Finite Group Databasebeta

← #10726750

Subgroups — #10726750

Order 768.

2662 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#67C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic, complemented
3C2×#4959C211yesmaximal, characteristic, complemented
4C2×#4959C211yesmaximal, characteristic, complemented
5C2×#4960C211yesmaximal, characteristic
6C2×#4676C211yesmaximal, characteristic, complemented
7C2×#4665C211yesmaximal, characteristic, complemented
8C2×#4667C211yesmaximal, characteristic, complemented
9C3×C22⋊#95C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13#69409C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#14732—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C2×C4×#67—24no—
27C2×C4×#67—24no—
28C2×C4×#67—24no—
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47#5213—24no—
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56#4960—24no—
57#4959—24no—
58#4959—24no—
59#4676—24no—
60#4667—24no—
61#4665—24no—
62C22×C4×D4—31no—
63C2×#396—31no—
64C2×#394—31no—
65C2×#394—31no—
66C2×#392—31no—
67C2×#386—31no—
68C2×#386—31no—
69C2×#380—31no—
70#1441—31no—
71#1440—31no—
72#1439—31no—
73#1438—31no—
74#1437—31no—
75#1436—31no—
76C22⋊#95D311yescharacteristic, complemented
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—41no—
86C23×C3×C4—41no—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—22no—
102C22×#67—22no—
103C22×#67—22no—
104C22×#67—41no—
105C22×#67—41no—
106C22×#67D414yes—
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C22×D12—22no—
114C22×D12—22no—
115C22×D12—22no—
116C22×D12—22no—
117C22×D12—22no—
118C22×D12—41no—
119C22×D12—41no—
120C22×C4×D3—22no—
121C22×C4×D3—22no—
122C22×C4×D3—22no—
123C22×C4×D3—22no—
124C22×C4×D3—41no—
125C22×C4×D3—41no—
126C22×C4×D3D414yescomplemented
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—41no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—41no—
138C2×#217D414yescomplemented
139C4×#67—232no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4—41no—
165C2×(C2×D3)⋊C4—41no—
166C2×(C2×D3)⋊C4—41no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—41no—
177C2×Dic3⋊C4—41no—
178C2×Dic3⋊C4D414yescomplemented
179C2×C4×Dic3—22no—
180C2×C4×Dic3—22no—
181C2×C4×Dic3—22no—
182C3×#95—22no—
183C3×#95—22no—
184C3×#95—22no—
185C3×#95—41no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—41no—
193C3⋊#95D414yescomplemented
194C23×D4—31no—
195C23×D4—31no—
196C23×D4—31no—
197C24×C4—31no—
198C24×C4C2×D311yescharacteristic
199C2×C4×D4—64no—
200C2×C4×D4—64no—
201C2×C4×D4—64no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4C2×D311yescharacteristic
218C22×C22⋊C4C2×D311yescharacteristic
219C22×C42—31no—
220#396—64no—
221#394—64no—
222#394—64no—
223#392—64no—
224#386—64no—
225#386—64no—
226#380—64no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95C2×D311yescharacteristic
236C2×#95C2×D311yescharacteristic
237C2×#95C2×D311yescharacteristic
238C2×#95C2×D311yescharacteristic
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3C2×D412yes—
252C24×C3C2×D412yes—
253C24×C3#4112yes—
254C24×C3C2411yescharacteristic
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3C2×D412yes—
282C23×D3C2×D412yes—
283C23×D3#4112yes—
284C23×D3#4112yes—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—28no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—44no—
324C22×C3×C4—44no—
325C22×C3×C4—44no—
326C22×C3×C4—44no—
327C22×C3×C4—44no—
328C22×C3×C4—44no—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4C2×D412yes—
332C22×C3×C4#4112yes—
333C22×C3×C4#4112yes—
334C2×#67—28no—
335C2×#67—28no—
336C2×#67—28no—
337C2×#67—28no—
338C2×#67—28no—
339C2×#67—28no—
340C2×#67—28no—
341C2×#67—28no—
342C2×#67—44no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C2×#67—44no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3—21no—
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380C22×Dic3—21no—
381C22×Dic3C2×D412yes—
382C22×Dic3C2×D412yes—
383C22×Dic3C2×D412yes—
384C22×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3C2×D412yes—
