Finite Group Databasebeta

← #11814432

Subgroups — #11814432

Order 1152.

1597 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#939C211yesmaximal, characteristic, complemented
2C2×#63969C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic, complemented
4C2×#63880C211yesmaximal, characteristic, complemented
5#10592922C211yesmaximal, characteristic, complemented
6C3×#5221C211yesmaximal, characteristic, complemented
7#10591724C211yesmaximal, characteristic, complemented
8#10591724C211yesmaximal, characteristic, complemented
9#10591722C211yesmaximal, characteristic, complemented
10#10591721C211yesmaximal, characteristic, complemented
11#10591718C211yesmaximal, characteristic, complemented
12#10591702C211yesmaximal, characteristic, complemented
13#10591311C211yesmaximal, characteristic, complemented
14#10591307C211yesmaximal, characteristic, complemented
15#10591193C211yesmaximal, characteristic, complemented
16#82657—31nomaximal
17#76446—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C3×#939—24no—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40#63969—24no—
41C2×#3724C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49#63952—24no—
50#63880—24no—
51#63658C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#121—31no—
58C2×#939D311yescharacteristic, complemented
59C2×#935—31no—
60C2×C4×#67—31no—
61C2×#883—31no—
62C2×#67⋊C4—31no—
63C2×#67⋊C4—31no—
64C2×C4×D12—31no—
65C3×#390—31no—
66#5223—31no—
67#5223—31no—
68#5223—31no—
69#5223—31no—
70#5223—61no—
71#5221D311yescharacteristic, complemented
72#5220—31no—
73#5210—31no—
74#4994—31no—
75#4994—31no—
76#4990—31no—
77#4978—31no—
78#4960—31no—
79#4960—31no—
80#4956—31no—
81#4956—31no—
82#4956—31no—
83#4951—31no—
84#4951—31no—
85#4950—31no—
86#4945—31no—
87#4933—31no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C2×C32×D4—22no—
93C2×C32×D4—22no—
94C2×C32×D4—41no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—22no—
97C2×#638—22no—
98C2×#638—22no—
99C2×#638—22no—
100C2×#638—41no—
101C2×#638—41no—
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—41no—
110C2×C3×#67—41no—
111C22×C3×Dic3—22no—
112C22×C3×Dic3—22no—
113C22×C3×Dic3—41no—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×#626—22no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#624—22no—
125C2×#624—22no—
126C2×#624—41no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3—41no—
130#3757—22no—
131#3757—41no—
132#3752—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217—22no—
137C3×#217—22no—
138C3×(C2×D3)⋊C4D414yescomplemented
139C3×C4⋊Dic3—41no—
140C3×Dic3⋊C4—22no—
141C3×C4×Dic3—22no—
142#3724D414yescomplemented
143Dic3⋊Dic3—22no—
144Dic3⋊Dic3—22no—
145#3722—22no—
146#3722—41no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
149Dic32—22no—
150#2456—91noSylow
151C22×C3×D4—21no—
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C22×C3×D4C2×D311yescharacteristic
155C22×C3×D4C2×D311yescharacteristic
156C23×C3×C4—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67—31no—
161C22×#67—31no—
162C22×#67—61no—
163C22×#67—61no—
164C22×#67C2×D311yescharacteristic
165C22×#67C2×D311yescharacteristic
166C23×Dic3—31no—
167C23×Dic3C2×D311yescharacteristic
168C22×D12—31no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C3×#121—64no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C42—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—61no—
189C2×#217—61no—
190C2×#217C2×D311yescharacteristic
191C2×#217C2×D311yescharacteristic
192C2×#217C2×D311yescharacteristic
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic
195#939—24no—
196#935—64no—
197C4×#67—64no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—61no—
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3C2×D311yescharacteristic
