Finite Group Databasebeta

← C2×#77787 #10967004

Subgroups — C2×#77787 #10967004

Order 768.

2446 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#889C211yesmaximal, characteristic
2C22×#889C211yesmaximal, characteristic
3C2×C3×#398C211yesmaximal, characteristic
4C2×#4982C211yesmaximal, characteristic
5C2×#4976C211yesmaximal, characteristic
6C2×#4976C211yesmaximal, characteristic
7C2×#4975C211yesmaximal, characteristic
8C2×#4975C211yesmaximal, characteristic
9C2×#4975C211yesmaximal, characteristic
10#77787C2116yesmaximal, direct product factor
11C2×#4661C211yesmaximal, characteristic
12C2×#4657C211yesmaximal, characteristic
13C2×#4647C211yesmaximal, characteristic
14C2×#4647C211yesmaximal, characteristic
15C2×#4649C211yesmaximal, characteristic
16C2×#4649C211yesmaximal, characteristic
17C2×#2552—31nomaximal, Sylow
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C22×C4⋊Dic3C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×Dic3⋊C4C2211yescharacteristic
27C22×Dic3⋊C4C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44C22×C4×Dic3C2211yescharacteristic
45C2×#889—28no—
46C2×#889—28no—
47C2×#889C2218yes—
48C2×#889C2218yes—
49C3×#398C2218yes—
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#4982C2218yes—
59#4976C2218yes—
60#4976C2218yes—
61#4975C2218yes—
62#4975C2218yes—
63#4975C2218yes—
64#4661C2218yes—
65#4657C2218yes—
66#4649C2218yes—
67#4649C2218yes—
68#4647C2218yes—
69#4647C2218yes—
70C22×#125—31no—
71C22×#125—31no—
72#2552—316no—
73C2×#398—31no—
74C2×#398—31no—
75C2×#398—31no—
76C2×#398D311yescharacteristic
77C2×#389—31no—
78C2×#389—31no—
79C2×#389—31no—
80C2×#389—31no—
81C2×#384—31no—
82C2×#384—31no—
83C2×#384—31no—
84C2×C4×C4⋊C4—31no—
85C2×C4×C4⋊C4—31no—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
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—42no—
104C2×C3×C4⋊C4—42no—
105C2×C3×C4⋊C4C2314yes—
106C2×C3×C4⋊C4C2314yes—
107C2×C3×C4⋊C4C2314yes—
108C2×C3×C4⋊C4C2314yes—
109C2×C4⋊Dic3—24no—
110C2×C4⋊Dic3—24no—
111C2×C4⋊Dic3—42no—
112C2×C4⋊Dic3—42no—
113C2×C4⋊Dic3C2314yes—
114C2×C4⋊Dic3C2314yes—
115C2×C4⋊Dic3C2314yes—
116C2×C4⋊Dic3C2314yes—
117C2×Dic3⋊C4—24no—
118C2×Dic3⋊C4—24no—
119C2×Dic3⋊C4—24no—
120C2×Dic3⋊C4—24no—
121C2×Dic3⋊C4—24no—
122C2×Dic3⋊C4—24no—
123C2×Dic3⋊C4—24no—
124C2×Dic3⋊C4—24no—
125C2×Dic3⋊C4—24no—
126C2×Dic3⋊C4—24no—
127C2×Dic3⋊C4—42no—
128C2×Dic3⋊C4—42no—
129C2×Dic3⋊C4D418yes—
130C2×Dic3⋊C4Q818yes—
131C2×Dic3⋊C4C2314yes—
132C2×Dic3⋊C4C2314yes—
133C2×Dic3⋊C4C2314yes—
134C2×Dic3⋊C4C2314yes—
135C2×Dic3⋊C4C2314yes—
136C2×Dic3⋊C4C2314yes—
137C2×Dic3⋊C4C2314yes—
138C2×Dic3⋊C4C2314yes—
139C2×Dic3⋊C4C2314yes—
140C2×Dic3⋊C4C2314yes—
141C2×Dic3⋊C4C2314yes—
142C2×Dic3⋊C4C2314yes—
143C2×Dic3⋊C4C2314yes—
144C2×Dic3⋊C4C2314yes—
145C2×C4×Dic3—24no—
146C2×C4×Dic3—24no—
147C2×C4×Dic3—24no—
