Finite Group Databasebeta

← #11900153

Subgroups — #11900153

Order 1152.

3227 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2#10595975C211yesmaximal, characteristic, complemented
3C3×#5504C211yesmaximal, characteristic, complemented
4C2×C3×#892C211yesmaximal, characteristic, complemented
5#10595056C214yesmaximal, complemented
6#10594990C211yesmaximal, characteristic, complemented
7#10594986C211yesmaximal, characteristic, complemented
8D3×#926C211yesmaximal, characteristic, complemented
9C4×#3804C214yesmaximal, complemented
10#10594604C212yesmaximal, complemented
11#10594602C212yesmaximal, complemented
12D3×#892C212yesmaximal, complemented
13#10594511C212yesmaximal, complemented
14#10594510C212yesmaximal, complemented
15#10594362C212yesmaximal, complemented
16#10594358C212yesmaximal, complemented
17#10594357C212yesmaximal, complemented
18#85885—31nomaximal
19#85731—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C2×D3×#67C2212yes—
24C2×#3804C2212yes—
25D3×#235C4116yescomplemented
26C2×D3×D12C2211yescharacteristic
27C2×C4×D32C2212yes—
28C2×#3799C2211yescharacteristic
29C2×#3798C2212yes—
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C4×#638C2214yescomplemented
34#64135C2211yescharacteristic, complemented
35#64102C2212yescomplemented
36#64101C2212yescomplemented
37C4⋊C4×C3⋊D3C2212yescomplemented
38#64096C2212yescomplemented
39C3×C4×#67C2214yescomplemented
40C2×C3×(C2×D3)⋊C4C2212yes—
41C3×#926C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43C2×C3×C4×Dic3C2212yescomplemented
44C3×#893C2212yescomplemented
45C3×#892C2212yes—
46C3×#892C2212yes—
47C3×#892C2212yescomplemented
48C3×#892C2212yescomplemented
49C3×#892C2212yescomplemented
50C3×D3×C4⋊C4C2212yescomplemented
51C3×#887C2212yescomplemented
52Dic3×#67C2214yescomplemented
53D3×#217C2212yes—
54#63955C2212yescomplemented
55#63952C2214yescomplemented
56#63921C2214yes—
57D3×(C2×D3)⋊C4C2214yes—
58C4×#627C2214yescomplemented
59C4×#626C2214yescomplemented
60#63902C2214yescomplemented
61#63900C2212yescomplemented
62#63898C2212yescomplemented
63#63894C2212yescomplemented
64D3×C4⋊Dic3C2212yescomplemented
65D3×C4⋊Dic3C2211yescharacteristic, complemented
66D3×C4⋊Dic3C2211yescharacteristic, complemented
67C4×#624C2214yescomplemented
68#63881C2214yescomplemented
69#63880C2214yescomplemented
70#63880C2214yescomplemented
71#63879C2214yescomplemented
72#63878C2214yes—
73#63877C2214yes—
74#63877C2214yescomplemented
75C4×D3×Dic3C2214yescomplemented
76C4×D3×Dic3C2212yescomplemented
77#63855C2212yes—
78#63849C2212yescomplemented
79#63844C2212yescomplemented
80#63843C2212yescomplemented
81#63841C2211yescharacteristic
82#63841C2211yescharacteristic
83#63841C2212yescomplemented
84#63837C2214yescomplemented
85#63836C2214yescomplemented
86C2×D3×#41—31no—
87C22×#235—31no—
88C3×#520—31no—
89C2×C3×#117—31no—
90#5827—31no—
91C2×#926—31no—
92C4×#239—32no—
93#5572—32no—
94#5545—34no—
95#5545—32no—
96C4×#237—34no—
97C4×#237—32no—
98#5523—31no—
99#5523—32no—
100#5523—32no—
101#5523—32no—
102#5522—32no—
