Finite Group Databasebeta

← #13168444

Subgroups — #13168444

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#11723677C211yesmaximal, characteristic, complemented
2#11723515C211yesmaximal, characteristic
3#11723447C211yesmaximal, characteristic, complemented
4Dic3×#634C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
7C3×#63857C211yesmaximal, characteristic, complemented
8#11723024C212yesmaximal, complemented
9#11722988C212yesmaximal, complemented
10#11722930C212yesmaximal, complemented
11#11722915C212yesmaximal, complemented
12#10594955—31nomaximal
13#10594444—31nomaximal
14#10593974—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6290C2212yes—
19C2×C3×#624C2212yes—
20C2×C3×D3×Dic3C2211yescharacteristic
21C2×C3×D3×Dic3C2211yescharacteristic
22C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4×Dic3C2211yescharacteristic
26#88814C2212yes—
27#88814C2212yes—
28#88807C2212yes—
29#88806C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38#64139—31no—
39#64099—31no—
40C4×#634—31no—
41C3×#924—31no—
42C2×C3×C4×Dic3—31no—
43C3×#897—31no—
44C3×#893—31no—
45C3×C4×D12—31no—
46C3×C42×D3—31no—
47#63966—32no—
48#63952—32no—
49#63908—31no—
50#63908—31no—
51#63908—61no—
52#63905—32no—
53C4×#625—32no—
54#63894D311yescharacteristic, complemented
55#63891—32no—
56#63879—32no—
57C4×D3×Dic3D311yescharacteristic, complemented
58#63869—31no—
59#63869—31no—
60#63869—61no—
61#63868—32no—
62#63864—31no—
63#63863—31no—
64#63860—31no—
65#63859—32no—
66#63858—32no—
67#63857D311yescharacteristic, complemented
68#63855—32no—
69Dic3×Dic6—31no—
70Dic3×Dic6—31no—
71Dic3×Dic6—61no—
72#63841—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2312yes—
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C3×C4⋊(C3⋊D3)—22no—
82C3×#634—22no—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88#6290—24no—
89C3×#624—24no—
90C3×D3×Dic3—22no—
91C3×D3×Dic3—22no—
92#5624—91no—
93#5557—91no—
94#5479—91no—
95C22×C32×C4—31no—
96C2×#638—32no—
97C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
98C2×#634C2×D311yescharacteristic
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C2×C3×D12—31no—
102C2×C3×D12—31no—
103C2×C3×D12—61no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×C4×D3C2×D311yescharacteristic
111C2×C3×Dic6—31no—
112C2×C3×Dic6—31no—
113C2×C3×Dic6—61no—
114C2×#625—32no—
115C2×#625—32no—
116C2×#625—62no—
117C2×#624C2×D312yes—
118C2×D3×Dic3C2×D311yescharacteristic
119C2×D3×Dic3C2×D311yescharacteristic
120C32×C4⋊C4—31no—
121C32×C42—31no—
122#3752—32no—
123C4⋊(C3⋊Dic3)—31no—
124C4⋊(C3⋊Dic3)—31no—
125C4⋊(C3⋊Dic3)—31no—
126C4⋊(C3⋊Dic3)—32no—
127C4⋊(C3⋊Dic3)—61no—
128C4⋊(C3⋊Dic3)—61no—
129C4⋊(C3⋊Dic3)—61no—
130C4⋊(C3⋊Dic3)—121no—
131#3750—32no—
132#3750—32no—
133C4×C3⋊Dic3—32no—
134C4×C3⋊Dic3C2×D311yescharacteristic
135C3×#217—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D311yescharacteristic
143C3×Dic3⋊C4—32no—
144C3×C4×Dic3—21no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—61no—
152C3×C4×Dic3C2×D311yescharacteristic
153C3×C4×Dic3C2×D311yescharacteristic
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#3722—32no—
165#3722—32no—
166#3722C2×D312yes—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—62no—
174(C2×D3)⋊Dic3C2×D312yes—
175Dic32—32no—
176Dic32—32no—
177Dic32—62no—
178Dic32C2×D311yescharacteristic
179Dic32C2×D311yescharacteristic
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—22no—
184C2×C32×D3—21no—
185C2×C32×D3—21no—
186C2×C32×D3#4112yes—
187C33×C4#4112yes—
188C3⋊(C3⋊Dic3)—22no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—21no—
192C32×Dic3—21no—
193C32×Dic3—22no—
194C32×Dic3—21no—
195C32×Dic3#4112yes—
196C3×C22⋊Q8—91no—
197C3×C4×D4—91no—
198C2×C3×C42—91no—
199#947—91no—
200Q8×Dic3—91no—
201#938—91no—
202#936—91no—
203#930—91no—
204#930—91no—
205#930—181no—
206#929—92no—
207C4×#67—92no—
208C4×#67—92no—
209#926—92no—
210#924—31no—
211C2×C4×Dic3—31no—
212#898—92no—
213#897—31no—
214#893—31no—
215#892—92no—
216#890—91no—
217#890—91no—
218#890—181no—
219#886—92no—
220#883—92no—
221#67⋊C4—92no—
222#879—92no—
223#876—92no—
224#875—91no—
225C4×D12—31no—
226#872—92no—
227C42×D3—31no—
228#870—91no—
229C4×Dic6—91no—
