Finite Group Databasebeta

← #10733667

Subgroups — #10733667

Order 768.

2442 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#895C211yesmaximal, characteristic
2C2×C3×#389C211yesmaximal, characteristic, complemented
3C2×#4994C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4991C211yesmaximal, characteristic, complemented
6C2×#4991C211yesmaximal, characteristic, complemented
7C2×#4989C211yesmaximal, characteristic, complemented
8C2×#4939C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71565C211yesmaximal, characteristic, complemented
11#71537C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69426C211yesmaximal, characteristic, complemented
15(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
16#15316—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×C4⋊Dic3C2211yescharacteristic
41C22×Dic3⋊C4C2211yescharacteristic
42C2×#895—24no—
43C2×#895—24no—
44C2×#895—24no—
45C3×#389—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
56#4994—24no—
57#4991—24no—
58#4991—24no—
59#4991—24no—
60#4989—24no—
61#4939—24no—
62C22×#121—31no—
63C2×#396—31no—
64C2×#394—31no—
65C2×#394—31no—
66C2×#394—31no—
67C2×#390—31no—
68C2×#389D311yescharacteristic, complemented
69C2×#385—31no—
70#1441—31no—
71#1439—31no—
72#1439—31no—
73#1438—31no—
74#1438—31no—
75#1437—31no—
76C22⋊#95—31no—
77C24×D3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
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—22no—
104C22×D12—22no—
105C22×D12—22no—
106C22×D12—41no—
107C22×D12—41no—
108C22×D12—41no—
109C22×D12—41no—
110C22×D12—41no—
111C22×D12—41no—
112C22×D12D414yes—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—41no—
119C22×C4×D3—41no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—41no—
130C2×C3×C4⋊C4D414yes—
131C2×C3×C4⋊C4D414yescomplemented
132C2×C3×C42—22no—
133C2×C3×C42—22no—
134C2×C3×C42—41no—
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—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—22no—
161C2×(C2×D3)⋊C4—22no—
162C2×(C2×D3)⋊C4—22no—
163C2×(C2×D3)⋊C4—22no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—41no—
166C2×(C2×D3)⋊C4—41no—
167C2×(C2×D3)⋊C4—41no—
168C2×(C2×D3)⋊C4—41no—
169C2×(C2×D3)⋊C4—41no—
170C2×(C2×D3)⋊C4—41no—
171C2×(C2×D3)⋊C4—41no—
172C2×(C2×D3)⋊C4—41no—
173C2×(C2×D3)⋊C4—41no—
174C2×(C2×D3)⋊C4—41no—
175C2×(C2×D3)⋊C4D414yes—
176C2×(C2×D3)⋊C4D414yescomplemented
177C2×C4⋊Dic3—22no—
178C2×C4⋊Dic3—22no—
179C2×C4⋊Dic3—41no—
180C2×Dic3⋊C4—22no—
181C2×Dic3⋊C4—22no—
182C2×Dic3⋊C4—41no—
183#895—232no—
184C3×#95—22no—
185C3×#95—22no—
186C3⋊#95—22no—
187C3⋊#95—22no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191C3⋊#95—22no—
192C3⋊#95—41no—
193C3⋊#95—41no—
194C23×D4—31no—
195C23×D4—31no—
196C23×D4—31no—
197C24×C4—31no—
198C2×#121—64no—
199C2×#121—64no—
200C2×#121—64no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4C2×D311yescharacteristic
204C22×C4⋊C4C2×D311yescharacteristic
205C22×C4⋊C4C2×D311yescharacteristic
206C22×C4⋊C4C2×D311yescharacteristic
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C42C2×D311yescharacteristic
222#396—64no—
223#394—64no—
224#394—64no—
225#394—64no—
226#390—64no—
227#389—24no—
228#385—64no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95C2×D311yescharacteristic
238C2×#95C2×D311yescharacteristic