148C2×C4×Dic3—24no—
149C2×C4×Dic3Q818yes—
150C2×C4×Dic3C2314yes—
151C2×C4×Dic3C2314yes—
152C2×C4×Dic3C2314yes—
153C2×C4×Dic3C2314yes—
154C2×C4×Dic3C2314yes—
155#889—232no—
156#889—232no—
157C3×#95C2314yes—
158C3×#95C2314yes—
159C3×#95C2314yes—
160C3⋊#95C2314yes—
161C3⋊#95C2314yes—
162C3⋊#95C2314yes—
163C3⋊#95C2314yes—
164C3⋊#95C2314yes—
165C2×#125—38no—
166C2×#125—38no—
167C2×#125—68no—
168C2×#125—68no—
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⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—31no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4C2×D311yescharacteristic
188C22×C4⋊C4C2×D311yescharacteristic
189C22×C4⋊C4C2×D311yescharacteristic
190C22×C4⋊C4C2×D311yescharacteristic
191C22×C42—31no—
192C22×C42—31no—
193C22×C42—31no—
194C22×C42—31no—
195C22×C42—31no—
196#398—38no—
197#398—38no—
198#398—38no—
199#398C2×D318yes—
200#389—38no—
201#389—38no—
202#389—38no—
203#389—38no—
204#384—38no—
205#384—38no—
206#384—38no—
207C4×C4⋊C4—38no—
208C4×C4⋊C4—38no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C2×#95C2×D311yescharacteristic
217C24×C3C2411yescharacteristic
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
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×C4C2×D414yes—
237C22×C3×C4C2×Q814yes—
238C22×C3×C4C2×Q814yes—
239C22×C3×C4C2412yes—
240C22×C3×C4C2412yes—
241C22×C3×C4C2412yes—
242C22×C3×C4C2412yes—
243C22×C3×C4C2412yes—
244C22×C3×C4C2412yes—
245C22×C3×C4C2412yes—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
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×Dic3C2×D414yes—
263C22×Dic3C2×D414yes—
264C22×Dic3C2×Q814yes—
265C22×Dic3C2×Q814yes—
266C22×Dic3C2×Q814yes—
267C22×Dic3C2×Q814yes—
268C22×Dic3#4114yes—
269C22×Dic3#4114yes—
270C22×Dic3C2412yes—
271C22×Dic3C2412yes—
272C22×Dic3C2412yes—
273C22×Dic3C2412yes—
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276C22×Dic3C2412yes—
277C22×Dic3C2412yes—
278C3×C4⋊C4—28no—
279C3×C4⋊C4—28no—
280C3×C4⋊C4—44no—
281C3×C4⋊C4—44no—
282C4⋊Dic3—28no—
283C4⋊Dic3—28no—
284C4⋊Dic3—44no—
285C4⋊Dic3—44no—
286Dic3⋊C4—28no—
287Dic3⋊C4—28no—
288Dic3⋊C4—28no—
289Dic3⋊C4—28no—
290Dic3⋊C4—28no—
291Dic3⋊C4—28no—
292Dic3⋊C4—28no—
293Dic3⋊C4—28no—
294Dic3⋊C4—28no—
295Dic3⋊C4—28no—
296Dic3⋊C4—44no—
297Dic3⋊C4—44no—
298Dic3⋊C4C2×D4116yes—
299Dic3⋊C4C2×Q8116yes—
300C4×Dic3—28no—
301C4×Dic3—28no—
302C4×Dic3—28no—
303C4×Dic3—28no—
304C4×Dic3C2×Q8116yes—
305C23×C4—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#125—632no—
321#125—632no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—38no—
325C2×C4⋊C4—38no—
326C2×C4⋊C4—34no—
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—34no—
337C2×C4⋊C4—34no—
338C2×C4⋊C4—34no—
339C2×C4⋊C4—34no—
340C2×C4⋊C4—34no—
341C2×C4⋊C4—34no—
342C2×C4⋊C4—34no—
343C2×C4⋊C4—34no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—64no—
