Finite Group Databasebeta

← #10733687

Subgroups — #10733687

Order 768.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#875C211yesmaximal, characteristic, complemented
2C2×#4988C211yesmaximal, characteristic, complemented
3C2×#4673C211yesmaximal, characteristic, complemented
4C2×#4671C211yesmaximal, characteristic
5C2×#4672C211yesmaximal, characteristic, complemented
6C2×#4646C211yesmaximal, characteristic, complemented
7C3×#1436C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71537C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69426C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#15317—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#875—24no—
41C2×#875—24no—
42C2×#875—24no—
43C2×C3×#95C2211yescharacteristic
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
55#4988—24no—
56#4673—24no—
57#4672—24no—
58#4671—24no—
59#4646—24no—
60C22×#124—31no—
61C2×#394—31no—
62C2×#393—31no—
63C2×#392—31no—
64C2×#391—31no—
65C2×#390—31no—
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1438—31no—
71#1438—31no—
72#1437—31no—
73#1437—31no—
74#1436D311yescharacteristic, complemented
75C24×D3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—22no—
102C22×D12—22no—
103C22×D12—41no—
104C22×D12—41no—
105C22×D12—41no—
106C22×D12—41no—
107C22×D12—41no—
108C22×D12—41no—
109C22×D12—41no—
110C22×D12—41no—
111C22×Dic6—22no—
112C22×Dic6—22no—
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—41no—
116C22×Dic6—41no—
117C22×Dic6D414yescomplemented
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—41no—
121C2×C3×C42—22no—
122C2×C3×C42—22no—
123C2×C3×C42—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
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—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—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×(C2×D3)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4—41no—
162C2×(C2×D3)⋊C4—41no—
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×(C2×D3)⋊C4D414yescomplemented
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—41no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3—41no—
175#875—232no—
176C3×#95—22no—
177C3×#95—22no—
178C3×#95—22no—
179C3×#95—41no—
180C3×#95D414yes—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—41no—
187C3⋊#95—41no—
188C23×Q8—31no—
189C23×D4—31no—
190C23×D4—31no—
191C23×D4—31no—
192C2×#124—64no—
193C2×#124—64no—
194C2×#124—64no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
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×C42—31no—
213C22×C42C2×D311yescharacteristic
214#394—64no—
215#393—64no—
216#392—64no—
217#391—64no—
218#390—64no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
231C24×C3C2411yescharacteristic
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
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—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
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×D3C2×D412yes—
275C23×D3C2×D412yes—
276C23×D3#4112yes—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—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×C4C2×D412yes—
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4#4112yes—
324C22×C3×C4#4112yes—
325C22×C3×C4#4112yes—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3C2×D412yes—
357C22×Dic3C2×D412yes—
358C22×Dic3C2×D412yes—
359C22×Dic3C2×D412yes—
360C22×Dic3#4112yes—
361C2×D12—28no—
362C2×D12—28no—
363C2×D12—44no—
364C2×D12—44no—
365C2×D12—44no—
366C2×D12—44no—
367C2×D12—44no—
368C2×D12—44no—
369C2×D12—44no—
370C2×D12—44no—
371C2×D12—44no—
372C2×D12—44no—
373C2×D12—44no—
374C2×D12—44no—
375C2×D12—44no—
376C2×D12—44no—
377C2×D12—44no—
378C2×D12—44no—
379C2×D12—44no—
380C2×D12—44no—
381C2×D12—44no—
382C2×Dic6—28no—
383C2×Dic6—28no—
384C2×Dic6—44no—
385C2×Dic6—44no—
386C2×Dic6—44no—
387C2×Dic6—44no—
388C2×Dic6—44no—
389C3×C4⋊C4—44no—
390C3×C42—28no—
391(C2×D3)⋊C4—28no—
392(C2×D3)⋊C4—28no—
393(C2×D3)⋊C4—28no—
394(C2×D3)⋊C4—28no—
395(C2×D3)⋊C4—44no—
396(C2×D3)⋊C4—44no—
397(C2×D3)⋊C4—44no—
398(C2×D3)⋊C4—44no—
399(C2×D3)⋊C4—44no—
