Finite Group Databasebeta

← #11802108

Subgroups — #11802108

Order 1152.

1897 conjugacy classes of subgroups.

The subgroup lattice has 767 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic, complemented
4C2×#63881C212yesmaximal, complemented
5C3×#4939C211yesmaximal, characteristic, complemented
6C3×#4928C211yesmaximal, characteristic, complemented
7#10591387C212yesmaximal, complemented
8#10591368C212yesmaximal, complemented
9#10591325C211yesmaximal, characteristic, complemented
10#10591283C212yesmaximal, complemented
11#10591274C211yesmaximal, characteristic, complemented
12#76291—31nomaximal
13#75964—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×#626C2212yes—
19C22×D3×Dic3C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C42×C3⋊D3—24no—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×#3722C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35#63916C418yescomplemented
36#63898—24no—
37#63881—28no—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41C2×#938—31no—
42C2×D4×Dic3—31no—
43C2×#895—31no—
44C2×#893—31no—
45C2×#893—32no—
46C2×#67⋊C4—32no—
47C2×C42×D3—31no—
48C2×C42×D3—31no—
49C2×C42×D3—61no—
50C3×#390—31no—
51C3×#389—31no—
52#4990—32no—
53#4987—31no—
54#4987—31no—
55Dic3×C4⋊C4—31no—
56Dic3×C4⋊C4—31no—
57#4956—32no—
58#4945—32no—
59Dic3×C22⋊C4—32no—
60#4939D311yescharacteristic, complemented
61#4928D311yescharacteristic, complemented
62#4666—32no—
63#4665—32no—
64C23×C3⋊D3C2311yescharacteristic
65C23×C3×D3C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3—22no—
79C2×C4×C3⋊D3C2×C414yescomplemented
80C2×C4×C3⋊D3D414yescomplemented
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C2×C3×D12—22no—
85C2×C3×D12—22no—
86C2×C3×D12C2×C414yescomplemented
87C2×#626—24no—
88C2×#626—24no—
89C2×#626C2×C418yescomplemented
90C2×D3×Dic3—24no—
91C2×D3×Dic3—24no—
92C2×D3×Dic3—24no—
93C32×C42—22no—
94C4×C3⋊Dic3—22no—
95C4×C3⋊Dic3—22no—
96C4×C3⋊Dic3D414yescomplemented
97C3×(C2×D3)⋊C4—24no—
98C3×(C2×D3)⋊C4—24no—
99C3×C4⋊Dic3—22no—
100C3×C4⋊Dic3—22no—
101C3×C4⋊Dic3C2×C414yescomplemented
102C3×Dic3⋊C4—24no—
103#3722—24no—
104(C2×D3)⋊Dic3—24no—
105(C2×D3)⋊Dic3C2×C418yescomplemented
106Dic32—24no—
107C4×#121—91noSylow
108C22×C3×D4—31no—
109C22×#67—32no—
110C23×Dic3—32no—
111C22×D12—32no—
112C22×D12C2×D311yescharacteristic
113C22×C4×D3—31no—
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×C4×D3—31no—
117C22×C4×D3—32no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C4×D3—61no—
121C22×C4×D3—61no—
122C22×C4×D3—61no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C22⋊C4—32no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C42—21no—
130C2×C3×C42C2×D311yescharacteristic
131C2×C3×C42C2×D311yescharacteristic
132C2×#217—32no—
133C2×#217—32no—
134#938—38no—
135D4×Dic3—64no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4C2×D312yes—
141C2×(C2×D3)⋊C4C2×D312yes—
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×C4⋊Dic3C2×D311yescharacteristic
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×Dic3⋊C4C2×D312yes—
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—32no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—61no—
155C2×C4×Dic3—61no—
156C2×C4×Dic3—61no—
157#895—38no—
158#893—64no—
159#893—68no—
160#67⋊C4—68no—
161C42×D3—64no—
162C42×D3—64no—
163C42×D3—68no—
164C3×#95—32no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95—32no—
168C3⋊#95—32no—
169C3⋊#95C2×D312yes—
170C23×C32C2411yescharacteristic
171C22×C3⋊D3—21no—
172C22×C3⋊D3—21no—
