Finite Group Databasebeta

← #10733092

Subgroups — #10733092

Order 768.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#924C211yesmaximal, characteristic, complemented
2C2×#5213C211yesmaximal, characteristic
3C2×#4959C211yesmaximal, characteristic
4C2×#4673C211yesmaximal, characteristic, complemented
5C2×#4646C211yesmaximal, characteristic, complemented
6C2×#4669C211yesmaximal, characteristic, complemented
7C3×C22⋊#95C211yesmaximal, characteristic, complemented
8#71550C211yesmaximal, characteristic
9#71548C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69415C211yesmaximal, characteristic, complemented
14#69414C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#15275—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×C4×Dic3C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43#5213—24no—
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
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#4959—24no—
57#4673—24no—
58#4669—24no—
59#4646—24no—
60C22×C22⋊Q8—31no—
61C2×#394—31no—
62C2×#393—31no—
63C2×#391—31no—
64C2×#388—31no—
65C2×#386—31no—
66#1442—31no—
67#1442—31no—
68#1441—31no—
69#1440—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1437—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—22no—
95C22×#67—41no—
96C22×#67—41no—
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—22no—
115C2×C3×C22⋊C4—22no—
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—22no—
139C2×(C2×D3)⋊C4—22no—
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—41no—
156C2×Dic3⋊C4D414yescomplemented
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—41no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—41no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—41no—
173C3⋊#95—41no—
174C3⋊#95—41no—
175C3⋊#95D414yes—
176C23×Q8—31no—
177C23×D4—31no—
178C24×C4C2×D311yescharacteristic
179C2×C22⋊Q8—64no—
180C2×C22⋊Q8—64no—
181C2×C22⋊Q8—64no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4C2×D311yescharacteristic
196C22×C22⋊C4C2×D311yescharacteristic
197C22×C42—31no—
198#394—64no—
199#393—64no—
200#391—64no—
201#388—64no—
202#386—64no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95C2×D311yescharacteristic
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
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×C3C2×D412yes—
232C24×C3#4112yes—
233C24×C3#4112yes—
234C24×C3C2411yescharacteristic
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
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#4112yes—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—28no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
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—44no—
289C22×C3×C4—44no—
290C22×C3×C4—44no—
291C22×C3×C4—44no—
292C22×C3×C4—44no—
293C22×C3×C4—44no—
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2×D412yes—
297C22×C3×C4#4112yes—
298C22×C3×C4#4112yes—
299C2×#67—28no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—44no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
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×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C22×Dic3C2×D412yes—
354C22×Dic3C2×D412yes—
355C2×Dic6—28no—
356C2×Dic6—28no—
357C2×Dic6—44no—
358C2×Dic6—44no—
359C2×Dic6—44no—
360C2×Dic6—44no—
361C2×Dic6—44no—
362C3×C22⋊C4—44no—
363C3×C22⋊C4—44no—
364#217—28no—
365#217—28no—
366#217—44no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—44no—
369(C2×D3)⋊C4—44no—
370(C2×D3)⋊C4—44no—
371(C2×D3)⋊C4—44no—
372(C2×D3)⋊C4—44no—
373C4⋊Dic3—28no—
374Dic3⋊C4—28no—
375Dic3⋊C4—28no—
376Dic3⋊C4—44no—
377C4×Dic3—44no—
378C25—31no—
379C25C22×D311yescharacteristic
380C22×Q8—34no—
381C22×Q8—62no—
382C22×Q8—62no—
383C22×Q8—62no—
384C22×Q8—62no—
385C22×Q8—121no—
386C22×Q8—121no—
387C22×D4—62no—
388C22×D4—62no—
389C22×D4—62no—
390C22×D4—62no—
391C22×D4—62no—
392C22×D4—121no—
393C22×D4—121no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—41no—
407C23×C4—41no—
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D311yescharacteristic
413C23×C4C22×D311yescharacteristic
414C22⋊Q8—632no—
415C2×C4⋊C4—34no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—121no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—41no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
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—121no—