239C24×C3C2411yescharacteristic
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×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3C2×D412yes—
281C23×D3C2×D412yes—
282C23×D3C2×D412yes—
283C23×D3C2×D412yes—
284C23×D3#4112yes—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2×D412yes—
325C22×C3×C4C2×D412yes—
326C22×C3×C4C2×D412yes—
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4#4112yes—
332C22×C3×C4#4112yes—
333C22×C3×C4#4112yes—
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×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3C2×D412yes—
368C22×Dic3C2×D412yes—
369C2×D12—28no—
370C2×D12—28no—
371C2×D12—28no—
372C2×D12—28no—
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×D12—44no—
383C2×D12—44no—
384C2×D12—44no—
385C2×D12—44no—
386C2×D12—44no—
387C2×D12—44no—
388C2×D12—44no—
389C2×D12—44no—
390C2×C4×D3—28no—
391C2×C4×D3—44no—
392C2×C4×D3—44no—
393C2×C4×D3—44no—
394C2×C4×D3—44no—
395C2×C4×D3—44no—
396C2×C4×D3—44no—
397C3×C4⋊C4—28no—
398C3×C4⋊C4—28no—
399C3×C4⋊C4—44no—
400C3×C4⋊C4—44no—
401C3×C42—44no—
402(C2×D3)⋊C4—28no—
403(C2×D3)⋊C4—28no—
404(C2×D3)⋊C4—28no—
405(C2×D3)⋊C4—44no—
406(C2×D3)⋊C4—44no—
407(C2×D3)⋊C4—44no—
408(C2×D3)⋊C4—44no—
409(C2×D3)⋊C4—44no—
410(C2×D3)⋊C4—44no—
411(C2×D3)⋊C4—44no—
412(C2×D3)⋊C4—44no—
413(C2×D3)⋊C4—44no—
414(C2×D3)⋊C4—44no—
415(C2×D3)⋊C4—44no—
416C4⋊Dic3—44no—
417Dic3⋊C4—44no—
418C25—31no—
419C25—31no—
420C25—31no—
421C22×D4—34no—
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—62no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—121no—
437C22×D4—121no—
438C22×D4—121no—
439C22×D4—121no—
440C22×D4—121no—
441C22×D4—121no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—31no—
447C23×C4—62no—
448C23×C4—62no—
449C23×C4—62no—
450C23×C4—62no—
451C23×C4—62no—
452C23×C4—121no—
453C23×C4—121no—
454C23×C4C22×D311yescharacteristic
455C23×C4C22×D311yescharacteristic
456C23×C4C22×D311yescharacteristic
457C23×C4C22×D311yescharacteristic
458C23×C4C22×D311yescharacteristic
459C23×C4C22×D311yescharacteristic
460C23×C4C22×D311yescharacteristic
461#121—632no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—62no—
473C2×C4⋊C4—62no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—121no—
477C2×C4⋊C4—121no—
478C2×C4⋊C4D1214yescomplemented
479C2×C4⋊C4#6714yes—
480C2×C22⋊C4—34no—
481C2×C22⋊C4—34no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—62no—
489C2×C22⋊C4—62no—
490C2×C22⋊C4—62no—
491C2×C22⋊C4—62no—
492C2×C22⋊C4—62no—
493C2×C22⋊C4—62no—
494C2×C22⋊C4—62no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—121no—
513C2×C22⋊C4—121no—
514C2×C22⋊C4—121no—
515C2×C22⋊C4—121no—
516C2×C22⋊C4—121no—
517C2×C22⋊C4—121no—
518C2×C22⋊C4—121no—
519C2×C22⋊C4—121no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4—121no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—41no—
525#95—22no—
526#95—22no—
527#95—62no—
528#95—62no—
529#95—62no—
530#95—62no—
531#95—62no—
532#95—62no—
533#95—121no—
534#95—121no—
535C23×C3C22×D411yescharacteristic
536C23×C3C22×D411yescharacteristic
537C23×C3C22×D411yescharacteristic
538C23×C3C22×D411yescharacteristic
539C23×C3C22×D411yescharacteristic
540C23×C3C2×#4111yescharacteristic
541C23×C3C2×#4111yescharacteristic
542C23×C3C2×#4111yescharacteristic
543C23×C3C2×#4111yescharacteristic