388C22×Dic3C2×D412yes—
389C22×Dic3#4112yes—
390C2×D12—28no—
391C2×D12—44no—
392C2×D12—44no—
393C2×D12—44no—
394C2×D12—44no—
395C2×D12—44no—
396C2×D12—44no—
397C2×C4×D3—28no—
398C2×C4×D3—28no—
399C2×C4×D3—44no—
400C2×C4×D3—44no—
401C2×C4×D3—44no—
402C2×C4×D3—44no—
403C2×C4×D3—44no—
404C3×C22⋊C4—44no—
405C3×C22⋊C4—44no—
406#217—28no—
407#217—44no—
408(C2×D3)⋊C4—28no—
409(C2×D3)⋊C4—44no—
410(C2×D3)⋊C4—44no—
411(C2×D3)⋊C4—44no—
412(C2×D3)⋊C4—44no—
413(C2×D3)⋊C4—44no—
414(C2×D3)⋊C4—44no—
415(C2×D3)⋊C4—44no—
416(C2×D3)⋊C4—44no—
417Dic3⋊C4—28no—
418Dic3⋊C4—44no—
419Dic3⋊C4—44no—
420Dic3⋊C4—44no—
421C4×Dic3—28no—
422C25—31no—
423C25—31no—
424C25C22×D311yescharacteristic
425C22×D4—34no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—62no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—62no—
437C22×D4—62no—
438C22×D4—62no—
439C22×D4—62no—
440C22×D4—62no—
441C22×D4—62no—
442C22×D4—121no—
443C22×D4—121no—
444C22×D4—121no—
445C22×D4—121no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4—31no—
455C23×C4—31no—
456C23×C4—34no—
457C23×C4—31no—
458C23×C4—41no—
459C23×C4—41no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4—62no—
464C23×C4—121no—
465C23×C4—121no—
466C23×C4C22×D311yescharacteristic
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469C23×C4C22×D311yescharacteristic
470C23×C4C22×D311yescharacteristic
471C23×C4C22×D311yescharacteristic
472C4×D4—632no—
473C2×C4⋊C4—34no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—62no—
478C2×C4⋊C4—62no—
479C2×C4⋊C4—62no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—121no—
484C2×C4⋊C4—121no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—34no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—62no—
513C2×C22⋊C4—62no—
514C2×C22⋊C4—62no—
515C2×C22⋊C4—62no—
516C2×C22⋊C4—62no—
517C2×C22⋊C4—62no—
518C2×C22⋊C4—62no—
519C2×C22⋊C4—121no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4—121no—
522C2×C22⋊C4—121no—
523C2×C22⋊C4—121no—
524C2×C42—62no—
525C2×C42—62no—
526C2×C42—62no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—34no—
531#95—41no—
532#95—62no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—62no—
537#95—62no—
538#95—121no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3#12114yes—
574C23×C3C22×D411yescharacteristic
575C23×C3C22×D411yescharacteristic
576C23×C3C22×D411yescharacteristic
577C23×C3C22×D411yescharacteristic
578C23×C3C22×D411yescharacteristic
579C23×C3C2×#4111yescharacteristic
580C23×C3C2×#4111yescharacteristic
581C23×C3C2×#4111yescharacteristic
582C23×C3C2×#4111yescharacteristic
583C23×C3C2×#4111yescharacteristic
584C23×C3C2×#4111yescharacteristic
585C23×C3H(5,𝔽2)11yescharacteristic
586C23×C3H(5,𝔽2)11yescharacteristic
587C23×C3H(5,𝔽2)11yescharacteristic
588C23×C32−1+411yescharacteristic
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3#12114yes—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—416no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4#12114yes—
702#67—232no—
703#67—416no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—22no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3—41no—
740C2×Dic3—41no—
741C2×Dic3—41no—
742C2×Dic3—41no—
743C2×Dic3—41no—
744C2×Dic3#12014yes—
745C2×Dic3#12114yes—
746D12—416no—
747C4×D3—416no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—32no—
761C24—32no—
762C24—32no—
763C24—32no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24—61no—
788C24—61no—
789C24—61no—
790C24#23512yes—
791C24D3×D412yes—
792C24D3×D412yes—
793C24C23×D311yescharacteristic
794C2×D4—68no—
795C2×D4—68no—
796C2×D4—68no—
797C2×D4—68no—
798C2×D4—68no—
799C2×D4—68no—
800C2×D4—68no—
801C2×D4—68no—
802C2×D4—68no—
803C2×D4—124no—
804C2×D4—124no—
805C2×D4—124no—
806C2×D4—124no—
807C2×D4—124no—
808C2×D4—124no—
809C2×D4—124no—
810C2×D4—124no—
811C2×D4—124no—
812C2×D4—124no—
813C2×D4—124no—
814C2×D4—124no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—28no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—32no—
