Finite Group Databasebeta

← C2×#86684 #11703444

Subgroups — C2×#86684 #11703444

Order 768.

7854 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic, complemented
2C2×#5834C212yesmaximal, complemented
3C2×#5832C212yesmaximal, complemented
4#86684C2132yesmaximal, direct product factor
5C2×#5721C211yesmaximal, characteristic, complemented
6C2×#5725C211yesmaximal, characteristic, complemented
7C2×#5661C214yesmaximal, complemented
8C2×#5663C214yesmaximal, complemented
9C2×#5631C212yesmaximal, complemented
10C2×#5624C212yesmaximal, complemented
11C2×#5599C212yesmaximal, complemented
12C2×#5619C212yesmaximal, complemented
13C2×#5557C211yesmaximal, characteristic, complemented
14C2×#5553C211yesmaximal, characteristic, complemented
15C2×#5553C211yesmaximal, characteristic, complemented
16C2×C4×#237C211yesmaximal, characteristic, complemented
17C2×#5514C212yesmaximal, complemented
18C2×#5504C212yesmaximal, complemented
19C2×#3517—31nomaximal, Sylow
20C22×C3×#41C2212yes—
21C22×#239C2212yes—
22C22×#237C2211yescharacteristic
23C22×#235C2212yes—
24C22×#235C2212yes—
25C3×#547C22116yescomplemented
26C2×C3×C4⋊Q8C2211yescharacteristic
27C2×C3×#123C2214yes—
28C2×C3×C22⋊Q8C2212yes—
29C2×C3×#121C2212yes—
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C4⋊C4C2212yes—
33#5834C22132yescomplemented
34#5832C22132yescomplemented
35C2×#947C2212yes—
36C2×Q8×Dic3C2212yes—
37C2×#944C2212yes—
38C2×#940C2212yes—
39C2×#940C2214yes—
40C2×#940C2212yes—
41C2×#939C2214yes—
42C2×#939C2214yes—
43C2×#938C2211yescharacteristic
44C2×#938C2214yes—
45C2×#936C2211yescharacteristic
46C2×D4×Dic3C2211yescharacteristic
47C2×#930C2212yes—
48C2×#930C2212yes—
49C2×#930C2214yes—
50C2×C4×#67C2212yes—
51C2×C4×#67C2214yes—
52C2×C4×#67C2214yes—
53C2×C4×#67C2214yes—
54C2×C4×#67C2212yes—
55C2×#926C2212yes—
56C22×C4×Dic3C2212yes—
57#5725C22116yescomplemented
58#5721C22116yescomplemented
59#5663C22164yescomplemented
60#5661C22164yescomplemented
61#5631C22132yescomplemented
62#5624C22132yescomplemented
63#5619C22132yescomplemented
64#5599C22132yescomplemented
65#5557C22116yescomplemented
66#5553C22116yescomplemented
67#5553C22116yescomplemented
68C4×#237C22116yescomplemented
69#5514C22132yescomplemented
70C2×#898C2214yes—
71C2×#897C2211yescharacteristic
72C2×#895C2212yes—
73C2×#895C2212yes—
74C2×#894C2214yes—
75#5504C22132yescomplemented
76C2×#893C2212yes—
77C2×#893C2212yes—
78C2×#893C2212yes—
79C2×#893C2212yes—
80C2×#892C2214yes—
81C2×#892C2211yescharacteristic