544C23×C3H(5,𝔽2)11yescharacteristic
545C23×C3H(5,𝔽2)11yescharacteristic
546C23×C3H(5,𝔽2)11yescharacteristic
547C23×C3H(5,𝔽2)11yescharacteristic
548C23×C32−1+411yescharacteristic
549C23×C32−1+411yescharacteristic
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
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—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3#12114yes—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4#12014yes—
702C2×C3×C4#12114yes—
703C2×C3×C4#12114yescomplemented
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
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—41no—
725C2×Dic3—41no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739D12—416no—
740D12—416no—
741D12—416no—
742C4×D3—416no—
743C24—32no—
744C24—32no—
745C24—32no—
746C24—32no—
747C24—32no—
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—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24—61no—
788C24C23×D311yescharacteristic
789C2×D4—68no—
790C2×D4—68no—
791C2×D4—68no—
792C2×D4—68no—
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—
803C2×D4—124no—
804C2×D4—124no—
805C2×D4—124no—
806C2×D4—124no—
807C2×D4—124no—
808C2×D4—124no—
809C2×D4—124no—
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—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—32no—
848C22×C4—32no—
849C22×C4—68no—
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×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—124no—
884C22×C4—124no—
885C22×C4—124no—
886C22×C4—124no—
887C22×C4—124no—
888C22×C4—124no—
889C22×C4C2×D1212yes—
890C22×C4C2×D1212yes—
891C22×C4C2×D1212yes—
892C22×C4#23512yes—
893C22×C4D3×D412yes—
894C22×C4D3×D412yes—
895C22×C4D3×D412yes—
896C22×C4#23912yes—
897C22×C4#23912yes—
898C22×C4C2×#6712yes—
899C22×C4C2×#6712yes—
900C22×C4C2×#6712yes—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—124no—
906C4⋊C4—124no—
907C22⋊C4—68no—
908C22⋊C4—68no—
909C22⋊C4—68no—
910C22⋊C4—124no—
911C22⋊C4—124no—
912C22⋊C4—124no—
913C22⋊C4—124no—
914C22⋊C4—124no—
915C22⋊C4—124no—
916C22⋊C4—124no—
917C22⋊C4—124no—
918C22⋊C4—124no—
919C22⋊C4—124no—
920C22⋊C4—124no—
921C42—44no—
922C22×C3C2×#12011yescharacteristic
923C22×C3C2×#12111yescharacteristic
924C22×C3C2×#12111yescharacteristic
925C22×C3C2×#12111yescharacteristic
926C22×C3#52911yescharacteristic
927C22×C3#53211yescharacteristic
928C22×C3#53411yescharacteristic
929C22×C3#53511yescharacteristic
930C22×C3#53611yescharacteristic
931C22×C3#53711yescharacteristic
932C22×C3#53711yescharacteristic
933C22×C3#53811yescharacteristic
934C22×C3#53911yescharacteristic
935C22×C3#54011yescharacteristic
936C22×C3#54211yescharacteristic
937C22×C3D4211yescharacteristic
938C22×C3D4211yescharacteristic
939C22×C3D4211yescharacteristic
940C22×C3D4211yescharacteristic
941C22×C3#54611yescharacteristic
942C22×C3#54611yescharacteristic
943C22×C3#54611yescharacteristic
944C22×C3#54611yescharacteristic
945C22×C3#54611yescharacteristic
946C22×C3#54711yescharacteristic
947C22×C3#54711yescharacteristic
948C22×C3#54711yescharacteristic
949C22×C3#54811yescharacteristic
950C22×C3#54811yescharacteristic
951C22×C3#54811yescharacteristic
952C22×C3#55011yescharacteristic
953C22×C3#55311yescharacteristic
954C22×C3#55311yescharacteristic
