Finite Group Databasebeta

← C2×#83993 #11661846

Subgroups — C2×#83993 #11661846

Order 768.

4742 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5964C211yesmaximal, characteristic
2C22×C3×#137C211yesmaximal, characteristic, complemented
3C2×#5816C211yesmaximal, characteristic, complemented
4C22×#942C211yesmaximal, characteristic, complemented
5C2×#5236C211yesmaximal, characteristic, complemented
6C2×#5205C214yesmaximal, complemented
7#83993C2116yesmaximal, direct product factor
8C2×#5202C214yesmaximal, complemented
9C2×#5139C211yesmaximal, characteristic, complemented
10C2×#5132C211yesmaximal, characteristic, complemented
11C2×#3022—31nomaximal, Sylow
12C22×C3×#41C2211yescharacteristic
13C23×C3×Q8C2211yescharacteristic, complemented
14#5964—24no—
15#5964—24no—
16#5964—24no—
17#5964C2218yes—
18C2×#1010—21no—
19C2×#1010C2212yes—
20C2×#1009—21no—
21C2×#1009C2212yes—
22C2×D3×#41—22no—
23C2×D3×#41—22no—
24C2×#1007—21no—
25C2×#1004—21no—
26C2×#1004—22no—
27C22×#235—22no—
28C22×#235C2211yescharacteristic
29C22×#235C2211yescharacteristic
30C2×C3×#137—22no—
31C2×C3×#137—24no—
32C2×C3×#137C2214yescomplemented
33C2×C3×#137C2218yescomplemented
34C22×C3×Q16—21no—
35C22×C3×SD16—21no—
36C22×C3×M16C2211yescharacteristic, complemented
37#5816—24no—
38#5816C2218yescomplemented
39C2×#947C2212yescomplemented
40C2×#946—22no—
41C2×#944C2212yescomplemented
42C22×#216—21no—
43C2×#942—22no—
44C2×#942—24no—
45C2×#942C2214yescomplemented
46C2×#942C2218yescomplemented
47C22×#215—21no—
48C2×#929—22no—
49C2×#926C2211yescharacteristic, complemented
50C22×#208C2211yescharacteristic, complemented
51#5236C2218yescomplemented
52C2×#837C2214yescomplemented
53#5205C22132yescomplemented
54#5202C22132yescomplemented
55#5139C2218yescomplemented
56C2×#825C2214yescomplemented
57C2×#824C2212yescomplemented
58#5132C2218yescomplemented
59C2×#823C2212yescomplemented
60C2×#585—31no—
61C22×#137—31no—
62C22×#137D311yescharacteristic, complemented
63C2×#536—31no—
64#3022—316no—
65C2×#456—34no—
66C2×#455—34no—
67C2×#421—31no—
68C2×#421—31no—
69C2×#413—31no—
70C2×C3×#41—21no—
71C2×C3×#41—21no—
72C2×C3×#41—22no—
73C2×C3×#41—22no—
74C2×C3×#41D412yes—
75C2×C3×#41D414yes—
76C2×C3×#41C2312yes—
77C2×C3×#41C2314yes—
78C22×C3×Q8—21no—
79C22×C3×Q8—22no—
80C22×C3×Q8—21no—
81C22×C3×Q8—21no—
82C22×C3×Q8—22no—
83C22×C3×Q8—21no—
84C22×C3×Q8—21no—
85C22×C3×Q8—22no—
86C22×C3×Q8D411yescharacteristic
87C22×C3×Q8C2312yes—
88C22×C3×Q8C2314yescomplemented
89C22×C3×D4—21no—
90C22×C3×D4D411yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C22×#67—24no—
95C22×#67—21no—
96C22×#67D412yes—
