Finite Group Databasebeta

← C2×#77977 #11430208

Subgroups — C2×#77977 #11430208

Order 768.

2526 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic
2C22×#898C211yesmaximal, characteristic
3C2×C3×#398C211yesmaximal, characteristic, complemented
4C2×#4989C211yesmaximal, characteristic
5C2×#4982C211yesmaximal, characteristic, complemented
6C2×#4979C211yesmaximal, characteristic, complemented
7C2×#4973C211yesmaximal, characteristic, complemented
8C2×#4990C211yesmaximal, characteristic
9C2×#4978C211yesmaximal, characteristic, complemented
10#77977C2116yesmaximal, direct product factor
11C2×#4675C211yesmaximal, characteristic
12C2×#4675C211yesmaximal, characteristic
13C2×#4664C211yesmaximal, characteristic
14C2×#4658C211yesmaximal, characteristic, complemented
15C2×#4647C211yesmaximal, characteristic, complemented
16C2×#4650C211yesmaximal, characteristic, complemented
17C2×#2698—31nomaximal, Sylow
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊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×C4⋊Dic3C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C2×#898—28no—
40C2×#898C2218yes—
41C2×#896—28no—
42C2×#896C2218yes—
43C3×#398C2218yescomplemented
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
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4990C2218yes—
59#4989C2218yes—
60#4982C2218yescomplemented
61#4979C2218yescomplemented
62#4978C2218yescomplemented
63#4973C2218yescomplemented
64#4675C2218yes—
65#4675C2218yes—
66#4664C2218yes—
67#4658C2218yescomplemented
68#4650C2218yescomplemented
69#4647C2218yescomplemented
70C22×#126—31no—
71C22×C22⋊Q8—31no—
72#2698—316no—
73C2×#400—31no—
74C2×#398—31no—
75C2×#398D311yescharacteristic, complemented
76C2×#397—31no—
77C2×#397—31no—
78C2×#395—31no—
79C2×#391—31no—
80C2×#389—31no—
81C2×#388—31no—
82C2×#387—31no—
83C2×#385—31no—
84C2×#382—31no—
85C2×#381—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
101C22×C4×D3—24no—
102C22×C4×D3—24no—
103C22×C4×D3—42no—
104C22×C4×D3C2314yes—
105C22×Dic6—24no—
106C22×Dic6—24no—
107C22×Dic6—42no—
108C22×Dic6C2314yes—
109C2×C3×C4⋊C4—24no—
110C2×C3×C4⋊C4—24no—
111C2×C3×C4⋊C4—42no—
112C2×C3×C4⋊C4—42no—
113C2×C3×C4⋊C4C2314yes—
114C2×C3×C4⋊C4C2314yes—
115C2×C3×C4⋊C4C2314yes—
116C2×C3×C4⋊C4C2314yes—
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)⋊C4D418yes—
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×C4⋊Dic3—24no—
130C2×C4⋊Dic3C2314yes—
131C2×Dic3⋊C4—24no—
132C2×Dic3⋊C4—24no—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—24no—
135C2×Dic3⋊C4—24no—
136C2×Dic3⋊C4—42no—
137C2×Dic3⋊C4C2314yes—
138C2×Dic3⋊C4C2314yes—
139C2×Dic3⋊C4C2314yes—
140C2×Dic3⋊C4C2314yes—
141C2×Dic3⋊C4C2314yes—
142C2×Dic3⋊C4C2314yes—
143C2×C4×Dic3—24no—
144C2×C4×Dic3—24no—
145C2×C4×Dic3C2314yes—
146C2×C4×Dic3C2314yes—
147#898—232no—
148#896—232no—
149C3×#95C2314yes—
150C3×#95C2314yes—
151C3×#95C2314yes—
152C3⋊#95C2314yes—
153C3⋊#95C2314yes—
154C3⋊#95C2314yes—
155C3⋊#95C2314yes—
156C3⋊#95C2314yes—
157C3⋊#95C2314yes—
158C3⋊#95C2314yes—
159C3⋊#95C2314yes—
160C3⋊#95C2314yes—
161C3⋊#95C2314yes—
162C3⋊#95C2314yes—
163C23×Q8—31no—
164C24×C4—31no—
165C2×#126—38no—
166C2×#126—68no—
167C2×C22⋊Q8—38no—
168C2×C22⋊Q8—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⋊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×C42—31no—
187C22×C42—31no—
188#400—38no—
189#398—38no—
190#398C2×D318yescomplemented
191#397—38no—
192#397—38no—
193#395—38no—
194#391—38no—
195#389—38no—
196#388—38no—
197#387—38no—
198#385—38no—
199#382—38no—
200#381—38no—
201C2×#95—31no—
202C2×#95—31no—
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×#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×D3C2×D414yes—
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×C4—22no—
244C22×C3×C4C2×D414yes—
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×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3C2×D414yes—