173C22×C3⋊D3—21no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3C22×C412yes—
176C22×C3⋊D3C2×D412yes—
177C22×C3⋊D3#4112yes—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3C22×C414yes—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C2×D412yes—
191C2×C32×C4C2×D412yes—
192C2×C32×C4#4112yes—
193C2×C32×C4#4112yes—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3C22×C412yes—
199C2×C3⋊Dic3C2×D412yes—
200C2×C3⋊Dic3C2×D412yes—
201C2×C3⋊Dic3C2×D412yes—
202C2×C3⋊Dic3#4112yes—
203C4×C3⋊D3—28no—
204C4×C3⋊D3—28no—
205C4×C3⋊D3—28no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3C22×C414yes—
215C3×D12—28no—
216#626—216no—
217D3×Dic3—48no—
218C2×#121—91no—
219C2×C4×D4—92no—
220C2×C4×D4—91no—
221C22×C42—91no—
222#390—31no—
223#389—31no—
224#388—92no—
225#386—92no—
226#380—91no—
227C4×C4⋊C4—91no—
228C4×C22⋊C4—92no—
229C24×C3—32no—
230C23×D3—31no—
231C23×D3—31no—
232C23×D3—61no—
233C23×D3C22×D312yes—
234C2×C3×D4—34no—
235C2×C3×D4—62no—
236C2×C3×D4—62no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—32no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—38no—
250C2×#67—64no—
251C2×#67—64no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261C22×Dic3—64no—
262C22×Dic3—64no—
263C22×Dic3—64no—
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D312yes—
266C22×Dic3C22×D312yes—
267C2×D12—22no—
268C2×D12—22no—
269C2×D12—38no—
270C2×D12—64no—
271C2×D12—64no—
272C2×D12C4×D314yescomplemented
273C2×C4×D3—34no—
274C2×C4×D3—34no—
275C2×C4×D3—34no—
276C2×C4×D3—34no—
277C2×C4×D3—64no—
278C2×C4×D3—64no—
279C2×C4×D3—62no—
280C2×C4×D3—62no—
281C2×C4×D3—62no—
282C2×C4×D3—62no—
283C2×C4×D3—62no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—64no—
288C2×C4×D3—64no—
289C2×C4×D3—64no—
290C2×C4×D3—64no—
291C2×C4×D3—64no—
292C2×C4×D3—64no—
293C2×C4×D3—64no—
294C2×C4×D3—62no—
295C2×C4×D3—62no—
296C2×C4×D3—62no—
297C2×C4×D3—62no—
298C2×C4×D3—62no—
299C2×C4×D3—62no—
300C2×C4×D3—64no—
301C2×C4×D3—64no—
302C2×C4×D3—64no—
303C3×C4⋊C4—34no—
304C3×C4⋊C4—64no—
305C3×C4⋊C4—62no—
306C3×C4⋊C4—62no—
307C3×C22⋊C4—64no—
308C3×C22⋊C4—64no—
309C3×C42—24no—
310C3×C42—22no—
311C3×C42—22no—
312#217—38no—
313#217—64no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—38no—
317(C2×D3)⋊C4—64no—
318(C2×D3)⋊C4—64no—
319(C2×D3)⋊C4—64no—
320C4⋊Dic3—22no—
321C4⋊Dic3—22no—
322C4⋊Dic3C4×D314yescomplemented
323Dic3⋊C4—24no—
324C4×Dic3—34no—
325C4×Dic3—34no—
326C4×Dic3—64no—
327C4×Dic3—64no—
328C4×Dic3—64no—
329C4×Dic3—62no—
330C4×Dic3—62no—
331C4×Dic3—62no—
332C4×Dic3—62no—
333C4×Dic3—64no—
334C4×Dic3—64no—
335C22×C32C23×C411yescharacteristic
336C22×C32C22×D411yescharacteristic
337C22×C32C22×D411yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C22×C32C2×#4111yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C2×C3⋊D3—22no—
343C2×C3⋊D3—22no—
344C2×C3⋊D3—22no—
345C2×C3⋊D3—22no—
346C2×C3⋊D3—22no—
347C2×C3⋊D3—22no—
348C2×C3⋊D3C4×D414yescomplemented
349C2×C3×D3—24no—
350C2×C3×D3—24no—
351C2×C3×D3—24no—
352C2×C3×D3—42no—
353C2×C3×D3—42no—
354C2×C3×D3—42no—
355C2×C3×D3—42no—
356C32×C4—22no—
357C32×C4—22no—
358C32×C4C4×D414yescomplemented
359C3⋊Dic3—22no—
360C3⋊Dic3—22no—
361C3⋊Dic3#12114yescomplemented
362C3×Dic3—24no—
363C3×Dic3—42no—
364C3×Dic3—42no—
365C22×D4—31no—
366C22×D4—92no—
367C23×C4—92no—
368C23×C4—91no—
369C23×C4—91no—
370C23×C4—91no—
371#121—98no—
372C4×D4—184no—
373C4×D4—188no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—31no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—32no—
380C2×C22⋊C4—92no—
381C2×C22⋊C4—92no—
382C2×C22⋊C4—92no—
383C2×C42—91no—
