Finite Group Databasebeta

← #11069361

Subgroups — #11069361

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5689C212yesmaximal, complemented
2C3×#2726C211yesmaximal, characteristic, complemented
3#83038C212yesmaximal, complemented
4#77986C212yesmaximal
5#77820C212yesmaximal, complemented
6#77790C212yesmaximal, complemented
7#77786C212yesmaximal, complemented
8#77745C212yesmaximal, complemented
9#77744C212yesmaximal, complemented
10#76261C211yesmaximal, characteristic
11#76261C211yesmaximal, characteristic
12#76221C212yesmaximal, complemented
13#76190C211yesmaximal, characteristic, complemented
14#76128C211yesmaximal, characteristic, complemented
15#76001C212yesmaximal, complemented
16#75967C211yesmaximal, characteristic, complemented
17#75961C211yesmaximal, characteristic
18#75305C212yesmaximal
19#75179C212yesmaximal, complemented
20#39365—31nomaximal, Sylow
21C2×C3×#125C2212yes—
22#5689—216no—
23C2×#897C2212yes—
24C2×#897C2212yes—
25C2×#897C2212yes—
26C2×#896C2212yes—
27C2×#896C2212yes—
28C2×#896C2212yes—
29C2×#893C2211yescharacteristic
30C2×#892C2212yes—
31C2×D3×C4⋊C4C2212yes—
32C2×#890C2212yes—
33C2×#889C2212yes—
34C2×#889C2212yes—
35C2×#888C2212yes—
36C2×#888C2212yes—
37C2×#888C2211yescharacteristic
38C2×#887C2212yes—
39C2×#872C2212yes—
40C2×#869C2212yes—
41C3×#398C2212yes—
42C3×#398C2212yes—
43C3×#398C2212yes—
44C3×#389C2211yescharacteristic
45C3×#389C2211yescharacteristic
46C3×#389C2212yes—
47C3×#389C2211yescharacteristic
48C3×#387C2212yes—
49#4994C2212yes—
50#4994C2212yes—
51#4994C2212yes—
52#4994C2212yes—
53#4994C2212yes—
54#4993C2212yes—
55#4993C2212yes—
56#4990C2212yes—
57#4990C2212yes—
58#4989C2212yes—
59#4988C2211yescharacteristic
60#4984C2211yescharacteristic
61#4984C2211yescharacteristic
62#4984C2212yes—
63#4982C2212yes—
64#4982C2212yes—
65#4980C2212yes—
66#4979C2212yes—
67#4976C2212yes—
68#4976C2212yes—
69#4976C2212yes—
70#4976C2212yes—
71#4975C2211yescharacteristic
72#4975C2211yescharacteristic
73#4975C2211yescharacteristic
74Dic3×C4⋊C4C2211yescharacteristic
75Dic3×C4⋊C4C2211yescharacteristic
76Dic3×C4⋊C4C2211yescharacteristic
77#4973C2212yes—
78#4972C2211yescharacteristic
79#4939C2211yescharacteristic
80C4×(C2×D3)⋊C4C2212yes—
81#4933C2212yes—
82C42×Dic3C2211yescharacteristic
83#4928C2211yescharacteristic
84#4928C2211yescharacteristic
85#4676C2212yes—
86#4670C2212yes—
87#4670C2212yes—
88#4668C2212yes—
89#4667C2212yes—
90#4667C2212yes—
91#4666C2212yes—
92#4666C2212yes—
93#4665C2212yes—
94#4665C2212yes—
95#4661C2212yes—
96#4661C2212yes—
97#4657C2212yes—
98#4656C2212yes—
99#4656C2212yes—
100#4656C2212yes—
101#4655C2212yes—
102#4650C2212yes—
103#4649C2212yes—
104#4647C2212yes—
105#4647C2212yes—
106#4647C2212yes—
107#4646C2212yes—
108#4646C2212yes—
109C2×#544—32no—
110#2859—31no—
111#2734—32no—
112#2732—32no—
113#2726—31no—
114#2726D311yescharacteristic, complemented
115#2683—31no—
116#2683—31no—
117#2629—32no—
118#2556—32no—
119#2556—32no—
120#2550—32no—
121#2441—32no—
122#2440—32no—
123#2429—32no—
124#2429—32no—
125#2352—32no—
126C4×C4⋊Q8—31no—
127#2293—31no—
128C22×D12C2311yescharacteristic
129C22×C4×D3C2312yes—
130C22×C4×D3C2312yes—
131C22×C4×D3C2312yes—
132C22×Dic6C2312yes—
133C22×Dic6C2312yes—
