Finite Group Databasebeta

← #10725786

Subgroups — #10725786

Order 768.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4672C211yesmaximal, characteristic
2C3×#1434C211yesmaximal, characteristic, complemented
3#71537C211yesmaximal, characteristic, complemented
4#71537C211yesmaximal, characteristic, complemented
5#69429C211yesmaximal, characteristic, complemented
6#69429C211yesmaximal, characteristic, complemented
7#69426C211yesmaximal, characteristic
8#69426C211yesmaximal, characteristic
9#69421C211yesmaximal, characteristic, complemented
10#69408C211yesmaximal, characteristic, complemented
11#69408C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14617—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
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#4672C418yescomplemented
53C2×#394—31no—
54#1445—31no—
55#1440—31no—
56#1440—31no—
57#1438—31no—
58#1438—31no—
59#1437—31no—
60#1437—31no—
61#1437—31no—
62#1437—31no—
63#1437—31no—
64#1437—31no—
65#1436—31no—
66#1434—31no—
67#1434D311yescharacteristic, complemented
68C24×D3C2311yescharacteristic
69C24×D3C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C22×D12—41no—
84C22×D12—41no—
85C22×D12—41no—
86C22×D12—41no—
87C22×D12—41no—
88C22×D12—41no—
89C22×D12C2×C414yes—
90C2×C3×C42—22no—
91C2×C3×C42—41no—
92C2×C3×C42—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—41no—
106C2×(C2×D3)⋊C4—41no—
107C2×(C2×D3)⋊C4—41no—
108C2×(C2×D3)⋊C4—41no—
109C2×(C2×D3)⋊C4—41no—
110C2×(C2×D3)⋊C4—41no—
111C2×(C2×D3)⋊C4—41no—
112C2×(C2×D3)⋊C4—41no—
113C2×(C2×D3)⋊C4—41no—
114C2×(C2×D3)⋊C4—41no—
115C2×(C2×D3)⋊C4—41no—
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)⋊C4C2×C414yes—
126C2×(C2×D3)⋊C4C2×C414yes—
127C2×(C2×D3)⋊C4C2×C414yes—
128C2×(C2×D3)⋊C4C2×C414yes—
129C2×Dic3⋊C4—41no—
130C2×Dic3⋊C4—41no—
131C2×Dic3⋊C4C2×C414yes—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—41no—
134C2×C4×Dic3—41no—
135C2×C4×Dic3—41no—
136C2×C4×Dic3—41no—
137C2×C4×Dic3—41no—
138C3×#95—22no—
139C3×#95—41no—
140C3×#95—41no—
141C3×#95—41no—
142C3×#95—41no—
143C3×#95C2×C414yes—
144C3⋊#95—22no—
145C3⋊#95—22no—
146C3⋊#95—22no—
147C3⋊#95—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95—41no—
155C3⋊#95—41no—
156C23×D4—31no—
157C22×C4⋊C4—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—31no—
165C22×C22⋊C4—31no—
166C22×C22⋊C4—31no—
167C22×C22⋊C4—31no—
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C42—31no—
171C22×C42—31no—
172C22×C42C2×D311yescharacteristic
173#394—38no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95C2×D311yescharacteristic
187C2×#95C2×D311yescharacteristic
188C2×#95C2×D311yescharacteristic
189C2×#95C2×D311yescharacteristic
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C24×C3C2411yescharacteristic
193C23×D3—21no—
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
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×D3C22×C412yes—
222C23×D3C22×C412yes—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
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×C4C22×C412yes—
267C22×C3×C4C22×C412yes—
268C22×C3×C4C22×C412yes—
269C22×C3×C4#4112yes—
270C22×C3×C4#4112yes—
271C22×C3×C4#4112yes—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
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×Dic3C22×C412yes—
310C22×Dic3C22×C412yes—
311C22×Dic3#4112yes—
312C22×Dic3#4112yes—
313C22×Dic3#4112yes—
314C2×D12—44no—
315C2×D12—44no—
316C2×D12—44no—
317C2×D12—44no—
318C2×D12—44no—
319C2×D12—44no—
320C2×D12—44no—