384C2×C42—92no—
385C2×C42—91no—
386C2×C42—91no—
387C2×C42—184no—
388C2×C42D3211yescharacteristic
389#95—32no—
390#95—92no—
391#95—92no—
392C23×C3—21no—
393C23×C3—34no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3C23×D311yescharacteristic
401C23×C3C23×D311yescharacteristic
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—22no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—32no—
409C22×D3—32no—
410C22×D3—32no—
411C22×D3—32no—
412C22×D3—32no—
413C22×D3—32no—
414C22×D3—62no—
415C22×D3—62no—
416C22×D3—62no—
417C22×D3—62no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—61no—
427C22×D3—61no—
428C22×D3—61no—
429C22×D3C2×C4×D314yes—
430C3×D4—68no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—34no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4C2×C4×D312yes—
458C2×C3×C4C2×C4×D312yes—
459C2×C3×C4D3×D412yes—
460C2×C3×C4D3×D412yes—
461C2×C3×C4D3×D412yes—
462C2×C3×C4D3×D412yes—
463C2×C3×C4#23712yes—
464C2×C3×C4#23712yes—
465C2×C3×C4#23912yes—
466C2×C3×C4#23912yes—
467#67—616no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—32no—
477C2×Dic3—32no—
478C2×Dic3—32no—
479C2×Dic3—32no—
480C2×Dic3—32no—
481C2×Dic3—32no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—128no—
504C2×Dic3C2×C4×D314yes—
505D12—28no—
506D12—616no—
507C4×D3—68no—
508C4×D3—68no—
509C4×D3—616no—
510C4×D3—616no—
511C4×D3—68no—
512C4×D3—68no—
513C4×D3—616no—
514C4×D3—68no—
515C4×D3—68no—
516C4×D3—128no—
517C2×C32C2×C4×D411yescharacteristic
518C2×C32C2×C4×D411yescharacteristic
519C2×C32C4×#4111yescharacteristic
520C2×C32C2×#12111yescharacteristic
521C2×C32#52511yescharacteristic
522C2×C32#52911yescharacteristic
523C2×C32#53211yescharacteristic
524C3⋊D3—24no—
525C3×D3—44no—
526C24—32no—
527C24—91no—
528C2×D4—34no—
529C2×D4—62no—
530C2×D4—62no—
531C2×D4—98no—
532C2×D4—184no—
533C2×D4—184no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—91no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—94no—
541C22×C4—94no—
542C22×C4—182no—
543C22×C4—182no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4—184no—
547C22×C4—184no—
548C22×C4—184no—
549C22×C4—182no—
550C22×C4—182no—
551C22×C4—182no—
552C22×C4C2×D3211yescharacteristic
553C22×C4C2×D3211yescharacteristic
554C22×C4C2×D3211yescharacteristic
555C4⋊C4—34no—
556C4⋊C4—62no—
557C4⋊C4—64no—
558C4⋊C4—62no—
559C22⋊C4—64no—
560C22⋊C4—64no—
561C22⋊C4—98no—
562C22⋊C4—184no—
563C22⋊C4—184no—
564C42—22no—
565C42—94no—
566C42—182no—
567C42—182no—
568C42—184no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—64no—
577C22×C3—64no—
578C22×C3—64no—
579C22×C3—122no—
580C22×C3—122no—
581C22×C3—122no—
582C22×C3—122no—
583C22×C3C22×C4×D311yescharacteristic
584C22×C3C22×C4×D311yescharacteristic
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C22×C3C2×D3×D411yescharacteristic
588C22×C3C2×D3×D411yescharacteristic
589C22×C3C2×#23711yescharacteristic
590C22×C3C2×#23711yescharacteristic
591C22×C3C2×#23911yescharacteristic
592C22×C3C2×#23911yescharacteristic
593C22×C3D3×#4111yescharacteristic
594C22×C3D3×#4111yescharacteristic
595C22×C3D3×#4111yescharacteristic
596C22×C3D3×#4111yescharacteristic
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—24no—
600C2×D3—34no—
601C2×D3—34no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—64no—
610C2×D3—64no—
611C2×D3—64no—
612C2×D3—64no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—62no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—24no—
632C3×C4—64no—
633C3×C4—122no—
634C3×C4—122no—
635C3×C4#67⋊C414yescomplemented
