Finite Group Databasebeta

← C2×#77771 #10964271

Subgroups — C2×#77771 #10964271

Order 768.

2466 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#898C211yesmaximal, characteristic
2C22×#889C211yesmaximal, characteristic, complemented
3C2×C3×#398C211yesmaximal, characteristic, complemented
4C2×#4993C211yesmaximal, characteristic
5C2×#4994C211yesmaximal, characteristic
6C2×#4976C211yesmaximal, characteristic, complemented
7C2×#4990C211yesmaximal, characteristic
8C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
9C2×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
10#77771C2116yesmaximal, direct product factor
11C2×#4657C211yesmaximal, characteristic, complemented
12C2×#4669C211yesmaximal, characteristic
13C2×#4669C211yesmaximal, characteristic
14C2×#4669C211yesmaximal, characteristic
15C2×#4652C211yesmaximal, characteristic, complemented
16C2×#4650C211yesmaximal, characteristic, complemented
17C2×#2519—31nomaximal, Sylow
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊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×C4⋊Dic3C2211yescharacteristic
30C22×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C2×#898—28no—
44C2×#898C2218yes—
45C2×#889—28no—
46C2×#889C2218yescomplemented
47C3×#398C2218yescomplemented
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4994C2218yes—
59#4993C2218yes—
60#4990C2218yes—
61#4976C2218yescomplemented
62Dic3×C4⋊C4C2218yescomplemented
63Dic3×C4⋊C4C2218yescomplemented
64#4669C2218yes—
65#4669C2218yes—
66#4669C2218yes—
67#4657C2218yescomplemented
68#4652C2218yescomplemented
69#4650C2218yescomplemented
70C22×#126—31no—
71C22×#125—31no—
72#2519—316no—
73C2×#399—31no—
74C2×#398—31no—
75C2×#398D311yescharacteristic, complemented
76C2×#396—31no—
77C2×#389—31no—
78C2×#388—31no—
79C2×#388—31no—
80C2×#388—31no—
81C2×#388—31no—
82C2×#387—31no—
83C2×#382—31no—
84C2×C4×C4⋊C4—31no—
85C2×C4×C4⋊C4—31no—
86C24×D3C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C2×C3×C4⋊C4—24no—
102C2×C3×C4⋊C4—24no—
103C2×C3×C4⋊C4—24no—
104C2×C3×C4⋊C4—24no—
105C2×C3×C4⋊C4C2314yes—
106C2×C3×C4⋊C4C2314yes—
107C2×C3×C4⋊C4C2314yes—
108C2×C3×C4⋊C4C2314yes—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4C2314yes—
117C2×(C2×D3)⋊C4C2314yes—
118C2×(C2×D3)⋊C4C2314yes—
119C2×(C2×D3)⋊C4C2314yes—
120C2×(C2×D3)⋊C4C2314yes—
121C2×(C2×D3)⋊C4C2314yes—
122C2×(C2×D3)⋊C4C2314yes—
123C2×C4⋊Dic3—24no—
124C2×C4⋊Dic3D418yes—
125C2×C4⋊Dic3C2314yes—
126C2×C4⋊Dic3C2314yes—
127C2×Dic3⋊C4—24no—
128C2×Dic3⋊C4—24no—
129C2×Dic3⋊C4—24no—
130C2×Dic3⋊C4—24no—
131C2×Dic3⋊C4—24no—
132C2×Dic3⋊C4—24no—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4C2314yes—
135C2×Dic3⋊C4C2314yes—
136C2×Dic3⋊C4C2314yes—
137C2×Dic3⋊C4C2314yes—
138C2×Dic3⋊C4C2314yes—
139C2×Dic3⋊C4C2314yes—
140C2×Dic3⋊C4C2314yes—
141C2×C4×Dic3—24no—
142C2×C4×Dic3—24no—
143C2×C4×Dic3—24no—
144C2×C4×Dic3—24no—
145C2×C4×Dic3—24no—
146C2×C4×Dic3C2314yes—
147C2×C4×Dic3C2314yes—
148C2×C4×Dic3C2314yes—
149C2×C4×Dic3C2314yes—
150C2×C4×Dic3C2314yes—
151#898—232no—
