Finite Group Databasebeta

← #11906235

Subgroups — #11906235

Order 1152.

2311 conjugacy classes of subgroups.

The subgroup lattice has 761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596093C211yesmaximal, characteristic, complemented
2C3×#5634C212yesmaximal, complemented
3#10595407C212yesmaximal, complemented
4#10595370C212yesmaximal, complemented
5C2×#63902C211yesmaximal, characteristic
6#10594971C212yesmaximal, complemented
7#10594810C211yesmaximal, characteristic, complemented
8#10594535C214yesmaximal, complemented
9#10594534C212yesmaximal, complemented
10#10594534C212yesmaximal, complemented
11#10594526C212yesmaximal, complemented
12#10594377C212yesmaximal, complemented
13#10594181C212yesmaximal
14D3×#878C214yesmaximal, complemented
15#10594033C212yesmaximal, complemented
16#86574—32nomaximal
17C22×#625C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×D3×Dic6C2214yescomplemented
20C32×C22⋊Q8C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22#64153C2211yescharacteristic, complemented
23#64133C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64098C2212yescomplemented
26#64097C2211yescharacteristic, complemented
27#64096C2212yescomplemented
28#64096C2211yescharacteristic, complemented
29#64087C2212yes—
30#64086C2212yes—
31C3×#946C2214yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yes—
33C3×#924C2212yes—
34C3×#897C2214yescomplemented
35C3×#896C2214yescomplemented
36C3×#896C2214yescomplemented
37C3×D3×C22⋊C4C2214yes—
38C3×#878C2214yes—
39#63982C2212yes—
40D3×#217C2214yes—
41C2×#3724C2211yescharacteristic
42#63964C2214yes—
43#63957C2212yes—
44#63919C2212yescomplemented
45#63919C2211yescharacteristic, complemented
46#63902C2212yes—
47#63902C2212yes—
48#63902C2212yes—
49#63902C2212yes—
50#63902C2212yes—
51#63902C2212yes—
52C4×#625C2212yes—
53C4×#625C2212yes—
54#63899C2214yescomplemented
55#63899C2214yescomplemented
56#63896C2214yescomplemented
57#63896C2214yescomplemented
58#63893C2214yescomplemented
59#63893C2214yescomplemented
60D3×C4⋊Dic3C2214yescomplemented
61#63887C2214yescomplemented
62#63887C2214yescomplemented
63#63879C2214yes—
64#63879C2214yes—
65D3×Dic3⋊C4C2214yescomplemented
66D3×Dic3⋊C4C2214yescomplemented
67#63873C2212yescomplemented
68#63873C2211yescharacteristic, complemented
69#63870C2212yescomplemented
70#63870C2212yescomplemented
71#63870C2212yescomplemented
72#63847C2214yescomplemented
73#63843C2212yescomplemented
74#63839C2214yescomplemented
75#63838C2212yescomplemented
76C3×#543—32no—
77#5636—34no—
78#5636—34no—
79#5636—34no—
80#5636—34no—
81#5635—34no—
82#5635—34no—
83#5634—32no—
84#5634D312yescomplemented
85#5632—34no—
86#5632—34no—
87D3×C22⋊Q8—34no—
88#5623—34no—
89#5622—32no—
90#5622—32no—
91#5622—61no—
92#5486—34no—