854C22×C4—32no—
855C22×C4—32no—
856C22×C4—32no—
857C22×C4—32no—
858C22×C4—32no—
859C22×C4—32no—
860C22×C4—32no—
861C22×C4—32no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—68no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—68no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4—61no—
900C22×C4—61no—
901C22×C4—61no—
902C22×C4—61no—
903C22×C4—124no—
904C22×C4—124no—
905C22×C4—124no—
906C22×C4—124no—
907C22×C4—124no—
908C22×C4#23512yes—
909C22×C4#23512yes—
910C22×C4D3×D412yes—
911C22×C4D3×D412yes—
912C22×C4D3×D412yes—
913C4⋊C4—68no—
914C4⋊C4—124no—
915C4⋊C4—124no—
916C4⋊C4—124no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—68no—
920C22⋊C4—68no—
921C22⋊C4—124no—
922C22⋊C4—124no—
923C22⋊C4—124no—
924C22⋊C4—124no—
925C22⋊C4—124no—
926C22⋊C4—124no—
927C22⋊C4—124no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C42—68no—
931C22×C3—24no—
932C22×C3—24no—
933C22×C3—24no—
934C22×C3—42no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—42no—
944C22×C3—42no—
945C22×C3—42no—
946C22×C3C2×#12011yescharacteristic
947C22×C3C2×#12111yescharacteristic
948C22×C3C2×#12111yescharacteristic
949C22×C3C2×#12111yescharacteristic
950C22×C3C2×#12111yescharacteristic
951C22×C3#52511yescharacteristic
952C22×C3#52511yescharacteristic
953C22×C3#52511yescharacteristic
954C22×C3#52511yescharacteristic
955C22×C3#52511yescharacteristic
956C22×C3#52911yescharacteristic
957C22×C3#52911yescharacteristic
958C22×C3#53211yescharacteristic
959C22×C3#53411yescharacteristic
960C22×C3#53711yescharacteristic
961C22×C3#53811yescharacteristic
962C22×C3#53911yescharacteristic
963C22×C3#54011yescharacteristic
964C22×C3#54211yescharacteristic
965C22×C3D4211yescharacteristic
966C22×C3D4211yescharacteristic
967C22×C3D4211yescharacteristic
968C22×C3#54611yescharacteristic
969C22×C3#54611yescharacteristic
970C22×C3#54611yescharacteristic
971C22×C3#54611yescharacteristic
972C22×C3#54611yescharacteristic
973C22×C3#54711yescharacteristic
974C22×C3#54711yescharacteristic
975C22×C3#54811yescharacteristic
976C22×C3#54811yescharacteristic
977C22×C3#55011yescharacteristic
978C22×C3#55111yescharacteristic
979C22×C3#55111yescharacteristic
980C22×C3#55311yescharacteristic
981C2×D3—24no—
982C2×D3—24no—
983C2×D3—24no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—42no—
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—81no—
1004C2×D3—81no—
1005C2×D3—81no—
1006C2×D3—81no—
1007C2×D3—81no—
1008C2×D3—81no—
1009C2×D3—81no—
1010C2×D3—81no—
1011C3×C4—24no—
1012C3×C4—42no—
1013C3×C4—42no—
1014C3×C4—81no—
1015C3×C4—81no—
1016C3×C4—81no—
1017Dic3—24no—
1018Dic3—24no—
1019Dic3—42no—
1020Dic3—42no—
1021Dic3—42no—
1022Dic3—81no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—34no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—62no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—62no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23—121no—
1120C23—121no—
1121C23—121no—
1122C23—121no—
1123C23—121no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23#88414yes—
1128C23C2×#23511yescharacteristic
1129C23C2×#23511yescharacteristic
1130C23C2×#23511yescharacteristic
1131C23C2×D3×D411yescharacteristic
1132C23C2×D3×D411yescharacteristic
1133C23C2×D3×D411yescharacteristic
1134C23C2×D3×D411yescharacteristic
1135C23C2×D3×D411yescharacteristic
1136C23#100411yescharacteristic
1137C23#100411yescharacteristic
1138C23#100711yescharacteristic
1139C23D3×#4111yescharacteristic
1140C23D3×#4111yescharacteristic
1141C23D3×#4111yescharacteristic
1142C23#100911yescharacteristic
1143D4—632no—
1144D4—1216no—
1145D4—1216no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—34no—
1159C2×C4—34no—
1160C2×C4—416no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—62no—
1191C2×C4—62no—
1192C2×C4—62no—
1193C2×C4—62no—
1194C2×C4—62no—
1195C2×C4—62no—
1196C2×C4—62no—
1197C2×C4—62no—
1198C2×C4—62no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—62no—
1202C2×C4—62no—
1203C2×C4—62no—
1204C2×C4—62no—
1205C2×C4—62no—