152#889—232no—
153C3×#95C2314yes—
154C3×#95C2314yes—
155C3×#95C2314yes—
156C3⋊#95C2314yes—
157C3⋊#95C2314yes—
158C3⋊#95C2314yes—
159C3⋊#95C2314yes—
160C3⋊#95C2314yes—
161C3⋊#95C2314yes—
162C3⋊#95C2314yes—
163C2×#126—38no—
164C2×#126—68no—
165C2×#125—38no—
166C2×#125—68no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4—31no—
170C22×C4⋊C4—31no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—31no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4C2×D311yescharacteristic
177C22×C4⋊C4C2×D311yescharacteristic
178C22×C4⋊C4C2×D311yescharacteristic
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C42—31no—
188C22×C42—31no—
189C22×C42—31no—
190C22×C42—31no—
191C22×C42—31no—
192#399—38no—
193#398—38no—
194#398C2×D318yescomplemented
195#396—38no—
196#389—38no—
197#388—38no—
198#388—38no—
199#388—38no—
200#388—38no—
201#387—38no—
202#382—38no—
203C4×C4⋊C4—38no—
204C4×C4⋊C4—38no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C24×C3C2411yescharacteristic
216C23×D3—22no—
217C23×D3—22no—
218C23×D3—22no—
219C23×D3—22no—
220C23×D3—22no—
221C23×D3—22no—
222C23×D3—22no—
223C23×D3C2412yes—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4C2×D414yes—
244C22×C3×C4#4114yes—
245C22×C3×C4C2412yes—
246C22×C3×C4C2412yes—
247C22×C3×C4C2412yes—
248C22×C3×C4C2412yes—
249C22×C3×C4C2412yes—
250C22×C3×C4C2412yes—
251C22×C3×C4C2412yes—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—22no—
255C22×Dic3—22no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3C2×D414yes—
269C22×Dic3C2×D414yes—
270C22×Dic3#4114yes—
271C22×Dic3#4114yes—
272C22×Dic3#4114yes—
273C22×Dic3C2412yes—
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276C22×Dic3C2412yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C3×C4⋊C4—28no—
281C3×C4⋊C4—28no—
282C3×C4⋊C4—28no—
283C3×C4⋊C4—28no—
284(C2×D3)⋊C4—28no—
285(C2×D3)⋊C4—28no—
286(C2×D3)⋊C4—28no—
287(C2×D3)⋊C4—28no—
288(C2×D3)⋊C4—28no—
289(C2×D3)⋊C4—28no—
290(C2×D3)⋊C4—28no—
291C4⋊Dic3—28no—
292C4⋊Dic3C2×D4116yes—
293Dic3⋊C4—28no—
294Dic3⋊C4—28no—
295Dic3⋊C4—28no—
296Dic3⋊C4—28no—
297Dic3⋊C4—28no—
298Dic3⋊C4—28no—
299Dic3⋊C4—28no—
300C4×Dic3—28no—
301C4×Dic3—28no—
302C4×Dic3—28no—
303C4×Dic3—28no—
304C4×Dic3—28no—
305C25—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4C22×D311yescharacteristic
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D311yescharacteristic
319C23×C4C22×D311yescharacteristic
320#126—632no—
321#125—632no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—38no—
327C2×C4⋊C4—34no—
328C2×C4⋊C4—34no—
329C2×C4⋊C4—34no—
330C2×C4⋊C4—34no—
331C2×C4⋊C4—34no—
332C2×C4⋊C4—34no—
333C2×C4⋊C4—34no—
334C2×C4⋊C4—34no—
335C2×C4⋊C4—34no—
336C2×C4⋊C4—64no—
337C2×C4⋊C4—64no—
338C2×C4⋊C4—64no—
339C2×C4⋊C4—64no—
340C2×C4⋊C4—64no—
341C2×C4⋊C4—64no—
342C2×C4⋊C4—64no—
343C2×C4⋊C4—64no—
344C2×C4⋊C4C22×D314yes—
345C2×C4⋊C4C22×D314yes—
346C2×C4⋊C4C22×D314yes—
347C2×C4⋊C4C22×D314yes—
348C2×C22⋊C4—34no—
349C2×C22⋊C4—34no—
350C2×C22⋊C4—34no—
351C2×C22⋊C4—34no—
352C2×C22⋊C4—34no—
353C2×C22⋊C4—34no—