230C4×Dic6—91no—
231C4×Dic6—181no—
232C23×C32—31no—
233C22×C3⋊D3C22×D312yes—
234C22×C3×D3—21no—
235C22×C3×D3—32no—
236C22×C3×D3—32no—
237C22×C3×D3—62no—
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—31no—
245C2×C32×C4—31no—
246C2×C32×C4—32no—
247C2×C32×C4—41no—
248C2×C32×C4—62no—
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×D311yescharacteristic
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—22no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—62no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C3×D12—62no—
289C3×D12—62no—
290C3×D12—122no—
291C3×C4×D3—22no—
292C3×C4×D3—22no—
293C3×C4×D3—42no—
294C3×C4×D3—64no—
295C3×C4×D3—62no—
296C3×C4×D3—62no—
297C3×C4×D3—64no—
298C3×Dic6—64no—
299C3×Dic6—62no—
300C3×Dic6—62no—
301#625—64no—
302#625—64no—
303#625—124no—
304#624—24no—
305D3×Dic3—22no—
306D3×Dic3—22no—
307#529—271noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—42no—
312C32×D3—22no—
313C2×C3×Q8—91no—
314C2×C3×D4—91no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C22×C3×C4—92no—
319C22×C3×C4—91no—
320C22×C3×C4—91no—
321C2×#67—92no—
322C2×#67—92no—
323C2×#67—92no—
324C2×#67—182no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—32no—
333C2×C4×D3—32no—
334C2×C4×D3D3211yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
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×C42—31no—
345C3×C42—31no—
346C3×C42—61no—
347C3×C42—91no—
348C3×C42—91no—
349C3×C42—91no—
350#217—32no—
351#217—92no—
352#217—92no—
353#217—92no—
354(C2×D3)⋊C4—32no—
355(C2×D3)⋊C4—32no—
356(C2×D3)⋊C4—32no—
357(C2×D3)⋊C4—92no—
358(C2×D3)⋊C4—92no—
359(C2×D3)⋊C4—92no—
360(C2×D3)⋊C4—92no—
361(C2×D3)⋊C4—92no—
362(C2×D3)⋊C4—92no—
363(C2×D3)⋊C4—182no—
364C4⋊Dic3—32no—
365C4⋊Dic3—92no—
366C4⋊Dic3—92no—
367C4⋊Dic3—91no—
368C4⋊Dic3—91no—
369C4⋊Dic3—91no—
370C4⋊Dic3—92no—
371C4⋊Dic3—182no—
372C4⋊Dic3—181no—
373C4⋊Dic3—181no—
374C4⋊Dic3—181no—
375C4⋊Dic3—361no—
376C4⋊Dic3D3211yescharacteristic
377Dic3⋊C4—32no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—92no—
382Dic3⋊C4—92no—
383Dic3⋊C4—92no—
384Dic3⋊C4—182no—
385Dic3⋊C4—182no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—92no—
394C4×Dic3—92no—
395C4×Dic3—92no—
396C4×Dic3—182no—
397C4×Dic3D3211yescharacteristic
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—32no—
402C22×C32—41no—
403C22×C32—61no—
404C22×C32—61no—
405C22×C32C23×D311yescharacteristic
406C22×C32C23×D311yescharacteristic
407C22×C32C23×D311yescharacteristic
408C2×C3⋊D3—22no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—22no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—62no—
421C2×C3×D3—62no—
422C2×C3×D3—62no—
423C2×C3×D3—62no—
424C2×C3×D3—122no—
425C2×C3×D3—122no—
426C2×C3×D3—122no—
427C2×C3×D3#23512yes—
428C2×C3×D3#23912yes—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—32no—
433C32×C4—42no—
434C32×C4—62no—
435C32×C4—61no—
436C32×C4—61no—
437C32×C4#23512yes—
438C32×C4#23512yes—
439C32×C4#23712yes—
440C3⋊Dic3—22no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
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—22no—
453C3×Dic3—21no—
454C3×Dic3—22no—
455C3×Dic3—21no—
456C3×Dic3—22no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—42no—
460C3×Dic3—64no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—121no—
468C3×Dic3—121no—
469C3×Dic3#23512yes—
470C3×Dic3#23712yes—
471#126—272no—
472#125—271no—
473#124—271no—
474#123—272no—
475C22⋊Q8—91no—
476#121—271no—
477C4×Q8—271no—
478C4×D4—91no—
479C4×D4—272no—
480#117—272no—
481C2×C42—91no—
482C33#52911yescharacteristic, complemented, Sylow
483C23×C3—31no—
484C23×C3—31no—
485C23×C3—61no—
486C23×C3—92no—
487C22×D3—32no—
488C22×D3—32no—
489C22×D3—62no—
490C22×D3C2×D3211yescharacteristic
491C3×Q8—182no—
492C3×D4—182no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—62no—
508C2×C3×C4—61no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—92no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—122no—
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—31no—
528C2×Dic3—31no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—62no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—92no—
537C2×Dic3—92no—