82C2×D3×C4⋊C4C2214yes—
83C2×#890C2211yescharacteristic
84C2×#890C2212yes—
85C2×#889C2214yes—
86C2×#887C2212yes—
87C2×#887C2211yescharacteristic
88C2×#886C2214yes—
89C2×#884C2214yes—
90C2×#884C2214yes—
91C2×#884C2214yes—
92C2×#883C2212yes—
93C2×#883C2214yes—
94C2×#67⋊C4C2214yes—
95C2×#67⋊C4C2212yes—
96C2×#879C2212yes—
97C2×#877C2212yes—
98C2×#874C2211yescharacteristic
99C2×C42×D3C2211yescharacteristic
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C2211yescharacteristic
102#3517—332no—
103C2×#557—31no—
104C2×#553—34no—
105C2×#553—32no—
106C2×#550—32no—
107C2×#550—32no—
108C2×#550—31no—
109C2×#550—31no—
110C2×#547—32no—
111C2×#547D311yescharacteristic, complemented
112C2×#540—34no—
113C2×#540—32no—
114C2×#532—32no—
115C2×#532—31no—
116C2×#529—32no—
117C2×#529—31no—
118C2×#520—32no—
119C2×C4×#41—31no—
120C2×C3×#41—48no—
121C2×C3×#41C23116yes—
122C22×C3×Q8C2312yes—
123C22×C3×D4C2311yescharacteristic
124C22×C3×D4C2311yescharacteristic
125C22×C3×D4C2314yes—
126C23×C3×C4C2312yes—
127C23×C3×C4C2312yes—
128C23×C3×C4C2314yes—
129C22×#67C2314yes—
130C22×#67C2312yes—
131C22×#67C2314yes—
132C22×#67C2314yes—
133C22×#67C2312yes—
134C22×#67C2314yes—
135C23×Dic3C2312yes—
136C23×Dic3C2312yes—
137C2×#239—48no—
138C2×#239C23116yes—
139C2×#237—28no—
140C2×#237C2318yes—
141C2×#235—216no—
142C2×#235—48no—
143C2×#235C23116yes—
144C2×#235C23116yes—
145C22×D12C2312yes—
146C22×D12C2312yes—
147C22×D12C2314yes—
148C22×D12C2312yes—
149C22×C4×D3C2314yes—
150C22×C4×D3C2311yescharacteristic
151C22×C4×D3C2311yescharacteristic
152C22×C4×D3C2314yes—
153C22×C4×D3C2314yes—
154C22×C4×D3C2311yescharacteristic
155C22×Dic6C2311yescharacteristic
156C22×Dic6C2311yescharacteristic
157C3×C4⋊Q8C2318yes—
158C3×#123C23132yes—
159C3×C22⋊Q8C23116yes—
160C3×#121C23116yes—
161C3×C4×D4C2318yes—
162C3×C4×D4C2318yes—
163C2×C3×C4⋊C4C2312yes—
164C2×C3×C4⋊C4C2311yescharacteristic
165C2×C3×C4⋊C4C2312yes—
166C2×C3×C4⋊C4C2311yescharacteristic
167C2×C3×C4⋊C4C2314yes—
168C2×C3×C4⋊C4C23116yes—
169C2×C3×C22⋊C4C2312yes—
170C2×C3×C22⋊C4C2312yes—
171C2×C3×C22⋊C4C2314yes—
172C2×C3×C42C2311yescharacteristic
173C2×#217C2312yes—
174C2×#217C2312yes—
175C2×#217C2312yes—
176C2×#217C2312yes—
177#947C23116yes—
178Q8×Dic3C23116yes—
179#944C23116yes—
180#940C23132yes—
181#940C23116yes—
182#940C23116yes—
183#939C23132yes—
184#939C23132yes—
185#938C23132yes—
186#938C2318yes—
187#936C2318yes—
188D4×Dic3C2318yes—
189#930C23132yes—
190#930C23116yes—
191#930C23116yes—
192C4×#67C23132yes—
193C4×#67C23132yes—