321C3×C42—44no—
322(C2×D3)⋊C4—44no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—44no—
325(C2×D3)⋊C4—44no—
326(C2×D3)⋊C4—44no—
327(C2×D3)⋊C4—44no—
328(C2×D3)⋊C4—44no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332(C2×D3)⋊C4—44no—
333(C2×D3)⋊C4—44no—
334Dic3⋊C4—44no—
335C4×Dic3—44no—
336C4×Dic3—44no—
337C25—31no—
338C25—31no—
339C22×D4—34no—
340C22×D4—121no—
341C22×D4—121no—
342C22×D4—121no—
343C22×D4—121no—
344C22×D4—121no—
345C22×D4—121no—
346C23×C4—31no—
347C23×C4—31no—
348C23×C4—31no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4C22×D311yescharacteristic
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C23×C4C22×D311yescharacteristic
358C23×C4C22×D311yescharacteristic
359C2×C4⋊C4—34no—
360C2×C4⋊C4—121no—
361C2×C4⋊C4—121no—
362C2×C22⋊C4—34no—
363C2×C22⋊C4—34no—
364C2×C22⋊C4—34no—
365C2×C22⋊C4—34no—
366C2×C22⋊C4—62no—
367C2×C22⋊C4—62no—
368C2×C22⋊C4—62no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—62no—
371C2×C22⋊C4—62no—
372C2×C22⋊C4—62no—
373C2×C22⋊C4—62no—
374C2×C22⋊C4—62no—
375C2×C22⋊C4—62no—
376C2×C22⋊C4—62no—
377C2×C22⋊C4—62no—
378C2×C22⋊C4—121no—
379C2×C22⋊C4—121no—
380C2×C22⋊C4—121no—
381C2×C22⋊C4—121no—
382C2×C22⋊C4—121no—
383C2×C22⋊C4—121no—
384C2×C22⋊C4—121no—
385C2×C22⋊C4—121no—
386C2×C22⋊C4—121no—
387C2×C22⋊C4—121no—
388C2×C22⋊C4—121no—
389C2×C22⋊C4—121no—
390C2×C22⋊C4—121no—
391C2×C22⋊C4—121no—
392C2×C22⋊C4—121no—
393C2×C22⋊C4—121no—
394C2×C22⋊C4—121no—
395C2×C22⋊C4—121no—
396C2×C22⋊C4—121no—
397C2×C22⋊C4—121no—
398C2×C42—22no—
399C2×C42—41no—
400C2×C42—41no—
401C2×C42—62no—
402C2×C42—121no—
403C2×C42—121no—
404C2×C42—121no—
405C2×C42—121no—
406C2×C42—121no—
407#95—22no—
408#95—41no—
409#95—41no—
410#95—41no—
411#95—41no—
412#95—62no—
413#95—62no—
414#95—62no—
415#95—121no—
416#95—121no—
417#95—121no—
418#95—121no—
419#95—121no—
420#95—121no—
421#95—121no—
422#95—121no—
423#95—121no—
424#95C4×D314yes—
425C23×C3C23×C411yescharacteristic
426C23×C3C2×#4111yescharacteristic
427C23×C3C2×#4111yescharacteristic
428C23×C3C2×#4111yescharacteristic
429C23×C3C2×#4111yescharacteristic
430C23×C3C2×#4111yescharacteristic
431C23×C3C2×#4111yescharacteristic
432C23×C3H(5,𝔽2)11yescharacteristic
433C23×C3H(5,𝔽2)11yescharacteristic
434C23×C3H(5,𝔽2)11yescharacteristic
435C23×C3H(5,𝔽2)11yescharacteristic
436C23×C3H(5,𝔽2)11yescharacteristic
437C23×C3H(5,𝔽2)11yescharacteristic
438C23×C3H(5,𝔽2)11yescharacteristic
439C23×C3H(5,𝔽2)11yescharacteristic
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
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—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
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×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601D12—416no—
602C24—32no—
603C24—32no—
604C24—61no—
605C24—61no—
606C24—61no—
607C24—61no—
608C24—61no—
609C24—61no—
610C24—61no—
611C24—61no—
612C24—61no—
613C24—61no—
614C24—61no—
615C24—61no—
616C24—61no—
617C24—61no—
618C24—61no—
619C24—61no—
620C24—61no—
621C24—61no—
622C24—61no—
623C24—61no—
624C24—61no—
625C24—61no—
626C24—61no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24—61no—
632C24C23×D311yescharacteristic
633C2×D4—124no—
634C2×D4—124no—
635C2×D4—124no—
636C2×D4—124no—
637C2×D4—124no—
638C2×D4—124no—
639C2×D4—124no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
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—32no—
684C22×C4—32no—
685C22×C4—32no—
686C22×C4—32no—
687C22×C4—32no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
