Finite Group Databasebeta

← #10718668

Subgroups — #10718668

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×#885C211yesmaximal, characteristic
2C22×C4×Dic6C211yesmaximal, characteristic, complemented
3C2×#4957C211yesmaximal, characteristic
4C2×#4957C211yesmaximal, characteristic
5C2×#4646C211yesmaximal, characteristic, complemented
6C3×#1437C211yesmaximal, characteristic, complemented
7#71547C211yesmaximal, characteristic, complemented
8#71546C211yesmaximal, characteristic, complemented
9#71545C211yesmaximal, characteristic, complemented
10#71537C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14Dic3⋊#95C211yesmaximal, characteristic, complemented
15Dic3×#95C211yesmaximal, characteristic, complemented
16#14026—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#885—24no—
41C2×#885—24no—
42C2×#885C418yescomplemented
43C2×C4×Dic6—24no—
44C2×C4×Dic6—24no—
45C2×C4×Dic6—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
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#1439—31no—
70#1437—31no—
71#1437—31no—
72#1437—31no—
73#1437D311yescharacteristic, complemented
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×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊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—41no—
113C2×C3×C22⋊C4C2×C414yes—
114C2×C3×C42—22no—
115C2×C3×C42—22no—
116C2×C3×C42—22no—
117C2×#217—22no—
118C2×#217—22no—
119C2×#217—22no—
120C2×#217—22no—
121C2×#217—22no—
122C2×#217—41no—
123C2×#217—41no—
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×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—22no—
147C2×Dic3⋊C4—22no—
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⋊C4D414yes—
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#885—232no—
169C4×Dic6—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⋊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⋊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×C42C2×D311yescharacteristic
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×C4C22×C412yes—
291C22×C3×C4C22×C412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2×D412yes—
296C22×C3×C4#4112yes—
297C22×C3×C4#4112yes—
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×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3C22×C412yes—
342C22×Dic3C22×C412yes—
343C22×Dic3C22×C412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
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×C22⋊C4—28no—
363C3×C22⋊C4—44no—
364C3×C22⋊C4—44no—
365C3×C42—28no—
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—
375C4⋊Dic3—28no—
376Dic3⋊C4—28no—
377Dic3⋊C4—28no—
378Dic3⋊C4—44no—
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—34no—
415C2×C4⋊C4—62no—
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×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—34no—
434C2×C22⋊C4—34no—
435C2×C22⋊C4—34no—
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—121no—
455C2×C22⋊C4—121no—
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—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—34no—
466C2×C42—34no—
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—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
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×C4C2×C22⋊C414yes—
615C2×C3×C4#12414yescomplemented
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—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—41no—
657C2×Dic3—41no—
658C2×Dic3C2×C22⋊C414yes—
659C2×Dic3C2×C22⋊C414yes—
660C2×Dic3C4×D414yes—
661C2×Dic3C4×D414yes—
662C2×Dic3#12014yes—
663C2×Dic3#12114yes—
664C2×Dic3#12114yes—
665C2×Dic3#12314yes—
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—32no—
746C22×C4—32no—
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—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×C4C2×C4×D312yes—
795C22×C4C2×C4×D312yes—
796C22×C4#23512yes—
797C22×C4#23512yes—
798C22×C4D3×D412yes—
799C22×C4D3×D412yes—
800C22×C4D3×D412yes—
801C22×C4D3×D412yes—
802C22×C4#23712yes—
803C4⋊C4—68no—