271C22×Dic3#4114yes—
272C22×Dic3#4114yes—
273C22×Dic3C2412yes—
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276C22×Dic3C2412yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C2×C4×D3—28no—
281C2×C4×D3—28no—
282C2×C4×D3—44no—
283C2×C4×D3—416no—
284C2×Dic6—28no—
285C2×Dic6—28no—
286C2×Dic6—44no—
287C2×Dic6—416no—
288C3×C4⋊C4—28no—
289C3×C4⋊C4—28no—
290C3×C4⋊C4—44no—
291C3×C4⋊C4—44no—
292(C2×D3)⋊C4—28no—
293(C2×D3)⋊C4—28no—
294(C2×D3)⋊C4—28no—
295(C2×D3)⋊C4—28no—
296(C2×D3)⋊C4—44no—
297(C2×D3)⋊C4C2×D4116yes—
298C4⋊Dic3—28no—
299Dic3⋊C4—28no—
300Dic3⋊C4—28no—
301Dic3⋊C4—28no—
302Dic3⋊C4—28no—
303Dic3⋊C4—28no—
304Dic3⋊C4—44no—
305C4×Dic3—28no—
306C4×Dic3—28no—
307C25—31no—
308C22×Q8—34no—
309C22×Q8—64no—
310C22×Q8—64no—
311C22×Q8—122no—
312C23×C4—31no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—34no—
320C23×C4—64no—
321C23×C4—64no—
322C23×C4—122no—
323C23×C4C22×D311yescharacteristic
324C23×C4C22×D311yescharacteristic
325C23×C4C22×D311yescharacteristic
326C23×C4C22×D311yescharacteristic
327C23×C4C22×D311yescharacteristic
328C23×C4C22×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330#126—632no—
331C22⋊Q8—632no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
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—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—64no—
344C2×C4⋊C4—64no—
345C2×C4⋊C4—64no—
346C2×C4⋊C4—64no—
347C2×C4⋊C4—64no—
348C2×C4⋊C4—64no—
349C2×C4⋊C4—122no—
350C2×C4⋊C4C22×D314yes—
351C2×C4⋊C4C22×D314yes—
352C2×C4⋊C4C22×D314yes—
353C2×C4⋊C4C22×D314yes—
354C2×C22⋊C4—38no—
355C2×C22⋊C4—34no—
356C2×C22⋊C4—34no—
357C2×C22⋊C4—34no—
358C2×C22⋊C4—34no—
359C2×C22⋊C4—34no—
360C2×C22⋊C4—34no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—122no—
366C2×C42—34no—
367C2×C42—34no—
368C2×C42—64no—
369C2×C42—64no—
370#95—34no—
371#95—34no—
372#95—34no—
373#95—34no—
374#95—34no—
375#95—34no—
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×C3C2×#4112yes—
386C23×C3C2×#4112yes—
387C23×C3H(5,𝔽2)12yes—
388C23×C32−1+412yes—
389C23×C32−1+412yes—
390C23×C32−1+412yes—
391C23×C3C2511yescharacteristic
392C22×D3—28no—
393C22×D3—28no—
394C22×D3—28no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—44no—
402C22×D3—44no—
403C22×D3—44no—
404C22×D3—44no—
405C22×D3C22×D414yes—
406C2×C3×C4—28no—
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—22no—
426C2×C3×C4—22no—
427C2×C3×C4—44no—
428C2×C3×C4—44no—
429C2×C3×C4—44no—
430C2×C3×C4—44no—
431C2×C3×C4—44no—
432C2×C3×C4—44no—
433C2×C3×C4C22×D414yes—
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—22no—
454C2×Dic3—22no—
455C2×Dic3—44no—
456C2×Dic3—44no—
457C2×Dic3—44no—
458C2×Dic3—44no—
459C2×Dic3C22×D414yes—
460C2×Dic3C2×#4114yes—
461C2×Dic3C2×#4114yes—
462C4×D3—416no—
463Dic6—416no—
464C24—34no—
465C24—32no—
466C24—62no—
467C24—62no—
468C24—62no—
469C24—62no—
470C24—62no—
471C24—62no—
472C24C23×D311yescharacteristic
473C2×Q8—68no—
474C2×Q8—68no—
475C2×Q8—124no—
476C2×Q8—1216no—
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—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—34no—
498C22×C4—34no—
499C22×C4—34no—
500C22×C4—32no—
501C22×C4—32no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—32no—
507C22×C4—68no—
508C22×C4—68no—
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—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—124no—
528C22×C4—1216no—
529C22×C4D3×D414yes—
530C22×C4C23×D312yes—
531C22×C4C23×D312yes—
532C22×C4C23×D312yes—
533C22×C4C23×D312yes—
534C22×C4C23×D312yes—
535C22×C4C23×D312yes—
536C22×C4C23×D312yes—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—44no—
540C4⋊C4—44no—
541C4⋊C4—68no—
542C4⋊C4—68no—
543C4⋊C4—68no—
544C4⋊C4—68no—
545C4⋊C4—68no—
546C4⋊C4—68no—
547C4⋊C4—124no—
548C22⋊C4—316no—
549C22⋊C4—68no—
550C22⋊C4—68no—
551C22⋊C4—68no—
552C22⋊C4—68no—