194C4×#67C23132yes—
195C4×#67C23116yes—
196C4×#67C23116yes—
197C2×(C2×D3)⋊C4C2312yes—
198C2×(C2×D3)⋊C4C2314yes—
199C2×(C2×D3)⋊C4C2312yes—
200C2×(C2×D3)⋊C4C2314yes—
201C2×(C2×D3)⋊C4C2314yes—
202C2×(C2×D3)⋊C4C2314yes—
203#926C23116yes—
204C2×C4⋊Dic3C2311yescharacteristic
205C2×C4⋊Dic3C2311yescharacteristic
206C2×C4⋊Dic3C2312yes—
207C2×C4⋊Dic3C2312yes—
208C2×C4⋊Dic3C2314yes—
209C2×Dic3⋊C4C2312yes—
210C2×Dic3⋊C4C2312yes—
211C2×Dic3⋊C4C2312yes—
212C2×Dic3⋊C4C2312yes—
213C2×Dic3⋊C4C2314yes—
214C2×Dic3⋊C4C2314yes—
215C2×C4×Dic3C2312yes—
216C2×C4×Dic3C2312yes—
217C2×C4×Dic3C2311yescharacteristic
218C2×C4×Dic3C2311yescharacteristic
219C2×C4×Dic3C2311yescharacteristic
220C2×C4×Dic3C2312yes—
221C2×C4×Dic3C2314yes—
222C2×C4×Dic3C2312yes—
223C2×C4×Dic3C23116yes—
224#898C23132yes—
225#897C2318yes—
226#895C23116yes—
227#895C23116yes—
228#894C23132yes—
229#893C23116yes—
230#893C23116yes—
231#893C23116yes—
232#893C23116yes—
233#892C23132yes—
234#892C2318yes—
235D3×C4⋊C4C23132yes—
236#890C23116yes—
237#890C2318yes—
238#889C23132yes—
239#887C23116yes—
240#887C2318yes—
241#886C23132yes—
242#884C23132yes—
243#884C23132yes—
244#884C23132yes—
245#883C23132yes—
246#883C23116yes—
247#67⋊C4C23132yes—
248#67⋊C4C23116yes—
249#879C23116yes—
250#877C23116yes—
251#874C2318yes—
252C42×D3C2318yes—
253C4×Dic6C2318yes—
254C4×Dic6C2318yes—
255C22×#41—32no—
256C22×#41—31no—
257C22×#41—32no—
258C22×#41—32no—
259C22×#41C2×D312yes—
260#557—316no—
261#553—364no—
262#553—332no—
263#550—332no—
264#550—332no—
265#550—316no—
266#550—316no—
267#547—332no—
268#547C2×D3116yescomplemented
269#540—364no—
270#540—332no—
271#532—332no—
272#532—316no—
273C2×C4⋊Q8—32no—
274C2×C4⋊Q8C2×D311yescharacteristic
275C2×#127—32no—
276C2×#127—34no—
277C2×#127—32no—
278C2×#127—31no—
279#529—332no—
280#529—316no—
281C2×#126—34no—
282C2×#126—32no—
283C2×#125—31no—
284C2×#125—34no—
285C2×#125—32no—
286C2×#124—32no—
287C2×#124—31no—
288C2×#123—34no—
289C2×#123—32no—
290C2×#123—34no—
291C2×#123—34no—
292C2×#123C2×D314yes—
293C2×C22⋊Q8—31no—
294C2×C22⋊Q8C2×D312yes—
295C2×#121—31no—
296C2×#121—34no—
297C2×#121—34no—
298C2×#121—34no—
299C2×#121—32no—
300C2×#121—34no—
301C2×#121—32no—
302C2×#121—32no—
303C2×#121—32no—
304C2×#121—34no—
305C2×#121—34no—
306C2×#121—34no—
307C2×#121C2×D312yes—
308#520—332no—
309C4×#41—316no—
310C2×C4×Q8—32no—
311C2×C4×Q8—31no—
312C2×C4×Q8—32no—
313C2×C4×Q8—31no—
314C2×C4×Q8—31no—
315C2×C4×D4—31no—
316C2×C4×D4—32no—
317C2×C4×D4—34no—
318C2×C4×D4—34no—
319C2×C4×D4—32no—
