Finite Group Databasebeta

← #11902004

Subgroups — #11902004

Order 1152.

2533 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×#5804C212yesmaximal, complemented
3#10595521C211yesmaximal, characteristic, complemented
4#10595518C211yesmaximal, characteristic, complemented
5#10595508C212yesmaximal, complemented
6#10595501C212yesmaximal, complemented
7C2×#67⋊Dic3C212yesmaximal, complemented
8#10595267C214yesmaximal, complemented
9#10595220C214yesmaximal, complemented
10#10595202C214yesmaximal, complemented
11#10595130C214yesmaximal, complemented
12#10594994C212yesmaximal, complemented
13#10594963C212yesmaximal, complemented
14#86295—32nomaximal
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic, complemented
18C22×C3×#67C2212yes—
19C2×#3805C2212yescomplemented
20C22×D3×Dic3C2212yescomplemented
21C2×#3757C2211yescharacteristic
22C2×#3757C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2214yescomplemented
24D4×C3⋊Dic3C2214yescomplemented
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C3×#953C2214yescomplemented
28C2×C3×#217C2212yes—
29C3×#939C2214yes—
30C3×#939C2214yes—
31C3×#937C2214yescomplemented
32C3×#935C2214yescomplemented
33C3×#929C2214yescomplemented
34#63982C2212yescomplemented
35#63982C2212yescomplemented
36#63982C2212yescomplemented
37#63980C2212yes—
38#63980C2212yes—
39#63980C2212yescomplemented
40#63976C2214yescomplemented
41#67⋊Dic3C2214yescomplemented
42#67⋊Dic3C2214yescomplemented
43#67⋊Dic3C2214yescomplemented
44#67⋊Dic3C2214yescomplemented
45#67⋊Dic3C2214yescomplemented
46#63970C2214yescomplemented
47#63969C2214yescomplemented
48C2×Dic3⋊Dic3C2212yescomplemented
49#63964C2214yescomplemented
50#63964C2214yescomplemented
51#63962C2214yescomplemented
52#63961C2214yescomplemented
53C2×(C2×D3)⋊Dic3C2212yescomplemented
54#63959C2214yescomplemented
55#63957C2212yescomplemented
56#63956C2214yescomplemented
57C2×Dic32C2212yescomplemented
58#63915C2212yescomplemented
59#63902C2212yescomplemented
60#63893C2214yescomplemented
61#63891C2214yescomplemented
62#63878C2214yescomplemented
63#63870C2212yescomplemented
64#63862C2214yescomplemented
65#63861C2214yescomplemented
66#63845C2214yescomplemented
67#63838C2212yescomplemented
68C3×#534—32no—
69#5804—32no—
70#5804D312yescomplemented
71C2×D4×Dic3—32no—
72C2×D4×Dic3—32no—
73C2×D4×Dic3—61no—
74#5665—34no—
75#5665—34no—
76#5649—34no—
77#5649—34no—
78#5617—34no—
79#5606—34no—
80#5602—34no—
81#5600—34no—
82#5593—34no—
83#5593—34no—
84#5586—34no—
85#5586—34no—
86C2×#67⋊C4—32no—
87#5483—32no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3C2312yes—
91C2×C32×D4—24no—
92C2×C32×D4C2314yes—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—42no—
95C22×C3⋊Dic3—42no—
96C22×C3⋊Dic3C2312yes—
97C22×C3⋊Dic3C2312yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2312yes—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2312yes—