97#1010—28no—
98#1010—24no—
99#1010—24no—
100#1010—28no—
101#1010—24no—
102#1010C2318yes—
103#1009—28no—
104#1009—24no—
105#1009—24no—
106#1009—28no—
107#1009—24no—
108#1009C2318yes—
109D3×#41—216no—
110D3×#41—216no—
111D3×#41—216no—
112D3×#41—216no—
113#1007—28no—
114#1007—28no—
115C2×#239—22no—
116C2×#239—22no—
117C2×D3×Q8—22no—
118C2×D3×Q8—22no—
119#1004—216no—
120#1004—28no—
121#1004—28no—
122#1004—216no—
123C2×#237—24no—
124C2×#237—22no—
125C2×#237—22no—
126C2×#237—24no—
127C2×D3×D4—24no—
128C2×D3×D4—22no—
129C2×D3×D4—24no—
130C2×D3×D4—22no—
131C2×#235—24no—
132C2×#235—24no—
133C2×#235—216no—
134C2×#235—21no—
135C2×#235—21no—
136C2×#235—21no—
137C2×#235—21no—
138C2×#235—21no—
139C2×#235—21no—
140C2×#235—22no—
141C2×#235—22no—
142C2×#235—22no—
143C2×#235—22no—
144C2×#235—216no—
145C2×#235—22no—
146C2×#235—22no—
147C2×#235D412yes—
148C2×#235D414yes—
149C2×#235D414yes—
150C2×#235C2312yes—
151C2×#235C2314yes—
152C2×#235C2314yes—
153C22×D12—22no—
154C22×D12D411yescharacteristic
155C22×D12C2311yescharacteristic
156C22×C4×D3—24no—
157C22×C4×D3—21no—
158C22×C4×D3D412yes—
159C22×Dic6—22no—
160C22×Dic6D411yescharacteristic
161C22×Dic6C2311yescharacteristic
162C3×#137—28no—
163C3×#137—216no—
164C3×#137C23116yescomplemented
165C2×C3×Q16—24no—
166C2×C3×Q16—28no—
167C2×C3×SD16—24no—
168C2×C3×SD16—28no—
169C2×C3×M16—21no—
170C2×C3×M16—22no—
171C2×C3×M16C2312yes—
172C2×C3×M16C2314yescomplemented
173C22×C3×C8—21no—
174C2×#217—21no—
175#947—24no—
176#947C2318yescomplemented
177#946—216no—
178#944—24no—
179#944C2318yescomplemented
180C2×#216—24no—
181C2×#216—28no—
182#942—28no—
183#942—216no—
184#942C23116yescomplemented
185C2×#215—24no—
186C2×#215—28no—
187#929—216no—
188C2×(C2×D3)⋊C4—24no—
189#926—22no—
190#926C2314yescomplemented
191C2×C4⋊Dic3—21no—
192C2×Dic3⋊C4—24no—
193C2×C4×Dic3C2312yes—
194C2×#208—21no—
195C2×#208—22no—
196C2×#208C2312yes—
197C2×#208C2314yescomplemented
198C22×C3⋊C8—21no—
199#837C23116yescomplemented
200#825C23116yescomplemented
201#824C2318yescomplemented
202#823C2318yescomplemented
203#585—38no—
204#585—64no—
205#585—64no—
206#585—64no—
207C2×2−1+4—32no—
208C2×2−1+4—61no—
209C2×2−1+4—61no—
210C2×H(5,𝔽2)—32no—
211C2×H(5,𝔽2)—62no—
212C2×H(5,𝔽2)—61no—
213C2×H(5,𝔽2)—61no—
214C22×#41—31no—
215C22×#41—31no—
216C22×#41—62no—
217C22×#41—62no—
218C22×#41—62no—
219C22×#41C2×D311yescharacteristic
220C23×Q8C2×D311yescharacteristic, complemented
221C2×#137—22no—
222C2×#137—24no—
223C2×#137—34no—
224C2×#137—38no—
225C2×#137—62no—
226C2×#137—64no—
227C2×#137C2×D314yescomplemented
228C2×#137C2×D318yescomplemented
229C22×Q16—21no—
