Finite Group Databasebeta

← C2×#75131 #10966593

Subgroups — C2×#75131 #10966593

Order 768.

2398 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#387C211yesmaximal, characteristic, complemented
2C2×#4993C211yesmaximal, characteristic
3C2×#4993C211yesmaximal, characteristic
4C2×#4973C211yesmaximal, characteristic, complemented
5C2×#4978C211yesmaximal, characteristic, complemented
6C2×#4933C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
8#75131C2116yesmaximal, direct product factor
9C2×#4673C211yesmaximal, characteristic
10C2×#4673C211yesmaximal, characteristic
11C2×#4664C211yesmaximal, characteristic
12C2×#4646C211yesmaximal, characteristic, complemented
13C2×#4646C211yesmaximal, characteristic, complemented
14C2×#4646C211yesmaximal, characteristic, complemented
15C2×#4652C211yesmaximal, characteristic, complemented
16C2×#4666C211yesmaximal, characteristic
17C2×#2607—31nomaximal, Sylow
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C22×C4×Dic3C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C3×#387C2218yescomplemented
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54#4993C2218yes—
55#4993C2218yes—
56#4978C2218yescomplemented
57#4973C2218yescomplemented
58C4×(C2×D3)⋊C4C2218yes—
59#4933C2218yescomplemented
60#4673C2218yes—
61#4673C2218yes—
62#4666C2218yes—
63#4664C2218yes—
64#4652C2218yescomplemented
65#4646C2218yescomplemented
66#4646C2218yescomplemented
67#4646C2218yescomplemented
68#2607—316no—
69C2×#399—31no—
70C2×#399—31no—
71C2×#393—31no—
72C2×#393—31no—
73C2×#391—31no—
74C2×#391—31no—
75C2×#391—31no—
76C2×#391—31no—
77C2×#387—31no—
78C2×#387—31no—
79C2×#387—31no—
80C2×#387D311yescharacteristic, complemented
81C2×#381—31no—
82C2×C4×C22⋊C4—31no—
83C2×C4×C22⋊C4—31no—
84C24×D3C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C22×C4×D3—42no—
100C22×C4×D3—42no—
101C22×C4×D3Q818yescomplemented
102C22×C4×D3C2314yes—
103C22×Dic6—24no—
104C22×Dic6—24no—
105C22×Dic6—24no—
106C22×Dic6—24no—
107C22×Dic6—42no—
108C22×Dic6—42no—
109C22×Dic6C2314yes—
110C22×Dic6C2314yes—
111C2×C3×C4⋊C4—24no—
112C2×C3×C4⋊C4—42no—
113C2×C3×C4⋊C4C2314yes—
114C2×C3×C4⋊C4C2314yes—
115C2×C3×C42—42no—
116C2×C3×C42C2314yes—
117C2×(C2×D3)⋊C4—24no—
118C2×(C2×D3)⋊C4—24no—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—42no—
122C2×(C2×D3)⋊C4—42no—
123C2×(C2×D3)⋊C4C2314yes—
124C2×(C2×D3)⋊C4C2314yes—
125C2×(C2×D3)⋊C4C2314yes—
126C2×(C2×D3)⋊C4C2314yes—
127C2×(C2×D3)⋊C4C2314yes—
128C2×(C2×D3)⋊C4C2314yes—
129C2×Dic3⋊C4—24no—
130C2×Dic3⋊C4—24no—
131C2×Dic3⋊C4—24no—
132C2×Dic3⋊C4—42no—
133C2×Dic3⋊C4C2314yes—
134C2×Dic3⋊C4C2314yes—
135C2×Dic3⋊C4C2314yes—
136C2×Dic3⋊C4C2314yes—
137C2×C4×Dic3—42no—
138C2×C4×Dic3—42no—
139C2×C4×Dic3—42no—
140C2×C4×Dic3C2314yes—
141C2×C4×Dic3C2314yes—
142C2×C4×Dic3C2314yes—
143C3×#95C2314yes—
144C3×#95C2314yes—
145C3×#95C2314yes—
146C3×#95C2314yes—
147C3⋊#95C2314yes—
148C3⋊#95C2314yes—
149C3⋊#95C2314yes—
150C3⋊#95C2314yes—
151C3⋊#95C2314yes—
152C3⋊#95C2314yes—
153C3⋊#95C2314yes—
154C3⋊#95C2314yes—
155C3⋊#95C2314yes—
156C3⋊#95C2314yes—
157C3⋊#95C2314yes—
158C3⋊#95C2314yes—
159C23×Q8—31no—