456C2×C22⋊C4—121no—
457C2×C22⋊C4—121no—
458C2×C22⋊C4—121no—
459C2×C22⋊C4—121no—
460C2×C42—62no—
461C2×C42—62no—
462C2×C42—121no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—34no—
467#95—41no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—62no—
476#95—121no—
477#95—121no—
478#95—121no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
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—41no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3#12414yes—
514C23×C3C22×D411yescharacteristic
515C23×C3C22×D411yescharacteristic
516C23×C3C22×D411yescharacteristic
517C23×C3C22×D411yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3C2×#4111yescharacteristic
521C23×C3C2×#4111yescharacteristic
522C23×C3C2×#4111yescharacteristic
523C23×C3H(5,𝔽2)11yescharacteristic
524C23×C3H(5,𝔽2)11yescharacteristic
525C23×C3H(5,𝔽2)11yescharacteristic
526C23×C32−1+411yescharacteristic
527C23×C32−1+411yescharacteristic
528C23×C32−1+411yescharacteristic
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
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—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—416no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
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#12114yes—
607#67—416no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
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—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
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#12014yes—
657Dic6—416no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—32no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24#23512yes—
686C24D3×D412yes—
687C24#23712yes—
688C24C23×D311yescharacteristic
689C2×Q8—68no—
690C2×Q8—68no—
691C2×Q8—124no—
692C2×Q8—124no—
693C2×Q8—124no—
694C2×Q8—124no—
695C2×Q8—124no—
696C2×D4—68no—
697C2×D4—124no—
698C2×D4—124no—
699C2×D4—124no—
700C2×D4—124no—
701C2×D4—124no—
702C2×D4—124no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—28no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
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—32no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
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#23512yes—
797C22×C4#23512yes—
798C22×C4D3×D412yes—
799C22×C4D3×D412yes—
800C22×C4D3×D412yes—
801C4⋊C4—68no—
802C4⋊C4—68no—
803C4⋊C4—68no—
804C4⋊C4—124no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—68no—
808C22⋊C4—68no—
809C22⋊C4—68no—
810C22⋊C4—124no—
811C22⋊C4—124no—
812C22⋊C4—124no—
813C22⋊C4—124no—
814C22⋊C4—124no—
815C22⋊C4—124no—
816C42—124no—
817C22×C3—24no—
818C22×C3—24no—
819C22×C3—24no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3C2×#12011yescharacteristic
833C22×C3C2×#12111yescharacteristic
834C22×C3#52511yescharacteristic
835C22×C3#52511yescharacteristic
836C22×C3C2×#12411yescharacteristic
837C22×C3#52911yescharacteristic
838C22×C3#53411yescharacteristic
839C22×C3#53611yescharacteristic
840C22×C3#53611yescharacteristic
841C22×C3#53711yescharacteristic
842C22×C3#53811yescharacteristic
843C22×C3#53911yescharacteristic
844C22×C3#53911yescharacteristic
845C22×C3#54211yescharacteristic
846C22×C3#54211yescharacteristic
847C22×C3D4211yescharacteristic
848C22×C3D4211yescharacteristic
849C22×C3#54611yescharacteristic
850C22×C3#54611yescharacteristic
851C22×C3#54611yescharacteristic
852C22×C3#54611yescharacteristic
853C22×C3#54711yescharacteristic
854C22×C3#54811yescharacteristic
855C22×C3#54811yescharacteristic
856C22×C3#54811yescharacteristic
857C22×C3#54811yescharacteristic
858C22×C3#54811yescharacteristic
859C22×C3#54811yescharacteristic
860C22×C3#55011yescharacteristic
861C22×C3#55111yescharacteristic
862C22×C3#55111yescharacteristic
863C22×C3#55211yescharacteristic
864C22×C3#55211yescharacteristic
865C22×C3#56211yescharacteristic
866C22×C3#56311yescharacteristic
867C2×D3—42no—
868C2×D3—42no—
869C2×D3—42no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—81no—
875C2×D3—81no—
876C2×D3—81no—
877C2×D3—81no—
878C2×D3—81no—
879C2×D3—81no—
880C2×D3—81no—
881C2×D3—81no—
882C3×C4—24no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—81no—
886C3×C4—81no—
887C3×C4—81no—
888Dic3—24no—
889Dic3—42no—
890Dic3—42no—
891Dic3—42no—
892Dic3—42no—
893Dic3—42no—
894Dic3—81no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