134C22×Dic6C2312yes—
135C3×#125—28no—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C4⋊C4C2312yes—
139C2×C3×C4⋊C4C2312yes—
140C2×C3×C4⋊C4C2312yes—
141C2×C3×C4⋊C4C2312yes—
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2312yes—
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C42C2312yes—
150C2×C3×C42C2311yescharacteristic
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2312yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2312yes—
156C2×(C2×D3)⋊C4C2312yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2312yes—
161C2×(C2×D3)⋊C4C2312yes—
162C2×C4⋊Dic3C2312yes—
163C2×C4⋊Dic3C2312yes—
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2312yes—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173C2×Dic3⋊C4C2312yes—
174C2×Dic3⋊C4C2312yes—
175C2×Dic3⋊C4C2312yes—
176C2×Dic3⋊C4C2312yes—
177C2×Dic3⋊C4C2312yes—
178C2×Dic3⋊C4C2312yes—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2312yes—
181C2×Dic3⋊C4C2312yes—
182C2×Dic3⋊C4C2312yes—
183C2×Dic3⋊C4C2312yes—
184C2×Dic3⋊C4C2312yes—
185C2×Dic3⋊C4C2312yes—
186C2×Dic3⋊C4C2312yes—
187C2×C4×Dic3C2312yes—
188C2×C4×Dic3C2312yes—
189C2×C4×Dic3C2311yescharacteristic
190C2×C4×Dic3C2311yescharacteristic
191C2×C4×Dic3C2311yescharacteristic
192C2×C4×Dic3C2311yescharacteristic
193C2×C4×Dic3C2312yes—
194C2×C4×Dic3C2312yes—
195C2×C4×Dic3C2311yescharacteristic
196C2×C4×Dic3C2311yescharacteristic
197#897—28no—
198#897—28no—
199#897—44no—
200#896—28no—
201#896—28no—
202#896—44no—
203#893Q818yescomplemented
204#892—28no—
205D3×C4⋊C4—28no—
206#890—28no—
207#889—28no—
208#889—28no—
209#888—28no—
210#888—28no—
211#888D418yescomplemented
212#887—44no—
213#872—28no—
214#869—28no—
215C3×#95C2312yes—
216C3×#95C2312yes—
217C3×#95C2312yes—
218C3×#95C2312yes—
219C3×#95C2312yes—
220C3×#95C2312yes—
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C3⋊#95C2312yes—
224C3⋊#95C2312yes—
225C3⋊#95C2312yes—
226C3⋊#95C2312yes—
227C3⋊#95C2312yes—
228C3⋊#95C2312yes—
229C3⋊#95C2312yes—
230C3⋊#95C2312yes—
231C3⋊#95C2312yes—
232C3⋊#95C2312yes—
233C3⋊#95C2312yes—
234#544—616no—
235C2×C4⋊Q8—31no—
236C2×C4⋊Q8—32no—
237C2×C4⋊Q8—32no—
238C2×C4⋊Q8—32no—
239C2×#125—32no—
240C2×#125—32no—
241C2×#125—32no—
242C2×#125C2×D312yes—
243C2×C22⋊Q8—32no—
244C2×C22⋊Q8—32no—
245C2×C22⋊Q8—32no—
246C2×C22⋊Q8—32no—
247C2×C22⋊Q8—32no—
248C2×C22⋊Q8—32no—
249C2×C4×Q8—32no—
250C2×C4×D4—31no—
251C2×#117—32no—
252C2×#117—32no—
253C22×C4⋊C4—32no—
254#399—32no—
255#399—32no—
256#398—32no—
257#398—32no—
258#398—32no—
259#398—32no—
260#398—32no—
261#398C2×D312yes—
262#398C2×D312yes—
263#398C2×D312yes—
264#396—32no—
265#396—32no—
266#396—32no—
267#396—32no—
268#396—32no—
269#396—32no—
270#395—32no—
271#395—32no—
272#395—32no—
273#395—32no—
274#391—32no—
275#391—32no—
276#391—32no—
277#390—31no—
278#390—31no—
279#389—32no—
280#389—31no—
281#389—32no—
282#389—31no—
283#389—32no—
284#389—32no—
285#389—32no—
286#389—31no—
287#389—31no—
288#389—31no—
289#389—32no—
290#389—32no—
291#389—32no—
292#389C2×D311yescharacteristic
293#389C2×D311yescharacteristic
294#389C2×D312yes—
295#389C2×D311yescharacteristic
296#388—32no—
297#388—32no—
298#388—32no—
299#388—32no—
300#387—32no—
301#387—32no—
302#387—32no—
303#387C2×D312yes—