347C2×C4⋊C4—64no—
348C2×C4⋊C4—64no—
349C2×C4⋊C4—64no—
350C2×C4⋊C4—64no—
351C2×C4⋊C4—64no—
352C2×C4⋊C4—64no—
353C2×C4⋊C4—64no—
354C2×C4⋊C4—64no—
355C2×C4⋊C4—64no—
356C2×C4⋊C4—64no—
357C2×C4⋊C4—64no—
358C2×C4⋊C4—122no—
359C2×C4⋊C4—122no—
360C2×C4⋊C4—122no—
361C2×C4⋊C4—122no—
362C2×C4⋊C4C22×D314yes—
363C2×C4⋊C4C22×D314yes—
364C2×C4⋊C4C22×D314yes—
365C2×C4⋊C4C22×D314yes—
366C2×C42—38no—
367C2×C42—34no—
368C2×C42—34no—
369C2×C42—34no—
370C2×C42—34no—
371C2×C42—34no—
372C2×C42—64no—
373C2×C42—64no—
374C2×C42—64no—
375C2×C42—64no—
376#95—34no—
377#95—34no—
378#95—34no—
379#95—34no—
380#95—34no—
381#95C22×D314yes—
382#95C22×D314yes—
383#95C22×D314yes—
384C23×C3C22×D412yes—
385C23×C3C22×Q812yes—
386C23×C3C22×Q812yes—
387C23×C3C2×#4112yes—
388C23×C3C2×#4112yes—
389C23×C3H(5,𝔽2)12yes—
390C23×C32−1+412yes—
391C23×C3C2511yescharacteristic
392C2×C3×C4—28no—
393C2×C3×C4—28no—
394C2×C3×C4—28no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
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—44no—
414C2×C3×C4—44no—
415C2×C3×C4—44no—
416C2×C3×C4—44no—
417C2×C3×C4C22×D414yes—
418C2×C3×C4C22×Q814yes—
419C2×C3×C4C22×Q814yes—
420C2×Dic3—28no—
421C2×Dic3—28no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—44no—
439C2×Dic3—44no—
440C2×Dic3—44no—
441C2×Dic3—44no—
442C2×Dic3#125116yescomplemented
443C2×Dic3C4⋊Q8116yes—
444C2×Dic3C22×D414yes—
445C2×Dic3C22×D414yes—
446C2×Dic3C22×Q814yes—
447C2×Dic3C22×Q814yes—
448C2×Dic3C22×Q814yes—
449C2×Dic3C22×Q814yes—
450C2×Dic3C2×#4114yes—
451C2×Dic3C2×#4114yes—
452C24C23×D311yescharacteristic
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—34no—
472C22×C4—34no—
473C22×C4—34no—
474C22×C4—34no—
475C22×C4—34no—
476C22×C4—34no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—34no—
480C22×C4—34no—
481C22×C4—32no—
482C22×C4—32no—
483C22×C4—32no—
484C22×C4—32no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4D3×D414yes—
504C22×C4D3×Q814yes—
505C22×C4D3×Q814yes—
506C22×C4C23×D312yes—
507C22×C4C23×D312yes—
508C22×C4C23×D312yes—
509C22×C4C23×D312yes—
510C22×C4C23×D312yes—
511C22×C4C23×D312yes—
512C22×C4C23×D312yes—
513C4⋊C4—28no—
514C4⋊C4—28no—
515C4⋊C4—316no—
516C4⋊C4—316no—
517C4⋊C4—44no—
518C4⋊C4—44no—
519C4⋊C4—68no—
520C4⋊C4—68no—
521C4⋊C4—68no—
522C4⋊C4—68no—
523C4⋊C4—68no—
524C4⋊C4—68no—
525C4⋊C4—68no—
526C4⋊C4—68no—
527C4⋊C4—68no—
528C4⋊C4—68no—
529C4⋊C4—68no—
530C4⋊C4—68no—
531C4⋊C4—124no—
532C4⋊C4—124no—
533C4⋊C4—124no—
534C4⋊C4—124no—
535C42—316no—
536C42—68no—
537C42—68no—
538C42—68no—
539C42—68no—
540C22×C3C2×#12514yes—
541C22×C3C2×C4⋊Q814yes—
542C22×C3#54414yes—
543C22×C3#54714yes—
544C22×C3#55014yes—
545C22×C3#55414yes—
546C22×C3#55714yes—
547C22×C3C23×D411yescharacteristic
548C22×C3C23×Q811yescharacteristic
549C22×C3C23×Q811yescharacteristic
550C22×C3C22×#4111yescharacteristic