320C2×C4×D4—34no—
321C2×C4×D4—32no—
322C2×C4×D4—32no—
323C2×C4×D4—32no—
324C2×C4×D4—32no—
325C2×C4×D4—32no—
326C2×C4×D4—34no—
327C2×C4×D4C2×D311yescharacteristic
328C2×C4×D4C2×D311yescharacteristic
329C2×#117—32no—
330C2×#117—31no—
331C2×#117—34no—
332C2×#117—32no—
333C22×C4⋊C4—34no—
334C22×C4⋊C4C2×D312yes—
335C22×C42—32no—
336C22×C42—31no—
337C24×C3C2412yes—
338C24×C3C2412yes—
339C23×D3C2414yes—
340C23×D3C2411yescharacteristic
341C3×#41—432no—
342C2×C3×Q8—28no—
343C2×C3×Q8C2418yes—
344C2×C3×D4—24no—
345C2×C3×D4—24no—
346C2×C3×D4—48no—
347C2×C3×D4C2414yes—
348C2×C3×D4C2414yes—
349C2×C3×D4C24116yes—
350C22×C3×C4—28no—
351C22×C3×C4—28no—
352C22×C3×C4—48no—
353C22×C3×C4C2412yes—
354C22×C3×C4C2418yes—
355C22×C3×C4C2411yescharacteristic
356C22×C3×C4C2414yes—
357C22×C3×C4C2412yes—
358C22×C3×C4C2418yes—
359C22×C3×C4C24116yes—
360C22×C3×C4C2411yescharacteristic
361C22×C3×C4C2411yescharacteristic
362C2×#67—216no—
363C2×#67—28no—
364C2×#67—48no—
365C2×#67—48no—
366C2×#67—44no—
367C2×#67—48no—
368C2×#67C2418yes—
369C2×#67C24116yes—
370C2×#67C24116yes—
371C2×#67C24116yes—
372C2×#67C2418yes—
373C2×#67C24116yes—
374C22×Dic3—28no—
375C22×Dic3—44no—
376C22×Dic3C2418yes—
377C22×Dic3C2411yescharacteristic
378C22×Dic3C2411yescharacteristic
379C22×Dic3C2412yes—
380C22×Dic3C2412yes—
381C22×Dic3C2411yescharacteristic
382C22×Dic3C2412yes—
383C22×Dic3C2418yes—
384C22×Dic3C2412yes—
385#239—432no—
386#237—232no—
387#235—264no—
388#235—432no—
389C2×D12—28no—
390C2×D12—28no—
391C2×D12—44no—
392C2×D12—48no—
393C2×D12C2418yes—
394C2×D12C2418yes—
395C2×D12C2418yes—
396C2×D12C24116yes—
397C2×C4×D3—24no—
398C2×C4×D3—24no—
399C2×C4×D3—216no—
400C2×C4×D3—42no—
401C2×C4×D3—48no—
402C2×C4×D3—48no—
403C2×C4×D3C2414yes—
404C2×C4×D3C2414yes—
405C2×C4×D3C24116yes—
406C2×C4×D3C2414yes—
407C2×C4×D3C24116yes—
408C2×C4×D3C24116yes—
409C2×Dic6—24no—
410C2×Dic6#4118yescomplemented
411C2×Dic6C2414yes—
412C2×Dic6C2414yes—
413C3×C4⋊C4C2418yes—
414C3×C4⋊C4C2414yes—
415C3×C4⋊C4C2418yes—
416C3×C4⋊C4C2414yes—
417C3×C4⋊C4C24116yes—
418C3×C22⋊C4C2418yes—
419C3×C22⋊C4C2418yes—
420C3×C22⋊C4C24116yes—
421C3×C42C2414yes—
422#217C2418yes—
423#217C2418yes—
424#217C2418yes—
425#217C2418yes—
426(C2×D3)⋊C4C2418yes—
427(C2×D3)⋊C4C24116yes—
428(C2×D3)⋊C4C2418yes—
429(C2×D3)⋊C4C24116yes—
430(C2×D3)⋊C4C24116yes—
431(C2×D3)⋊C4C24116yes—
432C4⋊Dic3C2414yes—
433C4⋊Dic3C2414yes—
434C4⋊Dic3C2418yes—
435C4⋊Dic3C2418yes—
436C4⋊Dic3C24116yes—
437Dic3⋊C4C2418yes—
438Dic3⋊C4C2418yes—
439Dic3⋊C4C2418yes—
