Finite Group Databasebeta

← #11058619

Subgroups — #11058619

Order 768.

2612 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#550C211yesmaximal, characteristic, complemented
2C2×#5557C211yesmaximal, characteristic, complemented
3#84097C212yesmaximal, complemented
4#84087C212yesmaximal, complemented
5#83192C211yesmaximal, characteristic, complemented
6#83186C212yesmaximal, complemented
7#83179C211yesmaximal, characteristic, complemented
8#83178C212yesmaximal, complemented
9#82716C214yesmaximal, complemented
10#82705C212yesmaximal, complemented
11#82690C214yesmaximal, complemented
12#82678C212yesmaximal, complemented
13C4×#946C211yesmaximal, characteristic, complemented
14#82482C211yesmaximal, characteristic, complemented
15#82408C212yesmaximal, complemented
16#82363C212yesmaximal, complemented
17D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
18#38909—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C3×#550—28no—
21C2×C3×#127C2212yes—
22C2×C3×#127C2211yescharacteristic
23C2×C3×#121C2214yes—
24C2×C3×#121C2212yes—
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2212yes—
27C2×C3×C4×D4C2211yescharacteristic
28C2×#946C2211yescharacteristic
29C2×#939C2214yes—
30C2×#938C2211yescharacteristic
31C2×#938C2212yes—
32C2×#938C2212yes—
33C2×#938C2212yes—
34C2×#936C2211yescharacteristic
35C2×#936C2212yes—
36C2×D4×Dic3C2212yes—
37C2×C4×#67C2212yes—
38C2×#926C2212yes—
39C22×C4⋊Dic3C2212yes—
40#5557—28no—
41C2×#897C2211yescharacteristic
42C2×#890C2211yescharacteristic
43C2×#883C2212yes—
44C2×#879C2212yes—
45C2×C42×D3C2211yescharacteristic
46C2×C4×Dic6C2211yescharacteristic
47#5229C2212yes—
48#5229C2211yescharacteristic
49#5223C2214yes—
50#5222C2214yes—
51#5222C2214yes—
52#5222C2214yes—
53#5222C2214yes—
54#5221C2212yes—
55#5221C2212yes—
56#5221C2212yes—
57#5221C2212yes—
58#5221C2212yes—
59#5221C2212yes—
60#5220C2214yes—
61#5220C2214yes—
62#5220C2214yes—
63#5213C2214yes—
64#5212C2214yes—
65#5212C2214yes—
66#5212C2212yes—
67#5210C2214yes—
68#4989C2212yes—
69#4987C2211yescharacteristic
70#4984C2212yes—
71#4982C2214yes—
72#4978C2212yes—
73#4972C2212yes—
74#4972C2211yescharacteristic
75#4961C2214yes—
76#4953C2214yes—
77#4950C2214yes—
78#4949C2214yes—
79#4948C2214yes—
80C4×(C2×D3)⋊C4C2212yes—
81#4935C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83C4×Dic3⋊C4C2212yes—
84#4929C2212yes—
85#4928C2212yes—
86C2×#550D311yescharacteristic, complemented
87C2×#529—31no—
88#2856—31no—
89#2691—34no—
90#2671—34no—
91#2624—32no—
92#2582—31no—
93#2548—31no—
94#2544—32no—
95#2454—32no—
96#2428—32no—
97#2427—32no—
98#2416—32no—
99#2407—32no—
100D4×C4⋊C4—31no—
101#2311—32no—
102C4×C22⋊Q8—31no—
103C2×C3×#41—28no—
104C2×C3×#41—28no—
105C2×C3×#41—44no—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×D4C2312yes—
108C22×C3×D4C2312yes—
109C22×C3×D4C2314yes—
110C22×C3×D4C2311yescharacteristic
111C22×C3×D4C2314yes—
112C22×C3×D4C2312yes—
113C23×C3×C4C2314yes—
114C23×C3×C4C2312yes—
115C22×#67C2312yes—
116C22×#67C2314yes—
117C23×Dic3C2314yes—
118C22×C4×D3C2311yescharacteristic
119C22×C4×D3C2311yescharacteristic
120C22×C4×D3C2311yescharacteristic
