Finite Group Databasebeta

← #11633930

Subgroups — #11633930

Order 768.

2534 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#533C211yesmaximal, characteristic, complemented
2C2×#5726C211yesmaximal, characteristic, complemented
3#83259C211yesmaximal, characteristic, complemented
4#83240C211yesmaximal, characteristic, complemented
5#83229C211yesmaximal, characteristic, complemented
6#83046C214yesmaximal, complemented
7#82812C212yesmaximal, complemented
8#82779C212yesmaximal, complemented
9#82778C212yesmaximal, complemented
10#82752C212yesmaximal, complemented
11#82495C212yesmaximal, complemented
12#82494C212yesmaximal, complemented
13#82490C212yesmaximal, complemented
14#82457C212yesmaximal, complemented
15#82279C214yesmaximal, complemented
16C4×#930C211yesmaximal, characteristic, complemented
17C4×#930C211yesmaximal, characteristic, complemented
18#59040—31nomaximal, Sylow
19C22×#239C2212yes—
20C3×#533—28no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×#125C2212yes—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×C22⋊Q8C2212yes—
26C2×C3×C4×Q8C2212yes—
27C2×C3×C4×Q8C2212yes—
28C2×C3×#117C2212yes—
29C22×C3×C42C2211yescharacteristic
30C2×#947C2212yes—
31C2×#946C2212yes—
32C2×#946C2212yes—
33C2×#946C2212yes—
34C2×Q8×Dic3C2212yes—
35C2×#930C2211yescharacteristic
36C2×#930C2211yescharacteristic
37C2×C4×#67C2212yes—
38C2×C4×#67C2212yes—
39#5726—28no—
40C2×#895C2212yes—
41C2×#894C2214yes—
42C2×D3×C4⋊C4C2212yes—
43C2×C4×D12C2211yescharacteristic
44C2×C4×D12C2211yescharacteristic
45#5229C2212yes—
46#5229C2212yes—
47#5213C2212yes—
48#5213C2212yes—
49#5212C2211yescharacteristic
50#5212C2211yescharacteristic
51#4994C2214yes—
52#4993C2214yes—
53#4993C2214yes—
54#4992C2214yes—
55#4991C2214yes—
56#4989C2214yes—
57#4988C2212yes—
58#4988C2214yes—
59#4987C2212yes—
60#4987C2214yes—
61#4987C2212yes—
62#4984C2212yes—
63#4983C2214yes—
64#4980C2214yes—
65#4976C2214yes—
66#4975C2212yes—
67Dic3×C4⋊C4C2212yes—
68#4960C2214yes—
69#4957C2214yes—
70#4956C2214yes—
71#4948C2214yes—
72#4940C2214yes—
73#4940C2212yes—
74#4940C2212yes—
75#4939C2211yescharacteristic
76#4939C2214yes—
77#4939C2211yescharacteristic
78C4×(C2×D3)⋊C4C2214yes—
79C4×(C2×D3)⋊C4C2212yes—
80C4×(C2×D3)⋊C4C2212yes—
81C4×C4⋊Dic3C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83#4933C2214yes—
84#4928C2211yescharacteristic
85#4928C2211yescharacteristic
86C2×#547—31no—
87C2×#533D311yescharacteristic, complemented
88#2694—34no—
89#2547—31no—
90#2542—31no—
91#2540—32no—
92#2538—32no—
93#2471—34no—
94#2426—32no—
95#2423—32no—
96#2417—32no—
97#2407—32no—
98#2365—31no—
99#2360—32no—
100#2341—32no—
101C4×#121—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×Q8C2312yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C22×#67C2312yes—
110C2×#239—28no—
111C2×#239—28no—
112C2×#239—44no—
113C22×D12C2311yescharacteristic
114C22×D12C2314yes—
115C22×D12C2311yescharacteristic
116C22×C4×D3C2312yes—
117C22×C4×D3C2312yes—
118C22×C4×D3C2314yes—
119C3×C4⋊Q8—24no—
120C3×C4⋊Q8D418yescomplemented
121C3×#125—28no—
122C3×C22⋊Q8—28no—
123C3×C22⋊Q8—28no—
124C3×C4×Q8—28no—
125C3×C4×Q8—28no—
126C3×#117—28no—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C4⋊C4C2314yes—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C42—24no—
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2314yes—
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C2×#217C2312yes—
141C2×#217C2312yes—
142#947—44no—