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—28no—
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—24no—
891C3×C4—42no—
892C3×C4—42no—
893C3×C4—42no—
894C3×C4—81no—
895Dic3—24no—
896Dic3—42no—
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×#23511yescharacteristic
974C23C2×#23511yescharacteristic
975C23C2×D3×D411yescharacteristic
976C23C2×D3×D411yescharacteristic
977C23C2×D3×D411yescharacteristic
978C23C2×D3×D411yescharacteristic
979C23C2×#23711yescharacteristic
980C23#100411yescharacteristic
981C23D3×#4111yescharacteristic
982C23D3×#4111yescharacteristic
983C23D3×#4111yescharacteristic
984C23#100911yescharacteristic
985C23#101011yescharacteristic
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—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—34no—
1011C2×C4—34no—
1012C2×C4—34no—
1013C2×C4—34no—
1014C2×C4—34no—
1015C2×C4—34no—
1016C2×C4—34no—
1017C2×C4—34no—
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—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—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—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—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4D3×C22⋊C414yes—
1079C2×C4#88514yescomplemented
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—
1127C22C4×#23511yescharacteristic
1128C22C2×D3×C22⋊C411yescharacteristic
1129C22#549011yescharacteristic
1130C22C2×#88511yescharacteristic
1131C22#552311yescharacteristic
1132C22#552811yescharacteristic
1133C22#553311yescharacteristic
1134C22C4×#23711yescharacteristic
1135C22#553811yescharacteristic
1136C22C4×D3×D411yescharacteristic
1137C22C4×D3×D411yescharacteristic
1138C22#554611yescharacteristic
1139C22#554811yescharacteristic
1140C22#555211yescharacteristic
1141C22#555211yescharacteristic
1142C22#555211yescharacteristic
1143C22#555311yescharacteristic
1144C22#555311yescharacteristic
1145C22#555911yescharacteristic
1146C22D3×#12011yescharacteristic
1147C22#559811yescharacteristic
1148C22#559811yescharacteristic
1149C22#559911yescharacteristic
1150C22D3×#12111yescharacteristic
1151C22D3×#12111yescharacteristic
1152C22#560711yescharacteristic
1153C22#564811yescharacteristic
1154C22D3×#12311yescharacteristic
1155C22#565411yescharacteristic
1156C22#566911yescharacteristic
1157C22#567711yescharacteristic
1158C22#568111yescharacteristic
1159C22#570211yescharacteristic
1160C22#571011yescharacteristic
1161C22#571811yescharacteristic
1162C4—24no—
1163C4—24no—
1164C4—38no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—64no—
1169C4—81no—
1170C4—122no—
1171C4—122no—
1172C4—122no—
1173C4—122no—
1174C4—241no—
1175C3#1402611yescharacteristic, complemented, Sylow
1176C2—82no—
1177C2—242no—
1178C2C4×#88511yescharacteristic
1179C2#7345411yescharacteristic
1180C2#7347211yescharacteristic
1181C2#7470011yescharacteristic
1182C2#7470111yescharacteristic
1183C2D3×#38611yescharacteristic
1184C2#7546211yescharacteristic
1185C2#7548211yescharacteristic
1186C2#7549911yescharacteristic
1187C2#7550111yescharacteristic
1188C2#7550211yescharacteristic
1189C2#7559311yescharacteristic
1190C2#7630111yescharacteristic
1191C2#7631211yescharacteristic
1192C2#7635311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenter#1437D3
hypocenterC3#14026
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic6C2semidirect
5. C2×#4646C2semidirect
6. C3×#1437C2semidirect
7. #71547C2semidirect
8. #71546C2semidirect
9. #71545C2semidirect
10. #71537C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
13. #69408C2semidirect
14. Dic3⋊#95C2semidirect
15. Dic3×#95C2semidirect
42. C2×#885C4semidirect
73. #1437D3semidirect
361. C2×Dic6C22⋊C4semidirect
615. C2×C3×C4#124semidirect
1079. C2×C4#885semidirect
1175. C3#14026semidirect

Maximal subgroups

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

subgroupindex
C22×#8852
C22×C4×Dic62
C2×#49572
C2×#46462
C3×#14372
#715472
#715462
#715452
#715372
#694282
#694272
#694082
Dic3⋊#952
Dic3×#952
#140263