Finite Group Databasebeta

← #11900136

Subgroups — #11900136

Order 1152.

3213 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2#10595987C211yesmaximal, characteristic, complemented
3C3×#5521C211yesmaximal, characteristic, complemented
4C3×D3×#117C211yesmaximal, characteristic, complemented
5#10594982C211yesmaximal, characteristic, complemented
6D3×#926C211yesmaximal, characteristic, complemented
7#10594828C211yesmaximal, characteristic, complemented
8#10594359C214yesmaximal, complemented
9#10594358C214yesmaximal, complemented
10#10594181C214yesmaximal, complemented
11D3×#877C214yesmaximal, complemented
12#10593887C214yesmaximal, complemented
13C4×#3795C214yesmaximal, complemented
14#85856—31nomaximal
15#85731—31nomaximal
16C22×#634C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×#625C2212yes—
20C22×D3×Dic3C2212yes—
21C2×#3795C4116yescomplemented
22C2×#3795C2212yes—
23C2×#3795C2212yes—
24C2×#3795C2212yes—
25C2×#3795C2212yes—
26C32×#117C2211yescharacteristic
27#64135C2211yescharacteristic
28#64096C2214yescomplemented
29#64086C2214yes—
30C4×#634C2214yescomplemented
31C3×#926C2211yescharacteristic
32C3×#926C2211yescharacteristic
33C3×#893C2214yescomplemented
34C3×#892C2212yescomplemented
35C3×D3×C4⋊C4C2212yescomplemented
36C3×D3×C22⋊C4C2212yes—
37C3×D3×C22⋊C4C2214yes—
38C3×#877C2212yes—
39C3×C4×D12C2214yescomplemented
40C3×#872C2212yescomplemented
41C3×C42×D3C2212yescomplemented
42D3×#217C2212yes—
43D3×#217C2214yes—
44#63957C2214yes—
45#63955C2212yes—
46#63902C2218yescomplemented
47C4×#625C2218yescomplemented
48#63898C2214yescomplemented
49Dic3×D12C2214yescomplemented
50D3×C4⋊Dic3C2212yescomplemented
51#63879C2218yescomplemented
52#63879C2218yescomplemented
53#63878C2218yescomplemented
54#63877C2218yescomplemented
55D3×Dic3⋊C4C2218yescomplemented
56C4×D3×Dic3C2212yescomplemented
57C4×D3×Dic3C2218yescomplemented
58#63855C2212yescomplemented
59#63844C2214yescomplemented
60#63844C2214yescomplemented
61#63841C2212yescomplemented
62C22×#237—31no—
63C22×#235—31no—
64C3×#518—31no—
65C2×C3×#117—31no—
66#5798—31no—
67C2×#926—31no—
68#5546—34no—
69#5546—34no—
70C4×#237—34no—
71C4×#237—34no—
72#5523—34no—
73#5522—34no—
74#5521—31no—
75#5521D311yescharacteristic, complemented
76D3×#117—31no—
77D3×#117—34no—
78D3×#117D311yescharacteristic, complemented
79#5516—31no—
80#5516—31no—
81#5516—31no—
82#5516—31no—
83#5516—61no—
84#5504—34no—
85#5486—34no—
86#5486—34no—
87C2×#877—34no—
88C4×#235—34no—
89C23×C3×D3C2312yes—
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2312yes—
93C2×#634C2×C418yescomplemented
94C2×#634C2312yes—
95C2×#634C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C2×C3×D12C2×C418yescomplemented
98C2×C3×D12C2312yes—
99C2×C3×D12C2312yes—
100C2×C3×C4×D3C2×C418yescomplemented
101C2×C3×C4×D3C2314yes—