143#946—28no—
144#946—28no—
145#946—44no—
146Q8×Dic3—44no—
147#930—24no—
148#930—24no—
149C4×#67—44no—
150C4×#67—44no—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2312yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2312yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2314yes—
170C2×C4⋊Dic3C2311yescharacteristic
171C2×Dic3⋊C4C2314yes—
172C2×Dic3⋊C4C2314yes—
173C2×Dic3⋊C4C2312yes—
174C2×Dic3⋊C4C2312yes—
175C2×Dic3⋊C4C2314yes—
176C2×C4×Dic3C2312yes—
177C2×C4×Dic3C2312yes—
178C2×C4×Dic3C2314yes—
179#895—28no—
180#894—216no—
181D3×C4⋊C4—28no—
182C4×D12—24no—
183C4×D12—24no—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C22×#41—32no—
195#547—68no—
196#533—28no—
197C2×C4⋊Q8C2×D311yescharacteristic
198C2×C4⋊Q8C2×D311yescharacteristic
199C2×#125C2×D312yes—
200C2×#124—32no—
201C2×#123—34no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8C2×D312yes—
206C2×C22⋊Q8C2×D312yes—
207C2×#121—31no—
208C2×#121—31no—
209C2×#121—32no—
210C2×C4×Q8—32no—
211C2×C4×Q8C2×D312yes—
212C2×C4×Q8C2×D312yes—
213C2×C4×D4—32no—
214C2×C4×D4—32no—
215C2×C4×D4—31no—
216C2×C4×D4—31no—
217C2×#117C2×D312yes—
218C22×C4⋊C4—32no—
219C22×C42C2×D311yescharacteristic
220#399—34no—
221#399—34no—
222#398—34no—
223#397—34no—
224#396—34no—
225#396—34no—
226#394—34no—
227#392—34no—
228#391—32no—
229#391—32no—
230#390—32no—
231#390—34no—
232#390—34no—
233#390—31no—
234#390—34no—
235#390—31no—
236#389—34no—
237#389—32no—
238#389—31no—
239#389—31no—
240#388—34no—
241#388—32no—
242#388—32no—
243#387—34no—
244#387—34no—
245#386—32no—
246#386—32no—
247#386—34no—
248#385—34no—
249#384—32no—
250#380—31no—
251#380—31no—
252#380—34no—
253#380—32no—
254#380—32no—
255C4×C4⋊C4—32no—
256C4×C4⋊C4—31no—
257C4×C4⋊C4—31no—
258C4×C22⋊C4—34no—
259C4×C22⋊C4—32no—
260C4×C22⋊C4—32no—
261C24×C3C2411yescharacteristic
262C23×D3C2412yes—
263C23×D3C2412yes—
264C2×C3×Q8—24no—
265C2×C3×Q8—24no—
266C2×C3×Q8—24no—
267C2×C3×Q8—24no—
268C2×C3×Q8—24no—
269C2×C3×Q8C2×D418yes—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2414yes—
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2414yes—
284C22×C3×C4C2411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2411yescharacteristic
287C2×#67—24no—
288C2×#67—24no—
289C2×#67—24no—
290C2×#67—24no—
291C2×#67—42no—
292C2×#67—42no—
293C22×Dic3C2412yes—
294C22×Dic3C2412yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299#239—432no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12—28no—
303C2×D12—22no—
304C2×D12—28no—
305C2×D12—22no—
306C2×D12—22no—
307C2×D12—44no—
308C2×D12#4114yes—
309C2×C4×D3—28no—
310C2×C4×D3—24no—
311C2×C4×D3—24no—
312C2×C4×D3—28no—
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—24no—
317C2×C4×D3—44no—
318C3×C4⋊C4—24no—
319C3×C4⋊C4—28no—
320C3×C4⋊C4—28no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4C2×D418yes—
323C3×C4⋊C4C2×D418yes—
324C3×C22⋊C4—28no—
325C3×C42—22no—
326C3×C42—22no—
327C3×C42—22no—
328C3×C42—28no—
329C3×C42C2×D414yes—
330#217—42no—
331#217—42no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345C4⋊Dic3—22no—
346C4⋊Dic3—22no—
347C4⋊Dic3—22no—
348C4⋊Dic3—22no—
349C4⋊Dic3—22no—
350C4⋊Dic3—44no—
351C4⋊Dic3#4114yescomplemented
352Dic3⋊C4—28no—
353Dic3⋊C4—28no—
354Dic3⋊C4—42no—
355Dic3⋊C4—42no—
356Dic3⋊C4—44no—
357C4×Dic3—24no—
358C4×Dic3—24no—
359C4×Dic3—44no—
360C2×#41—68no—
361C2×#41—68no—
362C2×#41—124no—
363C22×Q8C22×D312yes—
364C22×Q8C22×D312yes—
365C22×D4—32no—
366C22×D4—32no—
