Finite Group Databasebeta

← #10718665

Subgroups — #10718665

Order 768.

2358 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#887C211yesmaximal, characteristic, complemented
2C22×#885C211yesmaximal, characteristic
3C2×#4957C211yesmaximal, characteristic
4C2×#4957C211yesmaximal, characteristic
5C2×#4646C211yesmaximal, characteristic, complemented
6C3×#1439C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic, complemented
8#71547C211yesmaximal, characteristic, complemented
9#71545C211yesmaximal, characteristic, complemented
10#71545C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14026—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#887—24no—
41C2×#887—24no—
42C2×#887—24no—
43C2×#885—24no—
44C2×#885—24no—
45C2×#885C418yescomplemented
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
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4957—24no—
59#4957—24no—
60#4646—24no—
61C22×#124—31no—
62C22×C4×Q8—31no—
63C2×#391—31no—
64C2×#390—31no—
65C2×#390—31no—
66#1439—31no—
67#1439—31no—
68#1439—31no—
69#1439D311yescharacteristic, complemented
70#1437—31no—
71#1437—31no—
72#1437—31no—
73#1437—31no—
74C4⋊#95—31no—
75C4×#95—31no—
76C25×C3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67C2×C414yes—
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C22×Dic6—22no—
99C22×Dic6—22no—
100C22×Dic6—22no—
101C22×Dic6—22no—
102C22×Dic6C2×C414yes—
103C22×Dic6D414yes—
104C22×Dic6D414yes—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—41no—
114C2×C3×C22⋊C4—41no—
115C2×C3×C22⋊C4—41no—
116C2×C3×C22⋊C4C2×C414yes—
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×#217C2×C414yes—
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)⋊C4C2×C414yes—
143C2×(C2×D3)⋊C4C2×C414yes—
144C2×Dic3⋊C4—22no—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4D414yes—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—22no—
156C2×C4×Dic3—22no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160C2×C4×Dic3—22no—
161C2×C4×Dic3—22no—
162C2×C4×Dic3—22no—
163C2×C4×Dic3—22no—
164C2×C4×Dic3—22no—
165C2×C4×Dic3—22no—
166C2×C4×Dic3C2×C414yes—
167C2×C4×Dic3D414yes—
168#887—232no—
169#885—232no—
170C3×#95—22no—
171C3×#95—22no—
172C3×#95—41no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—41no—
180C3⋊#95—41no—
181C3⋊#95—41no—
182C23×Q8—31no—
183C23×D4—31no—
184C2×#124—38no—
185C2×#124—64no—
186C2×#124—64no—
187C2×C4×Q8—64no—
188C2×C4×Q8—64no—
189C2×C4×Q8—64no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4C2×D311yescharacteristic
204C22×C22⋊C4C2×D311yescharacteristic
205C22×C22⋊C4C2×D311yescharacteristic
206C22×C42—31no—
207C22×C42—31no—
208C22×C42—31no—
209C22×C42—31no—
210C22×C42—31no—
211#391—64no—
212#390—64no—
213#390—64no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95C2×D311yescharacteristic
224C2×#95C2×D311yescharacteristic
225C2×#95C2×D311yescharacteristic
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×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3C22×C412yes—
241C24×C3C2411yescharacteristic
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×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3C22×C412yes—
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—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4C22×C412yes—
293C22×C3×C4C22×C412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4#4112yes—
299C2×#67—28no—
300C2×#67—28no—
301C2×#67—28no—
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×Dic3C22×C412yes—
340C22×Dic3C22×C412yes—
