Finite Group Databasebeta

← #10729212

Subgroups — #10729212

Order 768.

2430 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#885C211yesmaximal, characteristic, complemented
2C2×#4979C211yesmaximal, characteristic, complemented
3C2×#4988C211yesmaximal, characteristic, complemented
4C2×#4959C211yesmaximal, characteristic, complemented
5C2×#4960C211yesmaximal, characteristic
6C2×#4957C211yesmaximal, characteristic, complemented
7C2×#4673C211yesmaximal, characteristic, complemented
8C2×#4669C211yesmaximal, characteristic, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10#71550C211yesmaximal, characteristic, complemented
11#71545C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14928—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C2×#885—24no—
43C2×#885—24no—
44C2×#885—24no—
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
55#4988—24no—
56#4979—24no—
57#4960—24no—
58#4959—24no—
59#4957—24no—
60#4673—24no—
61#4669—24no—
62C22×#124—31no—
63C2×#395—31no—
64C2×#394—31no—
65C2×#393—31no—
66C2×#392—31no—
67C2×#390—31no—
68C2×#390—31no—
69C2×#388—31no—
70#1439—31no—
71#1439D311yescharacteristic, complemented
72#1438—31no—
73#1438—31no—
74#1437—31no—
75#1437—31no—
76C4×#95—31no—
77C25×C3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—41no—
97C22×#67—41no—
98C22×#67—41no—
99C22×#67—41no—
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C22×D12—22no—
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—22no—
110C22×D12—22no—
111C22×D12—41no—
112C22×D12—41no—
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—22no—
116C22×Dic6—22no—
117C22×Dic6—22no—
118C22×Dic6—41no—
119C22×Dic6—41no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—41no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—41no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—41no—
137C2×#217D414yescomplemented
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
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×(C2×D3)⋊C4D414yescomplemented
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—41no—
174C2×C4×Dic3—22no—
175C2×C4×Dic3—22no—
176C2×C4×Dic3—22no—
177C2×C4×Dic3—22no—
178C2×C4×Dic3—22no—
179C2×C4×Dic3—22no—
180C2×C4×Dic3—41no—
181C2×C4×Dic3—41no—
182C2×C4×Dic3D414yescomplemented
183#885—232no—
184C3×#95—22no—
185C3×#95—22no—
186C3×#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95D414yes—
193C3⋊#95D414yescomplemented
194C23×Q8—31no—
195C23×D4—31no—
196C23×D4—31no—
197C23×D4—31no—
198C2×#124—64no—
199C2×#124—64no—
200C2×#124—64no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4C2×D311yescharacteristic
204C22×C22⋊C4—31no—
205C22×C22⋊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⋊C4C2×D311yescharacteristic
217C22×C22⋊C4C2×D311yescharacteristic
218C22×C22⋊C4C2×D311yescharacteristic
219C22×C42—31no—
220C22×C42—31no—
221C22×C42—31no—
222#395—64no—
223#394—64no—
224#393—64no—
225#392—64no—
226#390—64no—
227#390—64no—
228#388—64no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
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×C3—21no—
252C24×C3—21no—
253C24×C3C2×D412yes—
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×D3—21no—
282C23×D3—21no—
283C23×D3C2×D412yes—
284C23×D3#4112yes—
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—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×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4#4112yes—
326C22×C3×C4#4112yes—
327C2×#67—28no—
328C2×#67—28no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
332C2×#67—44no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—44no—
336C2×#67—44no—
337C2×#67—44no—
338C2×#67—44no—
339C2×#67—44no—
340C2×#67—44no—
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×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×Dic3C2×D412yes—
372C22×Dic3C2×D412yes—
373C22×Dic3C2×D412yes—
374C22×Dic3C2×D412yes—
375C22×Dic3C2×D412yes—
376C22×Dic3C2×D412yes—
377C22×Dic3C2×D412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3C2×D412yes—
