Finite Group Databasebeta

← C2×#79726 #11664962

Subgroups — C2×#79726 #11664962

Order 768.

1986 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5578C211yesmaximal, characteristic, complemented
2C2×#5580C211yesmaximal, characteristic
3C2×C3×C4×Q16C211yesmaximal, characteristic, complemented
4C2×#5189C211yesmaximal, characteristic, complemented
5C2×#5190C211yesmaximal, characteristic, complemented
6C2×C4×#216C211yesmaximal, characteristic, complemented
7C2×C4×#215C211yesmaximal, characteristic, complemented
8#79726C2116yesmaximal, direct product factor
9C2×#4886C211yesmaximal, characteristic
10C2×#4876C211yesmaximal, characteristic, complemented
11C2×#4816C211yesmaximal, characteristic, complemented
12C2×#4812C211yesmaximal, characteristic
13C2×#4797C211yesmaximal, characteristic, complemented
14C2×#4794C211yesmaximal, characteristic, complemented
15C2×C4×#204C211yesmaximal, characteristic, complemented
16C2×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
17C2×#3172—31nomaximal, Sylow
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×#947C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#944C2211yescharacteristic
25C22×#216C2211yescharacteristic
26C22×#215C2211yescharacteristic
27C22×#204C2211yescharacteristic
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30#5580—24no—
31#5580C2218yes—
32#5578—24no—
33#5578C2218yescomplemented
34C2×#898—21no—
35C2×#897C2211yescharacteristic
36C2×#896—21no—
37C2×#895C2211yescharacteristic
38C2×#894—21no—
39C2×#890C2211yescharacteristic
40C2×#889—21no—
41C2×#888C2211yescharacteristic
42C2×C4×D12—21no—
43C2×C4×D12C2211yescharacteristic
44C2×#872—21no—
45C2×#872—21no—
46C2×C42×D3C2211yescharacteristic
47C2×C4×Dic6—21no—
48C2×C4×Dic6C2211yescharacteristic
49C3×C4×Q16C2218yescomplemented
50C2×C3×#107C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#103C2211yescharacteristic
53C2×C3×C4×C8C2211yescharacteristic
54C2×#835C2211yescharacteristic
55C2×#835C2211yescharacteristic
56#5190C2218yescomplemented
57#5189C2218yescomplemented
58C2×#821C2211yescharacteristic
59C2×#817C2211yescharacteristic
60C2×#816C2211yescharacteristic
61C2×#815C2211yescharacteristic
62C2×#815C2211yescharacteristic
63C4×#216C2218yescomplemented
64C4×#215C2218yescomplemented
65C2×#810C2211yescharacteristic
66C2×#809C2211yescharacteristic
67C2×#808C2211yescharacteristic
68C2×#807C2211yescharacteristic
69C2×C4×C3⋊C8C2211yescharacteristic
70#4886C2218yes—
71#4876C2218yescomplemented
72#4816C2218yescomplemented
73#4812C2218yes—
74#4797C2218yescomplemented
75#4794C2218yescomplemented
76C4×#204C2218yescomplemented
77C4×ΓL(1,𝔽25)C2218yescomplemented
78C2×#533—31no—
79C2×#529—31no—
80#3172—316no—
81C2×#501—31no—
82C2×#497—31no—
83C2×#491—31no—
84C2×#489—31no—
85C2×#470—31no—
86C2×#470—31no—
87C2×#468—31no—
88C2×#468—31no—
89C2×C4×Q16—31no—
90C2×C4×Q16D311yescharacteristic, complemented
91C2×C4×SD16—31no—
92C2×C4×SD16—31no—
93C2×C4×M16—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×D12—21no—
97C22×D12C2311yescharacteristic
98C22×C4×D3—21no—
99C22×C4×D3D411yescharacteristic
100C22×C4×D3D411yescharacteristic
101C22×C4×D3C2311yescharacteristic
102C22×Dic6—21no—
103C22×Dic6C2311yescharacteristic
104C2×C3×Q16—24no—
105C2×C3×Q16C2314yes—
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×C4×Q8—22no—
109C3×C4×Q8—22no—
110C3×C4×Q8C2314yes—
111C3×C4×Q8C2314yes—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C42—21no—
117C2×C3×C42—21no—
118C2×C3×C42C2311yescharacteristic
119#947—22no—
120#947C2314yes—
121#946—22no—
122#946—22no—
123#946C2314yes—
124#946C2314yes—
125#944—22no—
