Finite Group Databasebeta

← #10733597

Subgroups — #10733597

Order 768.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#947C211yesmaximal, characteristic
2C2×#5230C211yesmaximal, characteristic, complemented
3C2×#4675C211yesmaximal, characteristic, complemented
4C2×#4665C211yesmaximal, characteristic
5C2×#4667C211yesmaximal, characteristic, complemented
6C2×#4672C211yesmaximal, characteristic
7C3×#1446C211yesmaximal, characteristic, complemented
8#69429C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69406C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#15311—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C2×#947—24no—
21C2×#947—24no—
22C2×#947—24no—
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×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45#5230—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#4675—24no—
57#4672—24no—
58#4667—24no—
59#4665—24no—
60C22×#124—31no—
61C2×#397—31no—
62C2×#395—31no—
63C2×#394—31no—
64C2×#386—31no—
65C2×#380—31no—
66#1446D311yescharacteristic, complemented
67#1440—31no—
68#1440—31no—
69#1439—31no—
70#1439—31no—
71#1439—31no—
72#1436—31no—
73#1436—31no—
74C22⋊#95—31no—
75C24×D3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—41no—
102C22×D12—41no—
103C22×D12D414yes—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—41no—
110C22×C4×D3—41no—
111#947—232no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—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—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4D414yes—
144C2×(C2×D3)⋊C4D414yes—
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×Dic3⋊C4—22no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—41no—
155C2×Dic3⋊C4—41no—
156C2×Dic3⋊C4—41no—
157C2×C4×Dic3—22no—
158C2×C4×Dic3—22no—
159C2×C4×Dic3—22no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—41no—
165C3×#95—41no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—41no—
175C3⋊#95D414yes—
176C23×Q8C2×D311yescharacteristic
177C23×D4—31no—
178C24×C4—31no—
179C2×#124—64no—
180C2×#124—64no—
181C2×#124—64no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C42—31no—
198#397—64no—
199#395—64no—
200#394—64no—
201#386—64no—
202#380—64no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C24×C3C2411yescharacteristic
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×D3—21no—
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×D3C2×D412yes—
247C23×D3C2×D412yes—
248C23×D3C2×D412yes—
249C23×D3C2×D412yes—
250C2×C3×Q8—28no—
251C2×C3×Q8—44no—
252C2×C3×Q8—44no—
253C2×C3×Q8—44no—
254C2×C3×Q8—44no—
255C2×C3×Q8—44no—
256C2×C3×Q8—44no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×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×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D412yes—
304C22×C3×C4#4112yes—
305C22×C3×C4#4112yes—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3#4112yes—
346C22×Dic3#4112yes—
347C22×Dic3#4112yes—
348C2×D12—28no—
349C2×D12—28no—
350C2×D12—44no—
351C2×D12—44no—
352C2×D12—44no—
353C2×D12—44no—
354C2×D12—44no—
355C2×C4×D3—28no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362(C2×D3)⋊C4—28no—
363(C2×D3)⋊C4—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—44no—
367(C2×D3)⋊C4—44no—
368(C2×D3)⋊C4—44no—
369(C2×D3)⋊C4—44no—
370(C2×D3)⋊C4—44no—
371(C2×D3)⋊C4—44no—
372(C2×D3)⋊C4—44no—
373Dic3⋊C4—44no—
374Dic3⋊C4—44no—
375Dic3⋊C4—44no—
376Dic3⋊C4—44no—
377C4×Dic3—28no—
378C25—31no—
379C25—31no—
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—22no—
384C22×Q8—22no—
385C22×Q8—41no—
386C22×Q8—41no—
387C22×D4—34no—
388C22×D4—62no—
389C22×D4—62no—
390C22×D4—62no—
391C22×D4—62no—
392C22×D4—121no—
393C22×D4—121no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—62no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—121no—
406C23×C4—121no—
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D311yescharacteristic
413C23×C4C22×D311yescharacteristic
414#124—632no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—121no—
425C2×C4⋊C4—121no—