121C22×Dic6C2311yescharacteristic
122C3×#127—28no—
123C3×#127—24no—
124C3×#121—28no—
125C3×#121—216no—
126C3×C4×Q8—24no—
127C3×C4×D4—28no—
128C3×C4×D4D418yescomplemented
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C42C2312yes—
135C2×C3×C42C2311yescharacteristic
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2314yes—
142C2×#217C2314yes—
143C2×#217C2314yes—
144C2×#217C2314yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147#946—24no—
148#939—48no—
149#938—24no—
150#938—44no—
151#938—44no—
152#938—44no—
153#936—24no—
154#936—44no—
155D4×Dic3—44no—
156C4×#67—28no—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160#926—28no—
161C2×C4⋊Dic3—44no—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2312yes—
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2314yes—
171C2×Dic3⋊C4C2312yes—
172C2×Dic3⋊C4C2312yes—
173C2×Dic3⋊C4C2312yes—
174C2×Dic3⋊C4C2314yes—
175C2×Dic3⋊C4C2312yes—
176C2×C4×Dic3C2311yescharacteristic
177C2×C4×Dic3C2312yes—
178C2×C4×Dic3C2312yes—
179C2×C4×Dic3C2311yescharacteristic
180C2×C4×Dic3C2311yescharacteristic
181#897—24no—
182#890—24no—
183#883—28no—
184#879—28no—
185C42×D3—24no—
186C4×Dic6—24no—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C3⋊#95C2312yes—
193C3⋊#95C2312yes—
194C3⋊#95C2312yes—
195C3⋊#95C2314yes—
196C22×#41C2×D312yes—
197#550—28no—
198C2×#127C2×D311yescharacteristic
199C2×#127C2×D312yes—
200#529—68no—
201C2×#126—32no—
202C2×#125—31no—
203C2×#124—31no—
204C2×#124—32no—
205C2×#123—32no—
206C2×C22⋊Q8—31no—
207C2×C22⋊Q8—31no—
208C2×#121—31no—
209C2×#121—32no—
210C2×#121—32no—
211C2×#121—32no—
212C2×#121—34no—
213C2×#121C2×D312yes—
214C2×#121C2×D314yes—
215C2×C4×Q8—31no—
216C2×C4×Q8C2×D311yescharacteristic
217C2×C4×D4—32no—
218C2×C4×D4—32no—
219C2×C4×D4C2×D312yes—
220C2×C4×D4C2×D311yescharacteristic
221C2×#117—32no—
222C22×C4⋊C4—32no—
223C22×C42—31no—
224#399—34no—
225#398—34no—
226#397—34no—
227#396—34no—
228#394—34no—
229#394—34no—
230#394—34no—
231#394—34no—
232#394—34no—
233#392—34no—
234#391—31no—
235#391—32no—
236#391—32no—
237#390—32no—
238#390—32no—
239#390—32no—
240#390—32no—
241#390—32no—
242#390—32no—
243#389—32no—
244#389—32no—
245#389—31no—
246#389—32no—
247#387—32no—
248#386—34no—
249#386—34no—
250#386—34no—
251#386—34no—
252#385—34no—
253#385—32no—
254#385—34no—
255#384—31no—
256#380—34no—
257#380—34no—
258#380—32no—
259#380—31no—
260C4×C4⋊C4—31no—
261C4×C4⋊C4—32no—
262C4×C22⋊C4—32no—
263C24×C3C2414yes—
264C24×C3C2412yes—
265C23×D3C2411yescharacteristic
266C3×#41—432no—
267C2×C3×Q8—22no—
268C2×C3×Q8—22no—
269C2×C3×Q8#4114yes—
270C2×C3×D4—28no—
271C2×C3×D4—28no—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—28no—
276C2×C3×D4—24no—
277C2×C3×D4—22no—
278C2×C3×D4—24no—
279C2×C3×D4—24no—
280C2×C3×D4—22no—
281C2×C3×D4—24no—
282C2×C3×D4—44no—
283C2×C3×D4—42no—
284C2×C3×D4—44no—
285C2×C3×D4—42no—
286C2×C3×D4—44no—
287C2×C3×D4C2×D414yes—
288C22×C3×C4—24no—
289C22×C3×C4—24no—
290C22×C3×C4—28no—
291C22×C3×C4—28no—
292C22×C3×C4—44no—
293C22×C3×C4C2×D418yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2412yes—
297C22×C3×C4C2412yes—