440Dic3⋊C4C2418yes—
441Dic3⋊C4C24116yes—
442Dic3⋊C4C24116yes—
443C4×Dic3C2418yes—
444C4×Dic3C2418yes—
445C4×Dic3C2414yes—
446C4×Dic3C2414yes—
447C4×Dic3C2414yes—
448C4×Dic3C2418yes—
449C4×Dic3C24116yes—
450C4×Dic3C2418yes—
451C2×#41—316no—
452C2×#41—38no—
453C2×#41—316no—
454C2×#41—316no—
455C2×#41—48no—
456C2×#41—616no—
457C2×#41—68no—
458C2×#41—128no—
459C2×#41—128no—
460C2×#41C22×D3116yes—
461C22×Q8—31no—
462C22×Q8—31no—
463C22×Q8C22×D312yes—
464C22×D4—34no—
465C22×D4—32no—
466C22×D4—34no—
467C22×D4—32no—
468C22×D4—34no—
469C22×D4—34no—
470C22×D4—32no—
471C22×D4—32no—
472C22×D4—32no—
473C22×D4—34no—
474C22×D4C22×D311yescharacteristic
475C22×D4C22×D311yescharacteristic
476C22×D4C22×D314yes—
477C23×C4—32no—
478C23×C4—32no—
479C23×C4—34no—
480C23×C4—31no—
481C23×C4—31no—
482C23×C4—34no—
483C23×C4—34no—
484C23×C4—31no—
485C23×C4C22×D312yes—
486C23×C4C22×D312yes—
487C23×C4C22×D314yes—
488C4⋊Q8—316no—
489C4⋊Q8C22×D318yes—
490#127—316no—
491#127—332no—
492#127—316no—
493#127—38no—
494#126—332no—
495#126—316no—
496#125—38no—
497#125—332no—
498#125—316no—
499#124—316no—
500#124—38no—
501#123—332no—
502#123—316no—
503#123—332no—
504#123—332no—
505#123C22×D3132yes—
506C22⋊Q8—38no—
507C22⋊Q8C22×D3116yes—
508#121—38no—
509#121—332no—
510#121—332no—
511#121—332no—
512#121—316no—
513#121—332no—
514#121—316no—
515#121—316no—
516#121—316no—
517#121—332no—
518#121—332no—
519#121—332no—
520#121C22×D3116yes—
521C4×Q8—316no—
522C4×Q8—38no—
523C4×Q8—316no—
524C4×Q8—38no—
525C4×Q8—38no—
526C4×D4—38no—
527C4×D4—316no—
528C4×D4—332no—
529C4×D4—332no—
530C4×D4—316no—
531C4×D4—332no—
532C4×D4—316no—
533C4×D4—316no—
534C4×D4—316no—
535C4×D4—316no—
536C4×D4—316no—
537C4×D4—332no—
538C4×D4C22×D318yes—
539C4×D4C22×D318yes—
540#117—316no—
541#117—38no—
542#117—332no—
543#117—316no—
544C2×C4⋊C4—32no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—34no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—32no—
549C2×C4⋊C4—31no—
550C2×C4⋊C4—32no—
551C2×C4⋊C4—34no—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—32no—
554C2×C4⋊C4—34no—
555C2×C4⋊C4—332no—
556C2×C4⋊C4C22×D314yes—
557C2×C4⋊C4C22×D311yescharacteristic
558C2×C4⋊C4C22×D312yes—
559C2×C4⋊C4C22×D3116yes—
560C2×C4⋊C4C22×D311yescharacteristic
561C2×C4⋊C4C22×D312yes—
562C2×C22⋊C4—32no—
563C2×C22⋊C4—32no—
564C2×C22⋊C4—32no—
565C2×C22⋊C4—32no—
566C2×C22⋊C4—34no—
567C2×C22⋊C4—32no—
568C2×C22⋊C4—34no—
569C2×C22⋊C4—34no—
570C2×C22⋊C4—32no—
571C2×C22⋊C4—34no—
572C2×C22⋊C4C22×D312yes—