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×C4C2×C4×D312yes—
726C22×C4C2×C4×D312yes—
727C22×C4C2×C4×D312yes—
728C22×C4#23512yes—
729C22×C4#23512yes—
730C22×C4#23912yes—
731C4⋊C4—124no—
732C22⋊C4—124no—
733C22⋊C4—124no—
734C22⋊C4—124no—
735C22⋊C4—124no—
736C22⋊C4—124no—
737C22⋊C4—124no—
738C22⋊C4—124no—
739C22⋊C4—124no—
740C22⋊C4—124no—
741C22⋊C4—124no—
742C22⋊C4—124no—
743C22⋊C4—124no—
744C42—44no—
745C42—124no—
746C42—124no—
747C22×C3C4×#4111yescharacteristic
748C22×C3C4×#4111yescharacteristic
749C22×C3C4×#4111yescharacteristic
750C22×C3#51811yescharacteristic
751C22×C3#51811yescharacteristic
752C22×C3#51811yescharacteristic
753C22×C3#51811yescharacteristic
754C22×C3#53811yescharacteristic
755C22×C3#53811yescharacteristic
756C22×C3#53811yescharacteristic
757C22×C3#53811yescharacteristic
758C22×C3#53811yescharacteristic
759C22×C3#53811yescharacteristic
760C22×C3#54011yescharacteristic
761C22×C3#54011yescharacteristic
762C22×C3#54011yescharacteristic
763C22×C3#54011yescharacteristic
764C22×C3#54011yescharacteristic
765C22×C3#54011yescharacteristic
766C22×C3#55111yescharacteristic
767C22×C3#55111yescharacteristic
768C22×C3#55111yescharacteristic
769C22×C3#55111yescharacteristic
770C22×C3#55311yescharacteristic
771C22×C3#55311yescharacteristic
772C22×C3#55311yescharacteristic
773C22×C3#55311yescharacteristic
774C22×C3#55511yescharacteristic
775C22×C3#55511yescharacteristic
776C22×C3#55911yescharacteristic
777C22×C3#55911yescharacteristic
778C22×C3#56011yescharacteristic
779C22×C3#56011yescharacteristic
780C22×C3#56011yescharacteristic
781C22×C3H(3,𝔽4)11yescharacteristic
782C2×D3—42no—
783C2×D3—42no—
784C2×D3—42no—
785C2×D3—42no—
786C2×D3—42no—
787C2×D3—42no—
788C2×D3—42no—
789C2×D3—42no—
790C2×D3—42no—
791C2×D3—42no—
792C2×D3—42no—
793C2×D3—42no—
794C2×D3—42no—
795C2×D3—42no—
796C2×D3—81no—
797C2×D3—81no—
798C2×D3—81no—
799C2×D3—81no—
800C2×D3—81no—
801C2×D3—81no—
802C2×D3—81no—
803C2×D3—81no—
804C2×D3—81no—
805C2×D3—81no—
806C2×D3—81no—
807C2×D3—81no—
808C2×D3—81no—
809C2×D3—81no—
810C2×D3—81no—
811C2×D3—81no—
812C3×C4—42no—
813C3×C4—42no—
814C3×C4—42no—
815C3×C4—42no—
816C3×C4—42no—
817C3×C4—42no—
818C3×C4—81no—
819Dic3—42no—
820Dic3—42no—
821Dic3—42no—
822Dic3—42no—
823Dic3—42no—
824Dic3—81no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—121no—
840C23—121no—
841C23—121no—
842C23—121no—
843C23—121no—
844C23—121no—
845C23—121no—
846C23—121no—
847C23—121no—
848C23—121no—
849C23—121no—
850C23—121no—
851C23—121no—
852C23—121no—
853C23—121no—
854C23—121no—
855C23—121no—
856C23—121no—
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—
895C23C22×C4×D311yescharacteristic
896C23C2×#23511yescharacteristic
897C23C2×#23511yescharacteristic
898C23#100411yescharacteristic
899C23#100411yescharacteristic
900C23#100411yescharacteristic
901C23C2×#23911yescharacteristic
902C23D3×#4111yescharacteristic
903C23D3×#4111yescharacteristic
904C23D3×#4111yescharacteristic
905C23#100911yescharacteristic
906C23#100911yescharacteristic
907C23#100911yescharacteristic
908C23#100911yescharacteristic
909C23#100911yescharacteristic
910D4—1216no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
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—62no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—121no—
976C2×C4—121no—
977C2×C4—121no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4—121no—
986C2×C4—121no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C3#233311yescharacteristic
