Finite Group Databasebeta

← #10733161

Subgroups — #10733161

Order 768.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#924C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C2×#4957C211yesmaximal, characteristic
4C2×#4676C211yesmaximal, characteristic, complemented
5C2×#4673C211yesmaximal, characteristic, complemented
6C2×#4646C211yesmaximal, characteristic, complemented
7C3×C22⋊#95C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic
9#71547C211yesmaximal, characteristic, complemented
10#71547C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69420C211yesmaximal, characteristic, complemented
14#69409C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#15280—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C2×#924—24no—
33C2×#924—24no—
34C2×#924—24no—
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45#5213—24no—
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
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#4957—24no—
57#4676—24no—
58#4673—24no—
59#4646—24no—
60C22×C22⋊Q8—31no—
61C2×#396—31no—
62C2×#393—31no—
63C2×#391—31no—
64C2×#390—31no—
65C2×#386—31no—
66#1444—31no—
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1436—31no—
74C22⋊#95D311yescharacteristic, complemented
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—41no—
83C23×C3×C4—41no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—41no—
95C22×#67—41no—
96C22×#67Q814yescomplemented
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C22×Dic6—22no—
105C22×Dic6—22no—
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—41no—
109C22×Dic6—41no—
110C22×Dic6D414yescomplemented
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C22⋊C4—41no—
116C2×C3×C22⋊C4—41no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—22no—
123C2×#217—22no—
124C2×#217—41no—
125C2×#217D414yes—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—22no—
147#924—232no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—41no—
159C2×Dic3⋊C4—41no—
160C2×Dic3⋊C4—41no—
161C2×Dic3⋊C4—41no—
162C2×Dic3⋊C4D414yescomplemented
163C2×C4×Dic3—22no—
164C2×C4×Dic3—22no—
165C2×C4×Dic3—41no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—41no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95D414yes—
180C23×Q8—31no—
181C23×D4—31no—
182C24×C4C2×D311yescharacteristic
183C2×C22⋊Q8—64no—
184C2×C22⋊Q8—64no—
185C2×C22⋊Q8—64no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4C2×D311yescharacteristic
202C22×C22⋊C4C2×D311yescharacteristic
203C22×C42—31no—
204#396—64no—
205#393—64no—
206#391—64no—
207#390—64no—
208#386—64no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C2×#95C2×D311yescharacteristic
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3C2×D412yes—
236C24×C3C2×Q812yes—
237C24×C3#4112yes—
238C24×C3C2411yescharacteristic
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3C2×Q812yes—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—28no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—44no—
293C22×C3×C4—44no—
294C22×C3×C4—44no—
295C22×C3×C4—44no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4#4112yes—
302C22×C3×C4#4112yes—
303C2×#67—28no—
304C2×#67—28no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—44no—
308C2×#67—44no—
309C2×#67—44no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C22×Dic3C2×D412yes—
354C22×Dic3C2×D412yes—
355C22×Dic3C2×D412yes—
356C22×Dic3C2×D412yes—
357C22×Dic3C2×Q812yes—
358C22×Dic3#4112yes—
359C2×Dic6—28no—
360C2×Dic6—28no—
361C2×Dic6—44no—
362C2×Dic6—44no—
363C2×Dic6—44no—
364C2×Dic6—44no—
365C2×Dic6—44no—
366C3×C22⋊C4—44no—
367C3×C22⋊C4—44no—
368#217—28no—
369#217—28no—
370#217—44no—
371(C2×D3)⋊C4—44no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374(C2×D3)⋊C4—44no—
375(C2×D3)⋊C4—44no—
376(C2×D3)⋊C4—44no—
377C4⋊Dic3—28no—
378Dic3⋊C4—28no—
379Dic3⋊C4—28no—
380Dic3⋊C4—44no—
381Dic3⋊C4—44no—
382Dic3⋊C4—44no—
383C4×Dic3—44no—
384C25—31no—
385C25C22×D311yescharacteristic
386C22×Q8—34no—
387C22×Q8—62no—
388C22×Q8—62no—
389C22×Q8—62no—
390C22×Q8—62no—
391C22×Q8—121no—
392C22×Q8—121no—
393C22×D4—34no—
394C22×D4—62no—
395C22×D4—62no—
396C22×D4—62no—
397C22×D4—62no—
398C22×D4—121no—
399C22×D4—121no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—41no—