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4C2×D311yescharacteristic
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3C2×D311yescharacteristic
219#883—64no—
220#67⋊C4—64no—
221#67⋊C4—64no—
222C4×D12—64no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—61no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32#4112yes—
250C23×C32C2411yescharacteristic
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3#4112yes—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3C2×D412yes—
265C32×D4—44no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D412yes—
269#638—28no—
270#638—44no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3C2×D412yes—
280C3×#67—44no—
281C3×#67—44no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—44no—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3C2×D412yes—
302C2×C3×Dic3C2×D412yes—
303C2×C3×Dic3#4112yes—
304#626—28no—
305#624—44no—
306D3×Dic3—44no—
307C2×#123—91no—
308C2×#121—31no—
309C2×C4×D4—91no—
310C2×C4×D4—91no—
311#396—91no—
312#392—91no—
313#392—91no—
314#392—91no—
315#390—31no—
316#388—91no—
317#388—91no—
318#387—91no—
319#386—91no—
320#386—91no—
321#385—91no—
322C24×C3—21no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C24×C3C22×D311yescharacteristic
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—61no—
332C23×D3C22×D311yescharacteristic
333C2×C3×D4—22no—
334C2×C3×D4—22no—
335C2×C3×D4—22no—
336C2×C3×D4—22no—
337C2×C3×D4—42no—
338C2×C3×D4—42no—
339C2×C3×D4—41no—
340C2×C3×D4—41no—
341C2×C3×D4—42no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—121no—
347C2×C3×D4—121no—
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—62no—
357C22×C3×C4—62no—
358C22×C3×C4—121no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C2×#67—22no—
362C2×#67—22no—
363C2×#67—22no—
364C2×#67—22no—
365C2×#67—41no—
366C2×#67—41no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—122no—
379C2×#67—122no—
380C2×#67—122no—
381C2×#67—122no—
382C2×#67—121no—
383C2×#67—121no—
384C2×#67—121no—
385C2×#67—121no—
386C2×#67—122no—
387C2×#67—122no—
388C22×Dic3—22no—
389C22×Dic3—22no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—41no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—62no—
401C22×Dic3—62no—
402C22×Dic3—121no—
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C2×D12—62no—
411C2×D12—62no—
412C2×D12—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—62no—
418C2×C4×D3—62no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C3×C4⋊C4—62no—
423C3×C4⋊C4—121no—
424C3×C22⋊C4—34no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—62no—
428C3×C22⋊C4—62no—
429C3×C22⋊C4—62no—
430C3×C42—62no—
431#217—22no—
432#217—22no—
433#217—22no—
434#217—22no—
435#217—22no—
436#217—62no—
437#217—62no—
438#217—62no—
439#217—122no—
440#217—121no—
441#217—121no—
442#217—121no—
443#217—122no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—122no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—121no—
453(C2×D3)⋊C4#6714yescomplemented
454C4⋊Dic3—41no—
455C4⋊Dic3—62no—
456C4⋊Dic3—62no—
457Dic3⋊C4—22no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—62no—
461Dic3⋊C4—62no—
462C4×Dic3—22no—
463C4×Dic3—62no—
464C4×Dic3—62no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C22×C32C22×D411yescharacteristic
481C22×C32C2×#4111yescharacteristic
482C22×C32C2×#4111yescharacteristic
483C22×C32C2×#4111yescharacteristic
484C22×C32H(5,𝔽2)11yescharacteristic
485C22×C32H(5,𝔽2)11yescharacteristic
486C2×C3⋊D3—22no—
487C2×C3⋊D3—22no—
488C2×C3⋊D3—22no—
489C2×C3⋊D3—41no—
490C2×C3⋊D3—41no—
491C2×C3⋊D3—41no—
492C2×C3⋊D3—41no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C32×C4—22no—
501C3⋊Dic3—22no—
502C3⋊Dic3—41no—