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C3×#67—28no—
105C2×C3×#67C2314yes—
106C2×C3×#67C2314yes—
107C2×C3×#67C2314yes—
108C2×C3×#67C2314yes—
109C22×C3×Dic3C2312yes—
110C22×C3×Dic3C2312yes—
111C22×C3×Dic3C2312yes—
112C2×#627C2312yes—
113C2×#627C2312yes—
114C2×#625C2312yes—
115C2×#625C2312yes—
116#3805—44no—
117C2×D3×Dic3—44no—
118C2×D3×Dic3C2314yes—
119C2×D3×Dic3C2314yes—
120#3757C2314yes—
121#3757C2314yes—
122C4⋊(C3⋊Dic3)C2314yes—
123C4×C3⋊Dic3C2312yes—
124C4×C3⋊Dic3C2312yes—
125C3×#217C2314yes—
126C3×#217C2314yes—
127C3×#217C2314yes—
128C3×#217C2314yes—
129C3×(C2×D3)⋊C4C2314yes—
130C3×(C2×D3)⋊C4C2314yes—
131C3×Dic3⋊C4C2314yes—
132C3×Dic3⋊C4C2314yes—
133#3724C2312yes—
134#3724C2312yes—
135#3724C2312yes—
136#3724C2312yes—
137Dic3⋊Dic3C2314yes—
138Dic3⋊Dic3C2314yes—
139Dic3⋊Dic3C2314yes—
140Dic3⋊Dic3C2314yes—
141(C2×D3)⋊Dic3C2314yes—
142(C2×D3)⋊Dic3C2314yes—
143(C2×D3)⋊Dic3C2314yes—
144(C2×D3)⋊Dic3C2314yes—
145Dic32C2314yes—
146Dic32C2314yes—
147#3459—91noSylow
148C22×C3×D4—21no—
149C22×C3×D4—32no—
150C22×C3×D4C2×D312yes—
151C22×#67C2×D312yes—
152C23×Dic3—32no—
153C23×Dic3—32no—
154C23×Dic3—32no—
155C23×Dic3—61no—
156C23×Dic3—61no—
157C2×#237—34no—
158C22×C4×D3—32no—
159C3×#123—34no—
160C3×#123—34no—
161C3×#121—34no—
162C3×#121—34no—
163C3×#120—34no—
164C3×#120—34no—
165C2×C3×C22⋊C4—32no—
166#953—34no—
167#953C2×D314yescomplemented
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—32no—
171C2×#217—61no—
172C2×#217—61no—
173C2×#217C2×D312yes—
174#939—34no—
175#939—34no—
176#939—34no—
177#939—34no—
178#939C2×D314yes—
179#939C2×D314yes—
180#938—34no—
181#937—34no—
182#937C2×D314yescomplemented
183#936—34no—
184#935—34no—
185#935—34no—
186#935—34no—
187#935C2×D314yescomplemented
188D4×Dic3—34no—
189D4×Dic3—34no—
190D4×Dic3—34no—
191D4×Dic3—34no—
192D4×Dic3—34no—
193D4×Dic3—34no—
194D4×Dic3—34no—
195D4×Dic3—34no—
196D4×Dic3—34no—
197D4×Dic3—64no—
198D4×Dic3—64no—
199#929—34no—
200#929C2×D314yescomplemented
201C2×(C2×D3)⋊C4—32no—
202C2×C4⋊Dic3—32no—
203C2×C4⋊Dic3—32no—
204C2×C4⋊Dic3—61no—
205#924—34no—
206#924—34no—
207C2×Dic3⋊C4—32no—
208C2×C4×Dic3—32no—
209C2×C4×Dic3—32no—
210C2×C4×Dic3—32no—
211C2×C4×Dic3—61no—
212#898—34no—
213#898—34no—
214#897—34no—
215#892—34no—
216#890—34no—
217#889—34no—
218#889—34no—
219#887—34no—
220#886—34no—
221#886—34no—
222#885—34no—
223#885—34no—
224#883—34no—
225#883—34no—
226#67⋊C4—34no—
227#67⋊C4—34no—
228#67⋊C4—34no—
229#67⋊C4—34no—
230#67⋊C4—34no—
231#67⋊C4—34no—
232#879—34no—
233#879—34no—
234#879—34no—
235#879—34no—
236#878—34no—
237#878—34no—
238#878—34no—
239#878—34no—
240#878—34no—
241#878—34no—
242#877—34no—
243#877—34no—
244C23×C32—22no—
245C23×C32—41no—
246C23×C32—41no—
247C23×C32—41no—
248C23×C32—41no—
249C23×C32#4114yescomplemented