103#5522—32no—
104#5521—32no—
105D3×#117—31no—
106D3×#117—32no—
107D3×#117—32no—
108D3×#117—32no—
109#5516—32no—
110#5504—31no—
111#5504—31no—
112#5504—31no—
113#5504—31no—
114#5504—32no—
115#5504—61no—
116#5504D311yescharacteristic, complemented
117C2×#892—32no—
118C2×#892D311yescharacteristic, complemented
119#5486—34no—
120C4×#235—34no—
121C23×C3×D3C2311yescharacteristic
122C22×D32C2312yes—
123C22×C32×C4C2312yes—
124C22×C32×C4C2311yescharacteristic
125C2×#638C2312yes—
126#3828C2×C418yescomplemented
127C2×C4⋊(C3⋊D3)C2311yescharacteristic
128C2×C4×C3⋊D3C2314yes—
129C2×C4×C3⋊D3C2312yes—
130C2×#634C2311yescharacteristic
131C2×C3×#67C2312yes—
132C22×C3×Dic3C2312yes—
133C22×C3×Dic3C2311yescharacteristic
134C3×#235C2×C418yescomplemented
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3C2×C418yescomplemented
137C2×C3×C4×D3C2314yes—
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×Dic6C2311yescharacteristic
144D3×#67C2×C4116yescomplemented
145C2×#627C2312yes—
146C2×#626C2312yes—
147C2×#626C2312yes—
148C2×#625C2312yes—
149C2×#624C2314yes—
150C2×#624C2312yes—
151#3804C2×C4116yescomplemented
152C2×D3×Dic3C2312yes—
153C2×D3×Dic3C2312yes—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2312yes—
156C2×D3×Dic3C2312yes—
157D3×D12C2×C418yescomplemented
158C4×D32C2×C4116yescomplemented
159#3799C2×C418yescomplemented
160#3798C2×C4116yescomplemented
161#3795C2×C418yescomplemented
162D3×Dic6C2×C418yescomplemented
163C32×C4⋊C4C2312yes—
164C32×C4⋊C4C2312yes—
165#3757C2312yes—
166#3752C2314yes—
167C4⋊(C3⋊Dic3)C2311yescharacteristic
168C4⋊(C3⋊Dic3)C2311yescharacteristic
169#3750C2314yes—
170C4×C3⋊Dic3C2312yes—
171C4×C3⋊Dic3C2314yes—
172C3×#217C2312yes—
173C3×(C2×D3)⋊C4C2314yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×(C2×D3)⋊C4C2314yes—
176C3×C4⋊Dic3C2311yescharacteristic
177C3×C4⋊Dic3C2312yes—
178C3×C4⋊Dic3C2312yes—
179C3×C4⋊Dic3C2311yescharacteristic
180C3×Dic3⋊C4C2314yes—
181C3×C4×Dic3C2314yes—
182C3×C4×Dic3C2312yes—
183C3×C4×Dic3C2314yes—
184C3×C4×Dic3C2314yes—
185#3724C2314yes—
186Dic3⋊Dic3C2314yes—
187Dic3⋊Dic3C2312yes—
188Dic3⋊Dic3C2312yes—
189#3722C2314yes—
190(C2×D3)⋊Dic3C2312yes—
191(C2×D3)⋊Dic3C2312yes—
192(C2×D3)⋊Dic3C2314yes—
193Dic32C2312yes—
194Dic32C2314yes—
195Dic32C2314yes—
196Dic32C2312yes—
197#3428—91noSylow
198C2×C3×#41—31no—
199C23×C3×C4—31no—
200C22×#67—32no—
201D3×#41—316no—
202C2×#239—31no—
203C2×D3×Q8—31no—
204C2×#237—32no—
205C2×#237—31no—
206C2×D3×D4—32no—
207C2×D3×D4—31no—
208C2×#235—31no—
209C2×#235—31no—
210C2×#235—32no—
211C2×#235—316no—
212C2×#235—31no—
213C2×#235—32no—
214C2×#235—32no—
215C2×#235—31no—
216C2×#235—61no—
217C2×#235C2×D311yescharacteristic
218C22×D12—31no—
219C22×C4×D3—32no—
220C22×C4×D3—32no—
221C22×C4×D3C2×D311yescharacteristic
222C22×Dic6—31no—
223C3×C4×Q8—32no—
224C3×C4×D4—34no—
225C3×C4×D4—32no—
226C3×#117—31no—
227C3×#117—32no—
228C3×#117—32no—
229C3×#117—32no—
230C3×#117—32no—
231C3×#117—32no—
232C2×C3×C4⋊C4—21no—
233C2×C3×C4⋊C4—31no—
234C2×C3×C4⋊C4—32no—