230C22×Q16—61no—
231C22×SD16—21no—
232C22×SD16—61no—
233C22×M16—31no—
234C22×M16C2×D311yescharacteristic, complemented
235#536—38no—
236#536—64no—
237C2×C4⋊Q8—32no—
238C2×#124—32no—
239C2×#123—62no—
240C2×C22⋊Q8—62no—
241C2×#117—31no—
242#456—332no—
243#455—332no—
244#421—38no—
245#421—38no—
246C2×#104—34no—
247C2×#104—34no—
248#413—38no—
249C2×#101—32no—
250C2×#100—32no—
251C24×C3—21no—
252C24×C3C2×D411yescharacteristic
253C23×D3—24no—
254C23×D3—21no—
255C23×D3C2×D412yes—
256C3×#41—24no—
257C3×#41—24no—
258C3×#41—24no—
259C3×#41—24no—
260C3×#41—22no—
261C3×#41—24no—
262C3×#41—22no—
263C3×#41C2×D418yes—
264C3×#41C2×D414yes—
265C3×#41C2414yes—
266C2×C3×Q8—21no—
267C2×C3×Q8—22no—
268C2×C3×Q8—22no—
269C2×C3×Q8—24no—
270C2×C3×Q8—22no—
271C2×C3×Q8—24no—
272C2×C3×Q8—22no—
273C2×C3×Q8—24no—
274C2×C3×Q8—22no—
275C2×C3×Q8—24no—
276C2×C3×Q8—22no—
277C2×C3×Q8—24no—
278C2×C3×Q8—41no—
279C2×C3×Q8—42no—
280C2×C3×Q8—41no—
281C2×C3×Q8—42no—
282C2×C3×Q8—42no—
283C2×C3×Q8—42no—
284C2×C3×Q8—42no—
285C2×C3×Q8C2×D412yes—
286C2×C3×Q8C2×D414yes—
287C2×C3×Q8C2414yes—
288C2×C3×D4—22no—
289C2×C3×D4—24no—
290C2×C3×D4—22no—
291C2×C3×D4—24no—
292C2×C3×D4—21no—
293C2×C3×D4—22no—
294C2×C3×D4C2×D412yes—
295C2×C3×D4C2×D414yes—
296C22×C3×C4—21no—
297C22×C3×C4—22no—
298C22×C3×C4—24no—
299C22×C3×C4—22no—
300C22×C3×C4—24no—
301C22×C3×C4—22no—
302C22×C3×C4—24no—
303C22×C3×C4—41no—
304C22×C3×C4—41no—
305C22×C3×C4—42no—
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2×D411yescharacteristic
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2411yescharacteristic
315C22×C3×C4C2412yes—
316C2×#67—24no—
317C2×#67—24no—
318C2×#67—232no—
319C2×#67—22no—
320C2×#67—22no—
321C2×#67—22no—
322C2×#67—24no—
323C2×#67—24no—
324C2×#67—22no—
325C2×#67—24no—
326C2×#67C2×D418yes—
327C22×Dic3—24no—
328C22×Dic3—21no—
329C22×Dic3—22no—
330C22×Dic3C2×D412yes—
331#239—28no—
332#239—216no—
333#239—28no—
334D3×Q8—28no—
335D3×Q8—216no—
336D3×Q8—28no—
337#237—216no—
338#237—232no—
339#237—28no—
340#237—216no—
341#237—28no—
342#237—216no—
343D3×D4—232no—
344D3×D4—216no—
345D3×D4—28no—
346D3×D4—216no—
347D3×D4—216no—
348D3×D4—28no—
349#235—232no—
350#235—232no—
351#235—28no—
352#235—28no—
353#235—24no—
354#235—24no—
355#235—24no—
356#235—24no—
357#235—24no—
358#235—24no—
359#235—24no—
360#235—24no—
361#235—24no—
362#235—24no—
363#235—24no—
364#235—24no—
365#235—22no—
366#235—24no—
367#235—22no—
368#235—28no—
369#235—28no—
370#235C2×D418yes—
371#235C2×D414yes—
372#235C2414yes—
373C2×D12—24no—
374C2×D12—28no—
375C2×D12—21no—
376C2×D12—22no—
377C2×D12—21no—
378C2×D12—21no—
379C2×D12—21no—