380C22×Dic3#4112yes—
381C22×Dic3#4112yes—
382C22×Dic3#4112yes—
383C2×D12—28no—
384C2×D12—44no—
385C2×D12—44no—
386C2×D12—44no—
387C2×D12—44no—
388C2×D12—44no—
389C2×D12—44no—
390C2×Dic6—28no—
391C2×Dic6—44no—
392C2×Dic6—44no—
393C2×Dic6—44no—
394C2×Dic6—44no—
395C2×Dic6—44no—
396C2×Dic6—44no—
397C3×C4⋊C4—44no—
398C3×C22⋊C4—28no—
399C3×C22⋊C4—44no—
400C3×C22⋊C4—44no—
401#217—28no—
402#217—44no—
403(C2×D3)⋊C4—28no—
404(C2×D3)⋊C4—28no—
405(C2×D3)⋊C4—28no—
406(C2×D3)⋊C4—44no—
407(C2×D3)⋊C4—44no—
408(C2×D3)⋊C4—44no—
409(C2×D3)⋊C4—44no—
410(C2×D3)⋊C4—44no—
411(C2×D3)⋊C4—44no—
412(C2×D3)⋊C4—44no—
413Dic3⋊C4—44no—
414Dic3⋊C4—44no—
415C4×Dic3—28no—
416C4×Dic3—44no—
417C4×Dic3—44no—
418C25—31no—
419C25—31no—
420C25C22×D311yescharacteristic
421C22×Q8—62no—
422C22×Q8—62no—
423C22×Q8—62no—
424C22×Q8—62no—
425C22×Q8—62no—
426C22×Q8—121no—
427C22×Q8—121no—
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—62no—
443C22×D4—121no—
444C22×D4—121no—
445C22×D4—121no—
446C22×D4—121no—
447C22×D4—121no—
448C22×D4—121no—
449C23×C4—31no—
450C23×C4—31no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4—31no—
455C23×C4C22×D311yescharacteristic
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C23×C4C22×D311yescharacteristic
461#124—632no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4—62no—
466C2×C4⋊C4—62no—
467C2×C4⋊C4—62no—
468C2×C4⋊C4—62no—
469C2×C4⋊C4—62no—
470C2×C4⋊C4—121no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—34no—
480C2×C22⋊C4—34no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
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—121no—
512C2×C22⋊C4—121no—
513C2×C22⋊C4—121no—
514C2×C22⋊C4—121no—
515C2×C22⋊C4—121no—
516C2×C42—34no—
517C2×C42—62no—
518C2×C42—62no—
519C2×C42—62no—
520C2×C42—62no—
521C2×C42—62no—
522C2×C42—62no—
523C2×C42—121no—
524C2×C42—121no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—34no—
529#95—34no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—62no—
534#95—62no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
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×C3C22×D411yescharacteristic
571C23×C3C22×D411yescharacteristic
572C23×C3C22×D411yescharacteristic
573C23×C3C22×D411yescharacteristic
574C23×C3C22×D411yescharacteristic
575C23×C3C2×#4111yescharacteristic
576C23×C3C2×#4111yescharacteristic
577C23×C3C2×#4111yescharacteristic
578C23×C3C2×#4111yescharacteristic
579C23×C3C2×#4111yescharacteristic
580C23×C3C2×#4111yescharacteristic
581C23×C3H(5,𝔽2)11yescharacteristic
582C23×C3H(5,𝔽2)11yescharacteristic
583C23×C3H(5,𝔽2)11yescharacteristic
584C23×C32−1+411yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
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—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
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—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
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—41no—
671C2×C3×C4—41no—
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#12414yescomplemented
697#67—416no—
698#67—416no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
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—22no—
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#12014yes—
739C2×Dic3#12414yescomplemented
740C2×Dic3#12714yes—
741D12—416no—
742Dic6—416no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—32no—
758C24—32no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
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—
787C24D3×D412yes—
788C24C23×D311yescharacteristic
789C2×Q8—68no—
790C2×Q8—124no—
791C2×Q8—124no—
792C2×Q8—124no—
793C2×Q8—124no—
794C2×Q8—124no—
795C2×Q8—124no—
796C2×D4—68no—
797C2×D4—68no—
798C2×D4—68no—
799C2×D4—124no—
800C2×D4—124no—
801C2×D4—124no—
802C2×D4—124no—
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—
815C2×D4—124no—
816C2×D4—124no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
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—32no—