235C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
236C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
237C2×C3×C22⋊C4—32no—
238C2×C3×C42—32no—
239C2×#217—32no—
240Q8×Dic3—32no—
241D4×Dic3—34no—
242D4×Dic3—32no—
243C4×#67—34no—
244C4×#67—34no—
245C4×#67—34no—
246C4×#67—34no—
247C4×#67—34no—
248C4×#67—34no—
249C4×#67—64no—
250C4×#67C2×D314yescomplemented
251C2×(C2×D3)⋊C4—34no—
252C2×(C2×D3)⋊C4C2×D312yes—
253#926—31no—
254#926—31no—
255#926—32no—
256#926—31no—
257#926—31no—
258#926—32no—
259#926—32no—
260#926—61no—
261#926C2×D311yescharacteristic, complemented
262C2×C4⋊Dic3—32no—
263C2×C4⋊Dic3—31no—
264C2×C4⋊Dic3—31no—
265C2×C4⋊Dic3C2×D311yescharacteristic, complemented
266C2×C4×Dic3—34no—
267C2×C4×Dic3—32no—
268C2×C4×Dic3C2×D312yescomplemented
269#893—32no—
270#893—32no—
271#893—32no—
272#893—34no—
273#893—32no—
274#893—62no—
275#893C2×D312yescomplemented
276#892—31no—
277#892—31no—
278#892—32no—
279#892—32no—
280#892—32no—
281#892—34no—
282#892—32no—
283#892—32no—
284#892—34no—
285#892—62no—
286#892C2×D312yes—
287#892C2×D312yes—
288#892C2×D312yescomplemented
289#892C2×D312yescomplemented
290#892C2×D312yescomplemented
291D3×C4⋊C4—31no—
292D3×C4⋊C4—32no—
293D3×C4⋊C4—31no—
294D3×C4⋊C4—32no—
295D3×C4⋊C4—32no—
296D3×C4⋊C4—32no—
297D3×C4⋊C4—32no—
298D3×C4⋊C4—62no—
299D3×C4⋊C4C2×D312yescomplemented
300#887—32no—
301#887—32no—
302#887—32no—
303#887—34no—
304#887—32no—
305#887—62no—
306#887C2×D312yescomplemented
307#67⋊C4—34no—
308#67⋊C4—34no—
309#67⋊C4—34no—
310#67⋊C4—34no—
311#67⋊C4—34no—
312#67⋊C4—34no—
313#67⋊C4—34no—
314D3×C22⋊C4—32no—
315D3×C22⋊C4—34no—
316D3×C22⋊C4—34no—
317D3×C22⋊C4—34no—
318#877—32no—
319#877—34no—
320#877—34no—
321#877—34no—
322C4×D12—34no—
323C4×D12—34no—
324C4×D12—34no—
325C4×D12—32no—
326#872—32no—
327#872—34no—
328#872—34no—
329#872—34no—
330C42×D3—34no—
331C42×D3—32no—
332C42×D3—34no—
333C42×D3—34no—
334C4×Dic6—32no—
335C4×Dic6—34no—
336C4×Dic6—34no—
337C4×Dic6—34no—
338C23×C32C2411yescharacteristic
339C22×C3⋊D3C2412yes—
340C22×C3×D3—41no—
341C22×C3×D3—41no—
342C22×C3×D3C22×C414yes—
343C22×C3×D3C2411yescharacteristic
344C22×C3×D3C2412yes—
345C22×C3×D3C2411yescharacteristic
346C2×D32—42no—
347C2×D32—42no—
348C2×D32C22×C418yes—
349C2×C32×C4—42no—
350C2×C32×C4C22×C414yes—
351C2×C32×C4C2414yes—
352C2×C32×C4C2411yescharacteristic
353C2×C32×C4C2411yescharacteristic
354#638C22×C418yes—
355C2×C3⋊Dic3C2412yes—
356C2×C3⋊Dic3C2412yes—
357C2×C3⋊Dic3C2412yes—
358C4⋊(C3⋊D3)C22×C414yes—
359C4×C3⋊D3—44no—
360C4×C3⋊D3C22×C418yes—
361#634C22×C414yes—
362C3×#67C22×C418yes—
363C2×C3×Dic3—42no—
364C2×C3×Dic3C22×C414yes—
365C2×C3×Dic3C2412yes—
366C2×C3×Dic3C2414yes—
367C2×C3×Dic3C2412yes—
368C2×C3×Dic3C2411yescharacteristic
369C2×C3×Dic3C2412yes—
370C2×C3×Dic3C2411yescharacteristic
371C3×D12C22×C414yes—
372C3×C4×D3—44no—
373C3×C4×D3C22×C414yes—
374C3×C4×D3C22×C414yes—
375C3×C4×D3C22×C414yes—
376C3×C4×D3C22×C418yes—
377C3×C4×D3C22×C414yes—
378C3×Dic6C22×C414yes—
379#627C22×C418yes—
380#626C22×C418yes—
381#626C22×C418yes—
382#625C22×C418yes—
383#624—44no—