955C22×C3#56211yescharacteristic
956C22×C3#56211yescharacteristic
957C2×D3—24no—
958C2×D3—24no—
959C2×D3—24no—
960C2×D3—42no—
961C2×D3—42no—
962C2×D3—42no—
963C2×D3—42no—
964C2×D3—42no—
965C2×D3—42no—
966C2×D3—42no—
967C2×D3—42no—
968C2×D3—42no—
969C2×D3—42no—
970C2×D3—42no—
971C2×D3—42no—
972C2×D3—42no—
973C2×D3—42no—
974C2×D3—42no—
975C2×D3—42no—
976C2×D3—42no—
977C2×D3—42no—
978C2×D3—42no—
979C2×D3—42no—
980C2×D3—42no—
981C2×D3—42no—
982C2×D3—42no—
983C2×D3—42no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—81no—
987C2×D3—81no—
988C2×D3—81no—
989C2×D3—81no—
990C2×D3—81no—
991C2×D3—81no—
992C2×D3—81no—
993C2×D3—81no—
994C2×D3—81no—
995C2×D3—81no—
996C2×D3—81no—
997C2×D3—81no—
998C2×D3—81no—
999C2×D3—81no—
1000C2×D3—81no—
1001C2×D3—81no—
1002C3×C4—24no—
1003C3×C4—24no—
1004C3×C4—24no—
1005C3×C4—42no—
1006C3×C4—42no—
1007C3×C4—42no—
1008C3×C4—81no—
1009Dic3—42no—
1010Dic3—42no—
1011Dic3—81no—
1012Dic3—81no—
1013Dic3—81no—
1014C23—34no—
1015C23—62no—
1016C23—62no—
1017C23—62no—
1018C23—62no—
1019C23—62no—
1020C23—62no—
1021C23—62no—
1022C23—62no—
1023C23—62no—
1024C23—62no—
1025C23—62no—
1026C23—62no—
1027C23—62no—
1028C23—62no—
1029C23—62no—
1030C23—62no—
1031C23—62no—
1032C23—62no—
1033C23—62no—
1034C23—62no—
1035C23—62no—
1036C23—62no—
1037C23—62no—
1038C23—62no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
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—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23C22×D1211yescharacteristic
1120C23C2×#23511yescharacteristic
1121C23C2×D3×D411yescharacteristic
1122C23C2×D3×D411yescharacteristic
1123C23C2×D3×D411yescharacteristic
1124C23#100411yescharacteristic
1125C23C2×#23911yescharacteristic
1126C23C2×#23911yescharacteristic
1127C23#100711yescharacteristic
1128C23#100711yescharacteristic
1129C23D3×#4111yescharacteristic
1130C23#100911yescharacteristic
1131C23#100911yescharacteristic
1132C23#100911yescharacteristic
1133C23C22×#6711yescharacteristic
1134D4—1216no—
1135D4—1216no—
1136D4—1216no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—62no—
1184C2×C4—62no—
1185C2×C4—62no—
1186C2×C4—62no—
1187C2×C4—62no—
1188C2×C4—62no—
1189C2×C4—1216no—
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—121no—
1205C2×C4—121no—
1206C2×C4—121no—
1207C2×C4—121no—
1208C2×C4—121no—
1209C2×C4—121no—
1210C2×C4—121no—
1211C2×C4—121no—
1212C2×C4—121no—
1213C2×C4—121no—
1214C2×C4—121no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4#89514yescomplemented
1220C2×C4#93014yes—
1221C2×C4#93714yes—
1222C2×C3#240811yescharacteristic
1223C2×C3#241011yescharacteristic
1224C2×C3#241611yescharacteristic
1225C2×C3#241611yescharacteristic
1226C2×C3#242511yescharacteristic
1227C2×C3#242611yescharacteristic
1228C2×C3#242811yescharacteristic
1229C2×C3#243211yescharacteristic
1230C2×C3#255911yescharacteristic
1231C2×C3#267211yescharacteristic
1232C2×C3#267611yescharacteristic
1233C2×C3#268111yescharacteristic
1234C2×C3#268211yescharacteristic
1235C2×C3#270111yescharacteristic
1236C2×C3#271111yescharacteristic
1237D3—44no—
1238D3—82no—
1239D3—82no—
1240C22—64no—
1241C22—64no—
1242C22—64no—
1243C22—122no—
1244C22—122no—
1245C22—122no—
1246C22—122no—
1247C22—122no—
1248C22—122no—
1249C22—122no—
1250C22—122no—
1251C22—122no—
1252C22—122no—
1253C22—122no—