426C2×C4⋊C4—121no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—121no—
455C2×C22⋊C4—121no—
456C2×C22⋊C4—121no—
457C2×C22⋊C4—121no—
458C2×C22⋊C4—121no—
459C2×C22⋊C4—121no—
460C2×C42—62no—
461C2×C42—62no—
462C2×C42—62no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—34no—
468#95—41no—
469#95—41no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—62no—
476#95—62no—
477#95—62no—
478#95—121no—
479C23×C3C22×D411yescharacteristic
480C23×C3C22×D411yescharacteristic
481C23×C3C22×D411yescharacteristic
482C23×C3C22×D411yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3C2×#4111yescharacteristic
486C23×C3C2×#4111yescharacteristic
487C23×C3C2×#4111yescharacteristic
488C23×C3H(5,𝔽2)11yescharacteristic
489C23×C3H(5,𝔽2)11yescharacteristic
490C23×C3H(5,𝔽2)11yescharacteristic
491C23×C32−1+411yescharacteristic
492C23×C32−1+411yescharacteristic
493C23×C32−1+411yescharacteristic
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3#12014yes—
564C3×Q8—416no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4#12114yes—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3#12414yescomplemented
656D12—416no—
657C4×D3—416no—
658C24—32no—
659C24—32no—
660C24—32no—
661C24—32no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24C23×D311yescharacteristic
689C2×Q8—28no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×D4—68no—
697C2×D4—68no—
698C2×D4—124no—
699C2×D4—124no—
700C2×D4—124no—
701C2×D4—124no—
702C2×D4—124no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—32no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—68no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—124no—
790C22×C4—124no—
791C22×C4—124no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4#23512yes—
796C22×C4D3×D412yes—
797C22×C4D3×D412yes—
798C22×C4D3×D412yes—
799C22×C4D3×D412yes—
800C22×C4#23912yes—
801C4⋊C4—124no—
802C4⋊C4—124no—
803C4⋊C4—124no—
804C4⋊C4—124no—
805C22⋊C4—68no—
806C22⋊C4—68no—
807C22⋊C4—68no—
808C22⋊C4—68no—
809C22⋊C4—124no—
810C22⋊C4—124no—
811C22⋊C4—124no—
812C22⋊C4—124no—
813C22⋊C4—124no—
814C22⋊C4—124no—
815C22⋊C4—124no—
816C42—68no—
817C22×C3C2×#12011yescharacteristic
818C22×C3C2×#12111yescharacteristic
819C22×C3#52511yescharacteristic
820C22×C3C2×#12411yescharacteristic
821C22×C3#52911yescharacteristic
822C22×C3#53211yescharacteristic
823C22×C3#53411yescharacteristic
824C22×C3#53611yescharacteristic
825C22×C3#53611yescharacteristic
826C22×C3#53711yescharacteristic
827C22×C3#53811yescharacteristic
828C22×C3#54211yescharacteristic
829C22×C3#54211yescharacteristic
830C22×C3#54211yescharacteristic
831C22×C3#54211yescharacteristic
832C22×C3D4211yescharacteristic
833C22×C3D4211yescharacteristic
834C22×C3#54611yescharacteristic
835C22×C3#54611yescharacteristic
836C22×C3#54611yescharacteristic
837C22×C3#54611yescharacteristic
838C22×C3#54611yescharacteristic
839C22×C3#54711yescharacteristic
840C22×C3#54711yescharacteristic
841C22×C3#54711yescharacteristic
842C22×C3#54711yescharacteristic
843C22×C3#54711yescharacteristic
844C22×C3#54711yescharacteristic
845C22×C3#54811yescharacteristic
846C22×C3#55111yescharacteristic
847C22×C3#55511yescharacteristic
848C22×C3#55611yescharacteristic
849C22×C3#55611yescharacteristic
850C22×C3#56211yescharacteristic
851C22×C3#56311yescharacteristic
852C2×D3—24no—
853C2×D3—24no—
854C2×D3—24no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—42no—
866C2×D3—42no—
867C2×D3—42no—
868C2×D3—42no—
869C2×D3—42no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—81no—
875C2×D3—81no—
876C2×D3—81no—
877C2×D3—81no—
878C2×D3—81no—
879C2×D3—81no—
880C2×D3—81no—
881C2×D3—81no—
882C3×C4—24no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—81no—
887C3×C4—81no—
888C3×C4—81no—
889Dic3—24no—
890Dic3—42no—
891Dic3—42no—
892Dic3—42no—
893Dic3—42no—
894Dic3—81no—
895C23—34no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23C2×#23511yescharacteristic
966C23C2×D3×D411yescharacteristic
967C23C2×D3×D411yescharacteristic
968C23C2×D3×D411yescharacteristic
969C23C2×D3×D411yescharacteristic
970C23#100411yescharacteristic
971C23#100411yescharacteristic