553C22⋊C4—124no—
554C42—68no—
555C42—68no—
556C22×C3#53614yes—
557C22×C3#54114yes—
558C22×C3#54214yes—
559C22×C3#54614yes—
560C22×C3#54714yes—
561C22×C3#55214yes—
562C22×C3#56314yes—
563C22×C3C23×D411yescharacteristic
564C22×C3C22×#4111yescharacteristic
565C22×C3C22×#4111yescharacteristic
566C22×C3C2×H(5,𝔽2)11yescharacteristic
567C22×C3C2×2−1+411yescharacteristic
568C22×C3C2×2−1+411yescharacteristic
569C22×C3C2×2−1+411yescharacteristic
570C2×D3—24no—
571C2×D3—24no—
572C2×D3—24no—
573C2×D3—42no—
574C2×D3—42no—
575C2×D3—416no—
576C2×D3—42no—
577C2×D3—42no—
578C3×C4—24no—
579C3×C4—42no—
580C3×C4—42no—
581C3×C4—42no—
582C3×C4—42no—
583C3×C4—42no—
584C3×C4—42no—
585Dic3—24no—
586Dic3—24no—
587Dic3—24no—
588Dic3—42no—
589Dic3—42no—
590Dic3—42no—
591Dic3—42no—
592C23—34no—
593C23—62no—
594C23—62no—
595C23—62no—
596C23—62no—
597C23—62no—
598C23—62no—
599C23—68no—
600C23—68no—
601C23—68no—
602C23—124no—
603C23—124no—
604C23—124no—
605C23—124no—
606C23C2×D3×D412yes—
607C23#100412yes—
608C23#100712yes—
609C23#100712yes—
610C23D3×#4112yes—
611C23D3×#4112yes—
612C23#101012yes—
613C23C24×D311yescharacteristic
614Q8—1216no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—28no—
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—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—34no—
637C2×C4—34no—
638C2×C4—34no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
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—68no—
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—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—1216no—
667C2×C4—124no—
668C2×C4—124no—
669C2×C4—124no—
670C2×C4—124no—
671C2×C4C2×D3×D414yes—
672C2×C3#269818yescomplemented
673C2×C3C2×#53611yescharacteristic
674C2×C3C2×#54111yescharacteristic
675C2×C3C2×#54211yescharacteristic
676C2×C3C2×#54611yescharacteristic
677C2×C3C2×#54711yescharacteristic
678C2×C3C2×#55211yescharacteristic
679C2×C3C2×#56311yescharacteristic
680D3—44no—
681C22—64no—
682C22—64no—
683C22—64no—
684C22—122no—
685C22—122no—
686C22—1216no—
687C22—122no—
688C22—122no—
689C22#561014yes—
690C22#562814yes—
691C22#563114yes—
692C22#566214yes—
693C22#569314yes—
694C22#569614yes—
695C22#573514yes—
696C22C22×D3×D411yescharacteristic
697C22C2×#100411yescharacteristic
698C22C2×#100711yescharacteristic
699C22C2×#100711yescharacteristic
700C22C2×D3×#4111yescharacteristic
701C22C2×D3×#4111yescharacteristic
702C22C2×#101011yescharacteristic
703C4—24no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—64no—
711C4—64no—
712C4—64no—
713C4—122no—
714C4—122no—
715C4—122no—
716C4—122no—
717C3C2×#269811yescharacteristic, complemented, Sylow
718C2—124no—
719C2#7797718yesdirect product factor
720C2C2×#561011yescharacteristic
721C2C2×#562811yescharacteristic
722C2C2×#563111yescharacteristic
723C2C2×#566211yescharacteristic
724C2C2×#569611yescharacteristic
725C2C2×#569311yescharacteristic
726C2C2×#573511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#398C2
socleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×#398D3
hypocenterC3C2×#2698
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. C2×C3×#398C2semidirect
5. C2×#4982C2semidirect
6. C2×#4979C2semidirect
7. C2×#4973C2semidirect
9. C2×#4978C2semidirect
10. #77977C2direct (N × H)
14. C2×#4658C2semidirect
15. C2×#4647C2semidirect
16. C2×#4650C2semidirect
43. C3×#398C22semidirect
60. #4982C22semidirect
61. #4979C22semidirect
62. #4978C22semidirect
63. #4973C22semidirect
67. #4658C22semidirect
68. #4650C22semidirect
69. #4647C22semidirect
75. C2×#398D3semidirect
190. #398C2×D3semidirect
672. C2×C3#2698semidirect
717. C3C2×#2698semidirect
719. C2#77977direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8962
C22×#8982
C2×C3×#3982
C2×#49892
C2×#49822
C2×#49792
C2×#49732
C2×#49902
C2×#49782
#779772
C2×#46752
C2×#46642
C2×#46582
C2×#46472
C2×#46502
C2×#26983