126#944C2314yes—
127C2×#216—24no—
128C2×#216C2314yes—
129C2×#215—24no—
130C2×#215C2314yes—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×Dic3⋊C4—21no—
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×C4×Dic3—21no—
150C2×C4×Dic3D411yescharacteristic
151C2×C4×Dic3D411yescharacteristic
152C2×C4×Dic3C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155C2×#204—24no—
156C2×#204C2314yes—
157C2×ΓL(1,𝔽25)—24no—
158C2×ΓL(1,𝔽25)—24no—
159C2×ΓL(1,𝔽25)C2314yes—
160C2×ΓL(1,𝔽25)C2314yes—
161#898—28no—
162#897—22no—
163#897C2314yes—
164#896—28no—
165#895—22no—
166#895C2314yes—
167#894—28no—
168#890—22no—
169#890C2314yes—
170#889—28no—
171#888—22no—
172#888C2314yes—
173C4×D12—28no—
174C4×D12—22no—
175C4×D12C2314yes—
176#872—28no—
177#872—28no—
178C42×D3D414yes—
179C42×D3C2314yes—
180C4×Dic6—22no—
181C4×Dic6—28no—
182C4×Dic6C2314yes—
183C3×#107C2314yes—
184C3×#103C2314yes—
185C3×#103C2314yes—
186C3×C4×C8C2314yes—
187#835C2314yes—
188#835C2314yes—
189#821C2314yes—
190#817C2314yes—
191#816C2314yes—
192#815C2314yes—
193#815C2314yes—
194#810C2314yes—
195#809C2314yes—
196#808C2314yes—
197#807C2314yes—
198C4×C3⋊C8C2314yes—
199C22×Q16—31no—
200C22×Q16C2×D311yescharacteristic
201C22×SD16—31no—
202C22×SD16—31no—
203C22×M16—31no—
204C22×M16—31no—
205#533—38no—
206#533—64no—
207C2×C4⋊Q8—31no—
208C2×C4⋊Q8—31no—
209#529—38no—
210#529—64no—
211C2×#126—61no—
212C2×#125—31no—
213C2×#125—61no—
214C2×#124—31no—
215C2×#123—61no—
216C2×C22⋊Q8—31no—
217C2×C22⋊Q8—31no—
218C2×C22⋊Q8—31no—
219C2×C22⋊Q8—61no—
220C2×#121—31no—
221C2×C4×Q8—31no—
222C2×C4×Q8—61no—
223C2×C4×Q8C2×D311yescharacteristic
224C2×C4×Q8C2×D311yescharacteristic
225C2×C4×D4—31no—
226C2×C4×D4—61no—
227C2×#117—61no—
228C2×#117—61no—
229C22×C42—31no—
230#501—38no—
231#497—38no—
232#491—38no—
233#489—38no—
234#470—38no—
235#470—38no—
236#468—38no—
237#468—38no—
238C4×Q16—38no—
239C4×Q16C2×D318yescomplemented
240C4×SD16—38no—
241C4×SD16—38no—
242C2×#107—31no—
243C2×#107C2×D311yescharacteristic
244C2×#106—31no—
245C2×#106—31no—
246C2×#103—31no—
247C2×#103—31no—
248C2×#103—31no—
249C2×#103—31no—
250C2×#103C2×D311yescharacteristic
251C2×#103C2×D311yescharacteristic
252C2×#102—31no—
253C2×#102—31no—
254C4×M16—38no—
255C2×#97—31no—
256C2×#97—31no—
257C2×C4×C8—31no—
258C2×C4×C8C2×D311yescharacteristic
259C23×D3—21no—
260C23×D3C2×D411yescharacteristic
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×Q8C2412yes—
268C2×C3×Q8C2412yes—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3C2×D411yescharacteristic
280C22×Dic3C2×D411yescharacteristic
281C22×Dic3C2×D411yescharacteristic
282C2×D12—22no—
283C2×D12—22no—
284C2×D12—24no—
285C2×D12—21no—
286C2×D12—44no—
287C2×D12C2412yes—
288C2×C4×D3—24no—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—24no—
292C2×C4×D3—42no—
293C2×C4×D3—44no—
294C2×C4×D3C2×D412yes—
295C2×C4×D3C2×D414yes—
296C2×C4×D3C2×D414yes—
297C2×C4×D3C2412yes—
298C2×Dic6—22no—
299C2×Dic6—22no—
300C2×Dic6—21no—
301C2×Dic6—24no—
302C2×Dic6—44no—
303C2×Dic6C2412yes—
304C3×Q16—28no—
305C2×C3×C8—22no—
306C2×C3×C8#4114yes—
307C2×C3×C8C2412yes—
308C2×C3×C8C2412yes—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—24no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—24no—
313C3×C4⋊C4C2412yes—
314C3×C4⋊C4C2412yes—
315C3×C42—24no—
316C3×C42—24no—
317C3×C42C2×D412yes—
318C3×C42C2412yes—
319#216—28no—
320#215—28no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—24no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—24no—
331C4⋊Dic3—24no—
332C4⋊Dic3C2412yes—
333C4⋊Dic3C2412yes—
334Dic3⋊C4—24no—