384#624C22×C418yes—
385D3×Dic3—42no—
386D3×Dic3—44no—
387D3×Dic3—42no—
388D3×Dic3C22×C418yes—
389D3×Dic3C22×C418yes—
390C22×#41—91no—
391#520—31no—
392#520—91no—
393#520—92no—
394#520—91no—
395#520—92no—
396#520—91no—
397#519—92no—
398#518—94no—
399#518—92no—
400C4×#41—94no—
401C4×#41—92no—
402C4×#41—92no—
403C2×#117—31no—
404C2×#117—92no—
405C2×#117—92no—
406C2×#117—91no—
407C24×C3—31no—
408C23×D3—32no—
409C23×D3—32no—
410C23×D3C22×D311yescharacteristic
411C3×#41—38no—
412C2×C3×Q8—31no—
413C2×C3×D4—32no—
414C2×C3×D4—31no—
415C22×C3×C4—21no—
416C22×C3×C4—22no—
417C22×C3×C4—31no—
418C22×C3×C4—38no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—32no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—32no—
425C22×C3×C4—34no—
426C22×C3×C4C22×D312yes—
427C22×C3×C4C22×D312yes—
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C2×#67—32no—
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—316no—
435C2×#67—32no—
436C2×#67—32no—
437C2×#67—62no—
438C2×#67C22×D312yes—
439C22×Dic3—32no—
440C22×Dic3—32no—
441C22×Dic3—32no—
442C22×Dic3—32no—
443C22×Dic3—34no—
444C22×Dic3C22×D312yes—
445C22×Dic3C22×D311yescharacteristic
446#239—38no—
447D3×Q8—38no—
448#237—316no—
449#237—38no—
450D3×D4—316no—
451D3×D4—38no—
452#235—38no—
453#235—38no—
454#235—316no—
455#235—38no—
456#235—316no—
457#235—316no—
458#235—38no—
459#235—68no—
460#235C4×D318yescomplemented
461C2×D12—32no—
462C2×D12—32no—
463C2×D12—31no—
464C2×D12—31no—
465C2×D12—38no—
466C2×D12—61no—
467C2×D12C22×D311yescharacteristic
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—32no—
471C2×C4×D3—32no—
472C2×C4×D3—32no—
473C2×C4×D3—32no—
474C2×C4×D3—316no—
475C2×C4×D3—316no—
476C2×C4×D3—32no—
477C2×C4×D3—34no—
478C2×C4×D3—32no—
479C2×C4×D3—34no—
480C2×C4×D3—34no—
481C2×C4×D3—34no—
482C2×C4×D3—34no—
483C2×C4×D3—62no—
484C2×C4×D3—64no—
485C2×C4×D3C4×D318yescomplemented
486C2×C4×D3C22×D314yes—
487C2×C4×D3C22×D311yescharacteristic
488C2×C4×D3C22×D311yescharacteristic
489C2×C4×D3C22×D311yescharacteristic
490C2×C4×D3C22×D312yes—
491C2×C4×D3C22×D311yescharacteristic
492C2×Dic6—31no—
493C2×Dic6—31no—
494C2×Dic6—32no—
495C2×Dic6—32no—
496C2×Dic6—38no—
497C2×Dic6—61no—
498C2×Dic6C22×D311yescharacteristic
499C3×C4⋊C4—22no—
500C3×C4⋊C4—22no—
501C3×C4⋊C4—32no—
502C3×C4⋊C4—34no—
503C3×C4⋊C4—31no—
504C3×C4⋊C4—32no—
505C3×C4⋊C4—31no—
506C3×C4⋊C4C22×D312yes—
507C3×C4⋊C4C22×D312yes—
508C3×C4⋊C4C22×D312yes—
509C3×C4⋊C4C22×D312yes—
510C3×C22⋊C4—32no—
511C3×C22⋊C4—34no—
512C3×C22⋊C4—34no—
513C3×C22⋊C4—34no—
514C3×C42—34no—
515C3×C42—34no—
516C3×C42—32no—
517C3×C42—34no—
518#217—32no—
519#217—32no—
520#217—32no—
521#217—32no—
522#217—34no—
523#217—62no—
524#217C22×D312yes—
525(C2×D3)⋊C4—32no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—32no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—34no—
532(C2×D3)⋊C4—64no—
533(C2×D3)⋊C4C22×D314yes—
534(C2×D3)⋊C4C22×D314yes—
535(C2×D3)⋊C4C22×D314yes—
536C4⋊Dic3—31no—
537C4⋊Dic3—31no—
538C4⋊Dic3—31no—
539C4⋊Dic3—31no—
540C4⋊Dic3—32no—
541C4⋊Dic3—32no—