1003C2×C3#233311yescharacteristic
1004C2×C3#233311yescharacteristic
1005C2×C3#237211yescharacteristic
1006C2×C3#237411yescharacteristic
1007C2×C3#237411yescharacteristic
1008C2×C3#237511yescharacteristic
1009C2×C3#275211yescharacteristic
1010C2×C3#275211yescharacteristic
1011C2×C3#275311yescharacteristic
1012C2×C3#275311yescharacteristic
1013C2×C3#275611yescharacteristic
1014C2×C3#275611yescharacteristic
1015C2×C3#280311yescharacteristic
1016C2×C3#280311yescharacteristic
1017D3—82no—
1018D3—82no—
1019C22—122no—
1020C22—122no—
1021C22—122no—
1022C22—122no—
1023C22—122no—
1024C22—122no—
1025C22—122no—
1026C22—122no—
1027C22—122no—
1028C22—122no—
1029C22—122no—
1030C22—122no—
1031C22—122no—
1032C22—122no—
1033C22—241no—
1034C22—241no—
1035C22—241no—
1036C22—241no—
1037C22—241no—
1038C22—241no—
1039C22—241no—
1040C22—241no—
1041C22—241no—
1042C22—241no—
1043C22—241no—
1044C22—241no—
1045C22—241no—
1046C22—241no—
1047C22—241no—
1048C22—241no—
1049C22C4×#23511yescharacteristic
1050C22#549411yescharacteristic
1051C22#551411yescharacteristic
1052C22#552111yescharacteristic
1053C22#552211yescharacteristic
1054C22#552711yescharacteristic
1055C22#552711yescharacteristic
1056C22#552711yescharacteristic
1057C22#553211yescharacteristic
1058C22#553211yescharacteristic
1059C22#553511yescharacteristic
1060C22#554011yescharacteristic
1061C22#554511yescharacteristic
1062C22#554511yescharacteristic
1063C22#554511yescharacteristic
1064C22#556011yescharacteristic
1065C22#556211yescharacteristic
1066C22C4×#23911yescharacteristic
1067C22#558511yescharacteristic
1068C22#561511yescharacteristic
1069C22#562011yescharacteristic
1070C22#563711yescharacteristic
1071C22#564411yescharacteristic
1072C22#566311yescharacteristic
1073C22#566311yescharacteristic
1074C22#566411yescharacteristic
1075C22#566611yescharacteristic
1076C22#567811yescharacteristic
1077C22#568311yescharacteristic
1078C22#569511yescharacteristic
1079C22#569711yescharacteristic
1080C22#570411yescharacteristic
1081C22#570411yescharacteristic
1082C22#570911yescharacteristic
1083C22#571111yescharacteristic
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—81no—
1091C4—122no—
1092C4—122no—
1093C4—122no—
1094C4—122no—
1095C4—122no—
1096C4—241no—
1097C3#1461711yescharacteristic, complemented, Sylow
1098C2—242no—
1099C2—242no—
1100C2#7339511yescharacteristic
1101C2#7357011yescharacteristic
1102C2#7366711yescharacteristic
1103C2#7398711yescharacteristic
1104C2#7410911yescharacteristic
1105C2#7424911yescharacteristic
1106C2#7431411yescharacteristic
1107C2#7495211yescharacteristic
1108C2#7497511yescharacteristic
1109C2#7527811yescharacteristic
1110C2#7542611yescharacteristic
1111C2#7573511yescharacteristic
1112C2#7580911yescharacteristic
1113C2#7583011yescharacteristic
1114C2#7584011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1434C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1434D3
hypocenterC3#14617
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C3×#1434C2semidirect
3. #71537C2semidirect
4. #71537C2semidirect
5. #69429C2semidirect
6. #69429C2semidirect
9. #69421C2semidirect
10. #69408C2semidirect
11. #69408C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. #69406C2semidirect
15. #69401C2semidirect
52. #4672C4semidirect
67. #1434D3semidirect
1097. C3#14617semidirect

Maximal subgroups

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

subgroupindex
C2×#46722
C3×#14342
#715372
#694292
#694262
#694212
#694082
#694062
#694012
#146173