298C22×C3×C4C2411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—28no—
303C2×#67—42no—
304C2×#67—44no—
305C2×#67—44no—
306C22×Dic3—44no—
307C22×Dic3—44no—
308C22×Dic3—44no—
309C22×Dic3C2411yescharacteristic
310C22×Dic3C2412yes—
311C22×Dic3C2412yes—
312C22×Dic3C2412yes—
313C22×Dic3C2414yes—
314C22×Dic3C2411yescharacteristic
315C22×Dic3C2411yescharacteristic
316C22×Dic3C2412yes—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3—22no—
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3—22no—
323C2×C4×D3—22no—
324C2×C4×D3—22no—
325C2×C4×D3—41no—
326C2×Dic6—22no—
327C2×Dic6—22no—
328C2×Dic6—22no—
329C3×C4⋊C4—24no—
330C3×C4⋊C4—22no—
331C3×C4⋊C4C2×D414yes—
332C3×C22⋊C4—28no—
333C3×C22⋊C4C2×D418yes—
334C3×C42—24no—
335C3×C42C2×D414yes—
336#217—24no—
337#217—24no—
338#217—24no—
339#217—44no—
340#217—44no—
341#217—44no—
342#217—44no—
343#217—44no—
344#217—44no—
345#217—44no—
346#217—44no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—24no—
349(C2×D3)⋊C4—24no—
350C4⋊Dic3—22no—
351C4⋊Dic3—24no—
352C4⋊Dic3—24no—
353C4⋊Dic3—22no—
354C4⋊Dic3—22no—
355C4⋊Dic3—24no—
356C4⋊Dic3—24no—
357C4⋊Dic3—44no—
358C4⋊Dic3—42no—
359Dic3⋊C4—24no—
360Dic3⋊C4—24no—
361Dic3⋊C4—24no—
362Dic3⋊C4—42no—
363Dic3⋊C4—44no—
364C4×Dic3—24no—
365C4×Dic3—22no—
366C4×Dic3—22no—
367C4×Dic3—22no—
368C4×Dic3—24no—
369C2×#41—28no—
370C2×#41—28no—
371C2×#41—44no—
372C22×Q8—31no—
373C22×Q8C22×D311yescharacteristic
374C22×D4—32no—
375C22×D4—34no—
376C22×D4C22×D312yes—
377C22×D4C22×D312yes—
378C22×D4C22×D314yes—
379C22×D4C22×D311yescharacteristic
380C22×D4C22×D314yes—
381C22×D4C22×D312yes—
382C23×C4—34no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4C22×D314yes—
387C23×C4C22×D312yes—
388#127—28no—
389#127—24no—
390#126—68no—
391#125—64no—
392#124—64no—
393#124—124no—
394#123—68no—
395C22⋊Q8—64no—
396C22⋊Q8—64no—
397#121—28no—
398#121—216no—
399#121—64no—
400#121—128no—
401#121—124no—
402#121—124no—
403#121—124no—
404C4×Q8—24no—
405C4×Q8—64no—
406C4×D4—28no—
407C4×D4—68no—
408C4×D4—124no—
409C4×D4#6718yescomplemented
410#117—68no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—32no—
413C2×C4⋊C4—32no—
414C2×C4⋊C4—32no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—32no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—32no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—34no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—34no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—124no—
426C2×C4⋊C4C22×D311yescharacteristic
427C2×C4⋊C4C22×D312yes—
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—32no—
430C2×C22⋊C4—32no—
431C2×C22⋊C4—32no—
432C2×C22⋊C4—32no—
433C2×C22⋊C4—32no—
434C2×C22⋊C4—32no—
435C2×C22⋊C4—34no—
436C2×C22⋊C4—34no—
437C2×C22⋊C4—34no—
438C2×C22⋊C4—34no—
439C2×C22⋊C4—34no—
440C2×C22⋊C4—34no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D312yes—
445C2×C42—31no—
446C2×C42—32no—
447C2×C42—32no—
448C2×C42—31no—
449C2×C42—31no—
450C2×C42—64no—
451C2×C42C22×D312yes—
452C2×C42C22×D311yescharacteristic
453#95—32no—
454#95—32no—
455#95—32no—
456#95—32no—
457#95—32no—
458#95—34no—
459#95—34no—
460#95—34no—