380C2×D12—21no—
381C2×D12—28no—
382C2×D12C2×D412yes—
383C2×D12C2×D412yes—
384C2×D12C2×D414yes—
385C2×D12C2412yes—
386C2×C4×D3—24no—
387C2×C4×D3—24no—
388C2×C4×D3—232no—
389C2×C4×D3—22no—
390C2×C4×D3—22no—
391C2×C4×D3—24no—
392C2×C4×D3—22no—
393C2×C4×D3—24no—
394C2×C4×D3—22no—
395C2×C4×D3—24no—
396C2×C4×D3C2×D418yes—
397C2×Dic6—24no—
398C2×Dic6—28no—
399C2×Dic6—21no—
400C2×Dic6—22no—
401C2×Dic6—21no—
402C2×Dic6—21no—
403C2×Dic6—21no—
404C2×Dic6—21no—
405C2×Dic6—28no—
406C2×Dic6C2×D412yes—
407C2×Dic6C2×D412yes—
408C2×Dic6C2×D414yes—
409C2×Dic6C2412yes—
410C3×Q16—216no—
411C3×SD16—216no—
412C3×M16—22no—
413C3×M16—24no—
414C3×M16C2414yes—
415C2×C3×C8—22no—
416C2×C3×C8—24no—
417#217—24no—
418#216—216no—
419#215—216no—
420(C2×D3)⋊C4—216no—
421C4⋊Dic3—24no—
422Dic3⋊C4—216no—
423C4×Dic3—22no—
424C4×Dic3C2414yes—
425#208—22no—
426#208—24no—
427#208C2414yes—
428C2×C3⋊C8—22no—
429C2×C3⋊C8—24no—
4302−1+4—38no—
4312−1+4—68no—
4322−1+4—64no—
4332−1+4—68no—
4342−1+4—64no—
4352−1+4—68no—
4362−1+4—64no—
4372−1+4—68no—
438H(5,𝔽2)—38no—
439H(5,𝔽2)—616no—
440H(5,𝔽2)—616no—
441H(5,𝔽2)—68no—
442H(5,𝔽2)—64no—
443H(5,𝔽2)—68no—
444H(5,𝔽2)—64no—
445H(5,𝔽2)—68no—
446H(5,𝔽2)—64no—
447H(5,𝔽2)—68no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—34no—
453C2×#41—34no—
454C2×#41—32no—
455C2×#41—34no—
456C2×#41—32no—
457C2×#41—34no—
458C2×#41—62no—
459C2×#41—62no—
460C2×#41—616no—
461C2×#41—64no—
462C2×#41—64no—
463C2×#41—616no—
464C2×#41—64no—
465C2×#41—616no—
466C2×#41—64no—
467C2×#41—62no—
468C2×#41—62no—
469C2×#41—616no—
470C2×#41—616no—
471C2×#41—616no—
472C2×#41—62no—
473C2×#41—62no—
474C2×#41—61no—
475C2×#41—61no—
476C2×#41—61no—
477C2×#41—62no—
478C2×#41—62no—
479C2×#41—61no—
480C2×#41—61no—
481C2×#41—61no—
482C2×#41—62no—
483C2×#41—62no—
484C2×#41#6712yes—
485C2×#41#6714yes—
486C2×#41C22×D312yes—
487C2×#41C22×D314yes—
488C22×Q8—21no—
489C22×Q8—22no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—22no—
496C22×Q8—31no—
497C22×Q8—31no—
498C22×Q8—62no—
499C22×Q8—62no—
500C22×Q8—62no—
501C22×Q8#6711yescharacteristic
502C22×Q8C22×D312yes—
503C22×Q8C22×D314yescomplemented
504C22×D4—21no—
505C22×D4—32no—
506C22×D4—31no—
507C22×D4—31no—
508C22×D4—62no—
509C22×D4—64no—
510C22×D4—64no—
511C22×D4—62no—
512C22×D4—64no—
513C22×D4—61no—
514C22×D4—62no—
515C22×D4#6711yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—32no—
519C23×C4—64no—
520C23×C4—61no—
521C23×C4C22×D311yescharacteristic
522#137—28no—
523#137—216no—
524#137—316no—
525#137—68no—
526#137—616no—
527#137C22×D3116yescomplemented
528C2×Q16—24no—
529C2×Q16—28no—
530C2×Q16—64no—