102C2×C3×C4×D3C2318yes—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#625C2×C4116yescomplemented
108C2×#625C2314yes—
109C2×#625C2314yes—
110C2×D3×Dic3C2×C4116yescomplemented
111C2×D3×Dic3C2318yes—
112C2×D3×Dic3C2314yes—
113C2×D3×Dic3C2314yes—
114C2×D3×Dic3C2314yes—
115#3795C2×C4116yescomplemented
116#3795C2×C4116yescomplemented
117#3795C2×C4116yescomplemented
118#3795C2×C4116yescomplemented
119C32×C4⋊C4C2312yes—
120C32×C22⋊C4C2312yes—
121C32×C42C2312yes—
122#3757C2312yes—
123C4⋊(C3⋊Dic3)C2312yes—
124#3750C2318yes—
125C4×C3⋊Dic3C2318yes—
126C4×C3⋊Dic3C2312yes—
127C3×#217C2312yes—
128C3×#217C2312yes—
129C3×(C2×D3)⋊C4C2314yes—
130C3×(C2×D3)⋊C4C2318yes—
131C3×C4⋊Dic3C2312yes—
132C3×C4⋊Dic3C2312yes—
133C3×Dic3⋊C4C2314yes—
134C3×C4×Dic3C2314yes—
135C3×C4×Dic3C2312yes—
136C3×C4×Dic3C2312yes—
137#3724C2318yes—
138Dic3⋊Dic3C2314yes—
139(C2×D3)⋊Dic3C2314yes—
140(C2×D3)⋊Dic3C2318yes—
141Dic32C2314yes—
142Dic32C2318yes—
143#3428—91noSylow
144C22×C3×D4—31no—
145C23×C3×C4—31no—
146C22×#67—32no—
147C22×#67—32no—
148C23×Dic3—32no—
149C2×#237—316no—
150C2×#237—32no—
151C2×#237—32no—
152C2×#237—32no—
153C2×#237—32no—
154C2×#235—316no—
155C2×#235—32no—
156C2×#235—32no—
157C2×#235—32no—
158C2×#235—32no—
159C22×D12C2×D311yescharacteristic
160C22×C4×D3—32no—
161C22×C4×D3C2×D311yescharacteristic
162C22×Dic6—31no—
163C22×Dic6—31no—
164C22×Dic6—61no—
165C3×C4×D4—34no—
166C3×C4×D4—34no—
167C3×#117—21no—
168C3×#117—31no—
169C3×#117—31no—
170C3×#117—32no—
171C3×#117—32no—
172C3×#117—32no—
173C3×#117C2×D311yescharacteristic
174C3×#117C2×D311yescharacteristic
175C2×C3×C4⋊C4—32no—
176C2×C3×C22⋊C4—34no—
177C2×C3×C22⋊C4—32no—
178C2×C3×C42—32no—
179C2×#217—34no—
180C2×#217—32no—
181D4×Dic3—34no—
182D4×Dic3—34no—
183C4×#67—38no—
184C4×#67—38no—
185C4×#67—38no—
186C4×#67—38no—
187#926—31no—
188#926—31no—
189#926—32no—
190#926—32no—
191#926—32no—
192#926—61no—
193#926C2×D311yescharacteristic
194#926C2×D311yescharacteristic
195C2×C4⋊Dic3—32no—
196C2×Dic3⋊C4—38no—
197C2×C4×Dic3—38no—
198C2×C4×Dic3—32no—
199#893—34no—
200#893C2×D314yescomplemented
201#892—32no—
202#892—38no—
203#892C2×D312yescomplemented
204D3×C4⋊C4—38no—
205D3×C4⋊C4—32no—
206D3×C4⋊C4C2×D312yescomplemented
207#887—34no—
208#887—34no—
209#887—34no—
210#887—34no—
211#887—64no—
212#67⋊C4—38no—
213#67⋊C4—38no—
214#67⋊C4—38no—
215#67⋊C4—38no—
216D3×C22⋊C4—32no—
217D3×C22⋊C4—34no—
218D3×C22⋊C4C2×D312yes—
219D3×C22⋊C4C2×D314yes—
220#877—32no—
221#877—34no—
222#877—34no—
223#877—34no—
224#877—34no—
225#877—38no—
226#877—38no—
227#877—64no—
228#877C2×D312yes—
229C4×D12—34no—
230C4×D12C2×D314yescomplemented
231#872—32no—
232#872—38no—
233#872C2×D312yescomplemented
234C42×D3—38no—
235C42×D3—32no—
236C42×D3C2×D312yescomplemented
237C4×Dic6—34no—
238C4×Dic6—34no—
239C4×Dic6—34no—
240C4×Dic6—34no—
241C4×Dic6—64no—
242C23×C32C2411yescharacteristic
243C22×C3×D3—42no—
244C22×C3×D3—44no—