335Dic3⋊C4—24no—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338Dic3⋊C4—24no—
339Dic3⋊C4—24no—
340Dic3⋊C4—24no—
341C4×Dic3—24no—
342C4×Dic3C2×D414yes—
343C4×Dic3C2×D412yes—
344C4×Dic3C2×D414yes—
345C4×Dic3C2412yes—
346C2×C3⋊C8—22no—
347C2×C3⋊C8#4114yes—
348C2×C3⋊C8C2412yes—
349C2×C3⋊C8C2412yes—
350#204—28no—
351ΓL(1,𝔽25)—28no—
352ΓL(1,𝔽25)—28no—
353C22×Q8—31no—
354C22×Q8—61no—
355C22×Q8C22×D311yescharacteristic
356C22×Q8C22×D311yescharacteristic
357C22×D4—31no—
358C22×D4—61no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—61no—
363C2×Q16—24no—
364C2×Q16—34no—
365C2×Q16—64no—
366C2×Q16C22×D314yes—
367C2×SD16—34no—
368C2×SD16—34no—
369C2×SD16—64no—
370C2×SD16—64no—
371C2×M16—34no—
372C2×M16—34no—
373C2×M16—64no—
374C2×M16—64no—
375C22×C8—31no—
376C22×C8—31no—
377C22×C8C22×D311yescharacteristic
378C22×C8C22×D311yescharacteristic
379C4⋊Q8—34no—
380C4⋊Q8—34no—
381C4⋊Q8—62no—
382C4⋊Q8—62no—
383#126—68no—
384#125—34no—
385#125—62no—
386#125—68no—
387#124—34no—
388#124—62no—
389#123—68no—
390C22⋊Q8—34no—
391C22⋊Q8—34no—
392C22⋊Q8—34no—
393C22⋊Q8—62no—
394C22⋊Q8—68no—
395C22⋊Q8—62no—
396C22⋊Q8—62no—
397#121—34no—
398#121—62no—
399C4×Q8—22no—
400C4×Q8—22no—
401C4×Q8—34no—
402C4×Q8—68no—
403C4×Q8—62no—
404C4×Q8C22×D314yes—
405C4×Q8C22×D314yes—
406C4×D4—34no—
407C4×D4—68no—
408C4×D4—62no—
409#117—68no—
410#117—68no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4—61no—
423C2×C4⋊C4—61no—
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—34no—
439C2×C42—34no—
440C2×C42—61no—
441C2×C42C22×D311yescharacteristic
442#107—34no—
443#107C22×D314yes—
444#106—34no—
445#106—34no—
446#103—34no—
447#103—34no—
448#103—34no—
449#103—34no—
450#103C22×D314yes—
451#103C22×D314yes—
452#102—34no—
453#102—34no—
454#97—34no—
455#97—34no—
456C4×C8—34no—
457C4×C8C22×D314yes—
458C23×C3C22×D411yescharacteristic
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—42no—
464C22×D3—42no—
465C22×D3—42no—
466C22×D3C22×D412yes—
467C3×Q8—22no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—42no—
472C3×Q8—42no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—42no—
479C2×C3×C4—42no—
480C2×C3×C4—42no—
481C2×C3×C4—42no—
482C2×C3×C4#13714yes—
483C2×C3×C4C22×D412yes—
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C22×D412yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4C2×#4112yes—
488C2×C3×C4C2511yescharacteristic
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—42no—
496C2×Dic3—42no—
497C2×Dic3—42no—
498C2×Dic3C22×D412yes—
499C2×Dic3C22×D412yes—
500C2×Dic3C22×D412yes—
501D12—22no—
502D12—22no—
503D12—48no—
504D12—42no—
505C4×D3—24no—
506C4×D3—28no—
507C4×D3—22no—
508C4×D3—22no—
509C4×D3—44no—
510C4×D3—48no—
511Dic6—22no—
512Dic6—22no—
513Dic6—48no—
514Dic6—42no—
515C3×C8—22no—
516C3×C8C2×#4114yes—
517C3⋊C8—22no—
518C3⋊C8C2×#4114yes—
519C24—31no—
520C24—61no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—32no—
528C2×Q8—64no—
529C2×Q8—61no—
530C2×Q8—62no—
531C2×Q8—62no—
532C2×Q8—124no—
533C2×Q8C23×D312yes—
534C2×Q8C23×D312yes—
535C2×D4—32no—
536C2×D4—64no—
537C2×D4—62no—
538C2×D4—61no—
539C2×D4—62no—
540C2×D4—124no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—34no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—34no—
552C22×C4—64no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—64no—
559C22×C4—122no—
560C22×C4—124no—
561C22×C4D3×D411yescharacteristic
562C22×C4D3×D411yescharacteristic
563C22×C4C23×D311yescharacteristic
564Q16—28no—
565Q16—68no—
566SD16—68no—
567SD16—68no—
568M16—68no—
569M16—68no—
570C2×C8—22no—
571C2×C8—34no—
572C2×C8—32no—
573C2×C8—32no—
574C2×C8—62no—
575C2×C8#23514yes—
576C2×C8C23×D312yes—
