Finite Group Databasebeta

← #10740317

Subgroups — #10740317

Order 768.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4672C211yesmaximal, characteristic
2C2×#4672C211yesmaximal, characteristic
3C2×#4647C211yesmaximal, characteristic, complemented
4C2×#4670C211yesmaximal, characteristic, complemented
5C3×#1443C211yesmaximal, characteristic, complemented
6#69429C211yesmaximal, characteristic, complemented
7#69428C211yesmaximal, characteristic, complemented
8#69428C211yesmaximal, characteristic, complemented
9#69427C211yesmaximal, characteristic, complemented
10#69426C211yesmaximal, characteristic
11#69414C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69406C211yesmaximal, characteristic, complemented
16#15777—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C22×(C2×D3)⋊C4C2211yescharacteristic
19C22×(C2×D3)⋊C4C2211yescharacteristic
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
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
52#4672—24no—
53#4672—24no—
54#4670—24no—
55#4647—24no—
56C2×#394—31no—
57C2×#394—31no—
58C2×#389—31no—
59C2×#388—31no—
60#1443D311yescharacteristic, complemented
61#1442—31no—
62#1440—31no—
63#1439—31no—
64#1439—31no—
65#1439—31no—
66#1438—31no—
67#1437—31no—
68#1437—31no—
69#1437—31no—
70#1436—31no—
71C24×D3C2311yescharacteristic
72C24×D3C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C22×D12—22no—
87C22×D12—22no—
88C22×D12—22no—
89C22×D12—41no—
90C22×D12—41no—
91C22×D12—41no—
92C22×D12—41no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—22no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—22no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—41no—
117C2×(C2×D3)⋊C4—41no—
118C2×(C2×D3)⋊C4—41no—
119C2×(C2×D3)⋊C4—41no—
120C2×(C2×D3)⋊C4—41no—
121C2×(C2×D3)⋊C4—41no—
122C2×(C2×D3)⋊C4—41no—
123C2×(C2×D3)⋊C4—41no—
124C2×(C2×D3)⋊C4—41no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4D414yes—
129C2×C4⋊Dic3—22no—
130C2×C4⋊Dic3—22no—
131C2×C4⋊Dic3—41no—
132C2×Dic3⋊C4—22no—
133C2×Dic3⋊C4—22no—
134C2×Dic3⋊C4—22no—
135C2×Dic3⋊C4—22no—
136C2×Dic3⋊C4—22no—
137C2×Dic3⋊C4—41no—
138C2×Dic3⋊C4—41no—
139C2×Dic3⋊C4—41no—
140C2×Dic3⋊C4D414yes—
141C2×C4×Dic3—22no—
142C2×C4×Dic3—22no—
143C2×C4×Dic3—41no—
144C2×C4×Dic3—41no—
145C2×C4×Dic3—41no—
146C2×C4×Dic3—41no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—41no—
153C3×#95—41no—
154C3⋊#95—22no—
155C3⋊#95—22no—
156C3⋊#95—22no—
157C3⋊#95—22no—
158C3⋊#95—22no—
159C3⋊#95—41no—
160C3⋊#95—41no—
161C3⋊#95—41no—
162C3⋊#95—41no—
163C23×D4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C42—31no—
181C22×C42—31no—
182#394—64no—
183#394—64no—
184#389—64no—
185#388—64no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95—31no—
189C2×#95—31no—
190C2×#95—31no—
191C2×#95—31no—
192C2×#95—31no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95C2×D311yescharacteristic
196C2×#95C2×D311yescharacteristic
197C2×#95C2×D311yescharacteristic
198C2×#95C2×D311yescharacteristic
199C2×#95C2×D311yescharacteristic
200C2×#95C2×D311yescharacteristic
201C2×#95C2×D311yescharacteristic
202C24×C3C2411yescharacteristic
203C23×D3—21no—
204C23×D3—21no—
205C23×D3—21no—
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3C2×D412yes—
232C23×D3#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D412yes—