250C23×C32C2412yes—
251C23×C32C2412yes—
252C23×C32C2411yescharacteristic
253C22×C3×D3—24no—
254C22×C3×D3—42no—
255C22×C3×D3—42no—
256C22×C3×D3C2414yes—
257C32×D4—28no—
258C2×C32×C4—22no—
259C2×C32×C4C2412yes—
260C2×C3⋊Dic3—22no—
261C2×C3⋊Dic3—24no—
262C2×C3⋊Dic3—24no—
263C2×C3⋊Dic3—42no—
264C2×C3⋊Dic3—42no—
265C2×C3⋊Dic3—41no—
266C2×C3⋊Dic3—41no—
267C2×C3⋊Dic3—41no—
268C2×C3⋊Dic3C2412yes—
269C2×C3⋊Dic3C2411yescharacteristic
270C2×C3⋊Dic3C2412yes—
271C2×C3⋊Dic3C2412yes—
272C2×C3⋊Dic3C2411yescharacteristic
273C3×#67—28no—
274C3×#67—28no—
275C3×#67—44no—
276C3×#67—44no—
277C2×C3×Dic3—24no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2414yes—
281C2×C3×Dic3C2414yes—
282C2×C3×Dic3C2414yes—
283#627—42no—
284#627—42no—
285#625—42no—
286#625—42no—
287D3×Dic3—28no—
288D3×Dic3—44no—
289#543—91no—
290#539—94no—
291#539—92no—
292#538—92no—
293#538—94no—
294#534—32no—
295#534—91no—
296#529—94no—
297#529—92no—
298#525—92no—
299#525—94no—
300C2×C4×D4—92no—
301C2×C4×D4—91no—
302C24×C3—21no—
303C24×C3—21no—
304C24×C3—32no—
305C24×C3C22×D312yes—
306C24×C3C22×D312yes—
307C23×D3C22×D312yes—
308C2×C3×D4—28no—
309C2×C3×D4—28no—
310C2×C3×D4—24no—
311C2×C3×D4—34no—
312C2×C3×D4—34no—
313C2×C3×D4—34no—
314C2×C3×D4—34no—
315C2×C3×D4—68no—
316C2×C3×D4C22×D314yes—
317C2×C3×D4C22×D314yes—
318C22×C3×C4—21no—
319C22×C3×C4—32no—
320C22×C3×C4—32no—
321C22×C3×C4—32no—
322C22×C3×C4C22×D312yes—
323C2×#67—28no—
324C2×#67—34no—
325C2×#67—34no—
326C2×#67C22×D314yes—
327C2×#67C22×D314yes—
328C2×#67C22×D314yes—
329C2×#67C22×D314yes—
330C22×Dic3—34no—
331C22×Dic3—32no—
332C22×Dic3—32no—
333C22×Dic3—32no—
334C22×Dic3—32no—
335C22×Dic3—32no—
336C22×Dic3—34no—
337C22×Dic3—32no—
338C22×Dic3—32no—
339C22×Dic3—32no—
340C22×Dic3—34no—
341C22×Dic3—34no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—62no—
347C22×Dic3—62no—
348C22×Dic3—62no—
349C22×Dic3—62no—
350C22×Dic3—124no—
351C22×Dic3—124no—
352C22×Dic3—124no—
353C22×Dic3—124no—
354C22×Dic3—124no—
355C22×Dic3C22×D312yes—
356C22×Dic3C22×D312yes—
357C22×Dic3C22×D312yes—
358#237—128no—
359C2×C4×D3—34no—
360C2×C4×D3—34no—
361C2×C4×D3—124no—
362C2×Dic6—34no—
363C2×Dic6—34no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—34no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—34no—
370C3×C22⋊C4—34no—
371C3×C22⋊C4—34no—
372#217—34no—
373#217—34no—
374#217—34no—
375#217—34no—
376#217—34no—
377#217—34no—
378#217—34no—
379#217—34no—
380#217—64no—
381#217—64no—
382#217C22×D314yes—
383#217C22×D314yes—
384#217C22×D314yes—
385#217C22×D314yes—
386(C2×D3)⋊C4—34no—
387(C2×D3)⋊C4—34no—
388(C2×D3)⋊C4—34no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4C22×D314yes—
391(C2×D3)⋊C4C22×D314yes—
392C4⋊Dic3—34no—
393C4⋊Dic3—34no—
394C4⋊Dic3—34no—
395C4⋊Dic3—34no—
396C4⋊Dic3—34no—
397C4⋊Dic3—34no—
398C4⋊Dic3—64no—
399Dic3⋊C4—34no—
400Dic3⋊C4—34no—