531C2×Q16—68no—
532C2×SD16—24no—
533C2×SD16—28no—
534C2×SD16—64no—
535C2×SD16—68no—
536C2×M16—21no—
537C2×M16—22no—
538C2×M16—32no—
539C2×M16—34no—
540C2×M16—61no—
541C2×M16—62no—
542C2×M16C22×D312yes—
543C2×M16C22×D314yescomplemented
544C22×C8—21no—
545C22×C8—61no—
546C4⋊Q8—38no—
547C4⋊Q8—64no—
548#124—38no—
549#124—64no—
550#123—616no—
551C22⋊Q8—616no—
552#117—34no—
553#117—62no—
554C2×C4⋊C4—64no—
555C2×C4⋊C4—61no—
556C2×C22⋊C4—64no—
557C2×C22⋊C4—61no—
558C2×C42—32no—
559#104—316no—
560#104—316no—
561#101—38no—
562#100—38no—
563C23×C3—22no—
564C23×C3—24no—
565C23×C3—42no—
566C23×C3—82no—
567C23×C3#12011yescharacteristic
568C23×C3#12011yescharacteristic
569C23×C3#12012yes—
570C23×C3C22×D411yescharacteristic
571C23×C3C22×D412yes—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—216no—
575C22×D3—22no—
576C22×D3—24no—
577C22×D3—44no—
578C22×D3—82no—
579C22×D3—88no—
580C22×D3C22×D414yes—
581C3×Q8—24no—
582C3×Q8—22no—
583C3×Q8—24no—
584C3×Q8—24no—
585C3×Q8—42no—
586C3×Q8—42no—
587C3×Q8—44no—
588C3×Q8—44no—
589C3×Q8C22×D414yes—
590C3×D4—28no—
591C3×D4—24no—
592C3×D4—24no—
593C3×D4—24no—
594C3×D4—22no—
595C3×D4C22×D414yes—
596C2×C3×C4—22no—
597C2×C3×C4—24no—
598C2×C3×C4—24no—
599C2×C3×C4—28no—
600C2×C3×C4—24no—
601C2×C3×C4—24no—
602C2×C3×C4—42no—
603C2×C3×C4—44no—
604C2×C3×C4—44no—
605C2×C3×C4—42no—
606C2×C3×C4#12011yescharacteristic
607C2×C3×C4#12012yes—
608C2×C3×C4#12011yescharacteristic
609C2×C3×C4#12012yes—
610C2×C3×C4#12012yes—
611C2×C3×C4#12012yes—
612C2×C3×C4#12012yes—
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D412yes—
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D412yes—
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D412yes—
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C22×D412yes—
621C2×C3×C4C22×D411yescharacteristic
622C2×C3×C4C22×D412yes—
623C2×C3×C4C2511yescharacteristic
624#67—216no—
625#67—216no—
626#67—28no—
627#67—28no—
628#67—28no—
629#67—24no—
630#67—24no—
631C2×Dic3—216no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—24no—
636C2×Dic3—24no—
637C2×Dic3—44no—
638C2×Dic3C22×D414yes—
639D12—216no—
640D12—22no—
641D12—22no—
642D12—22no—
643D12—24no—
644D12—22no—
645D12—22no—
646D12C22×D414yes—
647C4×D3—216no—
648C4×D3—216no—
649C4×D3—28no—
650C4×D3—28no—
651C4×D3—24no—
652C4×D3—28no—
653C4×D3—24no—
654Dic6—216no—
655Dic6—22no—
656Dic6—22no—
657Dic6—22no—
658Dic6—24no—
659Dic6—22no—
660Dic6—22no—
661Dic6C22×D414yes—
662C3×C8—24no—
663C3⋊C8—24no—
664C24—21no—
665C24—32no—
666C24—64no—
667C24—61no—
668C24D3×D411yescharacteristic
669#41—24no—
670#41—24no—
671#41—24no—
672#41—24no—