93C2×#67⋊C4—32no—
94#5483—32no—
95C2×#878—34no—
96C23×C3×D3C2312yes—
97C2×C32×Q8C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×#634C2312yes—
102C2×#634C2311yescharacteristic
103C22×C3×Dic3C2312yes—
104C2×C3×C4×D3C2314yes—
105C2×C3×C4×D3C2314yes—
106C2×C3×Dic6C2314yes—
107C2×C3×Dic6C2312yes—
108C2×#627C2312yes—
109C2×#627C2314yes—
110C2×#625Q818yescomplemented
111C2×#625C2312yes—
112C2×#625C2312yes—
113C2×D3×Dic3—44no—
114C2×D3×Dic3C2314yes—
115C2×D3×Dic3C2314yes—
116C2×D3×Dic3C2314yes—
117C2×D3×Dic3C2314yes—
118D3×Dic6—48no—
119C32×C4⋊C4C2311yescharacteristic
120C32×C4⋊C4C2312yes—
121C32×C22⋊C4C2312yes—
122#3757C2312yes—
123C4⋊(C3⋊Dic3)C2312yes—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750C2312yes—
126#3750C2312yes—
127#3750C2312yes—
128#3750C2312yes—
129#3750C2312yes—
130C4×C3⋊Dic3C2312yes—
131C4×C3⋊Dic3C2312yes—
132C4×C3⋊Dic3C2311yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134C4×C3⋊Dic3C2311yescharacteristic
135C4×C3⋊Dic3C2311yescharacteristic
136C3×#217C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×C4⋊Dic3C2314yes—
142C3×C4⋊Dic3C2312yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146#3724C2312yes—
147#3724C2312yes—
148#3724C2314yes—
149#3724C2312yes—
150#3724C2312yes—
151#3724C2312yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157Dic32C2314yes—
158#3501—91noSylow
159C22×#67—32no—
160C23×Dic3—32no—
161C2×D3×Q8—34no—
162C22×C4×D3—32no—
163C22×Dic6—34no—
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—34no—
166C3×C22⋊Q8—32no—
167C3×C22⋊Q8—34no—
168C3×C22⋊Q8—34no—
169C3×C22⋊Q8—34no—
170C3×C22⋊Q8—34no—
171C3×C22⋊Q8C2×D312yes—
172C2×C3×C22⋊C4—32no—
173C2×C3×C22⋊C4—34no—
174C2×#217—34no—
175#946—34no—
176#946—34no—
177#946C2×D314yescomplemented
178Q8×Dic3—32no—
179Q8×Dic3—32no—
180Q8×Dic3—61no—
181#944—32no—
182#944—34no—
183#944—32no—
184#944—34no—
185#944—61no—
186C4×#67—34no—
187C4×#67—34no—
188C4×#67—34no—
189C4×#67—34no—
190C2×(C2×D3)⋊C4C2×D312yes—
191C2×C4⋊Dic3—34no—
192#924—32no—
193#924—34no—
194#924—61no—
195#924C2×D312yes—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—34no—
198C2×Dic3⋊C4—34no—
199C2×C4×Dic3—32no—
200C2×C4×Dic3—61no—
201#897—34no—
202#897—34no—
203#897C2×D314yescomplemented
204#896—34no—
205#896—34no—
206#896—34no—
207#896—34no—
208#896C2×D314yescomplemented
209#896C2×D314yescomplemented
210D3×C4⋊C4—34no—
211D3×C4⋊C4—34no—
212D3×C4⋊C4—34no—
213#889—34no—
214#889—34no—
215#889—34no—
216#889—34no—
217#889—34no—
218#889—34no—
219#889—62no—
220#888—34no—
221#888—32no—
222#888—32no—
223#888—34no—
224#888—61no—
225#887—32no—
226#887—34no—
227#887—32no—
228#887—34no—
229#887—62no—
230#887—61no—
231#67⋊C4—34no—
232#67⋊C4—34no—
233#67⋊C4—34no—
234#67⋊C4—34no—
235#67⋊C4—34no—
236#67⋊C4—34no—