354C2×C22⋊C4—34no—
355C2×C22⋊C4—64no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4—64no—
358C2×C22⋊C4—64no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—64no—
362C2×C42—34no—
363C2×C42—34no—
364C2×C42—34no—
365C2×C42—34no—
366C2×C42—34no—
367C2×C42—64no—
368C2×C42—64no—
369C2×C42—64no—
370C2×C42—64no—
371C2×C42—64no—
372#95—34no—
373#95—34no—
374#95—34no—
375#95—34no—
376#95—34no—
377#95—34no—
378#95—34no—
379#95C22×D314yes—
380#95C22×D314yes—
381#95C22×D314yes—
382C23×C3C22×D412yes—
383C23×C3C2×#4112yes—
384C23×C3C2×#4112yes—
385C23×C3C2×#4112yes—
386C23×C3C2×#4112yes—
387C23×C32−1+412yes—
388C23×C32−1+412yes—
389C23×C3C2511yescharacteristic
390C22×D3—22no—
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—44no—
398C22×D3—44no—
399C22×D3—44no—
400C22×D3—44no—
401C22×D3—44no—
402C22×D3—44no—
403C22×D3—44no—
404C2×C3×C4—28no—
405C2×C3×C4—28no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—44no—
426C2×C3×C4—44no—
427C2×C3×C4—44no—
428C2×C3×C4—44no—
429C2×C3×C4—44no—
430C2×C3×C4C22×D414yes—
431C2×C3×C4C2×#4114yes—
432C2×Dic3—28no—
433C2×Dic3—28no—
434C2×Dic3—28no—
435C2×Dic3—28no—
436C2×Dic3—28no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—44no—
454C2×Dic3—44no—
455C2×Dic3C22×D414yes—
456C2×Dic3C22×D414yes—
457C2×Dic3C2×#4114yes—
458C2×Dic3C2×#4114yes—
459C2×Dic3C2×#4114yes—
460C24—32no—
461C24—62no—
462C24—62no—
463C24—62no—
464C24—62no—
465C24—62no—
466C24—62no—
467C24—62no—
468C24C23×D311yescharacteristic
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—34no—
489C22×C4—34no—
490C22×C4—34no—
491C22×C4—34no—
492C22×C4—34no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—32no—
499C22×C4—32no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4D3×D414yes—
517C22×C4#23714yes—
518C22×C4C23×D312yes—
519C22×C4C23×D312yes—
520C22×C4C23×D312yes—
521C22×C4C23×D312yes—
522C22×C4C23×D312yes—
523C22×C4C23×D312yes—
524C22×C4C23×D312yes—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—28no—
529C4⋊C4—316no—
530C4⋊C4—68no—
531C4⋊C4—68no—
532C4⋊C4—68no—
533C4⋊C4—68no—
534C4⋊C4—68no—
535C4⋊C4—68no—
536C4⋊C4—68no—
537C4⋊C4—68no—
538C22⋊C4—68no—
539C22⋊C4—68no—
540C22⋊C4—68no—
541C22⋊C4—68no—
542C22⋊C4—68no—
543C22⋊C4—68no—
544C22⋊C4—68no—
545C42—68no—
546C42—68no—
547C42—68no—
548C42—68no—
549C42—68no—
550C22×C3#52914yes—
551C22×C3#53214yes—
552C22×C3#54114yes—
553C22×C3#54714yes—
554C22×C3#54814yes—
555C22×C3#55214yes—
556C22×C3#55214yes—
557C22×C3C23×D411yescharacteristic
558C22×C3C22×#4111yescharacteristic
559C22×C3C22×#4111yescharacteristic
560C22×C3C22×#4111yescharacteristic
561C22×C3C22×#4111yescharacteristic
562C22×C3C2×2−1+411yescharacteristic
563C22×C3C2×2−1+411yescharacteristic
564C2×D3—42no—
565C2×D3—42no—
566C2×D3—42no—
567C2×D3—42no—
568C2×D3—42no—
569C2×D3—42no—
570C2×D3—42no—
571C2×D3—88no—
572C3×C4—24no—
573C3×C4—24no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—42no—
577C3×C4—42no—
578C3×C4—42no—
579Dic3—24no—
580Dic3—24no—
581Dic3—24no—
582Dic3—24no—