341C22×Dic3C22×C412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3#4112yes—
351C22×Dic3#4112yes—
352C22×Dic3#4112yes—
353C22×Dic3#4112yes—
354C22×Dic3#4112yes—
355C2×Dic6—28no—
356C2×Dic6—28no—
357C2×Dic6—28no—
358C2×Dic6—28no—
359C2×Dic6—28no—
360C2×Dic6—28no—
361C2×Dic6C22⋊C4116yescomplemented
362C3×C4⋊C4—28no—
363C3×C22⋊C4—28no—
364C3×C22⋊C4—44no—
365C3×C22⋊C4—44no—
366#217—28no—
367#217—44no—
368#217—44no—
369(C2×D3)⋊C4—28no—
370(C2×D3)⋊C4—28no—
371(C2×D3)⋊C4—44no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374(C2×D3)⋊C4—44no—
375Dic3⋊C4—28no—
376Dic3⋊C4—28no—
377Dic3⋊C4—44no—
378C4×Dic3—28no—
379C4×Dic3—28no—
380C4×Dic3—28no—
381C4×Dic3—28no—
382C4×Dic3—44no—
383C25—31no—
384C25C22×D311yescharacteristic
385C22×Q8—34no—
386C22×Q8—34no—
387C22×Q8—34no—
388C22×Q8—62no—
389C22×Q8—62no—
390C22×Q8—62no—
391C22×Q8—62no—
392C22×D4—34no—
393C22×D4—62no—
394C22×D4—62no—
395C22×D4—62no—
396C22×D4—62no—
397C22×D4—62no—
398C22×D4—62no—
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—31no—
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412#124—632no—
413C4×Q8—632no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—34no—
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×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—34no—
434C2×C22⋊C4—41no—
435C2×C22⋊C4—41no—
436C2×C22⋊C4—41no—
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—62no—
456C2×C22⋊C4—121no—
457C2×C22⋊C4—121no—
458C2×C22⋊C4—121no—
459C2×C22⋊C4—121no—
460C2×C22⋊C4—121no—
461C2×C22⋊C4C4×D314yes—
462C2×C42—34no—
463C2×C42—34no—
464C2×C42—62no—
465C2×C42—62no—
466C2×C42—62no—
467C2×C42—62no—
468C2×C42—62no—
469C2×C42—62no—
470C2×C42—62no—
471C2×C42—62no—
472C2×C42—62no—
473C2×C42—62no—
474C2×C42—62no—
475C2×C42—62no—
476C2×C42—62no—
477#95—22no—
478#95—22no—
479#95—41no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—121no—
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—41no—
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—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×C3—41no—
524C23×C3C23×C411yescharacteristic
525C23×C3C22×D411yescharacteristic
526C23×C3C22×D411yescharacteristic
527C23×C3C22×D411yescharacteristic
528C23×C3C22×D411yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3C2×#4111yescharacteristic
531C23×C3C2×#4111yescharacteristic
532C23×C3C2×#4111yescharacteristic
533C23×C3C2×#4111yescharacteristic
534C23×C3C2×#4111yescharacteristic
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—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
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×C4C2×C22⋊C414yes—
616#67—416no—
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—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—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—41no—
657C2×Dic3C2×C22⋊C414yes—
658C2×Dic3C2×C22⋊C414yes—
659C2×Dic3C4×D414yes—
660C2×Dic3C4×D414yes—
661C2×Dic3#12014yes—
662C2×Dic3#12114yes—
663C2×Dic3#12114yes—
664C2×Dic3#12314yes—
665C2×Dic3#12414yescomplemented
666Dic6—232no—
667C24—21no—
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—21no—
681C24—32no—
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—61no—
696C24C2×C4×D312yes—
697C24C23×D311yescharacteristic
698C2×Q8—316no—
699C2×Q8—68no—
700C2×Q8—68no—
701C2×Q8—68no—
702C2×Q8—68no—
703C2×Q8—68no—
704C2×Q8—68no—
705C2×D4—68no—
706C2×D4—68no—
707C2×D4—68no—
708C2×D4—124no—
709C2×D4—124no—
710C2×D4—124no—
711C2×D4—124no—
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—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—32no—