461#95—34no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—24no—
469C23×C3—24no—
470C23×C3—24no—
471C23×C3—24no—
472C23×C3—24no—
473C23×C3—24no—
474C23×C3—24no—
475C23×C3C22×D414yes—
476C23×C3C2511yescharacteristic
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3H(5,𝔽2)12yes—
484C3×Q8—28no—
485C3×D4—28no—
486C3×D4—416no—
487C3×D4—48no—
488C3×D4—48no—
489C3×D4—84no—
490C3×D4—88no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—21no—
497C2×C3×C4—216no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—416no—
502C2×C3×C4C22×D412yes—
503C2×C3×C4C22×D414yes—
504C2×C3×C4C22×D412yes—
505C2×C3×C4C22×D412yes—
506C2×C3×C4C2×#4114yes—
507C2×C3×C4C2×#4112yes—
508C2×C3×C4H(5,𝔽2)12yes—
509C2×C3×C4H(5,𝔽2)12yes—
510C2×C3×C42−1+412yes—
511#67—48no—
512#67—88no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—21no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—24no—
524C2×Dic3—22no—
525C2×Dic3—24no—
526C2×Dic3—24no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—22no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—88no—
538C4×D3—44no—
539C4×D3—44no—
540C4×D3—44no—
541Dic6—44no—
542C24—31no—
543C24C23×D314yes—
544C24C23×D312yes—
545#41—432no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—62no—
549C2×Q8—62no—
550C2×Q8—62no—
551C2×Q8#23714yes—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—44no—
565C2×D4—42no—
566C2×D4—44no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—64no—
570C2×D4—64no—
571C2×D4—68no—
572C2×D4—122no—
573C2×D4—124no—
574C2×D4—124no—
575C2×D4C2×#6714yes—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—31no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—34no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—32no—
588C22×C4—44no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—121no—
598C22×C4—124no—
599C22×C4—124no—
600C22×C4—124no—
601C22×C4C2×#6718yes—
602C22×C4C23×D312yes—
603C22×C4C23×D312yes—
604C22×C4C23×D311yescharacteristic
605C22×C4C23×D312yes—
606C22×C4C23×D311yescharacteristic
607C22×C4C23×D311yescharacteristic
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—64no—
611C4⋊C4—62no—
612C4⋊C4—62no—
613C4⋊C4—64no—
614C4⋊C4—64no—
615C4⋊C4—64no—
616C4⋊C4—64no—
617C4⋊C4—64no—
618C4⋊C4—62no—
619C4⋊C4—64no—
620C4⋊C4—124no—
621C4⋊C4—124no—
622C4⋊C4—122no—
623C4⋊C4—122no—
624C4⋊C4C2×#6714yes—
625C22⋊C4—28no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—64no—
632C22⋊C4—124no—
633C22⋊C4—124no—
634C22⋊C4—124no—
635C22⋊C4—124no—
636C22⋊C4—124no—
637C22⋊C4—124no—
638C22⋊C4—124no—
639C22⋊C4—124no—
640C22⋊C4C2×#6718yes—
641C42—24no—
642C42—64no—
643C42—62no—
644C42—62no—
645C42—62no—
646C42—64no—
647C42C2×#6714yes—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—44no—
656C22×C3—44no—
657C22×C3—44no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3C23×D411yescharacteristic
663C22×C3C22×#4111yescharacteristic
664C22×C3C2×H(5,𝔽2)11yescharacteristic
665C22×C3C2×H(5,𝔽2)11yescharacteristic
666C22×C3C2×H(5,𝔽2)11yescharacteristic
667C22×C3C2×2−1+411yescharacteristic
668C22×C3#58511yescharacteristic
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C3×C4—24no—