245C22×C3×D3C22×C418yes—
246C22×C3×D3C22×C414yes—
247C22×C3×D3C2411yescharacteristic
248C22×C3×D3C2414yes—
249C22×C3×D3C2411yescharacteristic
250C2×C32×C4C22×C414yes—
251C2×C32×C4C2414yes—
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3C22×C418yes—
255C2×C3⋊Dic3C2414yes—
256C2×C3⋊Dic3C2414yes—
257#634C22×C418yes—
258#634C22×C418yes—
259C2×C3×Dic3C22×C414yes—
260C2×C3×Dic3C2414yes—
261C2×C3×Dic3C2414yes—
262C2×C3×Dic3C2411yescharacteristic
263C2×C3×Dic3C2411yescharacteristic
264C3×D12C22×C418yes—
265C3×D12C22×C418yes—
266C3×C4×D3—44no—
267C3×C4×D3—48no—
268C3×C4×D3C22×C414yes—
269C3×C4×D3C22×C414yes—
270C3×C4×D3C22×C414yes—
271C3×C4×D3C22×C414yes—
272#625C22×C4116yes—
273#625C22×C4116yes—
274D3×Dic3—48no—
275D3×Dic3—44no—
276D3×Dic3C22×C4116yes—
277D3×Dic3C22×C4116yes—
278C22×#41—91no—
279#520—94no—
280#520—94no—
281#519—91no—
282#519—91no—
283#518—31no—
284#518—94no—
285#518—91no—
286C4×#41—94no—
287C4×#41—94no—
288C2×#117—31no—
289C2×#117—94no—
290C2×#117—91no—
291C24×C3—32no—
292C24×C3—31no—
293C23×D3C22×D312yes—
294C23×D3C22×D311yescharacteristic
295C2×C3×D4—38no—
296C2×C3×D4—32no—
297C2×C3×D4—32no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—38no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—38no—
306C22×C3×C4—34no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—316no—
310C2×#67—316no—
311C2×#67—34no—
312C2×#67—34no—
313C2×#67—34no—
314C2×#67—34no—
315C22×Dic3—32no—
316C22×Dic3—32no—
317C22×Dic3—316no—
318C22×Dic3—34no—
319C22×Dic3—34no—
320C22×Dic3—34no—
321C22×Dic3—38no—
322C22×Dic3—62no—
323C22×Dic3C22×D311yescharacteristic
324#237—316no—
325#237—316no—
326#237—316no—
327#237—316no—
328#235—316no—
329#235—316no—
330#235—316no—
331#235—316no—
332C2×D12C4×D318yescomplemented
333C2×D12C22×D312yes—
334C2×D12C22×D312yes—
335C2×C4×D3—316no—
336C2×C4×D3—34no—
337C2×C4×D3—34no—
338C2×C4×D3—38no—
339C2×C4×D3—34no—
340C2×C4×D3C4×D318yescomplemented
341C2×C4×D3C22×D318yes—
342C2×C4×D3C22×D314yes—
343C2×C4×D3C22×D311yescharacteristic
344C2×C4×D3C22×D311yescharacteristic
345C2×C4×D3C22×D311yescharacteristic
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6—38no—
348C2×Dic6—38no—
349C2×Dic6—32no—
350C2×Dic6—32no—
351C2×Dic6—32no—
352C2×Dic6—32no—
353C2×Dic6—62no—
354C2×Dic6—62no—
355C2×Dic6—68no—
356C3×C4⋊C4—22no—
357C3×C4⋊C4—32no—
358C3×C4⋊C4—32no—
359C3×C4⋊C4—34no—
360C3×C4⋊C4C22×D312yes—
361C3×C4⋊C4C22×D312yes—
362C3×C22⋊C4—22no—
363C3×C22⋊C4—32no—
364C3×C22⋊C4—32no—
365C3×C22⋊C4—38no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4C22×D312yes—
368C3×C22⋊C4C22×D312yes—
369C3×C42—22no—
370C3×C42—32no—
371C3×C42—32no—
372C3×C42—34no—
373C3×C42C22×D312yes—
374C3×C42C22×D312yes—
375#217—32no—
376#217—32no—
377#217—38no—
378#217—34no—
379#217—62no—
380#217C22×D312yes—
381#217C22×D312yes—