573C2×C22⋊C4C22×D314yes—
574C2×C22⋊C4C22×D312yes—
575C2×C42—32no—
576C2×C42—31no—
577C2×C42—32no—
578C2×C42—31no—
579C2×C42—34no—
580C2×C42—32no—
581C2×C42—32no—
582C2×C42—316no—
583C2×C42—31no—
584C2×C42—38no—
585C2×C42C22×D311yescharacteristic
586C23×C3—24no—
587C23×C3—24no—
588C23×C3—24no—
589C23×C3—24no—
590C23×C3—24no—
591C23×C3—24no—
592C23×C3C2514yes—
593C23×C3C2514yes—
594C23×C3C2511yescharacteristic
595C22×D3—28no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—28no—
599C22×D3—22no—
600C22×D3—28no—
601C22×D3C2518yes—
602C22×D3C2512yes—
603C3×Q8—216no—
604C3×D4—28no—
605C3×D4—28no—
606C3×D4—416no—
607C2×C3×C4—24no—
608C2×C3×C4—24no—
609C2×C3×C4—28no—
610C2×C3×C4—22no—
611C2×C3×C4—216no—
612C2×C3×C4—216no—
613C2×C3×C4—416no—
614C2×C3×C4C2×#4114yes—
615C2×C3×C4H(5,𝔽2)14yes—
616C2×C3×C4C2514yes—
617C2×C3×C4C2512yes—
618C2×C3×C4C2518yes—
619C2×C3×C4C2514yes—
620C2×C3×C4C2512yes—
621C2×C3×C4C2512yes—
622#67—232no—
623#67—216no—
624#67—416no—
625#67—416no—
626#67—48no—
627#67—416no—
628C2×Dic3—22no—
629C2×Dic3—24no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—24no—
633C2×Dic3—24no—
634C2×Dic3—216no—
635C2×Dic3—48no—
636C2×Dic3C2×#4118yes—
637C2×Dic3C2512yes—
638C2×Dic3C2512yes—
639C2×Dic3C2514yes—
640C2×Dic3C2514yes—
641C2×Dic3C2512yes—
642C2×Dic3C2514yes—
643C2×Dic3C2514yes—
644D12—216no—
645D12—216no—
646D12—48no—
647D12—416no—
648C4×D3—28no—
649C4×D3—28no—
650C4×D3—232no—
651C4×D3—44no—
652C4×D3—416no—
653C4×D3—416no—
654Dic6—28no—
655Dic6C2×#41116yescomplemented
656C24—31no—
657C24—34no—
658C24C23×D312yes—
659C24C23×D312yes—
660#41—432no—
661#41—664no—
662#41—632no—
663#41—1232no—
664#41—1232no—
665C2×Q8—28no—
666C2×Q8—38no—
667C2×Q8—34no—
668C2×Q8—34no—
669C2×Q8—64no—
670C2×Q8C23×D318yes—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—316no—
674C2×D4—38no—
675C2×D4—316no—
676C2×D4—38no—
677C2×D4—316no—
678C2×D4—316no—
679C2×D4—38no—
680C2×D4—38no—
681C2×D4—38no—
682C2×D4—316no—
683C2×D4—48no—
684C2×D4—616no—
685C2×D4—68no—
686C2×D4—68no—
687C2×D4—68no—
688C2×D4—128no—
689C2×D4—124no—
690C2×D4—128no—
691C2×D4—128no—
692C2×D4—128no—
693C2×D4—124no—
694C2×D4C23×D314yes—
695C2×D4C23×D314yes—
696C2×D4C23×D3116yes—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—32no—
700C22×C4—38no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—31no—
706C22×C4—32no—
707C22×C4—38no—
708C22×C4—34no—
709C22×C4—34no—
710C22×C4—316no—
711C22×C4—34no—
712C22×C4—316no—
713C22×C4—316no—
714C22×C4—48no—
715C22×C4—616no—