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—32no—
762C22×C4—32no—
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×C4C2×C4×D312yes—
797C22×C4C2×C4×D312yes—
798C22×C4D3×D412yes—
799C22×C4D3×D412yes—
800C22×C4D3×D412yes—
801C22×C4D3×D412yes—
802C22×C4#23712yes—
803C4⋊C4—28no—
804C4⋊C4—68no—
805C4⋊C4—68no—
806C4⋊C4—124no—
807C22⋊C4—28no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C22⋊C4—68no—
811C22⋊C4—68no—
812C22⋊C4—68no—
813C22⋊C4—124no—
814C22⋊C4—124no—
815C22⋊C4—124no—
816C22⋊C4—124no—
817C22⋊C4—124no—
818C22⋊C4—124no—
819C42—68no—
820C42—68no—
821C42—68no—
822C42—68no—
823C42—124no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3C22×C22⋊C411yescharacteristic
840C22×C3C2×C4×D411yescharacteristic
841C22×C3C2×C4×D411yescharacteristic
842C22×C3C4×#4111yescharacteristic
843C22×C3C4×#4111yescharacteristic
844C22×C3#52011yescharacteristic
845C22×C3#52011yescharacteristic
846C22×C3C2×#12011yescharacteristic
847C22×C3C2×#12111yescharacteristic
848C22×C3C2×#12111yescharacteristic
849C22×C3C2×#12311yescharacteristic
850C22×C3C2×#12411yescharacteristic
851C22×C3#52911yescharacteristic
852C22×C3#52911yescharacteristic
853C22×C3#53211yescharacteristic
854C22×C3#53511yescharacteristic
855C22×C3#53611yescharacteristic
856C22×C3#54211yescharacteristic
857C22×C3#54211yescharacteristic
858C22×C3#54611yescharacteristic
859C22×C3#54611yescharacteristic
860C22×C3#54811yescharacteristic
861C22×C3#54811yescharacteristic
862C22×C3#54811yescharacteristic
863C22×C3#54811yescharacteristic
864C22×C3#54811yescharacteristic
865C22×C3#54811yescharacteristic
866C22×C3#55011yescharacteristic
867C22×C3#55011yescharacteristic
868C22×C3#55011yescharacteristic
869C22×C3#55011yescharacteristic
870C22×C3#55611yescharacteristic
871C22×C3#55611yescharacteristic
872C22×C3#55911yescharacteristic
873C22×C3#55911yescharacteristic
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—42no—
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—81no—
882C2×D3—81no—
883C2×D3—81no—
884C2×D3—81no—
885C2×D3—81no—
886C2×D3—81no—
887C2×D3—81no—
888C2×D3—81no—
889C3×C4—24no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—42no—
893C3×C4—42no—
894C3×C4—81no—
895Dic3—24no—
896Dic3—24no—
897Dic3—42no—
898Dic3—42no—
899Dic3—42no—
900Dic3—81no—
901Dic3#38618yes—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
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—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
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—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23C22×C4×D311yescharacteristic
973C23C2×D3×D411yescharacteristic
974C23C2×D3×D411yescharacteristic
975C23C2×D3×D411yescharacteristic
976C23C2×D3×D411yescharacteristic
977C23C2×#23711yescharacteristic
978C23#100411yescharacteristic
979C23#100411yescharacteristic
980C23#100711yescharacteristic
981C23D3×#4111yescharacteristic
982C23D3×#4111yescharacteristic
983C23D3×#4111yescharacteristic
984C23D3×#4111yescharacteristic
985C23D3×#4111yescharacteristic
986C23#101011yescharacteristic
987Q8—632no—
988D4—1216no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
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—22no—
1007C2×C4—34no—
1008C2×C4—34no—
1009C2×C4—34no—
1010C2×C4—34no—
1011C2×C4—34no—
1012C2×C4—34no—
1013C2×C4—34no—
1014C2×C4—34no—
1015C2×C4—34no—
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—41no—
