C4—541no—
751C4—541no—
752C4#8896012yes—
753C3—21no—
754C3—21no—
755C3—21no—
756C3—41no—
757C3#1059455011yescharacteristic, complemented
758C3#1059455111yescharacteristic, complemented
759C3#1059497011yescharacteristic, complemented
760C2—121no—
761C2—182no—
762C2#1172437311yescharacteristic
763C2#1172439711yescharacteristic
764C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6290C22
hypercenterC2×C4D33
hypocenterC33#552
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. #11723450C2semidirect
4. #11723410C2semidirect
5. C3×#63900C2semidirect
6. C3×#63857C2semidirect
7. C3×#63841C2semidirect
8. #11723022C2semidirect
9. #11723014C2semidirect
11. #11722915C2semidirect
54. #63900D3semidirect
64. #63857D3semidirect
72. #63841D3semidirect
484. C33#552semidirect
689. C32#5513semidirect
690. C32#5529semidirect
691. C32#5639semidirect
757. C3#10594550semidirect
758. C3#10594551semidirect
759. C3#10594970semidirect

Maximal subgroups

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

subgroupindex
#117236742
C4×#62902
#117234502
#117234102
C3×#639002
C3×#638572
C3×#638412
#117230222
#117230142
#117229922
#117229152
#105949703
#105945513
#105945503