160C23×Q8—31no—
161C24×C4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4C2×D311yescharacteristic
167C22×C4⋊C4C2×D311yescharacteristic
168C22×C22⋊C4—31no—
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C42—31no—
175C22×C42—31no—
176C22×C42—31no—
177C22×C42C2×D311yescharacteristic
178#399—38no—
179#399—38no—
180#393—38no—
181#393—38no—
182#391—38no—
183#391—38no—
184#391—38no—
185#391—38no—
186#387—38no—
187#387—38no—
188#387—38no—
189#387C2×D318yescomplemented
190#381—38no—
191C4×C22⋊C4—38no—
192C4×C22⋊C4—38no—
193C2×#95—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95C2×D311yescharacteristic
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C24×C3C2411yescharacteristic
210C23×D3—22no—
211C23×D3—22no—
212C23×D3—22no—
213C23×D3—22no—
214C23×D3—22no—
215C23×D3—22no—
216C23×D3C2×Q814yes—
217C23×D3C2412yes—
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×C4—22no—
237C22×C3×C4C2×Q814yes—
238C22×C3×C4#4114yes—
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×Dic3—22no—
263C22×Dic3C2×Q814yes—
264C22×Dic3#4114yes—
265C22×Dic3#4114yes—
266C22×Dic3#4114yes—
267C22×Dic3C2412yes—
268C22×Dic3C2412yes—
269C22×Dic3C2412yes—
270C22×Dic3C2412yes—
271C22×Dic3C2412yes—
272C22×Dic3C2412yes—
273C22×Dic3C2412yes—
274C2×C4×D3—416no—
275C2×C4×D3—44no—
276C2×C4×D3—44no—
277C2×C4×D3C2×Q8116yescomplemented
278C2×Dic6—28no—
279C2×Dic6—28no—
280C2×Dic6—28no—
281C2×Dic6—28no—
282C2×Dic6—44no—
283C2×Dic6—44no—
284C2×Dic6—416no—
285C2×Dic6—416no—
286C3×C4⋊C4—28no—
287C3×C4⋊C4—44no—
288C3×C42—44no—
289(C2×D3)⋊C4—28no—
290(C2×D3)⋊C4—28no—
291(C2×D3)⋊C4—28no—
292(C2×D3)⋊C4—28no—
293(C2×D3)⋊C4—44no—
294(C2×D3)⋊C4—44no—
295Dic3⋊C4—28no—
296Dic3⋊C4—28no—
297Dic3⋊C4—28no—
298Dic3⋊C4—44no—
299C4×Dic3—44no—
300C4×Dic3—44no—
301C4×Dic3—44no—
302C25—31no—
303C22×Q8—34no—
304C22×Q8—34no—
305C22×Q8—64no—
306C22×Q8—64no—
307C22×Q8—64no—
308C22×Q8—64no—
309C22×Q8—122no—
310C22×Q8—122no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—38no—
316C23×C4—34no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—122no—
321C23×C4—122no—
322C23×C4C22×D311yescharacteristic
323C23×C4C22×D311yescharacteristic
324C23×C4C22×D311yescharacteristic
325C23×C4C22×D311yescharacteristic
326C23×C4C22×D311yescharacteristic
327C23×C4C22×D311yescharacteristic
328C23×C4C22×D311yescharacteristic
329C2×C4⋊C4—24no—
330C2×C4⋊C4—34no—
331C2×C4⋊C4—34no—
332C2×C4⋊C4—34no—
333C2×C4⋊C4—34no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—64no—
336C2×C4⋊C4—64no—
337C2×C4⋊C4—64no—
338C2×C4⋊C4—122no—
339C2×C4⋊C4C22×D314yes—
340C2×C4⋊C4C22×D314yes—
341C2×C22⋊C4—34no—
342C2×C22⋊C4—34no—
343C2×C22⋊C4—34no—
344C2×C22⋊C4—34no—
345C2×C22⋊C4—34no—
346C2×C22⋊C4—34no—
347C2×C22⋊C4—64no—
348C2×C22⋊C4—64no—
349C2×C22⋊C4—64no—
350C2×C22⋊C4—64no—
351C2×C22⋊C4—122no—
352C2×C22⋊C4—122no—
353C2×C42—34no—
354C2×C42—34no—
355C2×C42—34no—
356C2×C42—42no—
357C2×C42—122no—
358C2×C42—122no—
359C2×C42—122no—
360C2×C42C22×D314yes—
361#95—34no—
362#95—34no—
363#95—34no—
364#95—34no—
365#95—34no—
366#95—34no—
367#95—34no—
368#95—34no—
369#95—34no—
370#95—34no—
371#95—34no—