413C23×C4—41no—
414C23×C4C22×D311yescharacteristic
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C22⋊Q8—632no—
421C2×C4⋊C4—34no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—62no—
427C2×C4⋊C4—62no—
428C2×C4⋊C4—62no—
429C2×C4⋊C4—62no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—121no—
436C2×C4⋊C4—121no—
437C2×C4⋊C4—121no—
438C2×C4⋊C4—121no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—121no—
466C2×C22⋊C4—121no—
467C2×C22⋊C4—121no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C42—62no—
473C2×C42—62no—
474C2×C42—121no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—34no—
479#95—41no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—121no—
488#95—121no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3C22⋊Q814yes—
524C23×C3C22×D411yescharacteristic
525C23×C3C22×D411yescharacteristic
526C23×C3C22×D411yescharacteristic
527C23×C3C22×D411yescharacteristic
528C23×C3C22×Q811yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3C2×#4111yescharacteristic
531C23×C3C2×#4111yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3H(5,𝔽2)11yescharacteristic
534C23×C3H(5,𝔽2)11yescharacteristic
535C23×C3H(5,𝔽2)11yescharacteristic
536C23×C3H(5,𝔽2)11yescharacteristic
537C23×C32−1+411yescharacteristic
538C23×C32−1+411yescharacteristic
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—416no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4#12114yes—
617#67—416no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3#12014yes—
666C2×Dic3C22⋊Q814yescomplemented
667Dic6—416no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—32no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24#23512yes—
696C24D3×D412yes—
697C24D3×Q812yes—
698C24C23×D311yescharacteristic
699C2×Q8—68no—
700C2×Q8—68no—
701C2×Q8—124no—
702C2×Q8—124no—
703C2×Q8—124no—
704C2×Q8—124no—
705C2×Q8—124no—
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—124no—
709C2×D4—124no—
710C2×D4—124no—
711C2×D4—124no—
712C2×D4—124no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—28no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—32no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—32no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4#23512yes—
807C22×C4#23512yes—
808C22×C4D3×D412yes—
809C22×C4D3×D412yes—
810C22×C4D3×D412yes—
811C4⋊C4—68no—
812C4⋊C4—68no—
813C4⋊C4—68no—
814C4⋊C4—124no—
815C4⋊C4—124no—
816C4⋊C4—124no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—68no—
820C22⋊C4—68no—
821C22⋊C4—124no—
822C22⋊C4—124no—
823C22⋊C4—124no—
824C22⋊C4—124no—
825C22⋊C4—124no—
826C22⋊C4—124no—
827C22⋊C4—124no—
828C42—124no—
829C22×C3—24no—
830C22×C3—24no—
831C22×C3—24no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3C2×#12011yescharacteristic
845C22×C3C2×#12111yescharacteristic
846C22×C3C2×C22⋊Q811yescharacteristic
847C22×C3C2×C22⋊Q811yescharacteristic
848C22×C3#52911yescharacteristic
849C22×C3#53211yescharacteristic
850C22×C3#53411yescharacteristic
851C22×C3#53511yescharacteristic
852C22×C3#53611yescharacteristic
853C22×C3#53711yescharacteristic
854C22×C3#53811yescharacteristic
855C22×C3#53911yescharacteristic
856C22×C3#54211yescharacteristic
857C22×C3#54211yescharacteristic
858C22×C3#54311yescharacteristic
859C22×C3D4211yescharacteristic
860C22×C3D4211yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54611yescharacteristic
864C22×C3#54611yescharacteristic
865C22×C3#54611yescharacteristic
866C22×C3#54811yescharacteristic
867C22×C3#54811yescharacteristic
868C22×C3#54811yescharacteristic
869C22×C3D4×Q811yescharacteristic
870C22×C3D4×Q811yescharacteristic
871C22×C3#55011yescharacteristic
872C22×C3#55011yescharacteristic
873C22×C3#55111yescharacteristic
874C22×C3#55411yescharacteristic
875C22×C3#55411yescharacteristic
876C22×C3#55611yescharacteristic
877C22×C3#56211yescharacteristic
878C22×C3#56211yescharacteristic
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—42no—
885C2×D3—42no—
886C2×D3—81no—
887C2×D3—81no—
888C2×D3—81no—
889C2×D3—81no—
890C2×D3—81no—
891C2×D3—81no—
892C2×D3—81no—
893C2×D3—81no—
894C3×C4—24no—
895C3×C4—42no—
896C3×C4—42no—
897C3×C4—81no—
898C3×C4—81no—
899C3×C4—81no—
900Dic3—24no—
901Dic3—24no—
902Dic3—42no—
903Dic3—42no—
904Dic3—42no—
905Dic3—42no—