636C3×C4#89314yescomplemented
637Dic3—24no—
638Dic3—34no—
639Dic3—34no—
640Dic3—42no—
641Dic3—42no—
642Dic3—64no—
643Dic3—64no—
644Dic3—64no—
645Dic3—62no—
646Dic3—62no—
647Dic3—62no—
648Dic3—62no—
649C32C4×#12111yescharacteristic, complemented, Sylow
650C23—34no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23—92no—
658C23—92no—
659C23—92no—
660C23—181no—
661C23—181no—
662C23—181no—
663C23—181no—
664C23C22×D3211yescharacteristic
665D4—68no—
666D4—1816no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—34no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—92no—
681C2×C4—92no—
682C2×C4—92no—
683C2×C4—92no—
684C2×C4—92no—
685C2×C4—188no—
686C2×C4—188no—
687C2×C4—181no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—188no—
692C2×C4—368no—
693C2×C4#379612yes—
694C2×C4#379612yes—
695C2×C4C4×D3212yes—
696C2×C4#380212yes—
697C2×C4#381112yes—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—124no—
706C2×C3C2×#67⋊C411yescharacteristic
707C2×C3C2×#89311yescharacteristic
708C2×C3C4×#23711yescharacteristic
709C2×C3C4×D3×D411yescharacteristic
710C2×C3C4×D3×D411yescharacteristic
711C2×C3C4×#23911yescharacteristic
712C2×C3D3×#12111yescharacteristic
713C2×C3D3×#12111yescharacteristic
714C2×C3#560611yescharacteristic
715C2×C3#562711yescharacteristic
716C2×C3#568011yescharacteristic
717C2×C3#569111yescharacteristic
718C2×C3#571611yescharacteristic
719C2×C3#572511yescharacteristic
720D3—44no—
721D3—68no—
722D3—64no—
723D3—64no—
724C22—64no—
725C22—64no—
726C22—64no—
727C22—94no—
728C22—122no—
729C22—122no—
730C22—122no—
731C22—122no—
732C22—182no—
733C22—182no—
734C22—182no—
735C22—182no—
736C22—182no—
737C22—182no—
738C22C2×#379611yescharacteristic
739C22C2×#379611yescharacteristic
740C22C2×C4×D3211yescharacteristic
741C22C2×#380211yescharacteristic
742C22#6430611yescharacteristic
743C22#6430611yescharacteristic
744C22C2×#381111yescharacteristic
745C4—22no—
746C4—22no—
747C4—64no—
748C4—94no—
749C4—122no—
750C4—122no—
751C4—182no—
752C4—182no—
753C4#6388114yescomplemented
754C3—21no—
755C3#7596411yescharacteristic, complemented
756C3#7629111yescharacteristic, complemented
757C2—124no—
758C2—184no—
759C2C4×#379611yescharacteristic
760C2#1059390711yescharacteristic
761C2#1059394311yescharacteristic
762C2C4×#380211yescharacteristic
763C2C2×#6388111yescharacteristic
764C2#1059492211yescharacteristic
765C2#1059508111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63916C2
hypercenterC2×C42D32
hypocenterC32C4×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C42×C3⋊D3C2semidirect
3. C2×#63898C2semidirect
4. C2×#63881C2semidirect
5. C3×#4939C2semidirect
6. C3×#4928C2semidirect
7. #10591387C2semidirect
8. #10591368C2semidirect
9. #10591325C2semidirect
10. #10591283C2semidirect
11. #10591274C2semidirect
35. #63916C4semidirect
60. #4939D3semidirect
61. #4928D3semidirect
79. C2×C4×C3⋊D3C2×C4semidirect
80. C2×C4×C3⋊D3D4semidirect
86. C2×C3×D12C2×C4semidirect
89. C2×#626C2×C4semidirect
96. C4×C3⋊Dic3D4semidirect
101. C3×C4⋊Dic3C2×C4semidirect
105. (C2×D3)⋊Dic3C2×C4semidirect
272. C2×D12C4×D3semidirect
322. C4⋊Dic3C4×D3semidirect
348. C2×C3⋊D3C4×D4semidirect
358. C32×C4C4×D4semidirect
361. C3⋊Dic3#121semidirect
635. C3×C4#67⋊C4semidirect
636. C3×C4#893semidirect
649. C32C4×#121semidirect
753. C4#63881semidirect
755. C3#75964semidirect
756. C3#76291semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×#639162
C2×#638982
C2×#638812
C3×#49392
C3×#49282
#105913872
#105913682
#105913252
#105912832
#105912742
#762913
#759643