372#95—34no—
373#95C22×D314yes—
374#95C22×D314yes—
375#95C22×D314yes—
376#95C22×D314yes—
377C23×C3C22×Q812yes—
378C23×C3C2×#4112yes—
379C23×C3C2×#4112yes—
380C23×C3C2×#4112yes—
381C23×C3C2×#4112yes—
382C23×C3H(5,𝔽2)12yes—
383C23×C3H(5,𝔽2)12yes—
384C23×C3C2511yescharacteristic
385C22×D3—28no—
386C22×D3—28no—
387C22×D3—28no—
388C22×D3—22no—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—44no—
395C22×D3—44no—
396C22×D3—44no—
397C22×D3—44no—
398C22×D3C22×Q814yes—
399C2×C3×C4—28no—
400C2×C3×C4—28no—
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—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—44no—
421C2×C3×C4—44no—
422C2×C3×C4—44no—
423C2×C3×C4—44no—
424C2×C3×C4—44no—
425C2×C3×C4C22×Q814yes—
426C2×C3×C4C2×#4114yes—
427C2×Dic3—28no—
428C2×Dic3—28no—
429C2×Dic3—28no—
430C2×Dic3—28no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
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—44no—
449C2×Dic3—44no—
450C2×Dic3—44no—
451C2×Dic3C22×Q814yes—
452C2×Dic3C2×#4114yes—
453C2×Dic3C2×#4114yes—
454C2×Dic3C2×#4114yes—
455C4×D3—416no—
456Dic6—416no—
457Dic6—416no—
458C24—34no—
459C24—32no—
460C24—62no—
461C24—62no—
462C24—62no—
463C24—62no—
464C24—62no—
465C24—62no—
466C24C23×D311yescharacteristic
467C2×Q8—68no—
468C2×Q8—68no—
469C2×Q8—68no—
470C2×Q8—68no—
471C2×Q8—124no—
472C2×Q8—124no—
473C2×Q8—1216no—
474C2×Q8—1216no—
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—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—34no—
495C22×C4—34no—
496C22×C4—34no—
497C22×C4—34no—
498C22×C4—32no—
499C22×C4—32no—
500C22×C4—32no—
501C22×C4—32no—
502C22×C4—316no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—32no—
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×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—1216no—
524C22×C4—124no—
525C22×C4—124no—
526C22×C4#23514yes—
527C22×C4D3×Q814yes—
528C22×C4C23×D312yes—
529C22×C4C23×D312yes—
530C22×C4C23×D312yes—
531C22×C4C23×D312yes—
532C22×C4C23×D312yes—
533C22×C4C23×D312yes—
534C22×C4C23×D312yes—
535C4⋊C4—28no—
536C4⋊C4—44no—
537C4⋊C4—68no—
538C4⋊C4—68no—
539C4⋊C4—68no—
540C4⋊C4—124no—
541C22⋊C4—68no—
542C22⋊C4—68no—
543C22⋊C4—68no—
544C22⋊C4—68no—
545C22⋊C4—124no—
546C22⋊C4—124no—
547C42—44no—
548C42—124no—
549C42—124no—
550C42—124no—
551C22×C3#53314yes—
552C22×C3#53314yes—
553C22×C3#54314yes—
554C22×C3#55114yes—
555C22×C3#55114yes—
556C22×C3#55914yes—
557C22×C3#55914yes—
558C22×C3C23×Q811yescharacteristic
559C22×C3C22×#4111yescharacteristic
560C22×C3C22×#4111yescharacteristic
561C22×C3C22×#4111yescharacteristic
562C22×C3C22×#4111yescharacteristic
563C22×C3C2×H(5,𝔽2)11yescharacteristic
564C22×C3C2×H(5,𝔽2)11yescharacteristic
565C2×D3—24no—
566C2×D3—24no—
567C2×D3—24no—
568C2×D3—416no—
569C2×D3—42no—
570C2×D3—42no—
571C2×D3—42no—
572C2×D3—42no—
573C3×C4—24no—
574C3×C4—24no—
575C3×C4—42no—
576C3×C4—42no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—42no—
580Dic3—24no—
581Dic3—24no—
582Dic3—24no—
583Dic3—24no—
584Dic3—42no—
585Dic3—42no—
586Dic3—42no—
587C23—34no—
588C23—68no—
589C23—68no—
590C23—62no—
591C23—62no—
592C23—62no—