583Dic3—24no—
584Dic3—42no—
585Dic3—42no—
586C23—62no—
587C23—62no—
588C23—62no—
589C23—62no—
590C23—62no—
591C23—62no—
592C23—62no—
593C23—124no—
594C23—124no—
595C23—124no—
596C23—124no—
597C23—124no—
598C23—124no—
599C23—124no—
600C23C2×D3×D412yes—
601C23C2×#23712yes—
602C23#100712yes—
603C23#100712yes—
604C23D3×#4112yes—
605C23D3×#4112yes—
606C23D3×#4112yes—
607C23C24×D311yescharacteristic
608C2×C4—28no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—34no—
630C2×C4—34no—
631C2×C4—34no—
632C2×C4—34no—
633C2×C4—34no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—68no—
640C2×C4—68no—
641C2×C4—68no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—68no—
653C2×C4—68no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—124no—
661C2×C4—124no—
662C2×C4C2×D3×D414yes—
663C2×C4C2×#23714yes—
664C2×C3#251918yescomplemented
665C2×C3C2×#52911yescharacteristic
666C2×C3C2×#53211yescharacteristic
667C2×C3C2×#54111yescharacteristic
668C2×C3C2×#54711yescharacteristic
669C2×C3C2×#54811yescharacteristic
670C2×C3C2×#55211yescharacteristic
671C2×C3C2×#55211yescharacteristic
672D3—82no—
673C22—122no—
674C22—122no—
675C22—122no—
676C22—122no—
677C22—122no—
678C22—122no—
679C22—122no—
680C22—248no—
681C22#559614yes—
682C22#563114yes—
683C22#563314yes—
684C22#564914yes—
685C22#569314yes—
686C22#569314yes—
687C22#573114yes—
688C22C22×D3×D411yescharacteristic
689C22C22×#23711yescharacteristic
690C22C2×#100711yescharacteristic
691C22C2×#100711yescharacteristic
692C22C2×D3×#4111yescharacteristic
693C22C2×D3×#4111yescharacteristic
694C22C2×D3×#4111yescharacteristic
695C4—24no—
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—64no—
703C4—64no—
704C4—64no—
705C4—64no—
706C4—64no—
707C4—122no—
708C4—122no—
709C3C2×#251911yescharacteristic, complemented, Sylow
710C2—242no—
711C2#7777118yesdirect product factor
712C2C2×#559611yescharacteristic
713C2C2×#563111yescharacteristic
714C2C2×#563311yescharacteristic
715C2C2×#564911yescharacteristic
716C2C2×#569311yescharacteristic
717C2C2×#569311yescharacteristic
718C2C2×#573111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#398C2
socleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×#398D3
hypocenterC3C2×#2519
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×#889C2semidirect
3. C2×C3×#398C2semidirect
6. C2×#4976C2semidirect
8. C2×Dic3×C4⋊C4C2semidirect
9. C2×Dic3×C4⋊C4C2semidirect
10. #77771C2direct (N × H)
11. C2×#4657C2semidirect
15. C2×#4652C2semidirect
16. C2×#4650C2semidirect
46. C2×#889C22semidirect
47. C3×#398C22semidirect
61. #4976C22semidirect
62. Dic3×C4⋊C4C22semidirect
63. Dic3×C4⋊C4C22semidirect
67. #4657C22semidirect
68. #4652C22semidirect
69. #4650C22semidirect
75. C2×#398D3semidirect
194. #398C2×D3semidirect
664. C2×C3#2519semidirect
709. C3C2×#2519semidirect
711. C2#77771direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8982
C22×#8892
C2×C3×#3982
C2×#49932
C2×#49942
C2×#49762
C2×#49902
C2×Dic3×C4⋊C42
#777712
C2×#46572
C2×#46692
C2×#46522
C2×#46502
C2×#25193