Finite Group Databasebeta

← #13168629

Subgroups — #13168629

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
1C4×#6294C211yesmaximal, characteristic, complemented
2#11723522C211yesmaximal, characteristic
3#11723447C211yesmaximal, characteristic, complemented
4Dic6×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#63898C211yesmaximal, characteristic, complemented
6C3×#63871C211yesmaximal, characteristic, complemented
7C3×#63863C211yesmaximal, characteristic, complemented
8#11723026C212yesmaximal, complemented
9#11722998C212yesmaximal, complemented
10#11722936C212yesmaximal, complemented
11#11722914C212yesmaximal, complemented
12#10595377—31nomaximal
13#10595191—31nomaximal
14#10594444—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C32×D12C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6294C2211yescharacteristic
19C2×#6294C2211yescharacteristic
20C2×#6290C2212yes—
21C2×C3×D3×Dic3C2212yes—
22C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26#88813C2211yescharacteristic
27#88813C2211yescharacteristic
28#88806C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31(C2×D3)⋊(C3⋊Dic3)C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38Q8×C3⋊Dic3—31no—
39#64147—31no—
40#64099—31no—
41C3×#947—31no—
42C3×#946—31no—
43C3×#936—31no—
44C3×D4×Dic3—31no—
45C3×#897—31no—
46C3×#893—31no—
47#63975—32no—
48#63956—32no—
49#63955—32no—
50#63952—32no—
51#63908—31no—
52#63908—31no—
53#63908—61no—
54#63902—32no—
55#63898D311yescharacteristic, complemented
56#63891—32no—
57#63891—32no—
58C4×#624—31no—
59#63879—32no—
60#63878—32no—
61C4×D3×Dic3—31no—
62C4×D3×Dic3—31no—
63#63871D311yescharacteristic, complemented
64#63869—31no—
65#63869—31no—
66#63869—61no—
67#63863D311yescharacteristic, complemented
68#63861—32no—
69#63858—32no—
70Dic3×Dic6—31no—
71Dic3×Dic6—31no—
72Dic3×Dic6—61no—
73#63841—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C32×D12—22no—
87C32×Dic6—22no—
88#6294—22no—
89#6294—22no—
90#6290—24no—
91C3×D3×Dic3—24no—
92#5680—91no—
93#5624—91no—
94#5557—91no—
95C2×C32×Q8—31no—
96C2×C32×D4—31no—
97C2×#638—32no—
98C2×C4×C3⋊D3C2×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—61no—
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2×D311yescharacteristic
109C2×C3×Dic6C2×D311yescharacteristic
110C2×#625—32no—
111C2×#625—32no—
112C2×#625—62no—
113C2×#624—31no—
114C2×#624—31no—
115C2×D3×Dic3—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—31no—
118C2×D3×Dic3—31no—
119C2×D3×Dic3C2×D312yes—
120C32×C4⋊C4—31no—
121#3757—32no—
122C4⋊(C3⋊Dic3)—31no—
123C4⋊(C3⋊Dic3)—31no—
124C4⋊(C3⋊Dic3)—31no—
125C4⋊(C3⋊Dic3)—32no—
126C4⋊(C3⋊Dic3)—32no—
127C4⋊(C3⋊Dic3)—61no—
128C4⋊(C3⋊Dic3)—61no—
129C4⋊(C3⋊Dic3)—61no—
130C4⋊(C3⋊Dic3)—121no—
131#3750—32no—
132C4×C3⋊Dic3—32no—
133C4×C3⋊Dic3C2×D311yescharacteristic
134C4×C3⋊Dic3C2×D311yescharacteristic
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×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3—32no—
145C3×C4⋊Dic3C2×D311yescharacteristic
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×Dic3⋊C4—32no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—61no—
153C3×C4×Dic3—61no—
154#3724—32no—
155#3724—32no—
156#3724—62no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—62no—
162Dic3⋊Dic3—62no—
163Dic3⋊Dic3C2×D312yes—
164#3722C2×D312yes—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—62no—
168(C2×D3)⋊Dic3C2×D312yes—
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×#124—91no—
197C3×C22⋊Q8—91no—
198C3×C4×D4—91no—
199#947—31no—
200#946—31no—
201Q8×Dic3—91no—
202Q8×Dic3—91no—
203Q8×Dic3—181no—
204#938—91no—
205#938—91no—
206#938—181no—
207#936—31no—
208D4×Dic3—31no—
209#930—91no—
210C4×#67—92no—
211#926—92no—