237#67⋊C4—34no—
238#67⋊C4—34no—
239D3×C22⋊C4—34no—
240D3×C22⋊C4C2×D314yes—
241#878—34no—
242#878—34no—
243#878—34no—
244#878—34no—
245#878—34no—
246#878—34no—
247#878—34no—
248#878—34no—
249#878—34no—
250#878—34no—
251#878—34no—
252#878—62no—
253#878C2×D314yes—
254#877—34no—
255#877—34no—
256#877—62no—
257C23×C32C2411yescharacteristic
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3C2×Q818yescomplemented
261C22×C3×D3C2414yes—
262C32×Q8—41no—
263C2×C32×C4—41no—
264C2×C32×C4C2411yescharacteristic
265C2×C32×C4C2412yes—
266C2×C32×C4C2412yes—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—22no—
269C2×C3⋊Dic3C2×Q814yescomplemented
270C2×C3⋊Dic3C2412yes—
271C2×C3⋊Dic3C2412yes—
272C2×C3⋊Dic3C2411yescharacteristic
273C2×C3⋊Dic3C2411yescharacteristic
274C2×C3⋊Dic3C2411yescharacteristic
275C2×C3⋊Dic3C2411yescharacteristic
276#634—24no—
277#634—41no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3C2414yes—
280C2×C3×Dic3C2414yes—
281C2×C3×Dic3C2414yes—
282C3×C4×D3—44no—
283C3×C4×D3—44no—
284C3×Dic6—44no—
285C3×Dic6—42no—
286#627—24no—
287#627—44no—
288#625C2×Q818yescomplemented
289#625C2×Q818yescomplemented
290D3×Dic3—28no—
291D3×Dic3—44no—
292D3×Dic3—44no—
293D3×Dic3—44no—
294#554—92no—
295#554—94no—
296#554—92no—
297#554—92no—
298#554—92no—
299D4×Q8—92no—
300D4×Q8—92no—
301#544—92no—
302#543—32no—
303#543—92no—
304#533—91no—
305#533—91no—
306C2×C22⋊Q8—94no—
307#518—92no—
308C2×C4×D4—91no—
309C24×C3—32no—
310C23×D3C22×D312yes—
311C2×C3×Q8—21no—
312C2×C3×Q8—34no—
313C2×C3×Q8—32no—
314C2×C3×Q8C22×D312yes—
315C22×C3×C4—21no—
316C22×C3×C4—32no—
317C22×C3×C4—34no—
318C22×C3×C4—34no—
319C22×C3×C4C22×D312yes—
320C2×#67—316no—
321C2×#67—34no—
322C2×#67—34no—
323C22×Dic3—32no—
324C22×Dic3—32no—
325C22×Dic3—34no—
326C22×Dic3—34no—
327C22×Dic3—34no—
328C22×Dic3—34no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—124no—
332C22×Dic3C22×D312yes—
333D3×Q8—128no—
334C2×C4×D3—34no—
335C2×C4×D3—34no—
336C2×C4×D3—34no—
337C2×C4×D3—34no—
338C2×C4×D3—124no—
339C2×C4×D3C22×D314yes—
340C2×C4×D3C22×D314yes—
341C2×Dic6—34no—
342C2×Dic6—34no—
343C2×Dic6—32no—
344C2×Dic6—34no—
345C2×Dic6—34no—
346C2×Dic6—62no—
347C2×Dic6—61no—
348C2×Dic6—128no—
349C2×Dic6C22×D312yes—
350C2×Dic6C22×D314yes—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—32no—
354C3×C4⋊C4—34no—
355C3×C4⋊C4—34no—
356C3×C4⋊C4—34no—
357C3×C4⋊C4—34no—
358C3×C4⋊C4C22×D312yes—
359C3×C4⋊C4C22×D314yes—
360C3×C22⋊C4—22no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4C22×D314yes—
367#217—34no—
368#217—34no—
369#217—34no—
370#217—62no—
371#217C22×D314yes—
372(C2×D3)⋊C4—34no—
373(C2×D3)⋊C4—34no—
374(C2×D3)⋊C4C22×D314yes—
375(C2×D3)⋊C4C22×D314yes—
376(C2×D3)⋊C4C22×D314yes—
377(C2×D3)⋊C4C22×D314yes—
378C4⋊Dic3—32no—