401Dic3⋊C4—34no—
402Dic3⋊C4—34no—
403Dic3⋊C4—34no—
404Dic3⋊C4—34no—
405Dic3⋊C4—34no—
406Dic3⋊C4—34no—
407Dic3⋊C4C22×D314yes—
408Dic3⋊C4C22×D314yes—
409C4×Dic3—34no—
410C4×Dic3—34no—
411C4×Dic3—34no—
412C4×Dic3—34no—
413C4×Dic3—34no—
414C4×Dic3—34no—
415C4×Dic3—62no—
416C4×Dic3—62no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—44no—
425C22×C32—44no—
426C22×C32C2×#4114yes—
427C22×C32C2×#4112yes—
428C22×C32C2511yescharacteristic
429C2×C3×D3—24no—
430C2×C3×D3—24no—
431C2×C3×D3—24no—
432C2×C3×D3—48no—
433C32×C4—22no—
434C3⋊Dic3—21no—
435C3⋊Dic3—22no—
436C3⋊Dic3—22no—
437C3⋊Dic3—22no—
438C3⋊Dic3H(5,𝔽2)12yes—
439C3×Dic3—24no—
440C3×Dic3—24no—
441C3×Dic3—24no—
442C2×#41—92no—
443C22×D4—32no—
444C22×D4D3211yescharacteristic
445C23×C4—92no—
446C23×C4—91no—
447C23×C4—91no—
448#126—94no—
449#126—94no—
450#126—94no—
451#125—92no—
452#125—94no—
453#124—92no—
454#124—94no—
455#123—34no—
456#123—34no—
457#123—94no—
458#123—94no—
459#123—94no—
460#123—94no—
461C22⋊Q8—92no—
462C22⋊Q8—92no—
463C22⋊Q8—92no—
464C22⋊Q8—94no—
465C22⋊Q8—94no—
466C22⋊Q8—94no—
467#121—34no—
468#121—34no—
469#121—92no—
470#121—94no—
471#121—92no—
472#121—92no—
473#120—34no—
474#120—34no—
475#120—94no—
476C4×Q8—92no—
477C4×D4—92no—
478C4×D4—94no—
479C4×D4—94no—
480C4×D4—94no—
481C4×D4—94no—
482C4×D4—94no—
483C4×D4—94no—
484C4×D4—94no—
485#117—92no—
486#117—94no—
487C2×C4⋊C4—92no—
488C2×C4⋊C4—91no—
489C2×C22⋊C4—32no—
490C2×C22⋊C4—92no—
491C2×C22⋊C4—91no—
492C2×C22⋊C4—91no—
493C2×C42—92no—
494C2×C42—91no—
495C23×C3—24no—
496C23×C3—24no—
497C23×C3—21no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—24no—
501C23×C3—34no—
502C23×C3—42no—
503C23×C3—42no—
504C23×C3—42no—
505C23×C3—42no—
506C23×C3—42no—
507C23×C3—42no—
508C23×C3—42no—
509C23×C3—42no—
510C23×C3—64no—
511C23×C3—122no—
512C23×C3—122no—
513C23×C3#23718yescomplemented
514C23×C3C23×D314yes—
515C23×C3C23×D312yes—
516C23×C3C23×D312yes—
517C23×C3C23×D312yes—
518C22×D3—24no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3C23×D314yes—
522C3×D4—216no—
523C3×D4—28no—
524C3×D4—28no—
525C3×D4—68no—
526C3×D4—68no—
527C3×D4—124no—
528C3×D4—124no—
529C2×C3×C4—24no—
530C2×C3×C4—24no—
531C2×C3×C4—22no—
532C2×C3×C4—34no—
533C2×C3×C4—34no—
534C2×C3×C4—34no—
535C2×C3×C4—64no—
536C2×C3×C4—122no—
537C2×C3×C4—122no—
538C2×C3×C4C23×D314yes—
539#67—28no—
540#67—28no—
541#67—44no—
542#67—44no—
543#67—124no—
544#67—124no—
545C2×Dic3—24no—
546C2×Dic3—32no—
547C2×Dic3—34no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—34no—
552C2×Dic3—42no—
553C2×Dic3—42no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—68no—
560C2×Dic3—64no—
561C2×Dic3—68no—
562C2×Dic3—64no—
563C2×Dic3—64no—
564C2×Dic3—64no—
565C2×Dic3—124no—
566C2×Dic3—124no—
567C2×Dic3—124no—
568C2×Dic3—122no—
569C2×Dic3—122no—
570C2×Dic3—124no—
571C2×Dic3—122no—