577C2×C8C23×D312yes—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—32no—
583C4⋊C4—32no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—64no—
595C4⋊C4C23×D312yes—
596C4⋊C4C23×D312yes—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C42—24no—
605C42—24no—
606C42—34no—
607C42—32no—
608C42—34no—
609C42—32no—
610C42—64no—
611C42D3×D412yes—
612C42C23×D312yes—
613C22×C3#53212yes—
614C22×C3C2×#13712yes—
615C22×C3#57512yes—
616C22×C3C23×D411yescharacteristic
617C2×D3—22no—
618C2×D3—22no—
619C2×D3—22no—
620C2×D3—44no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—84no—
625C3×C4—22no—
626C3×C4—42no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4#53212yes—
631C3×C4C2×#13714yes—
632C3×C4C22×#4111yescharacteristic
633C3×C4C22×#4111yescharacteristic
634Dic3—22no—
635Dic3—22no—
636Dic3—22no—
637Dic3—42no—
638Dic3—42no—
639Dic3—42no—
640C23—32no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23C2×D3×D411yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—42no—
654Q8—42no—
655Q8—62no—
656Q8—62no—
657Q8—128no—
658Q8—122no—
659D4—62no—
660D4—62no—
661D4—128no—
662D4—122no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—68no—
681C2×C4—64no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—124no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4—122no—
689C2×C4—128no—
690C2×C4#91814yes—
691C2×C4C2×#23512yes—
692C2×C4C2×D3×D412yes—
693C2×C4C2×D3×D412yes—
694C2×C4C2×D3×D411yescharacteristic
695C2×C4D3×#4112yes—
696C2×C4C24×D311yescharacteristic
697C8—22no—
698C8—34no—
699C8—62no—
700C8C2×#23514yes—
701C2×C3#317214yescomplemented
702C2×C3C2×#53211yescharacteristic
703C2×C3C22×#13711yescharacteristic
704C2×C3C2×#57511yescharacteristic
705D3—42no—
706D3—82no—
707C22—62no—
708C22—62no—
709C22—62no—
710C22—124no—
711C22—122no—
712C22—122no—
713C22—122no—
714C22—244no—
715C22#554812yes—
716C22C2×#91812yes—
717C22#576812yes—
718C22C22×D3×D411yescharacteristic
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—62no—
725C4—62no—
726C4—62no—
727C4—122no—
728C4—122no—
729C4—122no—
730C4#554812yes—
731C4C2×#91814yes—
732C4C22×#23511yescharacteristic
733C4C2×D3×#4111yescharacteristic
734C3C2×#317211yescharacteristic, complemented, Sylow
735C2—122no—
736C2—242no—
737C2#7972614yesdirect product factor
738C2C2×#554811yescharacteristic
739C2C22×#91811yescharacteristic
740C2C2×#576811yescharacteristic
subgroupG/H
centerC22×C4D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×C4×Q16C2
socleC23×C3C22×D4
prime radicalC2×#895C22
hypercenterC2×C4×Q16D3
hypocenterC3C2×#3172
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#5578C2semidirect
3. C2×C3×C4×Q16C2semidirect
4. C2×#5189C2semidirect
5. C2×#5190C2semidirect
6. C2×C4×#216C2semidirect
7. C2×C4×#215C2semidirect
8. #79726C2direct (N × H)
10. C2×#4876C2semidirect
11. C2×#4816C2semidirect
13. C2×#4797C2semidirect
14. C2×#4794C2semidirect
15. C2×C4×#204C2semidirect
16. C2×C4×ΓL(1,𝔽25)C2semidirect
33. #5578C22semidirect
49. C3×C4×Q16C22semidirect
56. #5190C22semidirect
57. #5189C22semidirect
63. C4×#216C22semidirect
64. C4×#215C22semidirect
71. #4876C22semidirect
72. #4816C22semidirect
74. #4797C22semidirect
75. #4794C22semidirect
76. C4×#204C22semidirect
77. C4×ΓL(1,𝔽25)C22semidirect
90. C2×C4×Q16D3semidirect
239. C4×Q16C2×D3semidirect
701. C2×C3#3172semidirect
734. C3C2×#3172semidirect
737. C2#79726direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55782
C2×#55802
C2×C3×C4×Q162
C2×#51892
C2×#51902
C2×C4×#2162
C2×C4×#2152
#797262
C2×#48862
C2×#48762
C2×#48162
C2×#48122
C2×#47972
C2×#47942
C2×C4×#2042
C2×C4×ΓL(1,𝔽25)2
C2×#31723