863C22×C4—32no—
864C22×C4—32no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
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#23512yes—
896C22×C4D3×D412yes—
897C22×C4D3×D412yes—
898C22×C4D3×D412yes—
899C22×C4D3×D412yes—
900C22×C4#23712yes—
901C4⋊C4—44no—
902C4⋊C4—124no—
903C4⋊C4—124no—
904C22⋊C4—28no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—68no—
908C22⋊C4—68no—
909C22⋊C4—68no—
910C22⋊C4—68no—
911C22⋊C4—124no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C22⋊C4—124no—
915C22⋊C4—124no—
916C22⋊C4—124no—
917C22⋊C4—124no—
918C22⋊C4—124no—
919C42—68no—
920C42—124no—
921C42—124no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—42no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—81no—
930C22×C3—81no—
931C22×C3—81no—
932C22×C3—81no—
933C22×C3—81no—
934C22×C3—81no—
935C22×C3—81no—
936C22×C3—81no—
937C22×C3C2×#12011yescharacteristic
938C22×C3#52511yescharacteristic
939C22×C3#52511yescharacteristic
940C22×C3#52511yescharacteristic
941C22×C3C2×#12411yescharacteristic
942C22×C3C2×#12411yescharacteristic
943C22×C3C2×#12711yescharacteristic
944C22×C3#53211yescharacteristic
945C22×C3#53211yescharacteristic
946C22×C3#53211yescharacteristic
947C22×C3#53211yescharacteristic
948C22×C3#53211yescharacteristic
949C22×C3#53211yescharacteristic
950C22×C3#53511yescharacteristic
951C22×C3#53711yescharacteristic
952C22×C3#53811yescharacteristic
953C22×C3#53811yescharacteristic
954C22×C3#54211yescharacteristic
955C22×C3#54211yescharacteristic
956C22×C3D4211yescharacteristic
957C22×C3D4211yescharacteristic
958C22×C3D4211yescharacteristic
959C22×C3D4211yescharacteristic
960C22×C3#54611yescharacteristic
961C22×C3#54611yescharacteristic
962C22×C3#54611yescharacteristic
963C22×C3#54611yescharacteristic
964C22×C3#54711yescharacteristic
965C22×C3#54711yescharacteristic
966C22×C3#54811yescharacteristic
967C22×C3#54811yescharacteristic
968C22×C3#55111yescharacteristic
969C22×C3#55111yescharacteristic
970C22×C3#55511yescharacteristic
971C22×C3#55511yescharacteristic
972C2×D3—42no—
973C2×D3—42no—
974C2×D3—42no—
975C2×D3—42no—
976C2×D3—42no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—81no—
987C2×D3—81no—
988C2×D3—81no—
989C2×D3—81no—
990C2×D3—81no—
991C2×D3—81no—
992C2×D3—81no—
993C2×D3—81no—
994C2×D3—81no—
995C2×D3—81no—
996C2×D3—81no—
997C2×D3—81no—
998C2×D3—81no—
999C2×D3—81no—
1000C2×D3—81no—
1001C2×D3—81no—
1002C3×C4—24no—
1003C3×C4—42no—
1004C3×C4—42no—
1005C3×C4—42no—
1006C3×C4—81no—
1007C3×C4—81no—
1008Dic3—24no—
1009Dic3—24no—
1010Dic3—24no—
1011Dic3—42no—
1012Dic3—42no—
1013Dic3—42no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—62no—
1050C23—62no—
1051C23—62no—
1052C23—62no—
1053C23—62no—
1054C23—62no—
1055C23—62no—
1056C23—62no—
1057C23—62no—
1058C23—62no—
1059C23—62no—
1060C23—62no—
1061C23—62no—
1062C23—62no—
1063C23—121no—
1064C23—121no—
1065C23—121no—
1066C23—121no—
1067C23—121no—
1068C23—121no—
1069C23—121no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23—121no—
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—
1119C23C2×#23511yescharacteristic
1120C23C2×D3×D411yescharacteristic
1121C23C2×D3×D411yescharacteristic
1122C23C2×D3×D411yescharacteristic
1123C23C2×D3×D411yescharacteristic
1124C23C2×D3×D411yescharacteristic
1125C23C2×#23711yescharacteristic
1126C23#100411yescharacteristic
1127C23#100711yescharacteristic
1128C23D3×#4111yescharacteristic
1129C23D3×#4111yescharacteristic
1130C23D3×#4111yescharacteristic
1131C23D3×#4111yescharacteristic
1132C23#100911yescharacteristic
1133C23#100911yescharacteristic
1134Q8—1216no—
1135D4—1216no—
1136D4—1216no—
1137D4—1216no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—34no—
1154C2×C4—34no—
1155C2×C4—34no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
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—62no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—62no—
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—121no—