304#386—32no—
305#386—32no—
306#385—32no—
307#385—32no—
308#384—31no—
309#384—31no—
310#384—31no—
311#382—32no—
312#380—32no—
313#380—32no—
314C4×C4⋊C4—31no—
315C4×C4⋊C4—31no—
316C4×C4⋊C4—31no—
317C4×C4⋊C4—32no—
318C4×C22⋊C4—32no—
319C4×C22⋊C4—32no—
320C4×C22⋊C4—32no—
321C43—31no—
322C23×D3C2412yes—
323C22×C3×C4C2412yes—
324C22×C3×C4C2412yes—
325C22×C3×C4C2412yes—
326C22×C3×C4C2412yes—
327C22×C3×C4C2412yes—
328C22×C3×C4C2411yescharacteristic
329C22×C3×C4C2411yescharacteristic
330C22×C3×C4C2412yes—
331C22×C3×C4C2411yescharacteristic
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C22×Dic3C2412yes—
337C22×Dic3C2411yescharacteristic
338C22×Dic3C2411yescharacteristic
339C22×Dic3C2411yescharacteristic
340C22×Dic3C2411yescharacteristic
341C2×D12—41no—
342C2×D12—41no—
343C2×D12C2×Q814yes—
344C2×C4×D3—24no—
345C2×C4×D3—24no—
346C2×C4×D3—24no—
347C2×C4×D3—24no—
348C2×C4×D3—42no—
349C2×C4×D3—42no—
350C2×C4×D3—42no—
351C2×C4×D3—42no—
352C2×C4×D3C2×Q818yes—
353C2×Dic6—24no—
354C2×Dic6—24no—
355C2×Dic6—42no—
356C2×Dic6—42no—
357C2×Dic6—42no—
358C2×Dic6—42no—
359C2×Dic6—42no—
360C2×Dic6—42no—
361C2×Dic6C2×D418yes—
362C3×C4⋊C4—24no—
363C3×C4⋊C4—24no—
364C3×C4⋊C4—24no—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—24no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—41no—
370C3×C4⋊C4—41no—
371C3×C4⋊C4—41no—
372C3×C4⋊C4—42no—
373C3×C4⋊C4C2×D414yes—
374C3×C4⋊C4C2×Q814yes—
375C3×C42—24no—
376C3×C42—41no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—24no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4—42no—
384(C2×D3)⋊C4—42no—
385(C2×D3)⋊C4—42no—
386(C2×D3)⋊C4—42no—
387(C2×D3)⋊C4C2×Q818yes—
388C4⋊Dic3—22no—
389C4⋊Dic3—24no—
390C4⋊Dic3—24no—
391C4⋊Dic3—24no—
392C4⋊Dic3—24no—
393C4⋊Dic3—24no—
394C4⋊Dic3—42no—
395C4⋊Dic3—41no—
396C4⋊Dic3—41no—
397C4⋊Dic3—41no—
398C4⋊Dic3C2×D414yes—
399Dic3⋊C4—24no—
400Dic3⋊C4—24no—
401Dic3⋊C4—24no—
402Dic3⋊C4—24no—
403Dic3⋊C4—24no—
404Dic3⋊C4—24no—
405Dic3⋊C4—24no—
406Dic3⋊C4—24no—
407Dic3⋊C4—24no—
408Dic3⋊C4—42no—
409Dic3⋊C4—42no—
410Dic3⋊C4—42no—
411Dic3⋊C4—42no—
412Dic3⋊C4C2×D418yes—
413C4×Dic3—22no—
414C4×Dic3—24no—
415C4×Dic3—24no—
416C4×Dic3—22no—
417C4×Dic3—22no—
418C4×Dic3—42no—
419C4×Dic3—42no—
420C4×Dic3—41no—
421C4×Dic3C2×D414yes—
422C4×Dic3C2×Q814yes—
423C22×Q8—32no—
424C22×Q8—32no—
425C22×Q8—32no—
426C22×D4—31no—
427C23×C4—32no—
428C23×C4—32no—
429C23×C4—32no—
430C4⋊Q8—38no—
431C4⋊Q8—68no—
432C4⋊Q8—68no—
433C4⋊Q8—68no—
434#125—28no—
435#125—68no—
436#125—68no—
437#125—68no—
438C22⋊Q8—68no—
439C22⋊Q8—68no—
440C22⋊Q8—68no—
441C22⋊Q8—68no—
442C22⋊Q8—124no—
443C22⋊Q8—124no—
444C4×Q8—124no—
445C4×D4—38no—
446#117—68no—
447#117—68no—
448C2×C4⋊C4—32no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—32no—
452C2×C4⋊C4—32no—
453C2×C4⋊C4—32no—
454C2×C4⋊C4—32no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—32no—
457C2×C4⋊C4—32no—
458C2×C4⋊C4—32no—
459C2×C4⋊C4—32no—
460C2×C4⋊C4—32no—
461C2×C4⋊C4—32no—
462C2×C4⋊C4—32no—
463C2×C4⋊C4—32no—
464C2×C4⋊C4—32no—
465C2×C4⋊C4—32no—
466C2×C4⋊C4—32no—
467C2×C4⋊C4—32no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—32no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—32no—
473C2×C4⋊C4—68no—
474C2×C4⋊C4C22×D312yes—