280C22×C3×C4#4112yes—
281C22×C3×C4#4112yes—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
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×Dic3C2×D412yes—
318C22×Dic3C2×D412yes—
319C22×Dic3C2×D412yes—
320C22×Dic3#4112yes—
321C22×Dic3#4112yes—
322C22×Dic3#4112yes—
323C22×Dic3#4112yes—
324C2×D12—44no—
325C2×D12—44no—
326C2×D12—44no—
327C2×D12—44no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—44no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343C4⋊Dic3—44no—
344Dic3⋊C4—28no—
345Dic3⋊C4—44no—
346Dic3⋊C4—44no—
347C4×Dic3—44no—
348C4×Dic3—44no—
349C25—31no—
350C25—31no—
351C22×D4—62no—
352C22×D4—62no—
353C22×D4—62no—
354C22×D4—121no—
355C22×D4—121no—
356C22×D4—121no—
357C22×D4—121no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C2×C4⋊C4—34no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—62no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—121no—
380C2×C4⋊C4—121no—
381C2×C4⋊C4—121no—
382C2×C4⋊C4—121no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—62no—
388C2×C22⋊C4—62no—
389C2×C22⋊C4—62no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—62no—
393C2×C22⋊C4—62no—
394C2×C22⋊C4—62no—
395C2×C22⋊C4—62no—
396C2×C22⋊C4—62no—
397C2×C22⋊C4—62no—
398C2×C22⋊C4—62no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—121no—
408C2×C22⋊C4—121no—
409C2×C22⋊C4—121no—
410C2×C22⋊C4—121no—
411C2×C22⋊C4—121no—
412C2×C22⋊C4—121no—
413C2×C22⋊C4—121no—
414C2×C22⋊C4—121no—
415C2×C22⋊C4—121no—
416C2×C22⋊C4—121no—
417C2×C22⋊C4—121no—
418C2×C22⋊C4—121no—
419C2×C42—62no—
420C2×C42—62no—
421C2×C42—121no—
422C2×C42—121no—
423C2×C42—121no—
424C2×C42—121no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—41no—
431#95—41no—
432#95—62no—
433#95—62no—
434#95—62no—
435#95—62no—
436#95—62no—
437#95—121no—
438#95—121no—
439#95—121no—
440#95—121no—
441C23×C3C22×D411yescharacteristic
442C23×C3C22×D411yescharacteristic
443C23×C3C2×#4111yescharacteristic
444C23×C3C2×#4111yescharacteristic
445C23×C3C2×#4111yescharacteristic
446C23×C3C2×#4111yescharacteristic
447C23×C3C2×#4111yescharacteristic
448C23×C3C2×#4111yescharacteristic
449C23×C3C2×#4111yescharacteristic
450C23×C3H(5,𝔽2)11yescharacteristic
451C23×C3H(5,𝔽2)11yescharacteristic
452C23×C3H(5,𝔽2)11yescharacteristic
453C23×C3H(5,𝔽2)11yescharacteristic
454C23×C3H(5,𝔽2)11yescharacteristic
455C23×C32−1+411yescharacteristic
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3#12414yes—
617D12—416no—
618C24—32no—
619C24—32no—
620C24—61no—
621C24—61no—
622C24—61no—
623C24—61no—
624C24—61no—
625C24—61no—
626C24—61no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24—61no—
635C24—61no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24C23×D311yescharacteristic
649C2×D4—124no—
650C2×D4—124no—
651C2×D4—124no—
652C2×D4—124no—
653C2×D4—124no—
654C2×D4—124no—
655C2×D4—124no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—32no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4#23512yes—
744C22×C4D3×D412yes—
745C22×C4D3×D412yes—
746C22×C4#23912yes—
747C4⋊C4—68no—
748C4⋊C4—124no—
749C4⋊C4—124no—
750C4⋊C4—124no—
751C22⋊C4—68no—
752C22⋊C4—124no—
753C22⋊C4—124no—
754C22⋊C4—124no—
755C22⋊C4—124no—
756C22⋊C4—124no—
757C22⋊C4—124no—
758C22⋊C4—124no—
759C22⋊C4—124no—
760C22⋊C4—124no—
761C22⋊C4—124no—
762C22⋊C4—124no—
763C42—124no—