503C3⋊Dic3—41no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C22×D4—31no—
512C22×D4—31no—
513C22×D4—91no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4D3211yescharacteristic
517C23×C4—31no—
518C23×C4—91no—
519C23×C4—91no—
520#123—184no—
521#121—64no—
522C4×D4—184no—
523C4×D4—184no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C42—31no—
543C2×C42—91no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
548#95—91no—
549#95—91no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—22no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—22no—
579C23×C3—32no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3#23512yes—
599C23×C3#23712yes—
600C23×C3C23×D311yescharacteristic
601C23×C3C23×D311yescharacteristic
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—62no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3C2×#6712yes—
630C3×D4—44no—
631C3×D4—44no—
632C3×D4—48no—
633C3×D4—124no—
634C3×D4—124no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—22no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—124no—
664C2×C3×C4D3×D412yes—
665C2×C3×C4C2×#6712yes—
666#67—44no—
667#67—44no—
668#67—68no—
669#67—68no—
670#67—68no—
671#67—128no—
672#67—124no—
673#67—124no—
674#67—128no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—44no—
695C2×Dic3—62no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—62no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—121no—
719C2×Dic3—121no—
720C2×Dic3—124no—
721C2×Dic3D3×D412yes—
722C2×Dic3D3×D412yes—
723C2×Dic3#23712yes—
724C2×Dic3C2×#6712yes—
725D12—68no—
726C4×D3—124no—
727C4×D3—124no—
728C4×D3—124no—
729C2×C32—42no—
730C2×C32—81no—
731C2×C32#52511yescharacteristic
732C2×C32#52511yescharacteristic
733C2×C32#53811yescharacteristic
734C2×C32D4211yescharacteristic
735C2×C32#54611yescharacteristic
736C2×C32#55011yescharacteristic
737C2×C32#55311yescharacteristic
738C3⋊D3—42no—
739C3×D3—42no—
740C24—31no—
741C24—91no—
742C24C2×D3211yescharacteristic
743C24C2×D3211yescharacteristic
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—41no—
747C2×D4—62no—
748C2×D4—62no—
749C2×D4—62no—
750C2×D4—62no—
751C2×D4—121no—
752C2×D4—121no—
753C2×D4—182no—
754C2×D4—182no—
755C2×D4—182no—
756C2×D4—182no—
757C2×D4—182no—
758C2×D4—182no—
759C2×D4—182no—
760C2×D4—361no—
761C2×D4—361no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—62no—
770C22×C4—62no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—121no—
775C22×C4—182no—
776C22×C4—182no—
777C22×C4—182no—
778C22×C4—182no—
779C22×C4—361no—
780C22×C4—361no—
781C22×C4C2×D3211yescharacteristic
782C4⋊C4—62no—
783C4⋊C4—94no—
784C4⋊C4—121no—
785C4⋊C4—182no—
786C4⋊C4—182no—
787C22⋊C4—34no—
788C22⋊C4—62no—
789C22⋊C4—62no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—182no—
797C22⋊C4—361no—
798C22⋊C4—361no—
799C22⋊C4—361no—
800C42—62no—
801C42—182no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—81no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—81no—
851C22×C3—81no—
852C22×C3—81no—
853C22×C3—81no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3C2×#23511yescharacteristic
859C22×C3C2×D3×D411yescharacteristic
860C22×C3C2×D3×D411yescharacteristic
861C22×C3C2×D3×D411yescharacteristic
862C22×C3C2×#23711yescharacteristic
863C22×C3C2×#23711yescharacteristic
864C22×C3#100411yescharacteristic
865C22×C3#100411yescharacteristic
866C22×C3#100411yescharacteristic
867C22×C3D3×#4111yescharacteristic
868C22×C3D3×#4111yescharacteristic
869C22×C3D3×#4111yescharacteristic
870C22×C3#100911yescharacteristic
871C22×C3C22×#6711yescharacteristic
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—122no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—121no—
894C2×D3—121no—
895C2×D3—121no—
896C2×D3—241no—
897C2×D3—241no—
898C2×D3—241no—