212C2×C4×Dic3—91no—
213#898—92no—
214#897—31no—
215#893—31no—
216#892—92no—
217#890—91no—
218#890—91no—
219#890—181no—
220#886—92no—
221#883—92no—
222#883—92no—
223#67⋊C4—92no—
224#67⋊C4—92no—
225#879—92no—
226#879—92no—
227#877—92no—
228C42×D3—91no—
229C42×D3—91no—
230#870—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×Q8—62no—
241C32×D4—62no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—32no—
246C2×C32×C4—32no—
247C2×C32×C4—41no—
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251#638—64no—
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—32no—
254C2×C3⋊Dic3—32no—
255C2×C3⋊Dic3—62no—
256C2×C3⋊Dic3—62no—
257C2×C3⋊Dic3—62no—
258C2×C3⋊Dic3—122no—
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C4×C3⋊D3—22no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—64no—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C3×D12—22no—
288C3×D12—22no—
289C3×D12—42no—
290C3×C4×D3—64no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293C3×C4×D3—122no—
294C3×Dic6—24no—
295C3×Dic6—22no—
296C3×Dic6—22no—
297#625—64no—
298#625—64no—
299#625—124no—
300#624—62no—
301#624—62no—
302D3×Dic3—24no—
303D3×Dic3—62no—
304D3×Dic3—62no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307#529—271noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—22no—
312C32×D3—42no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—61no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—61no—
319C22×C3×C4—92no—
320C22×C3×C4—91no—
321C2×#67—92no—
322C2×#67—92no—
323C2×#67—92no—
324C2×#67—182no—
325C22×Dic3—32no—
326C22×Dic3—91no—
327C22×Dic3—91no—
328C2×D12D3211yescharacteristic
329C2×C4×D3—32no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—61no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×Dic6D3211yescharacteristic
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—92no—
342C3×C22⋊C4—92no—
343C3×C22⋊C4—92no—
344C3×C22⋊C4—92no—
345C3×C22⋊C4—92no—
346C3×C42—91no—
347C3×C42—91no—
348#217—32no—
349#217—32no—
350#217—32no—
351#217—92no—
352#217—92no—
353#217—182no—
354(C2×D3)⋊C4—32no—
355(C2×D3)⋊C4—32no—
356(C2×D3)⋊C4—32no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—92no—
360C4⋊Dic3—32no—
361C4⋊Dic3—92no—
362C4⋊Dic3—92no—
363C4⋊Dic3—92no—
364C4⋊Dic3—92no—
365C4⋊Dic3—91no—
366C4⋊Dic3—91no—
367C4⋊Dic3—91no—
368C4⋊Dic3—182no—
369C4⋊Dic3—182no—
370C4⋊Dic3—181no—
371C4⋊Dic3—181no—
372C4⋊Dic3—181no—
373C4⋊Dic3—361no—
374C4⋊Dic3D3211yescharacteristic
375Dic3⋊C4—32no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—182no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—92no—
395C4×Dic3—92no—
396C4×Dic3—92no—
397C4×Dic3—182no—
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#23912yes—
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—42no—
433C32×C4—62no—
434C32×C4—62no—
435C32×C4#23512yes—
436C32×C4#23712yes—
437C32×C4#23712yes—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—62no—
443C3⋊Dic3—62no—
444C3⋊Dic3—62no—
445C3⋊Dic3—122no—
446C3⋊Dic3—122no—
447C3⋊Dic3—122no—
448C3⋊Dic3—242no—
449C3⋊Dic3#23712yes—
450C3×Dic3—24no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—32no—
456C3×Dic3—32no—
457C3×Dic3—42no—
458C3×Dic3—62no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—121no—
468C3×Dic3—121no—
469C3×Dic3—121no—
470C3×Dic3—121no—
471#126—272no—
472#125—271no—
473#124—91no—
474#123—272no—
475C22⋊Q8—91no—
476#121—271no—
477C4×Q8—271no—
478C4×D4—91no—
479C4×D4—272no—
480#117—272no—
481C2×C42—271no—
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—64no—
492C3×Q8—62no—
493C3×Q8—62no—
494C3×D4—62no—
495C3×D4—62no—
496C3×D4—122no—
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—184no—
518#67—184no—
519#67—184no—