1254C22—122no—
1255C22—122no—
1256C22—122no—
1257C22—122no—
1258C22—122no—
1259C22—122no—
1260C22—122no—
1261C22—122no—
1262C22—122no—
1263C22—122no—
1264C22—122no—
1265C22—122no—
1266C22—122no—
1267C22—122no—
1268C22—122no—
1269C22—241no—
1270C22—241no—
1271C22—241no—
1272C22—241no—
1273C22—241no—
1274C22—241no—
1275C22—241no—
1276C22—241no—
1277C22—241no—
1278C22—241no—
1279C22—241no—
1280C22—241no—
1281C22—241no—
1282C22—241no—
1283C22—241no—
1284C22—241no—
1285C22C2×#89511yescharacteristic
1286C22#550711yescharacteristic
1287C22#551011yescharacteristic
1288C22#551411yescharacteristic
1289C22D4×D1211yescharacteristic
1290C22D4×D1211yescharacteristic
1291C22#555011yescharacteristic
1292C22#555011yescharacteristic
1293C22#557611yescharacteristic
1294C22#557711yescharacteristic
1295C22#558011yescharacteristic
1296C22#558211yescharacteristic
1297C22D3×#12111yescharacteristic
1298C22#560511yescharacteristic
1299C22#560911yescharacteristic
1300C22#561011yescharacteristic
1301C22#562911yescharacteristic
1302C22#563011yescharacteristic
1303C22#564411yescharacteristic
1304C22#564711yescharacteristic
1305C22#569211yescharacteristic
1306C22#569511yescharacteristic
1307C22#569711yescharacteristic
1308C22#570011yescharacteristic
1309C22#572411yescharacteristic
1310C22#572511yescharacteristic
1311C22#572611yescharacteristic
1312C22#572611yescharacteristic
1313C22C2×#93011yescharacteristic
1314C22C2×#93711yescharacteristic
1315C22D4×#6711yescharacteristic
1316C22#581711yescharacteristic
1317C22#581711yescharacteristic
1318C22#582911yescharacteristic
1319C22#583011yescharacteristic
1320C4—24no—
1321C4—24no—
1322C4—24no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—81no—
1327C4—122no—
1328C4—122no—
1329C4—241no—
1330C4—241no—
1331C4—241no—
1332C3#1531611yescharacteristic, complemented, Sylow
1333C2—124no—
1334C2—242no—
1335C2—242no—
1336C2#7607011yescharacteristic
1337C2#7621111yescharacteristic
1338C2#7621711yescharacteristic
1339C2#7622011yescharacteristic
1340C2#7625711yescharacteristic
1341C2#7625911yescharacteristic
1342C2#7626011yescharacteristic
1343C2#7626511yescharacteristic
1344C2#8219311yescharacteristic
1345C2#8240311yescharacteristic
1346C2#8249511yescharacteristic
1347C2#8270211yescharacteristic
1348C2#8282711yescharacteristic
1349C2#8307011yescharacteristic
1350C2#8325511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#389C2
prime radicalC22×#895C2
hypercenterC2×#389D3
hypocenterC3#15316
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×C3×#389C2semidirect
3. C2×#4994C2semidirect
4. C2×#4991C2semidirect
5. C2×#4991C2semidirect
6. C2×#4991C2semidirect
7. C2×#4989C2semidirect
8. C2×#4939C2semidirect
9. #71570C2semidirect
10. #71565C2semidirect
11. #71537C2semidirect
12. #69428C2semidirect
13. #69426C2semidirect
14. #69426C2semidirect
15. (C2×D3)⋊#95C2semidirect
68. C2×#389D3semidirect
131. C2×C3×C4⋊C4D4semidirect
176. C2×(C2×D3)⋊C4D4semidirect
478. C2×C4⋊C4D12semidirect
703. C2×C3×C4#121semidirect
1219. C2×C4#895semidirect
1332. C3#15316semidirect

Maximal subgroups

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

subgroupindex
C22×#8952
C2×C3×#3892
C2×#49942
C2×#49912
C2×#49892
C2×#49392
#715702
#715652
#715372
#694282
#694262
(C2×D3)⋊#952
#153163