382(C2×D3)⋊C4—38no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4C22×D318yes—
385(C2×D3)⋊C4C22×D314yes—
386C4⋊Dic3—32no—
387C4⋊Dic3—32no—
388C4⋊Dic3—34no—
389C4⋊Dic3—62no—
390C4⋊Dic3C22×D312yes—
391C4⋊Dic3C22×D312yes—
392Dic3⋊C4—38no—
393Dic3⋊C4—38no—
394Dic3⋊C4—38no—
395Dic3⋊C4—38no—
396Dic3⋊C4—34no—
397Dic3⋊C4—68no—
398Dic3⋊C4C22×D314yes—
399C4×Dic3—38no—
400C4×Dic3—38no—
401C4×Dic3—32no—
402C4×Dic3—32no—
403C4×Dic3—38no—
404C4×Dic3—38no—
405C4×Dic3—34no—
406C4×Dic3—34no—
407C4×Dic3—68no—
408C4×Dic3—62no—
409C4×Dic3C22×D312yes—
410C4×Dic3C22×D314yes—
411C4×Dic3C22×D312yes—
412C22×C32—22no—
413C22×C32C23×C412yes—
414C22×C32C2511yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—28no—
417C2×C3×D3—22no—
418C2×C3×D3—48no—
419C2×C3×D3—44no—
420C2×C3×D3C23×C418yes—
421C2×C3×D3C23×C412yes—
422C2×C3×D3C23×C412yes—
423C32×C4—24no—
424C32×C4C23×C412yes—
425C32×C4C23×C412yes—
426C3⋊Dic3—24no—
427C3⋊Dic3C23×C418yes—
428C3×Dic3—24no—
429C3×Dic3—24no—
430C3×Dic3C23×C412yes—
431C3×Dic3C23×C412yes—
432C2×#41—92no—
433C2×#41—92no—
434C2×#41—92no—
435C2×#41—92no—
436C2×#41—916no—
437C22×Q8—91no—
438C22×D4—31no—
439C22×D4—92no—
440C23×C4—31no—
441C23×C4—92no—
442C4×Q8—94no—
443C4×Q8—94no—
444C4×Q8—94no—
445C4×Q8—94no—
446C4×D4—34no—
447C4×D4—34no—
448C4×D4—94no—
449C4×D4—98no—
450C4×D4—98no—
451C4×D4—98no—
452C4×D4—94no—
453C4×D4—98no—
454#117—31no—
455#117—31no—
456#117—32no—
457#117—32no—
458#117—32no—
459#117—98no—
460#117—92no—
461#117—94no—
462#117—98no—
463#117—92no—
464#117—92no—
465#117—91no—
466#117—94no—
467#117D3211yescharacteristic
468C2×C4⋊C4—32no—
469C2×C4⋊C4—98no—
470C2×C4⋊C4—92no—
471C2×C22⋊C4—32no—
472C2×C22⋊C4—34no—
473C2×C22⋊C4—92no—
474C2×C22⋊C4—94no—
475C2×C42—32no—
476C2×C42—98no—
477C2×C42—92no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—34no—
481C23×C3—31no—
482C23×C3—38no—
483C23×C3—34no—
484C23×C3—124no—
485C23×C3—122no—
486C23×C3C23×D311yescharacteristic
487C23×C3C23×D311yescharacteristic
488C22×D3—42no—
489C22×D3—44no—
490C22×D3C2×C4×D318yes—
491C22×D3C2×C4×D314yes—
492C22×D3C23×D311yescharacteristic
493C22×D3C23×D314yes—
494C22×D3C23×D311yescharacteristic
495C3×D4—38no—
496C3×D4—38no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—24no—
500C2×C3×C4—24no—
501C2×C3×C4—34no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—34no—
505C2×C3×C4—34no—
506C2×C3×C4—34no—
507C2×C3×C4—34no—
508C2×C3×C4—34no—
509C2×C3×C4—34no—
510C2×C3×C4—128no—
511C2×C3×C4—124no—
512C2×C3×C4C2×C4×D314yes—
513C2×C3×C4C2×C4×D314yes—
514C2×C3×C4C23×D314yes—
515C2×C3×C4C23×D314yes—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—316no—
521#67—316no—
522#67—316no—
523#67—316no—
524C2×Dic3—38no—
525C2×Dic3—38no—
526C2×Dic3—34no—
527C2×Dic3—34no—
528C2×Dic3—316no—
529C2×Dic3—316no—
530C2×Dic3—34no—
531C2×Dic3—34no—
532C2×Dic3—68no—
533C2×Dic3—64no—
534C2×Dic3—64no—
535C2×Dic3—128no—