379C4⋊Dic3—34no—
380C4⋊Dic3—34no—
381C4⋊Dic3—34no—
382C4⋊Dic3—34no—
383C4⋊Dic3—62no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D312yes—
386C4⋊Dic3C22×D314yes—
387Dic3⋊C4—34no—
388Dic3⋊C4—34no—
389Dic3⋊C4—34no—
390Dic3⋊C4—34no—
391Dic3⋊C4—34no—
392Dic3⋊C4—34no—
393Dic3⋊C4—34no—
394Dic3⋊C4—34no—
395Dic3⋊C4—34no—
396Dic3⋊C4—34no—
397Dic3⋊C4—34no—
398Dic3⋊C4—34no—
399Dic3⋊C4—34no—
400Dic3⋊C4—34no—
401Dic3⋊C4—34no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404Dic3⋊C4—62no—
405Dic3⋊C4—62no—
406Dic3⋊C4—62no—
407Dic3⋊C4C22×D314yes—
408Dic3⋊C4C22×D314yes—
409Dic3⋊C4C22×D314yes—
410C4×Dic3—34no—
411C4×Dic3—34no—
412C4×Dic3—32no—
413C4×Dic3—32no—
414C4×Dic3—32no—
415C4×Dic3—32no—
416C4×Dic3—34no—
417C4×Dic3—34no—
418C4×Dic3—62no—
419C4×Dic3—62no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32C22×Q812yes—
427C22×C32C2511yescharacteristic
428C2×C3×D3—24no—
429C2×C3×D3—24no—
430C2×C3×D3—48no—
431C2×C3×D3C22×Q818yes—
432C32×C4—21no—
433C32×C4—22no—
434C32×C4—21no—
435C32×C4—22no—
436C3⋊Dic3—21no—
437C3⋊Dic3—22no—
438C3⋊Dic3—22no—
439C3⋊Dic3C22×Q812yes—
440C3⋊Dic3C22×Q812yes—
441C3⋊Dic3H(5,𝔽2)12yes—
442C3×Dic3—24no—
443C3×Dic3—24no—
444C3×Dic3—24no—
445C22×Q8—94no—
446C22×D4—91no—
447C23×C4—92no—
448C4⋊Q8—91no—
449C4⋊Q8—92no—
450C4⋊Q8—94no—
451C4⋊Q8—91no—
452C4⋊Q8—92no—
453C4⋊Q8—91no—
454C4⋊Q8—91no—
455#125—92no—
456#125—94no—
457#125—92no—
458#125—92no—
459#125—92no—
460C22⋊Q8—34no—
461C22⋊Q8—32no—
462C22⋊Q8—34no—
463C22⋊Q8—34no—
464C22⋊Q8—34no—
465C22⋊Q8—34no—
466C22⋊Q8—92no—
467C22⋊Q8—94no—
468C22⋊Q8—94no—
469C22⋊Q8—94no—
470C22⋊Q8—94no—
471C22⋊Q8—94no—
472C22⋊Q8—94no—
473C22⋊Q8—94no—
474C22⋊Q8—94no—
475C22⋊Q8—94no—
476C22⋊Q8—91no—
477C22⋊Q8—92no—
478C22⋊Q8D3211yescharacteristic
479C4×Q8—92no—
480C4×Q8—92no—
481C4×Q8—91no—
482C4×Q8—92no—
483C4×Q8—91no—
484C4×D4—92no—
485C4×D4—92no—
486C4×D4—92no—
487C4×D4—92no—
488C4×D4—92no—
489C4×D4—92no—
490C4×D4—94no—
491C4×D4—94no—
492C4×D4—92no—
493C4×D4—92no—
494#117—92no—
495#117—92no—
496C2×C4⋊C4—94no—
497C2×C4⋊C4—94no—
498C2×C4⋊C4—94no—
499C2×C4⋊C4—91no—
500C2×C22⋊C4—32no—
501C2×C22⋊C4—34no—
502C2×C22⋊C4—94no—
503C2×C42—91no—
504C23×C3—21no—
505C23×C3—34no—
506C23×C3—38no—
507C23×C3—122no—
508C23×C3—122no—
509C23×C3C23×D312yes—
510C22×D3—42no—
511C22×D3—42no—
512C22×D3D3×Q818yescomplemented
513C22×D3C23×D314yes—
514C3×Q8—42no—
515C3×Q8—42no—
516C3×Q8—124no—
517C3×Q8—122no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—34no—
523C2×C3×C4—34no—
524C2×C3×C4—34no—
525C2×C3×C4—42no—
526C2×C3×C4—42no—
527C2×C3×C4—124no—
528C2×C3×C4—124no—
529C2×C3×C4—122no—
530C2×C3×C4C23×D312yes—
531C2×C3×C4C23×D312yes—
532C2×C3×C4C23×D314yes—
533C2×C3×C4C23×D314yes—
534#67—316no—
535#67—316no—