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—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—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4D3×C22⋊C414yes—
1080C2×C3—82no—
1081C2×C3C2×#38611yescharacteristic
1082C2×C3C4×#12411yescharacteristic
1083C2×C3#232611yescharacteristic
1084C2×C3#234111yescharacteristic
1085C2×C3#234111yescharacteristic
1086C2×C3#236711yescharacteristic
1087C2×C3#236711yescharacteristic
1088C2×C3#242611yescharacteristic
1089C2×C3#242611yescharacteristic
1090C2×C3#243111yescharacteristic
1091C2×C3#243611yescharacteristic
1092C2×C3#244811yescharacteristic
1093C2×C3#244811yescharacteristic
1094C2×C3#254511yescharacteristic
1095C2×C3#254811yescharacteristic
1096D3—82no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—122no—
1119C22—241no—
1120C22—241no—
1121C22—241no—
1122C22—241no—
1123C22—241no—
1124C22—241no—
1125C22—241no—
1126C22—241no—
1127C22C2×D3×C22⋊C411yescharacteristic
1128C22#550411yescharacteristic
1129C22#552211yescharacteristic
1130C22C4×#23711yescharacteristic
1131C22C4×D3×D411yescharacteristic
1132C22C4×D3×D411yescharacteristic
1133C22#554611yescharacteristic
1134C22D3×#12011yescharacteristic
1135C22#559111yescharacteristic
1136C22#559211yescharacteristic
1137C22#559611yescharacteristic
1138C22#559811yescharacteristic
1139C22#559911yescharacteristic
1140C22#559911yescharacteristic
1141C22#559911yescharacteristic
1142C22D3×#12111yescharacteristic
1143C22D3×#12111yescharacteristic
1144C22#561011yescharacteristic
1145C22#562811yescharacteristic
1146C22#563311yescharacteristic
1147C22#563311yescharacteristic
1148C22#563311yescharacteristic
1149C22#564011yescharacteristic
1150C22#564111yescharacteristic
1151C22#564911yescharacteristic
1152C22D3×#12311yescharacteristic
1153C22#566211yescharacteristic
1154C22#566411yescharacteristic
1155C22#566411yescharacteristic
1156C22D3×#12411yescharacteristic
1157C22#567711yescharacteristic
1158C22#567711yescharacteristic
1159C22#570211yescharacteristic
1160C22#570611yescharacteristic
1161C22#571811yescharacteristic
1162C4—24no—
1163C4—38no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—64no—
1169C4—64no—
1170C4—81no—
1171C4—122no—
1172C4—122no—
1173C4—122no—
1174C4—241no—
1175C3#1402611yescharacteristic, complemented, Sylow
1176C2—82no—
1177C2—242no—
1178C2#7387711yescharacteristic
1179C2#7438611yescharacteristic
1180C2#7439811yescharacteristic
1181C2D3×#38611yescharacteristic
1182C2#7545411yescharacteristic
1183C2#7548111yescharacteristic
1184C2#7630111yescharacteristic
1185C2#7667211yescharacteristic
1186C2#7678111yescharacteristic
1187C2#7690111yescharacteristic
1188C2#7694611yescharacteristic
1189C2#7728611yescharacteristic
1190C2#7731511yescharacteristic
1191C2#7746911yescharacteristic
1192C2#7802211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1439C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#14026
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#887C2semidirect
5. C2×#4646C2semidirect
6. C3×#1439C2semidirect
7. #71570C2semidirect
8. #71547C2semidirect
9. #71545C2semidirect
10. #71545C2semidirect
11. #69428C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. Dic3⋊#95C2semidirect
15. Dic3×#95C2semidirect
45. C2×#885C4semidirect
69. #1439D3semidirect
361. C2×Dic6C22⋊C4semidirect
665. C2×Dic3#124semidirect
1175. C3#14026semidirect

Maximal subgroups

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

subgroupindex
C22×#8872
C22×#8852
C2×#49572
C2×#46462
C3×#14392
#715702
#715472
#715452
#694282
#694082
Dic3⋊#952
Dic3×#952
#140263