716C22×C4—68no—
717C22×C4—64no—
718C22×C4—64no—
719C22×C4—128no—
720C22×C4—128no—
721C22×C4—122no—
722C22×C4—124no—
723C22×C4C23×D318yes—
724C22×C4C23×D318yes—
725C22×C4C23×D312yes—
726C22×C4C23×D311yescharacteristic
727C22×C4C23×D314yes—
728C22×C4C23×D312yes—
729C22×C4C23×D3116yes—
730C22×C4C23×D311yescharacteristic
731C22×C4C23×D311yescharacteristic
732C4⋊C4—38no—
733C4⋊C4—38no—
734C4⋊C4—316no—
735C4⋊C4—38no—
736C4⋊C4—38no—
737C4⋊C4—34no—
738C4⋊C4—38no—
739C4⋊C4—316no—
740C4⋊C4—34no—
741C4⋊C4—38no—
742C4⋊C4—316no—
743C4⋊C4C23×D3116yes—
744C4⋊C4C23×D314yes—
745C4⋊C4C23×D318yes—
746C4⋊C4C23×D314yes—
747C4⋊C4C23×D318yes—
748C22⋊C4—38no—
749C22⋊C4—38no—
750C22⋊C4—38no—
751C22⋊C4—38no—
752C22⋊C4—316no—
753C22⋊C4—38no—
754C22⋊C4—316no—
755C22⋊C4—316no—
756C22⋊C4—38no—
757C22⋊C4—316no—
758C22⋊C4C23×D318yes—
759C22⋊C4C23×D3116yes—
760C22⋊C4C23×D318yes—
761C42—34no—
762C42—38no—
763C42—34no—
764C42—38no—
765C42—34no—
766C42—38no—
767C42—316no—
768C42—38no—
769C42C23×D314yes—
770C22×C3—24no—
771C22×C3—24no—
772C22×C3—24no—
773C22×C3—24no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—48no—
777C22×C3—48no—
778C22×C3C22×#4112yes—
779C22×C3C2×H(5,𝔽2)12yes—
780C22×C3#58512yes—
781C22×C3C2611yescharacteristic
782C2×D3—28no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—28no—
786C2×D3—22no—
787C2×D3—28no—
788C2×D3—416no—
789C2×D3—44no—
790C3×C4—24no—
791C3×C4—24no—
792C3×C4—28no—
793C3×C4—22no—
794C3×C4C22×#4114yes—
795C3×C4C2×H(5,𝔽2)14yes—
796Dic3—22no—
797Dic3—24no—
798Dic3—22no—
799Dic3—22no—
800Dic3—24no—
801Dic3—24no—
802Dic3C22×#4118yes—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—32no—
810C23—38no—
811C23—62no—
812C23—68no—
813C23—68no—
814C23—62no—
815C23—62no—
816C23—68no—
817C23C24×D314yes—
818C23C24×D314yes—
819C23C24×D311yescharacteristic
820Q8—216no—
821Q8—316no—
822Q8—68no—
823D4—28no—
824D4—28no—
825D4—416no—
826D4—632no—
827D4—616no—
828D4—616no—
829D4—616no—
830D4—1216no—
831D4—128no—
832D4—1216no—
833D4—1216no—
834D4—1216no—
835D4—128no—
836C2×C4—24no—
837C2×C4—28no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—216no—
841C2×C4—216no—
842C2×C4—38no—
843C2×C4—34no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—34no—
847C2×C4—34no—
848C2×C4—32no—
849C2×C4—34no—
850C2×C4—416no—
851C2×C4—632no—
852C2×C4—616no—
853C2×C4—62no—
854C2×C4—64no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—64no—
858C2×C4—64no—
859C2×C4—68no—
860C2×C4—68no—
861C2×C4—1216no—
862C2×C4—1216no—
863C2×C4—124no—