475C2×C4⋊C4C22×D312yes—
476C2×C4⋊C4C22×D312yes—
477C2×C4⋊C4C22×D311yescharacteristic
478C2×C4⋊C4C22×D312yes—
479C2×C4⋊C4C22×D312yes—
480C2×C4⋊C4C22×D312yes—
481C2×C4⋊C4C22×D311yescharacteristic
482C2×C4⋊C4C22×D311yescharacteristic
483C2×C4⋊C4C22×D311yescharacteristic
484C2×C4⋊C4C22×D312yes—
485C2×C4⋊C4C22×D311yescharacteristic
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—32no—
488C2×C22⋊C4—32no—
489C2×C22⋊C4—32no—
490C2×C22⋊C4—32no—
491C2×C22⋊C4—32no—
492C2×C22⋊C4—32no—
493C2×C22⋊C4—32no—
494C2×C22⋊C4—32no—
495C2×C22⋊C4—32no—
496C2×C22⋊C4—32no—
497C2×C22⋊C4—32no—
498C2×C42—31no—
499C2×C42—31no—
500C2×C42—32no—
501C2×C42—32no—
502C2×C42—31no—
503C2×C42—31no—
504C2×C42—31no—
505C2×C42—32no—
506C2×C42—32no—
507C2×C42—31no—
508C2×C42C22×D312yes—
509C2×C42C22×D311yescharacteristic
510#95—32no—
511#95—32no—
512#95—32no—
513#95—32no—
514#95—32no—
515#95—32no—
516#95—32no—
517#95—32no—
518#95—32no—
519#95—32no—
520#95—32no—
521#95—32no—
522#95—32no—
523#95C22×D312yes—
524#95C22×D312yes—
525#95C22×D312yes—
526#95C22×D312yes—
527#95C22×D312yes—
528#95C22×D312yes—
529C23×C3C2511yescharacteristic
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3C22×Q814yes—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—22no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4C22×D412yes—
560C2×C3×C4C22×D414yes—
561C2×C3×C4C22×Q812yes—
562C2×C3×C4C22×Q814yes—
563C2×C3×C4H(5,𝔽2)12yes—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—22no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3C22×D414yes—
585C2×Dic3C22×D412yes—
586C2×Dic3C22×D412yes—
587C2×Dic3C22×Q812yes—
588C2×Dic3C22×Q812yes—
589C2×Dic32−1+412yes—
590C2×Dic32−1+412yes—
591D12—44no—
592C4×D3—216no—
593C4×D3—84no—
594C4×D3—84no—
595Dic6—48no—
596Dic6—84no—
597Dic6—84no—
598C24—32no—
599C2×Q8—38no—
600C2×Q8—64no—
601C2×Q8—64no—
602C2×Q8—122no—
603C2×Q8—122no—
604C2×Q8—122no—
605C2×Q8—122no—
606C2×Q8—122no—
607C2×Q8—122no—
608C2×D4—34no—
609C2×D4—121no—
610C2×D4—121no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—32no—
615C22×C4—31no—
616C22×C4—38no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—64no—
622C22×C4—64no—
623C22×C4—64no—
624C22×C4—64no—
625C22×C4—122no—
626C22×C4—122no—
627C22×C4—122no—
628C22×C4—122no—
629C22×C4C23×D312yes—
630C22×C4C23×D312yes—
631C22×C4C23×D312yes—
632C22×C4C23×D312yes—
633C22×C4C23×D312yes—
634C22×C4C23×D311yescharacteristic
635C22×C4C23×D311yescharacteristic
636C22×C4C23×D312yes—
637C22×C4C23×D311yescharacteristic
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—38no—
646C4⋊C4—34no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—42no—
651C4⋊C4—64no—
652C4⋊C4—64no—
653C4⋊C4—64no—
654C4⋊C4—64no—
655C4⋊C4—64no—
656C4⋊C4—64no—
657C4⋊C4—64no—
658C4⋊C4—64no—
659C4⋊C4—64no—
660C4⋊C4—64no—
661C4⋊C4—64no—
662C4⋊C4—64no—
663C4⋊C4—64no—
664C4⋊C4—64no—
665C4⋊C4—62no—
666C4⋊C4—122no—
667C4⋊C4—122no—
668C4⋊C4—122no—
669C4⋊C4—122no—
670C4⋊C4—122no—
671C4⋊C4—121no—
672C4⋊C4—121no—
673C4⋊C4—121no—
674C4⋊C4D3×D414yes—
675C4⋊C4D3×Q814yes—
676C22⋊C4—38no—
677C22⋊C4—64no—
678C22⋊C4—64no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—64no—
682C22⋊C4—64no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—24no—