572C2×Dic3—122no—
573C2×Dic3—122no—
574C2×Dic3—124no—
575C2×Dic3—124no—
576C2×Dic3—122no—
577C2×Dic3—122no—
578C2×Dic3—122no—
579C2×Dic3C23×D314yes—
580C2×Dic3C23×D314yes—
581C2×Dic3C23×D314yes—
582C4×D3—68no—
583C4×D3—124no—
584Dic6—124no—
585Dic6—124no—
586C2×C32—22no—
587C2×C32—24no—
588C2×C32—42no—
589C2×C32C22×#4111yescharacteristic
590C2×C32C2×H(5,𝔽2)11yescharacteristic
591C2×C32#58511yescharacteristic
592C3×D3—44no—
593C24—32no—
594C24C2×D3211yescharacteristic
595C24C2×D3211yescharacteristic
596#41—364no—
597C2×Q8—92no—
598C2×Q8—92no—
599C2×D4—24no—
600C2×D4—34no—
601C2×D4—34no—
602C2×D4—34no—
603C2×D4—34no—
604C2×D4—68no—
605C2×D4—92no—
606C2×D4—92no—
607C2×D4C2×D3214yes—
608C22×C4—32no—
609C22×C4—32no—
610C22×C4—32no—
611C22×C4—94no—
612C22×C4—94no—
613C22×C4—91no—
614C22×C4—92no—
615C22×C4—92no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—92no—
619C22×C4—91no—
620C22×C4—92no—
621C22×C4—364no—
622C22×C4—362no—
623C22×C4—362no—
624C22×C4C2×D3211yescharacteristic
625C4⋊C4—34no—
626C4⋊C4—34no—
627C4⋊C4—94no—
628C4⋊C4—94no—
629C4⋊C4—92no—
630C4⋊C4—94no—
631C4⋊C4—92no—
632C4⋊C4—92no—
633C4⋊C4—94no—
634C4⋊C4—92no—
635C4⋊C4—94no—
636C22⋊C4—34no—
637C22⋊C4—34no—
638C22⋊C4—34no—
639C22⋊C4—34no—
640C22⋊C4—34no—
641C22⋊C4—34no—
642C22⋊C4—94no—
643C22⋊C4—94no—
644C22⋊C4—94no—
645C22⋊C4—94no—
646C22⋊C4—94no—
647C22⋊C4—94no—
648C42—94no—
649C42—94no—
650C42—92no—
651C42—92no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—22no—
665C22×C3—24no—
666C22×C3—21no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—48no—
672C22×C3—48no—
673C22×C3—48no—
674C22×C3—48no—
675C22×C3—64no—
676C22×C3—64no—
677C22×C3—64no—
678C22×C3—128no—
679C22×C3C2×#23714yes—
680C22×C3C2×#23714yes—
681C22×C3C2×#23714yes—
682C22×C3C24×D312yes—
683C2×D3—24no—
684C2×D3—24no—
685C2×D3—24no—
686C2×D3—48no—
687C3×C4—24no—
688C3×C4—24no—
689C3×C4—64no—
690C3×C4—64no—
691C3×C4—64no—
692Dic3—24no—
693Dic3—24no—
694Dic3—24no—
695Dic3—34no—
696Dic3—62no—
697Dic3—62no—
698Dic3—64no—
699Dic3—62no—
700Dic3—62no—
701Dic3—62no—
702Dic3—64no—
703Dic3—122no—
704Dic3—122no—
705Dic3—122no—
706C32#345911yescharacteristic, complemented, Sylow
707C23—22no—
708C23—34no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—64no—
714C23—122no—
715C23—122no—
716C23#380514yescomplemented
717C23C22×D3212yes—
718C23C22×D3211yescharacteristic
719C23C22×D3212yes—
720Q8—362no—
721Q8—362no—
722D4—28no—
723D4—68no—
724D4—68no—
725D4—124no—
726D4—124no—
727D4—362no—
728D4—362no—
729C2×C4—22no—
730C2×C4—34no—
731C2×C4—34no—
732C2×C4—34no—
733C2×C4—64no—
734C2×C4—91no—
735C2×C4—92no—
736C2×C4—91no—
737C2×C4—92no—
738C2×C4—92no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—188no—
742C2×C4—182no—
743C2×C4—184no—
744C2×C4—184no—
745C2×C4—364no—
746C2×C4—362no—
747C2×C4—362no—
748C2×C4—361no—