864C2×C4—128no—
865C2×C4#100414yes—
866C2×C4D3×#4114yes—
867C2×C4C24×D314yes—
868C2×C4C24×D312yes—
869C2×C4C24×D318yes—
870C2×C4C24×D314yes—
871C2×C4C24×D312yes—
872C2×C4C24×D312yes—
873C2×C3—44no—
874C2×C3—44no—
875C2×C3#351714yescomplemented
876C2×C3C23×#4111yescharacteristic
877C2×C3C22×H(5,𝔽2)11yescharacteristic
878C2×C3C2×#58511yescharacteristic
879D3—48no—
880D3—42no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—24no—
887C22—48no—
888C22—48no—
889C22—62no—
890C22—68no—
891C22—68no—
892C22—62no—
893C22—62no—
894C22—68no—
895C22—124no—
896C22—1216no—
897C22C2×#100412yes—
898C22C2×D3×#4112yes—
899C22#596812yes—
900C22C25×D311yescharacteristic
901C4—24no—
902C4—28no—
903C4—24no—
904C4—22no—
905C4—38no—
906C4—62no—
907C4—64no—
908C4—62no—
909C4—62no—
910C4—64no—
911C4—64no—
912C4C2×#100414yes—
913C4C2×D3×#4114yes—
914C3C2×#351711yescharacteristic, complemented, Sylow
915C2—44no—
916C2—44no—
917C2—122no—
918C2—128no—
919C2#8668414yesdirect product factor
920C2C22×#100411yescharacteristic
921C2C22×D3×#4111yescharacteristic
922C2C2×#596811yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#547C2
socleC23×C3C25
hypercenterC2×#547D3
hypocenterC3C2×#3517
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C3×#547C2semidirect
2. C2×#5834C2semidirect
3. C2×#5832C2semidirect
4. #86684C2direct (N × H)
5. C2×#5721C2semidirect
6. C2×#5725C2semidirect
7. C2×#5661C2semidirect
8. C2×#5663C2semidirect
9. C2×#5631C2semidirect
10. C2×#5624C2semidirect
11. C2×#5599C2semidirect
12. C2×#5619C2semidirect
13. C2×#5557C2semidirect
14. C2×#5553C2semidirect
15. C2×#5553C2semidirect
16. C2×C4×#237C2semidirect
17. C2×#5514C2semidirect
18. C2×#5504C2semidirect
25. C3×#547C22semidirect
33. #5834C22semidirect
34. #5832C22semidirect
57. #5725C22semidirect
58. #5721C22semidirect
59. #5663C22semidirect
60. #5661C22semidirect
61. #5631C22semidirect
62. #5624C22semidirect
63. #5619C22semidirect
64. #5599C22semidirect
65. #5557C22semidirect
66. #5553C22semidirect
67. #5553C22semidirect
68. C4×#237C22semidirect
69. #5514C22semidirect
75. #5504C22semidirect
111. C2×#547D3semidirect
268. #547C2×D3semidirect
410. C2×Dic6#41semidirect
655. Dic6C2×#41semidirect
875. C2×C3#3517semidirect
914. C3C2×#3517semidirect
919. C2#86684direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C2×#58342
C2×#58322
#866842
C2×#57212
C2×#57252
C2×#56612
C2×#56632
C2×#56312
C2×#56242
C2×#55992
C2×#56192
C2×#55572
C2×#55532
C2×C4×#2372
C2×#55142
C2×#55042
C2×#35173