400(C2×D3)⋊C4—44no—
401(C2×D3)⋊C4—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404(C2×D3)⋊C4—44no—
405(C2×D3)⋊C4—44no—
406Dic3⋊C4—44no—
407C4×Dic3—44no—
408C25—31no—
409C25—31no—
410C25—31no—
411C22×Q8—34no—
412C22×Q8—62no—
413C22×Q8—62no—
414C22×Q8—62no—
415C22×Q8—62no—
416C22×Q8—121no—
417C22×Q8—121no—
418C22×D4—62no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—62no—
429C22×D4—62no—
430C22×D4—62no—
431C22×D4—121no—
432C22×D4—121no—
433C22×D4—121no—
434C22×D4—121no—
435C22×D4—121no—
436C22×D4—121no—
437C22×D4—121no—
438C22×D4—121no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4C22×D311yescharacteristic
445C23×C4C22×D311yescharacteristic
446C23×C4C22×D311yescharacteristic
447C23×C4C22×D311yescharacteristic
448C23×C4C22×D311yescharacteristic
449C23×C4C22×D311yescharacteristic
450C23×C4C22×D311yescharacteristic
451#124—632no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—121no—
458C2×C22⋊C4—34no—
459C2×C22⋊C4—34no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
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—121no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4—121no—
502C2×C22⋊C4—121no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—62no—
507C2×C42—62no—
508C2×C42—121no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—41no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—121no—
519#95—121no—
520#95D1214yes—
521C23×C3C22×D411yescharacteristic
522C23×C3C22×D411yescharacteristic
523C23×C3C22×D411yescharacteristic
524C23×C3C22×D411yescharacteristic
525C23×C3C2×#4111yescharacteristic
526C23×C3C2×#4111yescharacteristic
527C23×C3C2×#4111yescharacteristic
528C23×C3C2×#4111yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3H(5,𝔽2)11yescharacteristic
531C23×C3H(5,𝔽2)11yescharacteristic
532C23×C3H(5,𝔽2)11yescharacteristic
533C23×C3H(5,𝔽2)11yescharacteristic
534C23×C3H(5,𝔽2)11yescharacteristic
535C23×C32−1+411yescharacteristic
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
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—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
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—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
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—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
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#12114yes—
689C2×C3×C4#12414yescomplemented
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—41no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3#12014yes—
725D12—416no—
726D12—416no—
727D12—416no—
728Dic6—416no—
729C24—32no—
730C24—32no—
731C24—32no—
732C24—61no—
733C24—61no—
734C24—61no—
735C24—61no—
736C24—61no—
737C24—61no—
738C24—61no—
739C24—61no—
740C24—61no—
741C24—61no—
742C24—61no—
743C24—61no—
744C24—61no—
745C24—61no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24—61no—
754C24—61no—
755C24—61no—
756C24—61no—
757C24—61no—
758C24—61no—
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—
774C24C23×D311yescharacteristic
775C2×Q8—68no—
776C2×Q8—68no—
777C2×Q8—124no—
778C2×Q8—124no—
779C2×Q8—124no—
780C2×Q8—124no—
781C2×Q8—124no—
782C2×D4—68no—
783C2×D4—68no—
784C2×D4—124no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—124no—
788C2×D4—124no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
796C2×D4—124no—
797C2×D4—124no—
798C2×D4—124no—
799C2×D4—124no—
800C2×D4—124no—
801C2×D4—124no—
802C2×D4—124no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
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—32no—
844C22×C4—32no—
845C22×C4—32no—
846C22×C4—32no—
847C22×C4—32no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
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×C4C2×D1212yes—
879C22×C4C2×D1212yes—
880C22×C4C2×D1212yes—
881C22×C4#23512yes—
882C22×C4#23512yes—
883C22×C4D3×D412yes—
884C22×C4D3×D412yes—
885C22×C4D3×D412yes—
886C22×C4#23912yes—
887C4⋊C4—44no—
888C4⋊C4—124no—
889C22⋊C4—68no—
890C22⋊C4—68no—
891C22⋊C4—68no—
892C22⋊C4—68no—
893C22⋊C4—124no—
894C22⋊C4—124no—
895C22⋊C4—124no—
896C22⋊C4—124no—