749C2×C4—361no—
750C2×C4—361no—
751C2×C4C22×D3212yes—
752C2×C3—24no—
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—24no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—44no—
760C2×C3—44no—
761C2×C3—44no—
762C2×C3—124no—
763C2×C3C22×#23712yes—
764C2×C3D3×H(5,𝔽2)12yes—
765C2×C3#596612yes—
766D3—44no—
767C22—22no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—44no—
775C22—44no—
776C22—64no—
777C22—64no—
778C22—64no—
779C22—128no—
780C22C2×#380512yes—
781C22C2×#380514yes—
782C22C23×D3211yescharacteristic
783C4—22no—
784C4—64no—
785C4—64no—
786C4—64no—
787C4—92no—
788C4—181no—
789C4—182no—
790C4—182no—
791C4—182no—
792C3—21no—
793C3#8629512yescomplemented
794C2—22no—
795C2—24no—
796C2—42no—
797C2—124no—
798C2#1059667511yescharacteristic
799C2#1059667911yescharacteristic
800C2C22×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3459
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. C3×#5804C2semidirect
3. #10595521C2semidirect
4. #10595518C2semidirect
5. #10595508C2semidirect
6. #10595501C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. #10595267C2semidirect
9. #10595220C2semidirect
10. #10595202C2semidirect
11. #10595130C2semidirect
12. #10594994C2semidirect
13. #10594963C2semidirect
17. C23×C3⋊Dic3C22semidirect
19. C2×#3805C22semidirect
20. C22×D3×Dic3C22semidirect
22. C2×#3757C22semidirect
23. D4×C3⋊Dic3C22semidirect
24. D4×C3⋊Dic3C22semidirect
25. C2×C4⋊(C3⋊Dic3)C22semidirect
26. C2×C4×C3⋊Dic3C22semidirect
27. C3×#953C22semidirect
31. C3×#937C22semidirect
32. C3×#935C22semidirect
33. C3×#929C22semidirect
34. #63982C22semidirect
35. #63982C22semidirect
36. #63982C22semidirect
39. #63980C22semidirect
40. #63976C22semidirect
41. #67⋊Dic3C22semidirect
42. #67⋊Dic3C22semidirect
43. #67⋊Dic3C22semidirect
44. #67⋊Dic3C22semidirect
45. #67⋊Dic3C22semidirect
46. #63970C22semidirect
47. #63969C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
49. #63964C22semidirect
50. #63964C22semidirect
51. #63962C22semidirect
52. #63961C22semidirect
53. C2×(C2×D3)⋊Dic3C22semidirect
54. #63959C22semidirect
55. #63957C22semidirect
56. #63956C22semidirect
57. C2×Dic32C22semidirect
58. #63915C22semidirect
59. #63902C22semidirect
60. #63893C22semidirect
61. #63891C22semidirect
62. #63878C22semidirect
63. #63870C22semidirect
64. #63862C22semidirect
65. #63861C22semidirect
66. #63845C22semidirect
67. #63838C22semidirect
70. #5804D3semidirect
167. #953C2×D3semidirect
182. #937C2×D3semidirect
187. #935C2×D3semidirect
200. #929C2×D3semidirect
249. C23×C32#41semidirect
513. C23×C3#237semidirect
706. C32#3459semidirect
716. C23#3805semidirect
793. C3#86295semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C3×#58042
#105955212
#105955182
#105955082
#105955012
C2×#67⋊Dic32
#105952672
#105952202
#105952022
#105951302
#105949942
#105949632
#862953