367C22×D4—31no—
368C22×D4—31no—
369C22×D4—34no—
370C23×C4—32no—
371C23×C4—32no—
372C23×C4—34no—
373C23×C4C22×D311yescharacteristic
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C4⋊Q8—24no—
377C4⋊Q8#6718yescomplemented
378#125—28no—
379#124—124no—
380#123—616no—
381C22⋊Q8—28no—
382C22⋊Q8—28no—
383C22⋊Q8—68no—
384C22⋊Q8—68no—
385C22⋊Q8—124no—
386#121—64no—
387#121—64no—
388#121—68no—
389C4×Q8—28no—
390C4×Q8—28no—
391C4×Q8—124no—
392C4×D4—64no—
393C4×D4—64no—
394C4×D4—124no—
395C4×D4—124no—
396#117—28no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—68no—
410C2×C4⋊C4C22×D312yes—
411C2×C4⋊C4C22×D314yes—
412C2×C4⋊C4C22×D314yes—
413C2×C4⋊C4C22×D312yes—
414C2×C4⋊C4C22×D312yes—
415C2×C4⋊C4C22×D312yes—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—32no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4C22×D314yes—
432C2×C42—24no—
433C2×C42—32no—
434C2×C42—32no—
435C2×C42—34no—
436C2×C42C22×D314yes—
437C2×C42C22×D311yescharacteristic
438C2×C42C22×D311yescharacteristic
439C2×C42C22×D311yescharacteristic
440C2×C42C22×D311yescharacteristic
441#95—32no—
442#95—32no—
443#95—34no—
444#95—32no—
445#95—32no—
446#95—34no—
447#95—32no—
448#95—32no—
449#95—34no—
450#95—34no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C32−1+412yes—
458C23×C3C2511yescharacteristic
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3C2×#4114yes—
473C3×Q8—216no—
474C3×Q8—48no—
475C2×C3×C4—28no—
476C2×C3×C4—21no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—24no—
491C2×C3×C4—44no—
492C2×C3×C4—44no—
493C2×C3×C4C22×D418yes—
494C2×C3×C4C22×D412yes—
495C2×C3×C4C22×D412yes—
496C2×C3×C4C22×D412yes—
497C2×C3×C4C2×#4112yes—
498C2×C3×C4C2×#4112yes—
499C2×C3×C4H(5,𝔽2)12yes—
500C2×C3×C4H(5,𝔽2)12yes—
501C2×C3×C42−1+412yes—
502#67—48no—
503#67—48no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3C2×#4114yes—
522D12—28no—
523D12—416no—
524D12—44no—
525C4×D3—416no—
526C4×D3—48no—
527C4×D3—48no—
528C24—32no—
529C24—32no—
530C24C23×D311yescharacteristic
531#41—1232no—
532C2×Q8—24no—
533C2×Q8—24no—
534C2×Q8—24no—
535C2×Q8—24no—
536C2×Q8—24no—
537C2×Q8C2×#6718yes—
538C2×D4—34no—
539C2×D4—68no—
540C2×D4—64no—
541C2×D4—64no—
542C2×D4—64no—
543C2×D4—64no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—62no—
548C2×D4—62no—
549C2×D4—68no—
550C2×D4—124no—
551C2×D4—122no—
552C2×D4—122no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—32no—
563C22×C4—32no—
564C22×C4—32no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—32no—
568C22×C4—68no—
569C22×C4—64no—
570C22×C4—64no—
571C22×C4—64no—
572C22×C4—64no—
573C22×C4—64no—
574C22×C4—68no—
575C22×C4—64no—
576C22×C4—124no—
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C22×C4C23×D314yes—
580C22×C4C23×D311yescharacteristic
581C22×C4C23×D311yescharacteristic
582C22×C4C23×D314yes—
583C22×C4C23×D311yescharacteristic
584C22×C4C23×D311yescharacteristic
585C4⋊C4—24no—
586C4⋊C4—28no—
587C4⋊C4—28no—
588C4⋊C4—24no—
589C4⋊C4—34no—
590C4⋊C4—68no—
591C4⋊C4—62no—
592C4⋊C4—62no—
593C4⋊C4—62no—
594C4⋊C4—62no—
595C4⋊C4—68no—
596C4⋊C4—62no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4—124no—
600C4⋊C4—124no—
601C4⋊C4C2×#6718yes—
602C4⋊C4C2×#6718yes—
603C22⋊C4—28no—
604C22⋊C4—64no—
605C22⋊C4—68no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—68no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C22⋊C4—124no—
615C22⋊C4—124no—
616C22⋊C4—124no—
617C22⋊C4—122no—
618C22⋊C4—122no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—28no—