897C22⋊C4—124no—
898C22⋊C4—124no—
899C22⋊C4—124no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C42—28no—
905C42—124no—
906C22×C3C2×#12011yescharacteristic
907C22×C3C2×#12111yescharacteristic
908C22×C3#52511yescharacteristic
909C22×C3C2×#12411yescharacteristic
910C22×C3#52911yescharacteristic
911C22×C3#53211yescharacteristic
912C22×C3#53411yescharacteristic
913C22×C3#53511yescharacteristic
914C22×C3#53511yescharacteristic
915C22×C3#53711yescharacteristic
916C22×C3#53811yescharacteristic
917C22×C3#53811yescharacteristic
918C22×C3#53811yescharacteristic
919C22×C3#54211yescharacteristic
920C22×C3#54211yescharacteristic
921C22×C3D4211yescharacteristic
922C22×C3D4211yescharacteristic
923C22×C3#54611yescharacteristic
924C22×C3#54611yescharacteristic
925C22×C3#54611yescharacteristic
926C22×C3#54611yescharacteristic
927C22×C3#54611yescharacteristic
928C22×C3#54611yescharacteristic
929C22×C3#54711yescharacteristic
930C22×C3#54811yescharacteristic
931C22×C3#54811yescharacteristic
932C22×C3#55011yescharacteristic
933C22×C3#55011yescharacteristic
934C22×C3#55011yescharacteristic
935C22×C3#55111yescharacteristic
936C22×C3#55511yescharacteristic
937C22×C3#55911yescharacteristic
938C22×C3#55911yescharacteristic
939C22×C3H(3,𝔽4)11yescharacteristic
940C22×C3#56211yescharacteristic
941C2×D3—42no—
942C2×D3—42no—
943C2×D3—42no—
944C2×D3—42no—
945C2×D3—42no—
946C2×D3—42no—
947C2×D3—42no—
948C2×D3—42no—
949C2×D3—42no—
950C2×D3—42no—
951C2×D3—42no—
952C2×D3—42no—
953C2×D3—42no—
954C2×D3—42no—
955C2×D3—42no—
956C2×D3—42no—
957C2×D3—42no—
958C2×D3—42no—
959C2×D3—42no—
960C2×D3—42no—
961C2×D3—42no—
962C2×D3—81no—
963C2×D3—81no—
964C2×D3—81no—
965C2×D3—81no—
966C2×D3—81no—
967C2×D3—81no—
968C2×D3—81no—
969C2×D3—81no—
970C2×D3—81no—
971C2×D3—81no—
972C2×D3—81no—
973C2×D3—81no—
974C2×D3—81no—
975C2×D3—81no—
976C2×D3—81no—
977C2×D3—81no—
978C2×D3—81no—
979C2×D3—81no—
980C2×D3—81no—
981C2×D3—81no—
982C2×D3—81no—
983C2×D3—81no—
984C2×D3—81no—
985C2×D3—81no—
986C3×C4—24no—
987C3×C4—24no—
988C3×C4—42no—
989C3×C4—42no—
990C3×C4—42no—
991C3×C4—81no—
992C3×C4—81no—
993Dic3—24no—
994Dic3—42no—
995Dic3—42no—
996Dic3—81no—
997Dic3—81no—
998C23—62no—
999C23—62no—
1000C23—62no—
1001C23—62no—
1002C23—62no—
1003C23—62no—
1004C23—62no—
1005C23—62no—
1006C23—62no—
1007C23—62no—
1008C23—62no—
1009C23—62no—
1010C23—62no—
1011C23—62no—
1012C23—62no—
1013C23—62no—
1014C23—62no—
1015C23—62no—
1016C23—62no—
1017C23—62no—
1018C23—62no—
1019C23—121no—
1020C23—121no—
1021C23—121no—
1022C23—121no—
1023C23—121no—
1024C23—121no—
1025C23—121no—
1026C23—121no—
1027C23—121no—
1028C23—121no—
1029C23—121no—
1030C23—121no—
1031C23—121no—
1032C23—121no—
1033C23—121no—
1034C23—121no—
1035C23—121no—
1036C23—121no—
1037C23—121no—
1038C23—121no—
1039C23—121no—
1040C23—121no—
1041C23—121no—
1042C23—121no—
1043C23—121no—
1044C23—121no—
1045C23—121no—
1046C23—121no—
1047C23—121no—
1048C23—121no—
1049C23—121no—
1050C23—121no—
1051C23—121no—
1052C23—121no—
1053C23—121no—
1054C23—121no—
1055C23—121no—
1056C23—121no—
1057C23—121no—
1058C23—121no—
1059C23—121no—
1060C23—121no—
1061C23—121no—
1062C23—121no—
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—
1103C23C22×D1211yescharacteristic
1104C23C2×#23511yescharacteristic
1105C23C2×#23511yescharacteristic
1106C23C2×D3×D411yescharacteristic
1107C23C2×D3×D411yescharacteristic
1108C23C2×D3×D411yescharacteristic
1109C23#100411yescharacteristic
1110C23C2×#23911yescharacteristic
1111C23#100711yescharacteristic
1112C23D3×#4111yescharacteristic
1113C23D3×#4111yescharacteristic
1114C23#100911yescharacteristic
1115C23#100911yescharacteristic
1116C23#100911yescharacteristic
1117C23#100911yescharacteristic
1118Q8—1216no—
1119D4—1216no—
1120D4—1216no—
1121D4—1216no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—34no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
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—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—62no—
1180C2×C4—62no—
1181C2×C4—62no—
1182C2×C4—121no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4#87514yescomplemented