593C23—62no—
594C23—62no—
595C23—62no—
596C23—68no—
597C23—124no—
598C23—124no—
599C23—124no—
600C23—124no—
601C23C2×#23512yes—
602C23#100412yes—
603C23C2×D3×Q812yes—
604C23D3×#4112yes—
605C23D3×#4112yes—
606C23D3×#4112yes—
607C23#100912yes—
608C23C24×D311yescharacteristic
609Q8—1216no—
610Q8—1216no—
611C2×C4—28no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—28no—
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—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—34no—
633C2×C4—34no—
634C2×C4—34no—
635C2×C4—34no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—68no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—68no—
645C2×C4—68no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—68no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—1216no—
663C2×C4—124no—
664C2×C4—124no—
665C2×C4—124no—
666C2×C4C2×#23514yes—
667C2×C4C2×D3×Q814yes—
668C2×C3#260718yescomplemented
669C2×C3C2×#53311yescharacteristic
670C2×C3C2×#53311yescharacteristic
671C2×C3C2×#54311yescharacteristic
672C2×C3C2×#55111yescharacteristic
673C2×C3C2×#55111yescharacteristic
674C2×C3C2×#55911yescharacteristic
675C2×C3C2×#55911yescharacteristic
676D3—44no—
677C22—64no—
678C22—64no—
679C22—64no—
680C22—122no—
681C22—122no—
682C22—1216no—
683C22—122no—
684C22—122no—
685C22#552714yes—
686C22#555914yes—
687C22#557814yes—
688C22#563414yes—
689C22#566414yes—
690C22#568814yes—
691C22#570514yes—
692C22C22×#23511yescharacteristic
693C22C2×#100411yescharacteristic
694C22C22×D3×Q811yescharacteristic
695C22C2×D3×#4111yescharacteristic
696C22C2×D3×#4111yescharacteristic
697C22C2×D3×#4111yescharacteristic
698C22C2×#100911yescharacteristic
699C4—24no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—64no—
707C4—64no—
708C4—64no—
709C4—64no—
710C4—122no—
711C4—122no—
712C4—122no—
713C3C2×#260711yescharacteristic, complemented, Sylow
714C2—124no—
715C2#7513118yesdirect product factor
716C2C2×#552711yescharacteristic
717C2C2×#555911yescharacteristic
718C2C2×#557811yescharacteristic
719C2C2×#563411yescharacteristic
720C2C2×#566411yescharacteristic
721C2C2×#568811yescharacteristic
722C2C2×#570511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#387C2
socleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×#387D3
hypocenterC3C2×#2607
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C2×C3×#387C2semidirect
4. C2×#4973C2semidirect
5. C2×#4978C2semidirect
6. C2×#4933C2semidirect
8. #75131C2direct (N × H)
12. C2×#4646C2semidirect
13. C2×#4646C2semidirect
14. C2×#4646C2semidirect
15. C2×#4652C2semidirect
37. C3×#387C22semidirect
56. #4978C22semidirect
57. #4973C22semidirect
59. #4933C22semidirect
64. #4652C22semidirect
65. #4646C22semidirect
66. #4646C22semidirect
67. #4646C22semidirect
80. C2×#387D3semidirect
101. C22×C4×D3Q8semidirect
189. #387C2×D3semidirect
277. C2×C4×D3C2×Q8semidirect
668. C2×C3#2607semidirect
713. C3C2×#2607semidirect
715. C2#75131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3872
C2×#49932
C2×#49732
C2×#49782
C2×#49332
C2×C4×(C2×D3)⋊C42
#751312
C2×#46732
C2×#46642
C2×#46462
C2×#46522
C2×#46662
C2×#26073