906Dic3—81no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23#89614yes—
977C23C2×#23511yescharacteristic
978C23C2×#23511yescharacteristic
979C23C2×#23511yescharacteristic
980C23C2×D3×D411yescharacteristic
981C23C2×D3×D411yescharacteristic
982C23C2×D3×D411yescharacteristic
983C23C2×D3×D411yescharacteristic
984C23#100411yescharacteristic
985C23#100411yescharacteristic
986C23#100411yescharacteristic
987C23C2×D3×Q811yescharacteristic
988C23D3×#4111yescharacteristic
989C23#100911yescharacteristic
990C23#101011yescharacteristic
991C23#101011yescharacteristic
992Q8—1216no—
993D4—1216no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—34no—
1007C2×C4—34no—
1008C2×C4—416no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4#88414yes—
1086C2×C3—44no—
1087C2×C3#240911yescharacteristic
1088C2×C3#241011yescharacteristic
1089C2×C3#242611yescharacteristic
1090C2×C3#243111yescharacteristic
1091C2×C3#243711yescharacteristic
1092C2×C3#245011yescharacteristic
1093C2×C3#245211yescharacteristic
1094C2×C3#253811yescharacteristic
1095C2×C3#256011yescharacteristic
1096C2×C3#267611yescharacteristic
1097C2×C3#268111yescharacteristic
1098C2×C3#269211yescharacteristic
1099C2×C3#270011yescharacteristic
1100C2×C3#273011yescharacteristic
1101C2×C3#273211yescharacteristic
1102D3—82no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—122no—
1119C22—122no—
1120C22—122no—
1121C22—122no—
1122C22—122no—
1123C22—122no—
1124C22—122no—
1125C22—241no—
1126C22—241no—
1127C22—241no—
1128C22—241no—
1129C22—241no—
1130C22—241no—
1131C22—241no—
1132C22—241no—
1133C22#547911yescharacteristic
1134C22C2×#88411yescharacteristic
1135C22#549011yescharacteristic
1136C22#549011yescharacteristic
1137C22#549011yescharacteristic
1138C22#549411yescharacteristic
1139C22C2×#89611yescharacteristic
1140C22#551111yescharacteristic
1141C22#551111yescharacteristic
1142C22#553311yescharacteristic
1143C22#553411yescharacteristic
1144C22#554811yescharacteristic
1145C22#555011yescharacteristic
1146C22#555211yescharacteristic
1147C22#555211yescharacteristic
1148C22#555211yescharacteristic
1149C22#555311yescharacteristic
1150C22#555611yescharacteristic
1151C22#556411yescharacteristic
1152C22D3×#12011yescharacteristic
1153C22#558911yescharacteristic
1154C22#559011yescharacteristic
1155C22#559011yescharacteristic
1156C22#559911yescharacteristic
1157C22#560711yescharacteristic
1158C22#560811yescharacteristic
1159C22#562111yescharacteristic
1160C22D3×C22⋊Q811yescharacteristic
1161C22#563211yescharacteristic
1162C22#563211yescharacteristic
1163C22#563411yescharacteristic
1164C22#564811yescharacteristic
1165C22#565411yescharacteristic
1166C22#566211yescharacteristic
1167C22#566711yescharacteristic
1168C4—24no—
1169C4—42no—
1170C4—42no—
1171C4—64no—
1172C4—64no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—122no—
1177C4—122no—
1178C4—122no—
1179C4—122no—
1180C4—241no—
1181C3#1528011yescharacteristic, complemented, Sylow
1182C2—44no—
1183C2—242no—
1184C2#7335111yescharacteristic
1185C2#7348511yescharacteristic
1186C2#7353811yescharacteristic
1187C2#7385411yescharacteristic
1188C2#7393611yescharacteristic
1189C2#7396111yescharacteristic
1190C2#7409811yescharacteristic
1191C2#7440511yescharacteristic
1192C2#7442511yescharacteristic
1193C2#7454111yescharacteristic
1194C2#7460711yescharacteristic
1195C2#7470011yescharacteristic
1196C2#7479411yescharacteristic
1197C2#7482911yescharacteristic
1198C2#7491611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#15280
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#924C2semidirect
4. C2×#4676C2semidirect
5. C2×#4673C2semidirect
6. C2×#4646C2semidirect
7. C3×C22⋊#95C2semidirect
9. #71547C2semidirect
10. #71547C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
13. #69420C2semidirect
14. #69409C2semidirect
15. #69406C2semidirect
74. C22⋊#95D3semidirect
96. C22×#67Q8semidirect
110. C22×Dic6D4semidirect
162. C2×Dic3⋊C4D4semidirect
666. C2×Dic3C22⋊Q8semidirect
1181. C3#15280semidirect

Maximal subgroups

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

subgroupindex
C22×#9242
C2×#52132
C2×#49572
C2×#46762
C2×#46732
C2×#46462
C3×C22⋊#952
#715502
#715472
#694282
#694272
#694202
#694092
#694062
#152803