542C4⋊Dic3—34no—
543C4⋊Dic3—61no—
544C4⋊Dic3—61no—
545C4⋊Dic3C22×D312yes—
546C4⋊Dic3C22×D311yescharacteristic
547C4⋊Dic3C22×D312yes—
548C4⋊Dic3C22×D311yescharacteristic
549Dic3⋊C4—34no—
550Dic3⋊C4—34no—
551Dic3⋊C4—32no—
552Dic3⋊C4—34no—
553Dic3⋊C4—34no—
554Dic3⋊C4—34no—
555Dic3⋊C4—32no—
556Dic3⋊C4—64no—
557Dic3⋊C4C22×D314yes—
558C4×Dic3—34no—
559C4×Dic3—34no—
560C4×Dic3—32no—
561C4×Dic3—32no—
562C4×Dic3—34no—
563C4×Dic3—34no—
564C4×Dic3—34no—
565C4×Dic3—32no—
566C4×Dic3—32no—
567C4×Dic3—32no—
568C4×Dic3—34no—
569C4×Dic3—32no—
570C4×Dic3—64no—
571C4×Dic3—62no—
572C4×Dic3C22×D314yes—
573C4×Dic3C22×D314yes—
574C4×Dic3C22×D314yes—
575C4×Dic3C22×D312yes—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32C23×C412yes—
579C22×C32C2511yescharacteristic
580C2×C3⋊D3—22no—
581C2×C3⋊D3—22no—
582C2×C3⋊D3C23×C414yes—
583C2×C3×D3—22no—
584C2×C3×D3—21no—
585C2×C3×D3—21no—
586C2×C3×D3—22no—
587C2×C3×D3—21no—
588C2×C3×D3—21no—
589C2×C3×D3—44no—
590C2×C3×D3C23×C412yes—
591C2×C3×D3C23×C414yes—
592C2×C3×D3C23×C412yes—
593D32—48no—
594C32×C4—24no—
595C32×C4C23×C412yes—
596C32×C4C23×C412yes—
597C3⋊Dic3—22no—
598C3⋊Dic3—22no—
599C3⋊Dic3C23×C414yes—
600C3×Dic3—22no—
601C3×Dic3—24no—
602C3×Dic3—22no—
603C3×Dic3C23×C412yes—
604C3×Dic3C23×C414yes—
605C3×Dic3C23×C412yes—
606C2×#41—31no—
607C2×#41—92no—
608C2×#41—92no—
609C2×#41—91no—
610C2×#41—91no—
611C2×#41—916no—
612C2×#41—91no—
613C22×Q8—91no—
614C22×D4—91no—
615C22×D4—92no—
616C23×C4—31no—
617C23×C4—92no—
618C4×Q8—32no—
619C4×Q8—94no—
620C4×Q8—94no—
621C4×Q8—92no—
622C4×Q8—92no—
623C4×Q8—92no—
624C4×D4—34no—
625C4×D4—32no—
626C4×D4—94no—
627C4×D4—94no—
628C4×D4—92no—
629C4×D4—94no—
630C4×D4—94no—
631C4×D4—94no—
632C4×D4—94no—
633C4×D4—94no—
634C4×D4—92no—
635C4×D4—94no—
636C4×D4—94no—
637C4×D4—92no—
638#117—31no—
639#117—32no—
640#117—32no—
641#117—32no—
642#117—32no—
643#117—32no—
644#117—94no—
645#117—94no—
646#117—94no—
647#117—92no—
648#117—94no—
649#117—92no—
650#117—92no—
651#117—91no—
652#117—91no—
653#117—92no—
654#117—91no—
655#117—92no—
656C2×C4⋊C4—31no—
657C2×C4⋊C4—32no—
658C2×C4⋊C4—92no—
659C2×C4⋊C4—91no—
660C2×C4⋊C4—92no—
661C2×C4⋊C4—91no—
662C2×C4⋊C4—92no—
663C2×C4⋊C4D3211yescharacteristic, complemented
664C2×C22⋊C4—32no—
665C2×C22⋊C4—94no—
666C2×C22⋊C4—94no—
667C2×C22⋊C4—92no—
668C2×C42—32no—
669C2×C42—94no—
670C2×C42—94no—
671C2×C42—92no—
672C23×C3—21no—
673C23×C3—31no—
674C23×C3—32no—
675C23×C3—31no—
676C23×C3—34no—
677C23×C3—121no—
678C23×C3—121no—
679C23×C3C23×D311yescharacteristic
680C23×C3C23×D311yescharacteristic
681C22×D3—32no—
682C22×D3—32no—
683C22×D3—38no—
684C22×D3—38no—
685C22×D3—41no—
686C22×D3—41no—
687C22×D3—62no—
688C22×D3—122no—
689C22×D3—122no—
690C22×D3—122no—
691C22×D3—122no—
692C22×D3C2×C4×D314yes—
693C22×D3C23×D311yescharacteristic
694C22×D3C23×D312yes—
695C22×D3C23×D311yescharacteristic
696C3×Q8—34no—
697C3×D4—38no—
698C3×D4—34no—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—24no—
702C2×C3×C4—24no—
703C2×C3×C4—34no—
704C2×C3×C4—31no—
705C2×C3×C4—32no—
706C2×C3×C4—31no—