673#41—24no—
674#41—22no—
675#41—22no—
676#41—38no—
677#41—34no—
678#41—34no—
679#41—68no—
680#41—68no—
681#41—632no—
682#41—632no—
683#41—68no—
684#41—68no—
685#41—616no—
686#41—616no—
687#41—632no—
688#41—616no—
689#41—68no—
690#41—616no—
691#41—68no—
692#41—68no—
693#41—68no—
694#41—64no—
695#41—64no—
696#41—64no—
697#41—64no—
698#41—64no—
699#41—64no—
700#41—64no—
701#41—64no—
702#41—64no—
703#41—64no—
704#41—62no—
705#41—64no—
706#41—64no—
707#41—62no—
708#41—64no—
709#41C2×#6718yes—
710#41C2×#6714yes—
711#41C23×D314yes—
712C2×Q8—21no—
713C2×Q8—22no—
714C2×Q8—24no—
715C2×Q8—22no—
716C2×Q8—22no—
717C2×Q8—24no—
718C2×Q8—22no—
719C2×Q8—24no—
720C2×Q8—22no—
721C2×Q8—24no—
722C2×Q8—22no—
723C2×Q8—24no—
724C2×Q8—32no—
725C2×Q8—32no—
726C2×Q8—32no—
727C2×Q8—34no—
728C2×Q8—42no—
729C2×Q8—42no—
730C2×Q8—42no—
731C2×Q8—42no—
732C2×Q8—42no—
733C2×Q8—41no—
734C2×Q8—41no—
735C2×Q8—68no—
736C2×Q8—64no—
737C2×Q8—68no—
738C2×Q8—616no—
739C2×Q8—68no—
740C2×Q8—68no—
741C2×Q8—61no—
742C2×Q8—62no—
743C2×Q8—61no—
744C2×Q8—61no—
745C2×Q8—61no—
746C2×Q8—61no—
747C2×Q8C2×#6712yes—
748C2×Q8C2×#6714yes—
749C2×Q8C23×D314yes—
750C2×D4—22no—
751C2×D4—24no—
752C2×D4—22no—
753C2×D4—24no—
754C2×D4—21no—
755C2×D4—22no—
756C2×D4—38no—
757C2×D4—32no—
758C2×D4—34no—
759C2×D4—32no—
760C2×D4—32no—
761C2×D4—68no—
762C2×D4—64no—
763C2×D4—68no—
764C2×D4—616no—
765C2×D4—632no—
766C2×D4—616no—
767C2×D4—616no—
768C2×D4—68no—
769C2×D4—64no—
770C2×D4—64no—
771C2×D4—632no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—64no—
775C2×D4—62no—
776C2×D4—64no—
777C2×D4—62no—
778C2×D4—64no—
779C2×D4—68no—
780C2×D4—61no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—61no—
785C2×D4—61no—
786C2×D4C2×#6712yes—
787C2×D4C2×#6714yes—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—24no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—22no—
794C22×C4—24no—
795C22×C4—32no—
796C22×C4—38no—
797C22×C4—42no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—64no—
801C22×C4—64no—
802C22×C4—632no—
803C22×C4—64no—
804C22×C4—61no—
805C22×C4—62no—
806C22×C4—62no—
807C22×C4—64no—
808C22×C4—62no—
809C22×C4—64no—
810C22×C4—62no—
811C22×C4—64no—
812C22×C4—62no—
813C22×C4D3×D411yescharacteristic
814C22×C4D3×D412yes—
815C22×C4D3×D411yescharacteristic
816C22×C4D3×D411yescharacteristic
817C22×C4D3×D412yes—
818C22×C4C2×#6711yescharacteristic
819C22×C4C2×#6711yescharacteristic
820C22×C4C2×#6712yes—
821C22×C4C23×D311yescharacteristic
822C22×C4C23×D312yes—
823Q16—216no—
824Q16—616no—
825SD16—216no—
826SD16—616no—
827M16—22no—
828M16—24no—
829M16—34no—
830M16—64no—
831M16—62no—