1210C2×C4—121no—
1211C2×C4—121no—
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#88514yescomplemented
1222C2×C3—82no—
1223C2×C3#238811yescharacteristic
1224C2×C3#243011yescharacteristic
1225C2×C3#243311yescharacteristic
1226C2×C3#246111yescharacteristic
1227C2×C3#246111yescharacteristic
1228C2×C3#247211yescharacteristic
1229C2×C3#247211yescharacteristic
1230C2×C3#249111yescharacteristic
1231C2×C3#249111yescharacteristic
1232C2×C3#254011yescharacteristic
1233C2×C3#255511yescharacteristic
1234C2×C3#255511yescharacteristic
1235C2×C3#261011yescharacteristic
1236C2×C3#266211yescharacteristic
1237C2×C3#285811yescharacteristic
1238D3—82no—
1239D3—82no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—122no—
1256C22—122no—
1257C22—122no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—122no—
1262C22—122no—
1263C22—122no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—241no—
1270C22—241no—
1271C22—241no—
1272C22—241no—
1273C22—241no—
1274C22—241no—
1275C22—241no—
1276C22—241no—
1277C22—241no—
1278C22—241no—
1279C22—241no—
1280C22—241no—
1281C22—241no—
1282C22—241no—
1283C22—241no—
1284C22—241no—
1285C22C2×#88511yescharacteristic
1286C22#550711yescharacteristic
1287C22#553211yescharacteristic
1288C22#554811yescharacteristic
1289C22#554811yescharacteristic
1290C22#555011yescharacteristic
1291C22#555611yescharacteristic
1292C22D3×#12011yescharacteristic
1293C22#559011yescharacteristic
1294C22#559011yescharacteristic
1295C22#559611yescharacteristic
1296C22#559611yescharacteristic
1297C22#559611yescharacteristic
1298C22#560611yescharacteristic
1299C22#560711yescharacteristic
1300C22#560911yescharacteristic
1301C22#560911yescharacteristic
1302C22#561711yescharacteristic
1303C22#562911yescharacteristic
1304C22#563111yescharacteristic
1305C22#563311yescharacteristic
1306C22#563311yescharacteristic
1307C22#564011yescharacteristic
1308C22#564311yescharacteristic
1309C22#565411yescharacteristic
1310C22#565411yescharacteristic
1311C22#565411yescharacteristic
1312C22#565611yescharacteristic
1313C22#565611yescharacteristic
1314C22#566811yescharacteristic
1315C22#567011yescharacteristic
1316C22D3×#12411yescharacteristic
1317C22#570411yescharacteristic
1318C22#570511yescharacteristic
1319C22D3×#12711yescharacteristic
1320C4—24no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—64no—
1325C4—64no—
1326C4—64no—
1327C4—81no—
1328C4—81no—
1329C4—122no—
1330C4—122no—
1331C4—122no—
1332C3#1492811yescharacteristic, complemented, Sylow
1333C2—82no—
1334C2—242no—
1335C2—242no—
1336C2#7391511yescharacteristic
1337C2#7443111yescharacteristic
1338C2#7460611yescharacteristic
1339C2#7472811yescharacteristic
1340C2#7559711yescharacteristic
1341C2#7590011yescharacteristic
1342C2#7642411yescharacteristic
1343C2#7667311yescharacteristic
1344C2#7679211yescharacteristic
1345C2#7688911yescharacteristic
1346C2#7694911yescharacteristic
1347C2#7729511yescharacteristic
1348C2#7734411yescharacteristic
1349C2#7747411yescharacteristic
1350C2#7803611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC2×#4960C2
hypercenter#1439D3
hypocenterC3#14928
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#885C2semidirect
2. C2×#4979C2semidirect
3. C2×#4988C2semidirect
4. C2×#4959C2semidirect
6. C2×#4957C2semidirect
7. C2×#4673C2semidirect
8. C2×#4669C2semidirect
9. C3×#1439C2semidirect
10. #71550C2semidirect
11. #71545C2semidirect
12. #69428C2semidirect
13. #69426C2semidirect
14. #69408C2semidirect
15. Dic3×#95C2semidirect
71. #1439D3semidirect
137. C2×#217D4semidirect
167. C2×(C2×D3)⋊C4D4semidirect
182. C2×C4×Dic3D4semidirect
193. C3⋊#95D4semidirect
696. C2×C3×C4#124semidirect
739. C2×Dic3#124semidirect
1221. C2×C4#885semidirect
1332. C3#14928semidirect

Maximal subgroups

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

subgroupindex
C22×#8852
C2×#49792
C2×#49882
C2×#49592
C2×#49602
C2×#49572
C2×#46732
C2×#46692
C3×#14392
#715502
#715452
#694282
#694262
#694082
Dic3×#952
#149283