623C42—64no—
624C42—64no—
625C42—124no—
626C42C2×#6714yes—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3C23×D411yescharacteristic
635C22×C3C22×#4111yescharacteristic
636C22×C3C22×#4111yescharacteristic
637C22×C3C2×H(5,𝔽2)11yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×2−1+411yescharacteristic
640C22×C3C2×2−1+411yescharacteristic
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—24no—
644C2×D3—42no—
645C2×D3—42no—
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—42no—
655C3×C4—28no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—44no—
661C3×C4#54614yes—
662C3×C4#55014yes—
663Dic3—24no—
664Dic3—42no—
665Dic3—42no—
666Dic3—42no—
667Dic3—42no—
668Dic3—42no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—34no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23—62no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23#100712yes—
690C23C24×D311yescharacteristic
691Q8—216no—
692Q8—48no—
693D4—68no—
694D4—1216no—
695D4—128no—
696D4—128no—
697D4—124no—
698C2×C4—28no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—24no—
714C2×C4—34no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—1216no—
735C2×C4—128no—
736C2×C4—128no—
737C2×C4#100712yes—
738C2×C4D3×#4112yes—
739C2×C4D3×#4112yes—
740C2×C4#100912yes—
741C2×C4#100912yes—
742C2×C4C22×#6712yes—
743C2×C4C22×#6718yes—
744C2×C4C22×#6712yes—
745C2×C4C22×#6712yes—
746C2×C3—42no—
747C2×C3C2×#54611yescharacteristic
748C2×C3C2×#55011yescharacteristic
749C2×C3#348211yescharacteristic
750C2×C3#348611yescharacteristic
751C2×C3#352011yescharacteristic
752C2×C3#352011yescharacteristic
753C2×C3#354811yescharacteristic
754D3—44no—
755D3—82no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—64no—
764C22—64no—
765C22—64no—
766C22—122no—
767C22—122no—
768C22—122no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22C2×#100711yescharacteristic
778C22C2×#100711yescharacteristic
779C22C2×D3×#4111yescharacteristic
780C22C2×D3×#4111yescharacteristic
781C22C2×#100911yescharacteristic
782C22C2×#100911yescharacteristic
783C22C23×#6711yescharacteristic
784C4—22no—
785C4—22no—
786C4—28no—
787C4—41no—
788C4—41no—
789C4—44no—
790C4—64no—
791C4—122no—
792C4—122no—
793C4—122no—
794C4—122no—
795C4—122no—
796C4#582914yes—
797C4#583414yes—
798C3#5904011yescharacteristic, complemented, Sylow
799C2—42no—
800C2—124no—
801C2—242no—
802C2#8627811yescharacteristic
803C2#8628511yescharacteristic
804C2#8628511yescharacteristic
805C2#8628811yescharacteristic
806C2#8725111yescharacteristic
807C2C2×#582911yescharacteristic
808C2C2×#583411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#533C2
hypercenterC2×#533D3
hypocenterC3#59040
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C3×#533C2semidirect
2. C2×#5726C2semidirect
3. #83259C2semidirect
4. #83240C2semidirect
5. #83229C2semidirect
6. #83046C2semidirect
7. #82812C2semidirect
8. #82779C2semidirect
9. #82778C2semidirect
10. #82752C2semidirect
11. #82495C2semidirect
12. #82494C2semidirect
13. #82490C2semidirect
14. #82457C2semidirect
15. #82279C2semidirect
16. C4×#930C2semidirect
17. C4×#930C2semidirect
87. C2×#533D3semidirect
120. C3×C4⋊Q8D4semidirect
351. C4⋊Dic3#41semidirect
377. C4⋊Q8#67semidirect
798. C3#59040semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5332
C2×#57262
#832592
#832402
#832292
#830462
#828122
#827792
#827782
#827522
#824952
#824942
#824902
#824572
#822792
C4×#9302
#590403