536C2×Dic3—124no—
537C2×Dic3C2×C4×D314yes—
538C2×Dic3C23×D314yes—
539C2×Dic3C23×D314yes—
540C2×Dic3C23×D311yescharacteristic
541C2×Dic3C23×D311yescharacteristic
542D12C2×C4×D318yes—
543D12C2×C4×D318yes—
544C4×D3—316no—
545C4×D3—316no—
546C4×D3—44no—
547C4×D3—48no—
548C4×D3—124no—
549C4×D3—128no—
550C4×D3C2×C4×D314yes—
551C4×D3C2×C4×D314yes—
552C4×D3C2×C4×D314yes—
553C4×D3C2×C4×D314yes—
554Dic6—38no—
555Dic6—38no—
556Dic6—38no—
557Dic6—38no—
558Dic6—68no—
559Dic6—68no—
560C2×C32—22no—
561C2×C32C24×C411yescharacteristic
562C2×C32#58512yes—
563C3×D3—28no—
564C3×D3—22no—
565C3×D3—22no—
566C24—31no—
567C24—32no—
568#41—916no—
569#41—916no—
570#41—916no—
571#41—916no—
572C2×Q8—92no—
573C2×Q8—92no—
574C2×Q8—98no—
575C2×D4—32no—
576C2×D4—32no—
577C2×D4—38no—
578C2×D4—94no—
579C2×D4—94no—
580C2×D4—916no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—38no—
587C22×C4—34no—
588C22×C4—38no—
589C22×C4—94no—
590C22×C4—94no—
591C22×C4—916no—
592C22×C4—98no—
593C22×C4—94no—
594C22×C4—92no—
595C22×C4C2×D3211yescharacteristic
596C4⋊C4—34no—
597C4⋊C4—32no—
598C4⋊C4—32no—
599C4⋊C4—94no—
600C4⋊C4—98no—
601C4⋊C4—98no—
602C4⋊C4—92no—
603C4⋊C4C2×D3212yes—
604C22⋊C4—32no—
605C22⋊C4—32no—
606C22⋊C4—34no—
607C22⋊C4—38no—
608C22⋊C4—98no—
609C22⋊C4—94no—
610C22⋊C4—92no—
611C22⋊C4C2×D3212yes—
612C42—34no—
613C42—32no—
614C42—32no—
615C42—94no—
616C42—98no—
617C42—98no—
618C42—92no—
619C42C2×D3212yes—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—38no—
625C22×C3—32no—
626C22×C3—32no—
627C22×C3—42no—
628C22×C3—68no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—124no—
632C22×C3—128no—
633C22×C3C22×C4×D312yes—
634C22×C3C22×C4×D312yes—
635C22×C3C24×D311yescharacteristic
636C22×C3C24×D311yescharacteristic
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—28no—
640C2×D3—48no—
641C2×D3—44no—
642C2×D3C22×C4×D318yes—
643C2×D3C22×C4×D312yes—
644C2×D3C22×C4×D312yes—
645C3×C4—24no—
646C3×C4—24no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—32no—
650C3×C4—32no—
651C3×C4—44no—
652C3×C4—64no—
653C3×C4—64no—
654C3×C4C22×C4×D312yes—
655C3×C4C22×C4×D312yes—
656C3×C4C22×C4×D312yes—
657C3×C4C22×C4×D312yes—
658Dic3—24no—
659Dic3—24no—
660Dic3—38no—
661Dic3—38no—
662Dic3—68no—
663Dic3—64no—
664Dic3—64no—
665Dic3—124no—
666Dic3C22×C4×D312yes—
667Dic3C22×C4×D312yes—
668C32#342811yescharacteristic, complemented, Sylow
669C23—31no—
670C23—34no—
671C23—31no—
672C23—34no—
673C23—38no—
674C23—122no—
675C23—124no—
676C23C22×D3211yescharacteristic
677Q8—98no—
678Q8—98no—
679D4—38no—
680D4—38no—
681D4—916no—
682D4—916no—
683C2×C4—34no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—34no—
687C2×C4—34no—
688C2×C4—34no—
689C2×C4—34no—
690C2×C4—34no—
691C2×C4—34no—
692C2×C4—916no—
693C2×C4—916no—
694C2×C4—98no—
695C2×C4—94no—
696C2×C4—94no—
697C2×C4—128no—
698C2×C4—124no—
699C2×C4—364no—