536C2×Dic3—38no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—34no—
542C2×Dic3—34no—
543C2×Dic3—42no—
544C2×Dic3—64no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—68no—
552C2×Dic3—64no—
553C2×Dic3—122no—
554C2×Dic3—124no—
555C2×Dic3—124no—
556C2×Dic3—124no—
557C2×Dic3C23×D314yes—
558C2×Dic3C23×D314yes—
559C2×Dic3C23×D314yes—
560C4×D3—44no—
561C4×D3—44no—
562C4×D3—68no—
563C4×D3—124no—
564C4×D3—124no—
565C4×D3—124no—
566Dic6—44no—
567Dic6—42no—
568Dic6—68no—
569Dic6—68no—
570Dic6—124no—
571Dic6—124no—
572Dic6—124no—
573Dic6—122no—
574Dic6—122no—
575C2×C32—22no—
576C2×C32C23×Q811yescharacteristic
577C2×C32C2×H(5,𝔽2)11yescharacteristic
578C2×C32#58511yescharacteristic
579C3×D3—28no—
580C24—32no—
581C2×Q8—32no—
582C2×Q8—34no—
583C2×Q8—92no—
584C2×Q8—94no—
585C2×Q8—92no—
586C2×Q8—91no—
587C2×Q8—368no—
588C2×Q8C2×D3211yescharacteristic
589C2×D4—92no—
590C2×D4—92no—
591C2×D4—98no—
592C22×C4—32no—
593C22×C4—34no—
594C22×C4—34no—
595C22×C4—94no—
596C22×C4—94no—
597C22×C4—94no—
598C22×C4—94no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—364no—
602C22×C4C2×D3211yescharacteristic
603C4⋊C4—34no—
604C4⋊C4—34no—
605C4⋊C4—34no—
606C4⋊C4—34no—
607C4⋊C4—32no—
608C4⋊C4—94no—
609C4⋊C4—92no—
610C4⋊C4—92no—
611C4⋊C4—92no—
612C4⋊C4—94no—
613C4⋊C4—94no—
614C4⋊C4—94no—
615C4⋊C4—92no—
616C4⋊C4—92no—
617C4⋊C4—92no—
618C4⋊C4—92no—
619C4⋊C4—92no—
620C4⋊C4—92no—
621C4⋊C4—92no—
622C4⋊C4—92no—
623C4⋊C4—91no—
624C4⋊C4C2×D3212yes—
625C4⋊C4C2×D3211yescharacteristic
626C22⋊C4—34no—
627C22⋊C4—34no—
628C22⋊C4—34no—
629C22⋊C4—34no—
630C22⋊C4—34no—
631C22⋊C4—94no—
632C22⋊C4—94no—
633C22⋊C4—92no—
634C22⋊C4C2×D3212yes—
635C42—94no—
636C42—91no—
637C42—91no—
638C42—91no—
639C42—91no—
640C42—92no—
641C42—92no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—38no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—128no—
652C22×C3C2×D3×Q814yes—
653C22×C3C24×D312yes—
654C2×D3—24no—
655C2×D3—24no—
656C2×D3—48no—
657C2×D3C2×D3×Q818yes—
658C3×C4—22no—
659C3×C4—24no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—24no—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—42no—
666C3×C4—64no—
667C3×C4—64no—
668C3×C4—64no—
669Dic3—24no—
670Dic3—24no—
671Dic3—24no—
672Dic3—34no—
673Dic3—34no—
674Dic3—34no—
675Dic3—62no—
676Dic3—62no—
677Dic3—62no—
678Dic3—64no—
679Dic3—62no—
680Dic3—64no—
681Dic3—122no—
682Dic3—122no—
683Dic3—121no—
684C32#350111yescharacteristic, complemented, Sylow
685C23—34no—
686C23—38no—
687C23—122no—
688C23—122no—
689C23C22×D3211yescharacteristic
690Q8—41no—
691Q8—124no—
692Q8—122no—
693Q8—184no—
694Q8—184no—
695Q8—361no—
696Q8—364no—
697D4—98no—
698D4—98no—
699C2×C4—34no—
700C2×C4—34no—
701C2×C4—34no—
702C2×C4—41no—
703C2×C4—94no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—92no—