688C42—34no—
689C42—34no—
690C42—41no—
691C42—64no—
692C42—64no—
693C42—62no—
694C42—62no—
695C42—62no—
696C42—122no—
697C42—122no—
698C42—121no—
699C22×C3C23×D411yescharacteristic
700C22×C3C23×Q811yescharacteristic
701C22×C3C2×H(5,𝔽2)11yescharacteristic
702C22×C3C2×2−1+411yescharacteristic
703C22×C3C2×2−1+411yescharacteristic
704C22×C3#58511yescharacteristic
705C22×C3#58511yescharacteristic
706C2×D3—24no—
707C2×D3—24no—
708C2×D3—24no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C3×C4—22no—
714C3×C4—24no—
715C3×C4—24no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—42no—
722Dic3—22no—
723Dic3—24no—
724Dic3—22no—
725Dic3—22no—
726Dic3—42no—
727Dic3—42no—
728Dic3—42no—
729Dic3—42no—
730Dic3D4×Q814yes—
731C23—34no—
732C23—62no—
733C23—62no—
734C23—62no—
735C23—62no—
736C23—62no—
737C23—62no—
738C23C24×D311yescharacteristic
739Q8—128no—
740Q8—244no—
741Q8—244no—
742D4—124no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—34no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—616no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—244no—
794C2×C4—244no—
795C2×C4C2×D3×D414yes—
796C2×C4C2×D3×D412yes—
797C2×C4C2×D3×Q812yes—
798C2×C4C2×D3×Q814yes—
799C2×C4#100912yes—
800C2×C3#345811yescharacteristic
801C2×C3C2×D4×Q811yescharacteristic
802C2×C3#349611yescharacteristic
803C2×C3#349711yescharacteristic
804C2×C3#350311yescharacteristic
805C2×C3#355911yescharacteristic
806C2×C3#356311yescharacteristic
807D3—44no—
808C22—64no—
809C22—64no—
810C22—64no—
811C22—122no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22C22×D3×D411yescharacteristic
816C22C22×D3×Q811yescharacteristic
817C22C2×#100911yescharacteristic
818C22#596611yescharacteristic
819C22D3×2−1+411yescharacteristic
820C22D3×2−1+411yescharacteristic
821C22#596811yescharacteristic
822C4—22no—
823C4—22no—
824C4—22no—
825C4—24no—
826C4—24no—
827C4—34no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—62no—
833C4—64no—
834C4—62no—
835C4—62no—
836C4—122no—
837C4—122no—
838C4—122no—
839C4—122no—
840C3#3936511yescharacteristic, complemented, Sylow
841C2—124no—
842C2#8636711yescharacteristic
843C2#8644211yescharacteristic
844C2#8658111yescharacteristic
845C2#8670211yescharacteristic
846C2D3×D4×Q811yescharacteristic
847C2#8701811yescharacteristic
848C2#8714411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2726C2
prime radicalC22×D12C23
hypercenter#2726D3
hypocenterC3#39365
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2726

Complements

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

NH ≅ G/Ntype
1. C2×#5689C2semidirect
2. C3×#2726C2semidirect
3. #83038C2semidirect
5. #77820C2semidirect
6. #77790C2semidirect
7. #77786C2semidirect
8. #77745C2semidirect
9. #77744C2semidirect
12. #76221C2semidirect
13. #76190C2semidirect
14. #76128C2semidirect
15. #76001C2semidirect
16. #75967C2semidirect
19. #75179C2semidirect
114. #2726D3semidirect
203. #893Q8semidirect
211. #888D4semidirect
840. C3#39365semidirect

Maximal subgroups

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

subgroupindex
C2×#56892
C3×#27262
#830382
#779862
#778202
#777902
#777862
#777452
#777442
#762612
#762212
#761902
#761282
#760012
#759672
#759612
#753052
#751792
#393653