707C2×C3×C4—34no—
708C2×C3×C4—34no—
709C2×C3×C4—38no—
710C2×C3×C4—34no—
711C2×C3×C4—34no—
712C2×C3×C4—32no—
713C2×C3×C4—34no—
714C2×C3×C4—32no—
715C2×C3×C4—42no—
716C2×C3×C4—42no—
717C2×C3×C4—82no—
718C2×C3×C4—124no—
719C2×C3×C4—122no—
720C2×C3×C4C2×C4×D314yes—
721C2×C3×C4C2×C4×D314yes—
722C2×C3×C4C23×D314yes—
723C2×C3×C4C23×D314yes—
724C2×C3×C4C23×D311yescharacteristic
725C2×C3×C4C23×D311yescharacteristic
726C2×C3×C4C23×D311yescharacteristic
727C2×C3×C4C23×D311yescharacteristic
728#67—38no—
729#67—38no—
730#67—38no—
731#67—38no—
732#67—38no—
733#67—38no—
734#67—68no—
735#67C2×C4×D318yes—
736C2×Dic3—32no—
737C2×Dic3—32no—
738C2×Dic3—38no—
739C2×Dic3—38no—
740C2×Dic3—32no—
741C2×Dic3—32no—
742C2×Dic3—32no—
743C2×Dic3—32no—
744C2×Dic3—42no—
745C2×Dic3—62no—
746C2×Dic3—62no—
747C2×Dic3—62no—
748C2×Dic3—124no—
749C2×Dic3—122no—
750C2×Dic3—122no—
751C2×Dic3C2×C4×D314yes—
752C2×Dic3C23×D312yes—
753C2×Dic3C23×D314yes—
754C2×Dic3C23×D312yes—
755C2×Dic3C23×D311yescharacteristic
756C2×Dic3C23×D312yes—
757C2×Dic3C23×D311yescharacteristic
758D12—38no—
759D12—38no—
760D12—34no—
761D12—34no—
762D12—64no—
763D12C2×C4×D314yes—
764C4×D3—38no—
765C4×D3—38no—
766C4×D3—38no—
767C4×D3—38no—
768C4×D3—38no—
769C4×D3—38no—
770C4×D3—44no—
771C4×D3—68no—
772C4×D3—124no—
773C4×D3—124no—
774C4×D3—124no—
775C4×D3—124no—
776C4×D3—122no—
777C4×D3—122no—
778C4×D3—124no—
779C4×D3—244no—
780C4×D3C2×C4×D314yes—
781C4×D3C2×C4×D318yes—
782C4×D3C2×C4×D314yes—
783C4×D3C2×C4×D314yes—
784C4×D3C2×C4×D314yes—
785Dic6—34no—
786Dic6—34no—
787Dic6—38no—
788Dic6—38no—
789Dic6—64no—
790Dic6C2×C4×D314yes—
791C2×C32—22no—
792C2×C32C24×C411yescharacteristic
793C2×C32#58511yescharacteristic
794C2×C32#58511yescharacteristic
795C3⋊D3—24no—
796C3×D3—22no—
797C3×D3—24no—
798C3×D3—22no—
799C24—31no—
800C24—92no—
801#41—38no—
802#41—916no—
803#41—916no—
804#41—98no—
805#41—98no—
806#41—98no—
807C2×Q8—31no—
808C2×Q8—92no—
809C2×Q8—98no—
810C2×Q8—91no—
811C2×D4—32no—
812C2×D4—31no—
813C2×D4—98no—
814C2×D4—92no—
815C2×D4—92no—
816C2×D4—916no—
817C2×D4—92no—
818C2×D4—92no—
819C2×D4—91no—
820C22×C4—31no—
821C22×C4—31no—
822C22×C4—32no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—38no—
827C22×C4—32no—
828C22×C4—34no—
829C22×C4—92no—
830C22×C4—916no—
831C22×C4—94no—
832C22×C4—92no—
833C22×C4—92no—
834C22×C4—92no—
835C22×C4—94no—
836C22×C4—92no—
837C22×C4—92no—
838C22×C4—94no—
839C22×C4C2×D3212yes—
840C22×C4C2×D3211yescharacteristic
841C4⋊C4—31no—
842C4⋊C4—32no—
843C4⋊C4—32no—
844C4⋊C4—34no—
845C4⋊C4—31no—
846C4⋊C4—94no—
847C4⋊C4—92no—
848C4⋊C4—92no—
849C4⋊C4—94no—
850C4⋊C4—91no—
851C4⋊C4—91no—
852C4⋊C4—94no—
853C4⋊C4C2×D3212yes—
854C4⋊C4C2×D3212yes—
855C22⋊C4—32no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—94no—
860C22⋊C4—92no—
861C22⋊C4—92no—
862C22⋊C4—94no—
863C22⋊C4—92no—
864C22⋊C4—94no—
865C42—34no—
866C42—34no—
867C42—34no—
868C42—32no—
869C42—92no—
870C42—92no—
871C42—94no—
872C42—94no—
873C42—94no—
874C42—92no—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—22no—