1205C2×C4#89514yes—
1206C2×C3#240711yescharacteristic
1207C2×C3#241011yescharacteristic
1208C2×C3#242611yescharacteristic
1209C2×C3#243111yescharacteristic
1210C2×C3#245911yescharacteristic
1211C2×C3#247211yescharacteristic
1212C2×C3#249111yescharacteristic
1213C2×C3#254811yescharacteristic
1214C2×C3#255711yescharacteristic
1215C2×C3#267011yescharacteristic
1216C2×C3#267611yescharacteristic
1217C2×C3#271011yescharacteristic
1218C2×C3#271211yescharacteristic
1219C2×C3#273011yescharacteristic
1220C2×C3#273311yescharacteristic
1221D3—82no—
1222D3—82no—
1223D3—82no—
1224C22—122no—
1225C22—122no—
1226C22—122no—
1227C22—122no—
1228C22—122no—
1229C22—122no—
1230C22—122no—
1231C22—122no—
1232C22—122no—
1233C22—122no—
1234C22—122no—
1235C22—122no—
1236C22—122no—
1237C22—122no—
1238C22—122no—
1239C22—122no—
1240C22—122no—
1241C22—122no—
1242C22—122no—
1243C22—122no—
1244C22—122no—
1245C22—241no—
1246C22—241no—
1247C22—241no—
1248C22—241no—
1249C22—241no—
1250C22—241no—
1251C22—241no—
1252C22—241no—
1253C22—241no—
1254C22—241no—
1255C22—241no—
1256C22—241no—
1257C22—241no—
1258C22—241no—
1259C22—241no—
1260C22—241no—
1261C22—241no—
1262C22—241no—
1263C22—241no—
1264C22—241no—
1265C22—241no—
1266C22—241no—
1267C22—241no—
1268C22—241no—
1269C22C2×#87511yescharacteristic
1270C22#549011yescharacteristic
1271C22C2×#89511yescharacteristic
1272C22#550711yescharacteristic
1273C22#552511yescharacteristic
1274C22#552711yescharacteristic
1275C22#553211yescharacteristic
1276C22#554711yescharacteristic
1277C22#554811yescharacteristic
1278C22D4×D1211yescharacteristic
1279C22D4×D1211yescharacteristic
1280C22#555311yescharacteristic
1281C22#555311yescharacteristic
1282C22#555411yescharacteristic
1283C22#556011yescharacteristic
1284C22#557611yescharacteristic
1285C22#558211yescharacteristic
1286C22#558511yescharacteristic
1287C22#558511yescharacteristic
1288C22D3×#12011yescharacteristic
1289C22#559911yescharacteristic
1290C22#560711yescharacteristic
1291C22#562911yescharacteristic
1292C22#563011yescharacteristic
1293C22#563011yescharacteristic
1294C22#563311yescharacteristic
1295C22#565311yescharacteristic
1296C22#565411yescharacteristic
1297C22#565411yescharacteristic
1298C22#568311yescharacteristic
1299C22#569111yescharacteristic
1300C22#570011yescharacteristic
1301C22#570411yescharacteristic
1302C22#570411yescharacteristic
1303C22#573311yescharacteristic
1304C4—24no—
1305C4—24no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—64no—
1310C4—81no—
1311C4—81no—
1312C4—122no—
1313C4—122no—
1314C4—241no—
1315C4—241no—
1316C3#1531711yescharacteristic, complemented, Sylow
1317C2—242no—
1318C2—242no—
1319C2—242no—
1320C2#7359411yescharacteristic
1321C2#7371211yescharacteristic
1322C2#7378811yescharacteristic
1323C2#7440411yescharacteristic
1324C2#7460111yescharacteristic
1325C2#7470011yescharacteristic
1326C2#7532611yescharacteristic
1327C2#7535811yescharacteristic
1328C2#7538911yescharacteristic
1329C2#7539911yescharacteristic
1330C2#7571211yescharacteristic
1331C2#7591311yescharacteristic
1332C2#7621811yescharacteristic
1333C2#7626811yescharacteristic
1334C2#7665211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC2×#4671C2
hypercenter#1436D3
hypocenterC3#15317
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×#875C2semidirect
2. C2×#4988C2semidirect
3. C2×#4673C2semidirect
5. C2×#4672C2semidirect
6. C2×#4646C2semidirect
7. C3×#1436C2semidirect
8. #71570C2semidirect
9. #71537C2semidirect
10. #69429C2semidirect
11. #69428C2semidirect
12. #69426C2semidirect
13. #69426C2semidirect
14. #69426C2semidirect
15. #69408C2semidirect
74. #1436D3semidirect
117. C22×Dic6D4semidirect
167. C2×(C2×D3)⋊C4D4semidirect
168. C2×(C2×D3)⋊C4D4semidirect
689. C2×C3×C4#124semidirect
1204. C2×C4#875semidirect
1316. C3#15317semidirect

Maximal subgroups

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

subgroupindex
C22×#8752
C2×#49882
C2×#46732
C2×#46712
C2×#46722
C2×#46462
C3×#14362
#715702
#715372
#694292
#694282
#694262
#694082
#153173