677C3×C4—24no—
678C3×C4—22no—
679C3×C4—42no—
680C3×C4#53714yes—
681C3×C4#54614yes—
682Dic3—42no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—42no—
687Dic3—42no—
688Dic3—42no—
689Dic3—44no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—32no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—61no—
709C23—61no—
710C23C22×#6714yes—
711C23C24×D311yescharacteristic
712Q8—28no—
713Q8—124no—
714D4—28no—
715D4—416no—
716D4—48no—
717D4—48no—
718D4—84no—
719D4—88no—
720D4—128no—
721D4—248no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—216no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—416no—
733C2×C4—62no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—61no—
741C2×C4—62no—
742C2×C4—64no—
743C2×C4—61no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—61no—
747C2×C4—62no—
748C2×C4—64no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—124no—
758C2×C4—124no—
759C2×C4—124no—
760C2×C4—248no—
761C2×C4C2×#23714yes—
762C2×C4C2×#23712yes—
763C2×C4#100412yes—
764C2×C4#100912yes—
765C2×C4#101012yes—
766C2×C4C22×#6712yes—
767C2×C4C22×#6714yes—
768C2×C4C22×#6712yes—
769C2×C4C22×#6712yes—
770C2×C3—44no—
771C2×C3—84no—
772C2×C3C2×#53711yescharacteristic
773C2×C3C2×#54611yescharacteristic
774C2×C3#348811yescharacteristic
775C2×C3#351711yescharacteristic
776C2×C3#352211yescharacteristic
777C2×C3#354311yescharacteristic
778C2×C3#355411yescharacteristic
779D3—42no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—62no—
795C22—62no—
796C22—62no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22C22×#23711yescharacteristic
802C22C2×#100411yescharacteristic
803C22C2×#100911yescharacteristic
804C22C2×#101011yescharacteristic
805C22D3×H(5,𝔽2)11yescharacteristic
806C22#596611yescharacteristic
807C22C23×#6711yescharacteristic
808C4—24no—
809C4—24no—
810C4—22no—
811C4—42no—
812C4—122no—
813C4—124no—
814C4—121no—
815C4—121no—
816C4—122no—
817C4—122no—
818C4—121no—
819C4—122no—
820C4#580614yes—
821C4#583314yes—
822C3#3890911yescharacteristic, complemented, Sylow
823C2—44no—
824C2—84no—
825C2—122no—
826C2#8677311yescharacteristic
827C2#8677611yescharacteristic
828C2#8678711yescharacteristic
829C2#8678911yescharacteristic
830C2C2×#580611yescharacteristic
831C2C2×#583311yescharacteristic
832C2#8728511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#550C2
hypercenterC2×#550D3
hypocenterC3#38909
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×C3×#550C2semidirect
2. C2×#5557C2semidirect
3. #84097C2semidirect
4. #84087C2semidirect
5. #83192C2semidirect
6. #83186C2semidirect
7. #83179C2semidirect
8. #83178C2semidirect
9. #82716C2semidirect
10. #82705C2semidirect
11. #82690C2semidirect
12. #82678C2semidirect
13. C4×#946C2semidirect
14. #82482C2semidirect
15. #82408C2semidirect
16. #82363C2semidirect
17. D4×C4⋊Dic3C2semidirect
86. C2×#550D3semidirect
128. C3×C4×D4D4semidirect
409. C4×D4#67semidirect
822. C3#38909semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5502
C2×#55572
#840972
#840872
#831922
#831862
#831792
#831782
#827162
#827052
#826902
#826782
C4×#9462
#824822
#824082
#823632
D4×C4⋊Dic32
#389093