1206C2×C4—62no—
1207C2×C4—62no—
1208C2×C4—62no—
1209C2×C4—62no—
1210C2×C4—62no—
1211C2×C4—1216no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C4—121no—
1227C2×C4—121no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4#88414yes—
1232C2×C3—44no—
1233C2×C3#239211yescharacteristic
1234C2×C3#240711yescharacteristic
1235C2×C3#241011yescharacteristic
1236C2×C3#241611yescharacteristic
1237C2×C3#242411yescharacteristic
1238C2×C3#242511yescharacteristic
1239C2×C3#242711yescharacteristic
1240C2×C3#242811yescharacteristic
1241C2×C3#245711yescharacteristic
1242C2×C3#246111yescharacteristic
1243C2×C3#246311yescharacteristic
1244C2×C3#246711yescharacteristic
1245C2×C3#253411yescharacteristic
1246C2×C3#263011yescharacteristic
1247C2×C3#284711yescharacteristic
1248D3—44no—
1249D3—82no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—64no—
1266C22—64no—
1267C22—64no—
1268C22—122no—
1269C22—122no—
1270C22—122no—
1271C22—122no—
1272C22—122no—
1273C22—122no—
1274C22—122no—
1275C22—122no—
1276C22—122no—
1277C22—122no—
1278C22—122no—
1279C22—122no—
1280C22—122no—
1281C22—122no—
1282C22—122no—
1283C22—122no—
1284C22—122no—
1285C22—122no—
1286C22—122no—
1287C22—241no—
1288C22—241no—
1289C22—241no—
1290C22—241no—
1291C22—241no—
1292C22—241no—
1293C22—241no—
1294C22—241no—
1295C22#547911yescharacteristic
1296C22C2×#88411yescharacteristic
1297C22C2×#88411yescharacteristic
1298C22#549011yescharacteristic
1299C22#549011yescharacteristic
1300C22#549011yescharacteristic
1301C22#550711yescharacteristic
1302C22#550711yescharacteristic
1303C22#551511yescharacteristic
1304C22#552811yescharacteristic
1305C22#553011yescharacteristic
1306C22#554711yescharacteristic
1307C22#554711yescharacteristic
1308C22#554711yescharacteristic
1309C22#554711yescharacteristic
1310C22#554811yescharacteristic
1311C22#555311yescharacteristic
1312C22#555611yescharacteristic
1313C22#556011yescharacteristic
1314C22D3×#12011yescharacteristic
1315C22#558911yescharacteristic
1316C22#559011yescharacteristic
1317C22#559011yescharacteristic
1318C22D3×#12111yescharacteristic
1319C22D3×#12111yescharacteristic
1320C22#560911yescharacteristic
1321C22#561011yescharacteristic
1322C22#562911yescharacteristic
1323C22#563311yescharacteristic
1324C22#563311yescharacteristic
1325C22#564011yescharacteristic
1326C22#565411yescharacteristic
1327C22#565611yescharacteristic
1328C22#565911yescharacteristic
1329C22#566311yescharacteristic
1330C4—24no—
1331C4—42no—
1332C4—42no—
1333C4—64no—
1334C4—64no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—122no—
1339C4—122no—
1340C4—122no—
1341C4—241no—
1342C3#1473211yescharacteristic, complemented, Sylow
1343C2—44no—
1344C2—124no—
1345C2—242no—
1346C2#7334911yescharacteristic
1347C2#7349911yescharacteristic
1348C2#7358111yescharacteristic
1349C2#7385411yescharacteristic
1350C2#7388711yescharacteristic
1351C2#7389511yescharacteristic
1352C2#7406911yescharacteristic
1353C2#7440411yescharacteristic
1354C2#7443111yescharacteristic
1355C2#7461311yescharacteristic
1356C2#7462211yescharacteristic
1357C2#7469811yescharacteristic
1358C2#7489311yescharacteristic
1359C2#7490111yescharacteristic
1360C2#7493511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC2×#4960C2
hypercenterC22⋊#95D3
hypocenterC3#14732
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×C4×#67C2semidirect
2. C2×#5213C2semidirect
3. C2×#4959C2semidirect
4. C2×#4959C2semidirect
6. C2×#4676C2semidirect
7. C2×#4665C2semidirect
8. C2×#4667C2semidirect
9. C3×C22⋊#95C2semidirect
10. #71547C2semidirect
11. #69429C2semidirect
12. #69426C2semidirect
13. #69409C2semidirect
14. #69408C2semidirect
15. #69406C2semidirect
76. C22⋊#95D3semidirect
126. C22×C4×D3D4semidirect
138. C2×#217D4semidirect
178. C2×Dic3⋊C4D4semidirect
193. C3⋊#95D4semidirect
1342. C3#14732semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#672
C2×#52132
C2×#49592
C2×#49602
C2×#46762
C2×#46652
C2×#46672
C3×C22⋊#952
#715472
#694292
#694262
#694092
#694082
#694062
#147323