700C2×C4—368no—
701C2×C4C4×D3214yes—
702C2×C4C22×D3214yes—
703C2×C4C22×D3211yescharacteristic
704C2×C4C22×D3211yescharacteristic
705C2×C3—22no—
706C2×C3—22no—
707C2×C3—21no—
708C2×C3—22no—
709C2×C3—42no—
710C2×C3—62no—
711C2×C3—62no—
712C2×C3—68no—
713C2×C3C23×C4×D311yescharacteristic
714C2×C3C23×C4×D311yescharacteristic
715C2×C3#596412yes—
716C2×C3#596612yes—
717D3—28no—
718D3—22no—
719D3—22no—
720C22—22no—
721C22—32no—
722C22—32no—
723C22—38no—
724C22—62no—
725C22—68no—
726C22—62no—
727C22—124no—
728C22—128no—
729C22C2×C4×D3212yes—
730C22C23×D3211yescharacteristic
731C4—24no—
732C4—32no—
733C4—32no—
734C4—64no—
735C4—64no—
736C4—98no—
737C4—184no—
738C4C2×C4×D3212yes—
739C4C2×C4×D3212yes—
740C3—21no—
741C3#8573111yescharacteristic, complemented
742C3#8585611yescharacteristic, complemented
743C2—22no—
744C2—62no—
745C2—62no—
746C2—68no—
747C2C22×C4×D3211yescharacteristic
748C2#1059669612yes—
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC32×#117C22
socle, cosocleC22×C32C25
prime radicalC22×#3795C2
hypercenter#117D32
hypocenterC32#3428
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10595987C2semidirect
3. C3×#5521C2semidirect
4. C3×D3×#117C2semidirect
5. #10594982C2semidirect
6. D3×#926C2semidirect
7. #10594828C2semidirect
8. #10594359C2semidirect
9. #10594358C2semidirect
10. #10594181C2semidirect
11. D3×#877C2semidirect
12. #10593887C2semidirect
13. C4×#3795C2semidirect
21. C2×#3795C4semidirect
28. #64096C22semidirect
30. C4×#634C22semidirect
33. C3×#893C22semidirect
34. C3×#892C22semidirect
35. C3×D3×C4⋊C4C22semidirect
39. C3×C4×D12C22semidirect
40. C3×#872C22semidirect
41. C3×C42×D3C22semidirect
46. #63902C22semidirect
47. C4×#625C22semidirect
48. #63898C22semidirect
49. Dic3×D12C22semidirect
50. D3×C4⋊Dic3C22semidirect
51. #63879C22semidirect
52. #63879C22semidirect
53. #63878C22semidirect
54. #63877C22semidirect
55. D3×Dic3⋊C4C22semidirect
56. C4×D3×Dic3C22semidirect
57. C4×D3×Dic3C22semidirect
58. #63855C22semidirect
59. #63844C22semidirect
60. #63844C22semidirect
61. #63841C22semidirect
75. #5521D3semidirect
78. D3×#117D3semidirect
93. C2×#634C2×C4semidirect
97. C2×C3×D12C2×C4semidirect
100. C2×C3×C4×D3C2×C4semidirect
107. C2×#625C2×C4semidirect
110. C2×D3×Dic3C2×C4semidirect
115. #3795C2×C4semidirect
116. #3795C2×C4semidirect
117. #3795C2×C4semidirect
118. #3795C2×C4semidirect
200. #893C2×D3semidirect
203. #892C2×D3semidirect
206. D3×C4⋊C4C2×D3semidirect
230. C4×D12C2×D3semidirect
233. #872C2×D3semidirect
236. C42×D3C2×D3semidirect
332. C2×D12C4×D3semidirect
340. C2×C4×D3C4×D3semidirect
668. C32#3428semidirect
741. C3#85731semidirect
742. C3#85856semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
#105959872
C3×#55212
C3×D3×#1172
#105949822
D3×#9262
#105948282
#105943592
#105943582
#105941812
D3×#8772
#105938872
C4×#37952
#858563
#857313