551C22×C3C22×#4111yescharacteristic
552C22×C3C2×H(5,𝔽2)11yescharacteristic
553C22×C3C2×2−1+411yescharacteristic
554C3×C4—24no—
555C3×C4—24no—
556C3×C4—24no—
557C3×C4—42no—
558C3×C4—42no—
559C3×C4—42no—
560C3×C4—42no—
561Dic3—24no—
562Dic3—24no—
563Dic3—42no—
564Dic3—42no—
565Dic3—42no—
566Dic3—42no—
567Dic3C2×#12518yescomplemented
568Dic3C2×C4⋊Q818yes—
569C23C2×D3×D412yes—
570C23#100412yes—
571C23C2×D3×Q812yes—
572C23C2×D3×Q812yes—
573C23D3×#4112yes—
574C23D3×#4112yes—
575C23#101012yes—
576C23C24×D311yescharacteristic
577C2×C4—28no—
578C2×C4—28no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—28no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—316no—
599C2×C4—34no—
600C2×C4—34no—
601C2×C4—34no—
602C2×C4—34no—
603C2×C4—34no—
604C2×C4—34no—
605C2×C4—316no—
606C2×C4—34no—
607C2×C4—34no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—44no—
612C2×C4—68no—
613C2×C4—68no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—62no—
622C2×C4—62no—
623C2×C4—62no—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—124no—
631C2×C4—124no—
632C2×C4—124no—
633C2×C4—124no—
634C2×C4C2×D3×D414yes—
635C2×C4C2×D3×Q814yes—
636C2×C4C2×D3×Q814yes—
637C2×C3#255218yescomplemented
638C2×C3C22×#12511yescharacteristic
639C2×C3C22×C4⋊Q811yescharacteristic
640C2×C3C2×#54411yescharacteristic
641C2×C3C2×#54711yescharacteristic
642C2×C3C2×#55011yescharacteristic
643C2×C3C2×#55411yescharacteristic
644C2×C3C2×#55711yescharacteristic
645C22#559914yes—
646C22#562314yes—
647C22#563614yes—
648C22#565514yes—
649C22#568514yes—
650C22D3×#12514yes—
651C22D3×C4⋊Q814yes—
652C22C22×D3×D411yescharacteristic
653C22C2×#100411yescharacteristic
654C22C22×D3×Q811yescharacteristic
655C22C22×D3×Q811yescharacteristic
656C22C2×D3×#4111yescharacteristic
657C22C2×D3×#4111yescharacteristic
658C22C2×#101011yescharacteristic
659C4—24no—
660C4—24no—
661C4—24no—
662C4—38no—
663C4—38no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—64no—
669C4—64no—
670C4—122no—
671C4—122no—
672C4—122no—
673C4—122no—
674C3C2×#255211yescharacteristic, complemented, Sylow
675C2#7778718yesdirect product factor
676C2C2×#559911yescharacteristic
677C2C2×#562311yescharacteristic
678C2C2×#563611yescharacteristic
679C2C2×#565511yescharacteristic
680C2C2×#568511yescharacteristic
681C2C2×D3×#12511yescharacteristic
682C2C2×D3×C4⋊Q811yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#398C2
socle, prime radicalC24×C3C24
hypercenterC2×#398D3
hypocenterC3C2×#2552
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
10. #77787C2direct (N × H)
442. C2×Dic3#125semidirect
567. Dic3C2×#125semidirect
637. C2×C3#2552semidirect
674. C3C2×#2552semidirect
675. C2#77787direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8892
C2×C3×#3982
C2×#49822
C2×#49762
C2×#49752
#777872
C2×#46612
C2×#46572
C2×#46472
C2×#46492
C2×#25523