880C22×C3—21no—
881C22×C3—32no—
882C22×C3—34no—
883C22×C3—32no—
884C22×C3—41no—
885C22×C3—41no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3—61no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—124no—
893C22×C3C22×C4×D312yes—
894C22×C3C22×C4×D312yes—
895C22×C3C24×D311yescharacteristic
896C22×C3C24×D311yescharacteristic
897C2×D3—21no—
898C2×D3—21no—
899C2×D3—21no—
900C2×D3—21no—
901C2×D3—22no—
902C2×D3—22no—
903C2×D3—34no—
904C2×D3—34no—
905C2×D3—44no—
906C2×D3—64no—
907C2×D3—62no—
908C2×D3—62no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—122no—
912C2×D3—122no—
913C2×D3—128no—
914C2×D3—128no—
915C2×D3C22×C4×D312yes—
916C2×D3C22×C4×D314yes—
917C2×D3C22×C4×D312yes—
918C3×C4—24no—
919C3×C4—24no—
920C3×C4—22no—
921C3×C4—22no—
922C3×C4—32no—
923C3×C4—34no—
924C3×C4—32no—
925C3×C4—44no—
926C3×C4—62no—
927C3×C4—62no—
928C3×C4—64no—
929C3×C4C22×C4×D312yes—
930C3×C4C22×C4×D312yes—
931C3×C4C22×C4×D312yes—
932C3×C4C22×C4×D312yes—
933Dic3—24no—
934Dic3—22no—
935Dic3—22no—
936Dic3—34no—
937Dic3—34no—
938Dic3—64no—
939Dic3—62no—
940Dic3—62no—
941Dic3—62no—
942Dic3—62no—
943Dic3—122no—
944Dic3—122no—
945Dic3C22×C4×D312yes—
946Dic3C22×C4×D314yes—
947Dic3C22×C4×D312yes—
948C32#342811yescharacteristic, complemented, Sylow
949C23—31no—
950C23—31no—
951C23—32no—
952C23—34no—
953C23—98no—
954C23—92no—
955C23—121no—
956C23—121no—
957C23—362no—
958C23—362no—
959C23C22×D3211yescharacteristic
960Q8—34no—
961Q8—98no—
962Q8—94no—
963D4—38no—
964D4—34no—
965D4—98no—
966D4—98no—
967D4—98no—
968D4—98no—
969D4—94no—
970C2×C4—34no—
971C2×C4—31no—
972C2×C4—31no—
973C2×C4—32no—
974C2×C4—34no—
975C2×C4—34no—
976C2×C4—34no—
977C2×C4—34no—
978C2×C4—38no—
979C2×C4—32no—
980C2×C4—34no—
981C2×C4—32no—
982C2×C4—42no—
983C2×C4—98no—
984C2×C4—98no—
985C2×C4—98no—
986C2×C4—92no—
987C2×C4—98no—
988C2×C4—92no—
989C2×C4—92no—
990C2×C4—124no—
991C2×C4—122no—
992C2×C4—364no—
993C2×C4—364no—
994C2×C4—362no—
995C2×C4—364no—
996C2×C4—362no—
997C2×C4C4×D3214yes—
998C2×C4C22×D3214yes—
999C2×C4C22×D3211yescharacteristic
1000C2×C4C22×D3211yescharacteristic
1001C2×C3—22no—
1002C2×C3—22no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—42no—
1007C2×C3—62no—
1008C2×C3—62no—
1009C2×C3—64no—
1010C2×C3C23×C4×D311yescharacteristic
1011C2×C3C23×C4×D311yescharacteristic
1012C2×C3#596411yescharacteristic
1013C2×C3#596411yescharacteristic
1014C2×C3#596611yescharacteristic
1015C2×C3#596811yescharacteristic
1016D3—24no—
1017D3—22no—
1018D3—22no—
1019D3—64no—
1020D3—64no—
1021D3—124no—
1022C22—21no—
1023C22—21no—
1024C22—32no—
1025C22—32no—
1026C22—34no—
1027C22—62no—
1028C22—61no—
1029C22—61no—
1030C22—61no—
1031C22—62no—
1032C22—61no—
1033C22—94no—
1034C22—124no—
1035C22—182no—
1036C22—182no—
1037C22—368no—
1038C22C2×C4×D3212yes—
1039C22C23×D3211yescharacteristic
1040C4—24no—
1041C4—32no—
1042C4—32no—
1043C4—34no—
1044C4—62no—
1045C4—64no—
1046C4—62no—
1047C4—94no—
1048C4—182no—
1049C4—182no—
1050C4C2×C4×D3212yes—
1051C4C2×C4×D3212yes—
1052C3—21no—
1053C3#8573111yescharacteristic, complemented