709C2×C4—92no—
710C2×C4—124no—
711C2×C4—124no—
712C2×C4—122no—
713C2×C4—188no—
714C2×C4—182no—
715C2×C4—364no—
716C2×C4—364no—
717C2×C4—364no—
718C2×C4C22×D3211yescharacteristic
719C2×C4C22×D3211yescharacteristic
720C2×C4C22×D3212yes—
721C2×C4C22×D3212yes—
722C2×C3—24no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—68no—
728C2×C3C22×D3×Q812yes—
729C2×C3D3×H(5,𝔽2)12yes—
730C2×C3#596612yes—
731D3—28no—
732C22—21no—
733C22—21no—
734C22—38no—
735C22—64no—
736C22—64no—
737C22—128no—
738C22D32×Q812yes—
739C22C23×D3211yescharacteristic
740C4—21no—
741C4—21no—
742C4—22no—
743C4—22no—
744C4—64no—
745C4—64no—
746C4—64no—
747C4—92no—
748C4—92no—
749C4—92no—
750C4—182no—
751C4—181no—
752C4—182no—
753C3—21no—
754C3#8657412yescomplemented
755C2—22no—
756C2—68no—
757C2#1059667911yescharacteristic
758C2C2×D32×Q811yescharacteristic
759C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
prime radicalC22×#625C22
hypercenterC22⋊Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596093C2semidirect
2. C3×#5634C2semidirect
3. #10595407C2semidirect
4. #10595370C2semidirect
6. #10594971C2semidirect
7. #10594810C2semidirect
8. #10594535C2semidirect
9. #10594534C2semidirect
10. #10594534C2semidirect
11. #10594526C2semidirect
12. #10594377C2semidirect
14. D3×#878C2semidirect
15. #10594033C2semidirect
19. C2×D3×Dic6C22semidirect
21. Q8×C3⋊Dic3C22semidirect
22. #64153C22semidirect
25. #64098C22semidirect
26. #64097C22semidirect
27. #64096C22semidirect
28. #64096C22semidirect
31. C3×#946C22semidirect
34. C3×#897C22semidirect
35. C3×#896C22semidirect
36. C3×#896C22semidirect
44. #63919C22semidirect
45. #63919C22semidirect
54. #63899C22semidirect
55. #63899C22semidirect
56. #63896C22semidirect
57. #63896C22semidirect
58. #63893C22semidirect
59. #63893C22semidirect
60. D3×C4⋊Dic3C22semidirect
61. #63887C22semidirect
62. #63887C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. D3×Dic3⋊C4C22semidirect
67. #63873C22semidirect
68. #63873C22semidirect
69. #63870C22semidirect
70. #63870C22semidirect
71. #63870C22semidirect
72. #63847C22semidirect
73. #63843C22semidirect
74. #63839C22semidirect
75. #63838C22semidirect
84. #5634D3semidirect
110. C2×#625Q8semidirect
177. #946C2×D3semidirect
203. #897C2×D3semidirect
208. #896C2×D3semidirect
209. #896C2×D3semidirect
260. C22×C3×D3C2×Q8semidirect
269. C2×C3⋊Dic3C2×Q8semidirect
288. #625C2×Q8semidirect
289. #625C2×Q8semidirect
512. C22×D3D3×Q8semidirect
684. C32#3501semidirect
754. C3#86574semidirect

Maximal subgroups

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

subgroupindex
#105960932
C3×#56342
#105954072
#105953702
C2×#639022
#105949712
#105948102
#105945352
#105945342
#105945262
#105943772
#105941812
D3×#8782
#105940332
#865743