538C2×Dic3—92no—
539C2×Dic3—182no—
540C2×Dic3—182no—
541C2×Dic3—182no—
542C2×Dic3—362no—
543C2×Dic3C2×D3211yescharacteristic
544C2×Dic3C2×D3211yescharacteristic
545C2×Dic3C2×D3212yes—
546C2×Dic3C2×D3211yescharacteristic
547D12—62no—
548D12—62no—
549D12—122no—
550C4×D3—22no—
551C4×D3—64no—
552C4×D3—62no—
553C4×D3—62no—
554C4×D3—64no—
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—62no—
571C2×C32C2×#23511yescharacteristic
572C2×C32C2×#23511yescharacteristic
573C2×C32C2×#23511yescharacteristic
574C2×C32C2×#23511yescharacteristic
575C2×C32C2×#23711yescharacteristic
576C2×C32C2×#23711yescharacteristic
577C2×C32C2×#23911yescharacteristic
578C2×C32D3×#4111yescharacteristic
579C2×C32D3×#4111yescharacteristic
580C3⋊D3—42no—
581C3×D3—22no—
582C3×D3—22no—
583C3×D3—42no—
584C3×D3—122no—
585C3×D3—122no—
586C3×D3—242no—
587C2×Q8—91no—
588C2×D4—91no—
589C2×D4—272no—
590C22×C4—31no—
591C22×C4—92no—
592C22×C4—91no—
593C22×C4—91no—
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—272no—
603C22⋊C4—272no—
604C22⋊C4—272no—
605C42—31no—
606C42—91no—
607C42—91no—
608C42—91no—
609C42—272no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—32no—
614C22×C3—32no—
615C22×C3—41no—
616C22×C3—62no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—182no—
624C22×C3—182no—
625C22×C3—182no—
626C22×C3C22×D3211yescharacteristic
627C22×C3C22×D3211yescharacteristic
628C22×C3C22×D3211yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—122no—
638C2×D3—122no—
639C2×D3—122no—
640C2×D3#379912yes—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—32no—
645C3×C4—32no—
646C3×C4—42no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—62no—
653C3×C4—61no—
654C3×C4—121no—
655C3×C4—122no—
656C3×C4—121no—
657C3×C4—182no—
658C3×C4—181no—
659C3×C4—181no—
660C3×C4#379512yes—
661C3×C4#379812yes—
662C3×C4#380412yes—
663Dic3—21no—
664Dic3—22no—
665Dic3—21no—
666Dic3—64no—
667Dic3—62no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—62no—
673Dic3—121no—
674Dic3—121no—
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#562411yescharacteristic, complemented
690C23—31no—
691C23—92no—
692Q8—182no—
693D4—182no—
694D4—544no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—32no—
699C2×C4—62no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—92no—
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—62no—
721C2×C3—62no—
722C2×C3—122no—
723C2×C3—362no—
724C2×C3C2×#379511yescharacteristic
725C2×C3C2×#379511yescharacteristic
726C2×C3C2×#379811yescharacteristic
727C2×C3C2×#379911yescharacteristic
728C2×C3D3×#23511yescharacteristic
729C2×C3D3×#23511yescharacteristic
730C2×C3D3×#23711yescharacteristic
731C2×C3D3×#23911yescharacteristic
732C2×C3C2×#380411yescharacteristic
733D3—22no—
734D3—122no—
735D3—122no—
736D3—242no—
737C22—32no—
738C22—61no—
739C22—61no—
740C22—182no—
741C22—182no—
742C22—182no—
743C22C2×D3311yescharacteristic
744C4—32no—
745C4—62no—
746C4—61no—
747C4—61no—
748C4—181no—
749C4—181no—
750C4—182no—
751C4—542no—
752C4#8896012yes—
753C3—21no—
754C3—21no—
755C3—21no—
756C3—41no—
757C3#1059397411yescharacteristic, complemented
758C3#1059444411yescharacteristic, complemented
759C3#1059495511yescharacteristic, complemented
760C2—62no—
761C2—362no—
762C2D3×#379511yescharacteristic
763C2D3×#379911yescharacteristic
764C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723515C2
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. #11723677C2semidirect
3. #11723447C2semidirect
4. Dic3×#634C2semidirect
5. C3×#63894C2semidirect
6. C3×C4×D3×Dic3C2semidirect
7. C3×#63857C2semidirect
8. #11723024C2semidirect
9. #11722988C2semidirect
10. #11722930C2semidirect
11. #11722915C2semidirect
54. #63894D3semidirect
57. C4×D3×Dic3D3semidirect
67. #63857D3semidirect
482. C33#529semidirect
687. C32#5479semidirect
688. C32#5557semidirect
689. C32#5624semidirect
757. C3#10593974semidirect
758. C3#10594444semidirect
759. C3#10594955semidirect

Maximal subgroups

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

subgroupindex
#117236772
#117235152
#117234472
Dic3×#6342
C3×#638942
C3×C4×D3×Dic32
C3×#638572
#117230242
#117229882
#117229302
#117229152
#105949553
#105944443
#105939743