1054C3#8588511yescharacteristic, complemented
1055C2—22no—
1056C2—62no—
1057C2—62no—
1058C2—64no—
1059C2—184no—
1060C2C22×C4×D3211yescharacteristic
1061C2#1059667811yescharacteristic
1062C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC22×C32C25
prime radicalC2×D3×#235C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3428
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10595975C2semidirect
3. C3×#5504C2semidirect
4. C2×C3×#892C2semidirect
5. #10595056C2semidirect
6. #10594990C2semidirect
7. #10594986C2semidirect
8. D3×#926C2semidirect
9. C4×#3804C2semidirect
10. #10594604C2semidirect
11. #10594602C2semidirect
12. D3×#892C2semidirect
13. #10594511C2semidirect
14. #10594510C2semidirect
15. #10594362C2semidirect
16. #10594358C2semidirect
17. #10594357C2semidirect
25. D3×#235C4semidirect
32. C2×C32×C4⋊C4C22semidirect
33. C4×#638C22semidirect
34. #64135C22semidirect
35. #64102C22semidirect
36. #64101C22semidirect
37. C4⋊C4×C3⋊D3C22semidirect
38. #64096C22semidirect
39. C3×C4×#67C22semidirect
41. C3×#926C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. C2×C3×C4×Dic3C22semidirect
44. C3×#893C22semidirect
47. C3×#892C22semidirect
48. C3×#892C22semidirect
49. C3×#892C22semidirect
50. C3×D3×C4⋊C4C22semidirect
51. C3×#887C22semidirect
52. Dic3×#67C22semidirect
54. #63955C22semidirect
55. #63952C22semidirect
58. C4×#627C22semidirect
59. C4×#626C22semidirect
60. #63902C22semidirect
61. #63900C22semidirect
62. #63898C22semidirect
63. #63894C22semidirect
64. D3×C4⋊Dic3C22semidirect
65. D3×C4⋊Dic3C22semidirect
66. D3×C4⋊Dic3C22semidirect
67. C4×#624C22semidirect
68. #63881C22semidirect
69. #63880C22semidirect
70. #63880C22semidirect
71. #63879C22semidirect
74. #63877C22semidirect
75. C4×D3×Dic3C22semidirect
76. C4×D3×Dic3C22semidirect
78. #63849C22semidirect
79. #63844C22semidirect
80. #63843C22semidirect
83. #63841C22semidirect
84. #63837C22semidirect
85. #63836C22semidirect
116. #5504D3semidirect
118. C2×#892D3semidirect
126. #3828C2×C4semidirect
134. C3×#235C2×C4semidirect
136. C2×C3×C4×D3C2×C4semidirect
144. D3×#67C2×C4semidirect
151. #3804C2×C4semidirect
157. D3×D12C2×C4semidirect
158. C4×D32C2×C4semidirect
159. #3799C2×C4semidirect
160. #3798C2×C4semidirect
161. #3795C2×C4semidirect
162. D3×Dic6C2×C4semidirect
235. C2×C3×C4⋊C4C2×D3semidirect
236. C2×C3×C4⋊C4C2×D3semidirect
250. C4×#67C2×D3semidirect
261. #926C2×D3semidirect
265. C2×C4⋊Dic3C2×D3semidirect
268. C2×C4×Dic3C2×D3semidirect
275. #893C2×D3semidirect
288. #892C2×D3semidirect
289. #892C2×D3semidirect
290. #892C2×D3semidirect
299. D3×C4⋊C4C2×D3semidirect
306. #887C2×D3semidirect
460. #235C4×D3semidirect
485. C2×C4×D3C4×D3semidirect
663. C2×C4⋊C4D32semidirect
948. C32#3428semidirect
1053. C3#85731semidirect
1054. C3#85885semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
#105959752
C3×#55042
C2×C3×#8922
#105950562
#105949902
#105949862
D3×#9262
C4×#38042
#105946042
#105946022
D3×#8922
#105945112
#105945102
#105943622
#105943582
#105943572
#858853
#857313