832M16C23×D314yes—
833C2×C8—22no—
834C2×C8—24no—
835C2×C8—64no—
836C2×C8—62no—
837C4⋊C4—616no—
838C4⋊C4—64no—
839C22⋊C4—616no—
840C22⋊C4—64no—
841C42—34no—
842C42—62no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—24no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—44no—
850C22×C3—84no—
851C22×C3C2×#12011yescharacteristic
852C22×C3C2×#12012yes—
853C22×C3C2×#12012yes—
854C22×C3C2×#12011yescharacteristic
855C22×C3C23×D411yescharacteristic
856C2×D3—24no—
857C2×D3—24no—
858C2×D3—44no—
859C2×D3—44no—
860C2×D3—44no—
861C2×D3—82no—
862C2×D3—84no—
863C2×D3—816no—
864C3×C4—24no—
865C3×C4—44no—
866C3×C4C2×#12011yescharacteristic
867C3×C4C2×#12011yescharacteristic
868C3×C4C2×#12012yes—
869C3×C4C2×#12012yes—
870C3×C4C23×D411yescharacteristic
871C3×C4C23×D411yescharacteristic
872Dic3—24no—
873Dic3—24no—
874Dic3—44no—
875C23—22no—
876C23—24no—
877C23—34no—
878C23—42no—
879C23—616no—
880C23—62no—
881C23—62no—
882C23—64no—
883C23—62no—
884C23—82no—
885C23—124no—
886C23—242no—
887C23—248no—
888C23#93711yescharacteristic
889C23#93711yescharacteristic
890C23#93712yes—
891C23C2×D3×D411yescharacteristic
892C23C2×D3×D412yes—
893Q8—24no—
894Q8—22no—
895Q8—24no—
896Q8—24no—
897Q8—34no—
898Q8—44no—
899Q8—42no—
900Q8—44no—
901Q8—42no—
902Q8—616no—
903Q8—62no—
904Q8—62no—
905Q8—62no—
906Q8—62no—
907Q8—62no—
908Q8—64no—
909Q8C22×#6714yes—
910D4—24no—
911D4—28no—
912D4—24no—
913D4—24no—
914D4—22no—
915D4—34no—
916D4—616no—
917D4—616no—
918D4—616no—
919D4—64no—
920D4—68no—
921D4—68no—
922D4—68no—
923D4—64no—
924D4—62no—
925D4—62no—
926D4—62no—
927D4—62no—
928D4—64no—
929D4—62no—
930D4C22×#6714yes—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—34no—
938C2×C4—44no—
939C2×C4—42no—
940C2×C4—44no—
941C2×C4—42no—
942C2×C4—616no—
943C2×C4—616no—
944C2×C4—616no—
945C2×C4—62no—
946C2×C4—64no—
947C2×C4—62no—
948C2×C4—62no—
949C2×C4—64no—
950C2×C4—68no—
951C2×C4—68no—
952C2×C4—68no—
953C2×C4—64no—
954C2×C4—64no—
955C2×C4—124no—
956C2×C4#93712yes—
957C2×C4#93712yes—
958C2×C4#93712yes—
959C2×C4#93712yes—
960C2×C4#93712yes—
961C2×C4#93711yescharacteristic
962C2×C4#93711yescharacteristic
963C2×C4C2×D3×D412yes—
964C2×C4C2×D3×D412yes—
965C2×C4C2×D3×D411yescharacteristic
966C2×C4C2×D3×D411yescharacteristic
967C2×C4C2×D3×D411yescharacteristic
968C2×C4C2×D3×D412yes—
969C2×C4C22×#6712yes—
970C2×C4C22×#6712yes—
971C2×C4C22×#6711yescharacteristic
972C2×C4C22×#6711yescharacteristic
973C2×C4C24×D311yescharacteristic
974C8—24no—
975C8—64no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—22no—
979C2×C3—22no—
980C2×C3—44no—
981C2×C3#302212yescomplemented