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#88514yes—
965C23C2×#23511yescharacteristic
966C23C2×#23511yescharacteristic
967C23C2×#23511yescharacteristic
968C23C2×D3×D411yescharacteristic
969C23C2×D3×D411yescharacteristic
970C23C2×D3×D411yescharacteristic
971C23C2×D3×D411yescharacteristic
972C23C2×#23711yescharacteristic
973C23#100411yescharacteristic
974C23#100411yescharacteristic
975C23#100711yescharacteristic
976C23D3×#4111yescharacteristic
977C23#100911yescharacteristic
978C23#101011yescharacteristic
979C23#101011yescharacteristic
980Q8—1216no—
981D4—1216no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—34no—
995C2×C4—416no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
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—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
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—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
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#88414yes—
1074C2×C3—44no—
1075C2×C3#240711yescharacteristic
1076C2×C3#241011yescharacteristic
1077C2×C3#242611yescharacteristic
1078C2×C3#243611yescharacteristic
1079C2×C3#246311yescharacteristic
1080C2×C3#247211yescharacteristic
1081C2×C3#247711yescharacteristic
1082C2×C3#248811yescharacteristic
1083C2×C3#253611yescharacteristic
1084C2×C3#267411yescharacteristic
1085C2×C3#268111yescharacteristic
1086C2×C3#268711yescharacteristic
1087C2×C3#270211yescharacteristic
1088C2×C3#272811yescharacteristic
1089C2×C3#273011yescharacteristic
1090D3—82no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—122no—
1107C22—122no—
1108C22—122no—
1109C22—122no—
1110C22—122no—
1111C22—122no—
1112C22—122no—
1113C22—241no—
1114C22—241no—
1115C22—241no—
1116C22—241no—
1117C22—241no—
1118C22—241no—
1119C22—241no—
1120C22—241no—
1121C22#547911yescharacteristic
1122C22C2×#88411yescharacteristic
1123C22#549011yescharacteristic
1124C22#549011yescharacteristic
1125C22C2×#88511yescharacteristic
1126C22#549511yescharacteristic
1127C22#550711yescharacteristic
1128C22#551311yescharacteristic
1129C22#551511yescharacteristic
1130C22#552911yescharacteristic
1131C22#553411yescharacteristic
1132C22#554711yescharacteristic
1133C22#555011yescharacteristic
1134C22#555211yescharacteristic
1135C22#555211yescharacteristic
1136C22#555211yescharacteristic
1137C22#555311yescharacteristic
1138C22#555611yescharacteristic
1139C22#556111yescharacteristic
1140C22D3×#12011yescharacteristic
1141C22#558911yescharacteristic
1142C22#559011yescharacteristic
1143C22#559011yescharacteristic
1144C22#559811yescharacteristic
1145C22#559811yescharacteristic
1146C22#560611yescharacteristic
1147C22#561711yescharacteristic
1148C22#562811yescharacteristic
1149C22#562911yescharacteristic
1150C22#563311yescharacteristic
1151C22#564611yescharacteristic
1152C22#564811yescharacteristic
1153C22#565411yescharacteristic
1154C22#566011yescharacteristic
1155C22#566711yescharacteristic
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—64no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—122no—
1164C4—122no—
1165C4—122no—
1166C4—122no—
1167C4—122no—
1168C4—241no—
1169C3#1527511yescharacteristic, complemented, Sylow
1170C2—44no—
1171C2—242no—
1172C2#7335211yescharacteristic
1173C2#7348511yescharacteristic
1174C2#7350211yescharacteristic
1175C2#7385411yescharacteristic
1176C2#7393411yescharacteristic
1177C2#7396511yescharacteristic
1178C2#7409411yescharacteristic
1179C2#7440411yescharacteristic
1180C2#7450811yescharacteristic
1181C2#7463211yescharacteristic
1182C2#7464111yescharacteristic
1183C2#7470111yescharacteristic
1184C2#7472811yescharacteristic
1185C2#7482811yescharacteristic
1186C2#7490011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#15275
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×#4673C2semidirect
5. C2×#4646C2semidirect
6. C2×#4669C2semidirect
7. C3×C22⋊#95C2semidirect
9. #71548C2semidirect
10. #71545C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
13. #69415C2semidirect
14. #69414C2semidirect
15. #69409C2semidirect
74. C22⋊#95D3semidirect
110. C22×Dic6D4semidirect
156. C2×Dic3⋊C4D4semidirect
1169. C3#15275semidirect

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×#49592
C2×#46732
C2×#46462
C2×#46692
C3×C22⋊#952
#715502
#715482
#715452
#694282
#694272
#694152
#694142
#694092
#152753