972C23C2×#23911yescharacteristic
973C23#100711yescharacteristic
974C23#100711yescharacteristic
975C23#100711yescharacteristic
976C23D3×#4111yescharacteristic
977C23D3×#4111yescharacteristic
978C23D3×#4111yescharacteristic
979C23#100911yescharacteristic
980Q8—416no—
981D4—1216no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—34no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—1216no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4#88414yes—
1074C2×C3#240611yescharacteristic
1075C2×C3#241011yescharacteristic
1076C2×C3#242711yescharacteristic
1077C2×C3#243011yescharacteristic
1078C2×C3#247211yescharacteristic
1079C2×C3#247411yescharacteristic
1080C2×C3#249111yescharacteristic
1081C2×C3#252111yescharacteristic
1082C2×C3#254711yescharacteristic
1083C2×C3#267211yescharacteristic
1084C2×C3#267411yescharacteristic
1085C2×C3#268611yescharacteristic
1086C2×C3#270011yescharacteristic
1087C2×C3#271511yescharacteristic
1088C2×C3#271711yescharacteristic
1089D3—44no—
1090D3—82no—
1091C22—64no—
1092C22—64no—
1093C22—64no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22—122no—
1102C22—122no—
1103C22—122no—
1104C22—122no—
1105C22—122no—
1106C22—122no—
1107C22—122no—
1108C22—122no—
1109C22—122no—
1110C22—122no—
1111C22—122no—
1112C22—122no—
1113C22—241no—
1114C22—241no—
1115C22—241no—
1116C22—241no—
1117C22—241no—
1118C22—241no—
1119C22—241no—
1120C22—241no—
1121C22C2×#88411yescharacteristic
1122C22#549011yescharacteristic
1123C22#549011yescharacteristic
1124C22#556811yescharacteristic
1125C22#556811yescharacteristic
1126C22#558011yescharacteristic
1127C22#558211yescharacteristic
1128C22D3×#12011yescharacteristic
1129C22#558911yescharacteristic
1130C22#559011yescharacteristic
1131C22#559011yescharacteristic
1132C22#562711yescharacteristic
1133C22#562911yescharacteristic
1134C22#563011yescharacteristic
1135C22#563111yescharacteristic
1136C22#563111yescharacteristic
1137C22#563111yescharacteristic
1138C22#563111yescharacteristic
1139C22#563311yescharacteristic
1140C22#563711yescharacteristic
1141C22#564011yescharacteristic
1142C22#564011yescharacteristic
1143C22#564711yescharacteristic
1144C22#566811yescharacteristic
1145C22#567011yescharacteristic
1146C22D3×#12411yescharacteristic
1147C22#567611yescharacteristic
1148C22#567611yescharacteristic
1149C22#567811yescharacteristic
1150C22#572411yescharacteristic
1151C22#572411yescharacteristic
1152C22#572611yescharacteristic
1153C22#572611yescharacteristic
1154C22#573311yescharacteristic
1155C22#573511yescharacteristic
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—64no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—122no—
1165C4—122no—
1166C4—122no—
1167C4—122no—
1168C4—241no—
1169C3#1531111yescharacteristic, complemented, Sylow
1170C2—124no—
1171C2—242no—
1172C2#7385411yescharacteristic
1173C2#7651511yescharacteristic
1174C2#7653611yescharacteristic
1175C2#7662411yescharacteristic
1176C2#7663511yescharacteristic
1177C2#7664911yescharacteristic
1178C2#7665311yescharacteristic
1179C2#7679011yescharacteristic
1180C2#7679211yescharacteristic
1181C2#7686411yescharacteristic
1182C2#7687711yescharacteristic
1183C2#7724911yescharacteristic
1184C2#7725911yescharacteristic
1185C2#7726011yescharacteristic
1186C2#7726811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1446C2
prime radicalC23×D12C22
hypercenter#1446D3
hypocenterC3#15311
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. C2×#5230C2semidirect
3. C2×#4675C2semidirect
5. C2×#4667C2semidirect
7. C3×#1446C2semidirect
8. #69429C2semidirect
9. #69429C2semidirect
10. #69428C2semidirect
11. #69428C2semidirect
12. #69428C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69406C2semidirect
15. #69405C2semidirect
66. #1446D3semidirect
655. C2×Dic3#124semidirect
1169. C3#15311semidirect

Maximal subgroups

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

subgroupindex
C22×#9472
C2×#52302
C2×#46752
C2×#46652
C2×#46672
C2×#46722
C3×#14462
#694292
#694282
(C2×D3)⋊#952
#694062
#694052
#153113