764C42—124no—
765C22×C3#52511yescharacteristic
766C22×C3#52511yescharacteristic
767C22×C3C2×#12411yescharacteristic
768C22×C3#52911yescharacteristic
769C22×C3#52911yescharacteristic
770C22×C3#53211yescharacteristic
771C22×C3#53411yescharacteristic
772C22×C3#53411yescharacteristic
773C22×C3#53811yescharacteristic
774C22×C3#53811yescharacteristic
775C22×C3#53811yescharacteristic
776C22×C3#54011yescharacteristic
777C22×C3#54211yescharacteristic
778C22×C3#54211yescharacteristic
779C22×C3#54211yescharacteristic
780C22×C3D4211yescharacteristic
781C22×C3#54611yescharacteristic
782C22×C3#54611yescharacteristic
783C22×C3#54611yescharacteristic
784C22×C3#54711yescharacteristic
785C22×C3#54811yescharacteristic
786C22×C3#55011yescharacteristic
787C22×C3#55111yescharacteristic
788C22×C3#55211yescharacteristic
789C22×C3#55311yescharacteristic
790C22×C3#55311yescharacteristic
791C22×C3#55311yescharacteristic
792C22×C3#55311yescharacteristic
793C22×C3#55311yescharacteristic
794C22×C3#55311yescharacteristic
795C22×C3#55311yescharacteristic
796C22×C3#55511yescharacteristic
797C22×C3#55911yescharacteristic
798C22×C3#56011yescharacteristic
799C22×C3#56211yescharacteristic
800C2×D3—42no—
801C2×D3—42no—
802C2×D3—42no—
803C2×D3—42no—
804C2×D3—42no—
805C2×D3—42no—
806C2×D3—42no—
807C2×D3—42no—
808C2×D3—42no—
809C2×D3—42no—
810C2×D3—42no—
811C2×D3—42no—
812C2×D3—42no—
813C2×D3—42no—
814C2×D3—81no—
815C2×D3—81no—
816C2×D3—81no—
817C2×D3—81no—
818C2×D3—81no—
819C2×D3—81no—
820C2×D3—81no—
821C2×D3—81no—
822C2×D3—81no—
823C2×D3—81no—
824C2×D3—81no—
825C2×D3—81no—
826C2×D3—81no—
827C2×D3—81no—
828C2×D3—81no—
829C2×D3—81no—
830C3×C4—42no—
831C3×C4—42no—
832C3×C4—42no—
833C3×C4—42no—
834C3×C4—81no—
835C3×C4—81no—
836C3×C4—81no—
837Dic3—24no—
838Dic3—42no—
839Dic3—42no—
840Dic3—42no—
841Dic3—42no—
842Dic3—81no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—121no—
858C23—121no—
859C23—121no—
860C23—121no—
861C23—121no—
862C23—121no—
863C23—121no—
864C23—121no—
865C23—121no—
866C23—121no—
867C23—121no—
868C23—121no—
869C23—121no—
870C23—121no—
871C23—121no—
872C23—121no—
873C23—121no—
874C23—121no—
875C23—121no—
876C23—121no—
877C23—121no—
878C23—121no—
879C23—121no—
880C23—121no—
881C23—121no—
882C23—121no—
883C23—121no—
884C23—121no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23C2×#23511yescharacteristic
914C23C2×D3×D411yescharacteristic
915C23C2×D3×D411yescharacteristic
916C23#100411yescharacteristic
917C23C2×#23911yescharacteristic
918C23D3×#4111yescharacteristic
919C23D3×#4111yescharacteristic
920C23D3×#4111yescharacteristic
921C23D3×#4111yescharacteristic
922C23D3×#4111yescharacteristic
923C23#100911yescharacteristic
924C23#100911yescharacteristic
925C23#100911yescharacteristic
926C23#100911yescharacteristic
927C23#101011yescharacteristic
928D4—1216no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—34no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—62no—
992C2×C4—62no—
993C2×C4—62no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C3#245611yescharacteristic
1021C2×C3#245811yescharacteristic
1022C2×C3#247011yescharacteristic
1023C2×C3#249011yescharacteristic
1024C2×C3#249111yescharacteristic
1025C2×C3#251811yescharacteristic
1026C2×C3#255911yescharacteristic
1027C2×C3#259111yescharacteristic