982C2×C3C22×#12011yescharacteristic
983D3—44no—
984D3—44no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—24no—
989C22—42no—
990C22—42no—
991C22—44no—
992C22—64no—
993C22—64no—
994C22—84no—
995C22—124no—
996C22—124no—
997C22—124no—
998C22—242no—
999C22—244no—
1000C22—2416no—
1001C22C2×#93712yes—
1002C22C2×#93711yescharacteristic
1003C22C2×#93712yes—
1004C22C2×#93711yescharacteristic
1005C22C22×D3×D411yescharacteristic
1006C4—24no—
1007C4—44no—
1008C4—64no—
1009C4—64no—
1010C4—124no—
1011C4C2×#93712yes—
1012C4C2×#93711yescharacteristic
1013C4C2×#93712yes—
1014C4C2×#93711yescharacteristic
1015C4C22×D3×D411yescharacteristic
1016C4C23×#6711yescharacteristic
1017C3C2×#302211yescharacteristic, complemented, Sylow
1018C2—21no—
1019C2—22no—
1020C2—21no—
1021C2—22no—
1022C2—44no—
1023C2—124no—
1024C2—124no—
1025C2#8399312yesdirect product factor
1026C2C22×#93711yescharacteristic
subgroupG/H
centerC22C2×#937
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#137C2
socleC22×C3C2×#120
prime radicalC2×#5964C2
hypercenterC22×#137D3
hypocenterC3C2×#3022
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C22×C3×#137C2semidirect
3. C2×#5816C2semidirect
4. C22×#942C2semidirect
5. C2×#5236C2semidirect
6. C2×#5205C2semidirect
7. #83993C2direct (N × H)
8. C2×#5202C2semidirect
9. C2×#5139C2semidirect
10. C2×#5132C2semidirect
13. C23×C3×Q8C22semidirect
32. C2×C3×#137C22semidirect
33. C2×C3×#137C22semidirect
36. C22×C3×M16C22semidirect
38. #5816C22semidirect
39. C2×#947C22semidirect
41. C2×#944C22semidirect
45. C2×#942C22semidirect
46. C2×#942C22semidirect
49. C2×#926C22semidirect
50. C22×#208C22semidirect
51. #5236C22semidirect
52. C2×#837C22semidirect
53. #5205C22semidirect
54. #5202C22semidirect
55. #5139C22semidirect
56. C2×#825C22semidirect
57. C2×#824C22semidirect
58. #5132C22semidirect
59. C2×#823C22semidirect
62. C22×#137D3semidirect
88. C22×C3×Q8C23semidirect
164. C3×#137C23semidirect
172. C2×C3×M16C23semidirect
176. #947C23semidirect
179. #944C23semidirect
184. #942C23semidirect
190. #926C23semidirect
197. C2×#208C23semidirect
199. #837C23semidirect
200. #825C23semidirect
201. #824C23semidirect
202. #823C23semidirect
220. C23×Q8C2×D3semidirect
227. C2×#137C2×D3semidirect
228. C2×#137C2×D3semidirect
234. C22×M16C2×D3semidirect
503. C22×Q8C22×D3semidirect
527. #137C22×D3semidirect
543. C2×M16C22×D3semidirect
981. C2×C3#3022semidirect
1017. C3C2×#3022semidirect
1025. C2#83993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#59642
C22×C3×#1372
C2×#58162
C22×#9422
C2×#52362
C2×#52052
#839932
C2×#52022
C2×#51392
C2×#51322
C2×#30223