899C2×D3—241no—
900C3×C4—22no—
901C3×C4—22no—
902C3×C4—42no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—62no—
906C3×C4—62no—
907C3×C4—121no—
908C3×C4—121no—
909C3×C4—121no—
910Dic3—22no—
911Dic3—22no—
912Dic3—22no—
913Dic3—22no—
914Dic3—41no—
915Dic3—41no—
916Dic3—41no—
917Dic3—62no—
918Dic3—62no—
919Dic3—122no—
920Dic3—122no—
921Dic3—121no—
922Dic3—121no—
923Dic3—121no—
924Dic3—121no—
925Dic3—241no—
926C32#245611yescharacteristic, complemented, Sylow
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—32no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—92no—
948C23—181no—
949C23—181no—
950C23—181no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23#380412yes—
955C23C22×D3211yescharacteristic
956D4—44no—
957D4—124no—
958D4—124no—
959D4—188no—
960D4—188no—
961D4—364no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—32no—
965C2×C4—32no—
966C2×C4—32no—
967C2×C4—32no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—92no—
986C2×C4—124no—
987C2×C4—181no—
988C2×C4—181no—
989C2×C4—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—364no—
996C2×C4—364no—
997C2×C4D3×#6712yes—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—42no—
1006C2×C3—42no—
1007C2×C3—82no—
1008C2×C3—82no—
1009C2×C3—81no—
1010C2×C3—81no—
1011C2×C3—122no—
1012C2×C3#549011yescharacteristic
1013C2×C3#554711yescharacteristic
1014C2×C3#556511yescharacteristic
1015C2×C3#559911yescharacteristic
1016C2×C3#560111yescharacteristic
1017C2×C3#560611yescharacteristic
1018C2×C3#560611yescharacteristic
1019C2×C3#560911yescharacteristic
1020C2×C3#561311yescharacteristic
1021C2×C3#567811yescharacteristic
1022C2×C3#571811yescharacteristic
1023C2×C3D4×#6711yescharacteristic
1024C2×C3#580611yescharacteristic
1025C2×C3#582811yescharacteristic
1026D3—42no—
1027D3—122no—
1028D3—122no—
1029D3—242no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—121no—
1048C22—121no—
1049C22—121no—
1050C22—121no—
1051C22—182no—
1052C22—182no—
1053C22—182no—
1054C22—361no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22D32×D411yescharacteristic
1059C22D3×#23711yescharacteristic
1060C22#6431211yescharacteristic
1061C22#6431411yescharacteristic
1062C22C2×#380411yescharacteristic
1063C22C2×D3×#6711yescharacteristic
1064C22#6433011yescharacteristic
1065C4—22no—
1066C4—62no—
1067C4—62no—
1068C4—62no—
1069C4—62no—
1070C4—121no—
1071C4—121no—
1072C4—121no—
1073C4—182no—
1074C4—361no—
1075C4—361no—
1076C3—21no—
1077C3#7644611yescharacteristic, complemented
1078C3#8265711yescharacteristic, complemented
1079C2—42no—
1080C2—81no—
1081C2—122no—
1082C2—362no—
1083C2#1059513811yescharacteristic
1084C2#1059519611yescharacteristic
1085C2#1059520711yescharacteristic
1086C2#1059522711yescharacteristic
1087C2#1059528811yescharacteristic
1088C2#1059530111yescharacteristic
1089C2#1059549311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2456
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#939C2semidirect
2. C2×#63969C2semidirect
3. C2×#63952C2semidirect
4. C2×#63880C2semidirect
5. #10592922C2semidirect
6. C3×#5221C2semidirect
7. #10591724C2semidirect
8. #10591724C2semidirect
9. #10591722C2semidirect
10. #10591721C2semidirect
11. #10591718C2semidirect
12. #10591702C2semidirect
13. #10591311C2semidirect
14. #10591307C2semidirect
15. #10591193C2semidirect
58. C2×#939D3semidirect
71. #5221D3semidirect
138. C3×(C2×D3)⋊C4D4semidirect
142. #3724D4semidirect
453. (C2×D3)⋊C4#67semidirect
926. C32#2456semidirect
1077. C3#76446semidirect
1078. C3#82657semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9392
C2×#639692
C2×#639522
C2×#638802
#105929222
C3×#52212
#105917242
#105917222
#105917212
#105917182
#105917022
#105913112
#105913072
#105911932
#826573
#764463