1028C2×C3#260211yescharacteristic
1029C2×C3#266811yescharacteristic
1030C2×C3#270111yescharacteristic
1031C2×C3#273011yescharacteristic
1032C2×C3#277911yescharacteristic
1033C2×C3#280111yescharacteristic
1034C2×C3#280311yescharacteristic
1035D3—82no—
1036D3—82no—
1037C22—122no—
1038C22—122no—
1039C22—122no—
1040C22—122no—
1041C22—122no—
1042C22—122no—
1043C22—122no—
1044C22—122no—
1045C22—122no—
1046C22—122no—
1047C22—122no—
1048C22—122no—
1049C22—122no—
1050C22—122no—
1051C22—241no—
1052C22—241no—
1053C22—241no—
1054C22—241no—
1055C22—241no—
1056C22—241no—
1057C22—241no—
1058C22—241no—
1059C22—241no—
1060C22—241no—
1061C22—241no—
1062C22—241no—
1063C22—241no—
1064C22—241no—
1065C22—241no—
1066C22—241no—
1067C22#552711yescharacteristic
1068C22#552811yescharacteristic
1069C22#553211yescharacteristic
1070C22#554811yescharacteristic
1071C22#555211yescharacteristic
1072C22#556011yescharacteristic
1073C22#558511yescharacteristic
1074C22#559911yescharacteristic
1075C22#560911yescharacteristic
1076C22#561011yescharacteristic
1077C22#562711yescharacteristic
1078C22#562711yescharacteristic
1079C22#564411yescharacteristic
1080C22#565311yescharacteristic
1081C22#565311yescharacteristic
1082C22#565411yescharacteristic
1083C22#565511yescharacteristic
1084C22#566111yescharacteristic
1085C22#566311yescharacteristic
1086C22D3×#12411yescharacteristic
1087C22#567611yescharacteristic
1088C22#568411yescharacteristic
1089C22#569411yescharacteristic
1090C22#569511yescharacteristic
1091C22#569511yescharacteristic
1092C22#570411yescharacteristic
1093C22#570611yescharacteristic
1094C22#570911yescharacteristic
1095C22#570911yescharacteristic
1096C22#570911yescharacteristic
1097C22#570911yescharacteristic
1098C22#571011yescharacteristic
1099C22#571011yescharacteristic
1100C22#571011yescharacteristic
1101C22#571111yescharacteristic
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—64no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—122no—
1111C4—122no—
1112C4—122no—
1113C4—122no—
1114C4—241no—
1115C3#1577711yescharacteristic, complemented, Sylow
1116C2—242no—
1117C2—242no—
1118C2#7426911yescharacteristic
1119C2#7498911yescharacteristic
1120C2#7527811yescharacteristic
1121C2#7537411yescharacteristic
1122C2#7554611yescharacteristic
1123C2#7570811yescharacteristic
1124C2#7588711yescharacteristic
1125C2#7729211yescharacteristic
1126C2#7748711yescharacteristic
1127C2#7768911yescharacteristic
1128C2#7769811yescharacteristic
1129C2#7814011yescharacteristic
1130C2#7835811yescharacteristic
1131C2#7839911yescharacteristic
1132C2#7842611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1443C2
prime radicalC23×D12C22
hypercenter#1443D3
hypocenterC3#15777
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
3. C2×#4647C2semidirect
4. C2×#4670C2semidirect
5. C3×#1443C2semidirect
6. #69429C2semidirect
7. #69428C2semidirect
8. #69428C2semidirect
9. #69427C2semidirect
11. #69414C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. #69408C2semidirect
15. #69406C2semidirect
60. #1443D3semidirect
1115. C3#15777semidirect

Maximal subgroups

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

subgroupindex
C2×#46722
C2×#46472
C2×#46702
C3×#14432
#694292
#694282
#694272
#694262
#694142
#694082
#694062
#157773