520#67—364no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—64no—
537C2×Dic3—92no—
538C2×Dic3—92no—
539C2×Dic3—92no—
540C2×Dic3—182no—
541C2×Dic3—182no—
542C2×Dic3—182no—
543C2×Dic3—182no—
544C2×Dic3—182no—
545C2×Dic3—362no—
546C2×Dic3C2×D3212yes—
547C2×Dic3C2×D3212yes—
548D12—22no—
549C4×D3—64no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—122no—
553C4×D3—182no—
554C4×D3—182no—
555C4×D3—182no—
556C4×D3—182no—
557Dic6—22no—
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×#23711yescharacteristic
573C2×C32C2×#23711yescharacteristic
574C2×C32C2×#23711yescharacteristic
575C2×C32C2×#23911yescharacteristic
576C2×C32D3×#4111yescharacteristic
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—31no—
588C2×D4—31no—
589C2×D4—272no—
590C22×C4—92no—
591C22×C4—91no—
592C22×C4—271no—
593C22×C4—271no—
594C4⋊C4—31no—
595C4⋊C4—92no—
596C4⋊C4—272no—
597C4⋊C4—272no—
598C4⋊C4—272no—
599C4⋊C4—271no—
600C22⋊C4—92no—
601C22⋊C4—92no—
602C22⋊C4—92no—
603C22⋊C4—92no—
604C22⋊C4—272no—
605C42—91no—
606C42—91no—
607C42—272no—
608C42—271no—
609C42—271no—
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—42no—
645C3×C4—64no—
646C3×C4—62no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—62no—
650C3×C4—92no—
651C3×C4—122no—
652C3×C4—181no—
653C3×C4—181no—
654C3×C4—181no—
655C3×C4—181no—
656C3×C4#379512yes—
657C3×C4#380412yes—
658C3×C4#380512yes—
659Dic3—22no—
660Dic3—22no—
661Dic3—32no—
662Dic3—32no—
663Dic3—62no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—182no—
677Dic3—182no—
678Dic3—182no—
679Dic3—362no—
680Dic3—362no—
681Dic3—362no—
682Dic3—722no—
683C32—21no—
684C32—21no—
685C32—21no—
686C32—41no—
687C32#555711yescharacteristic, complemented
688C32#562411yescharacteristic, complemented
689C32#568011yescharacteristic, complemented
690C23—32no—
691C23—91no—
692Q8—62no—
693D4—62no—
694D4—544no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—184no—
703C2×C4—182no—
704C2×C4—272no—
705C2×C4—542no—
706C2×C4—542no—
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×C3D3×#23711yescharacteristic
726C2×C3D3×#23711yescharacteristic
727C2×C3#6431211yescharacteristic
728C2×C3D3×#23911yescharacteristic
729C2×C3D3×#23911yescharacteristic
730C2×C3#6431911yescharacteristic
731C2×C3C2×#380411yescharacteristic
732C2×C3C2×#380511yescharacteristic
733D3—42no—
734D3—62no—
735D3—62no—
736D3—122no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—92no—
741C22—181no—
742C22—181no—
743C22C2×D3311yescharacteristic
744C4—62no—
745C4—62no—
746C4—92no—
747C4—181no—
748C4—181no—
749C4—181no—
750C4—181no—
751C4—542no—
752C4#8896112yes—
753C3—21no—
754C3—21no—
755C3—21no—
756C3—41no—
757C3#1059444411yescharacteristic, complemented
758C3#1059519111yescharacteristic, complemented
759C3#1059537711yescharacteristic, complemented
760C2—122no—
761C2—182no—
762C2#1172437411yescharacteristic
763C2#1172437711yescharacteristic
764C2C2×#8896111yescharacteristic
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. C4×#6294C2semidirect
3. #11723447C2semidirect
4. Dic6×C3⋊Dic3C2semidirect
5. C3×#63898C2semidirect
6. C3×#63871C2semidirect
7. C3×#63863C2semidirect
8. #11723026C2semidirect
9. #11722998C2semidirect
10. #11722936C2semidirect
11. #11722914C2semidirect
55. #63898D3semidirect
63. #63871D3semidirect
67. #63863D3semidirect
482. C33#529semidirect
687. C32#5557semidirect
688. C32#5624semidirect
689. C32#5680semidirect
757. C3#10594444semidirect
758. C3#10595191semidirect
759. C3#10595377semidirect

Maximal subgroups

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

subgroupindex
C4×#62942
#117235222
#117234472
Dic6×C3⋊Dic32
C3×#638982
C3×#638712
C3×#638632
#117230262
#117229982
#117229362
#117229142
#105953773
#105951913
#105944443