Finite Group Databasebeta

← #11430879

Subgroups — #11430879

Order 768.

2120 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5728C212yesmaximal, complemented
2C3×#2734C211yesmaximal, characteristic, complemented
3#83267C212yesmaximal, complemented
4#77852C212yesmaximal, complemented
5#77739C212yesmaximal, complemented
6#77220C212yesmaximal, complemented
7#77215C212yesmaximal
8#77171C212yesmaximal, complemented
9#77170C212yesmaximal, complemented
10#76656C211yesmaximal, characteristic
11#76477C211yesmaximal, characteristic, complemented
12#76261C211yesmaximal, characteristic
13#76128C211yesmaximal, characteristic, complemented
14#75967C211yesmaximal, characteristic, complemented
15#75961C211yesmaximal, characteristic
16#75390C212yesmaximal, complemented
17#75158C212yesmaximal, complemented
18#74941C212yesmaximal, complemented
19#74937C212yesmaximal
20#52162—31nomaximal, Sylow
21C2×C3×C4⋊Q8C2212yes—
22C2×#946C2212yes—
23C2×#946C2212yes—
24C2×Q8×Dic3C2212yes—
25C2×Q8×Dic3C2211yescharacteristic
26#5728—216no—
27C2×#897C2212yes—
28C2×#897C2212yes—
29C2×#896C2212yes—
30C2×#893C2211yescharacteristic
31C2×#892C2212yes—
32C2×#892C2212yes—
33C2×#890C2212yes—
34C2×#890C2212yes—
35C2×#888C2211yescharacteristic
36C2×#887C2212yes—
37C2×#887C2212yes—
38C2×C42×D3C2212yes—
39C2×#869C2212yes—
40C3×#398C2212yes—
41C3×#395C2212yes—
42C3×#395C2212yes—
43C3×#391C2211yescharacteristic
44C3×#389C2211yescharacteristic
45C3×#389C2211yescharacteristic
46C3×#387C2212yes—
47C3×#387C2212yes—
48#5231C2212yes—
49#5230C2212yes—
50#5229C2211yescharacteristic
51#4994C2212yes—
52#4994C2212yes—
53#4994C2212yes—
54#4994C2212yes—
55#4993C2212yes—
56#4990C2212yes—
57#4989C2212yes—
58#4989C2212yes—
59#4988C2211yescharacteristic
60#4986C2212yes—
61#4984C2211yescharacteristic
62#4982C2212yes—
63#4982C2212yes—
64#4982C2212yes—
65#4981C2212yes—
66#4980C2212yes—
67#4976C2212yes—
68#4975C2211yescharacteristic
69Dic3×C4⋊C4C2211yescharacteristic
70Dic3×C4⋊C4C2212yes—
71Dic3×C4⋊C4C2211yescharacteristic
72Dic3×C4⋊C4C2211yescharacteristic
73Dic3×C4⋊C4C2211yescharacteristic
74#4972C2211yescharacteristic
75#4940C2212yes—
76#4939C2211yescharacteristic
77#4933C2212yes—
78C42×Dic3C2211yescharacteristic
79#4928C2211yescharacteristic
80#4928C2211yescharacteristic
81#4677C2212yes—
82#4673C2212yes—
83#4670C2212yes—
84#4669C2212yes—
85#4668C2212yes—
86#4668C2212yes—
87#4667C2212yes—
88#4666C2212yes—
89#4666C2212yes—
90#4666C2212yes—
91#4665C2212yes—
92#4665C2212yes—
93#4661C2212yes—
94#4661C2212yes—
95#4661C2212yes—
96#4660C2212yes—
97#4656C2212yes—
98#4656C2212yes—
99#4656C2212yes—
100#4654C2212yes—
101#4653C2212yes—
102#4649C2212yes—
103#4649C2212yes—
104#4649C2212yes—
105#4648C2212yes—
106#4647C2212yes—
107#4646C2212yes—
108#4646C2212yes—
109C2×#533—32no—
110#2734D311yescharacteristic, complemented
111#2732—31no—
112#2729—32no—
113#2726—31no—
114#2720—32no—
115#2713—32no—
116#2704—32no—
117#2692—32no—
118#2683—31no—
119#2677—32no—
120#2399—32no—
121#2396—32no—
122#2396—32no—
123C4×C4⋊Q8—31no—
124C4×C22⋊Q8—32no—
125#2295—31no—
126#2293—31no—
127#2290—32no—
128C22×C3×Q8C2312yes—
129C22×C3×Q8C2311yescharacteristic
130C22×D12C2311yescharacteristic
131C22×C4×D3C2312yes—
132C22×C4×D3C2312yes—
133C22×C4×D3C2312yes—
134C22×Dic6C2312yes—
135C22×Dic6C2312yes—
136C3×C4⋊Q8—28no—
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C4⋊C4C2312yes—
139C2×C3×C4⋊C4C2312yes—
140C2×C3×C4⋊C4C2312yes—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2312yes—
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C42C2312yes—
148C2×C3×C42C2311yescharacteristic
149#946—28no—
150#946—28no—
151Q8×Dic3—28no—
152Q8×Dic3D418yescomplemented
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×(C2×D3)⋊C4C2312yes—
163C2×(C2×D3)⋊C4C2312yes—
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2312yes—
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4⋊Dic3C2312yes—
172C2×C4⋊Dic3C2311yescharacteristic
173C2×C4⋊Dic3C2311yescharacteristic
174C2×C4⋊Dic3C2312yes—
175C2×C4⋊Dic3C2311yescharacteristic
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×C4×Dic3C2312yes—
187C2×C4×Dic3C2312yes—
188C2×C4×Dic3C2311yescharacteristic
189C2×C4×Dic3C2312yes—
190C2×C4×Dic3C2312yes—
191C2×C4×Dic3C2312yes—
192C2×C4×Dic3C2311yescharacteristic
193C2×C4×Dic3C2311yescharacteristic
194C2×C4×Dic3C2311yescharacteristic
195C2×C4×Dic3C2312yes—
196C2×C4×Dic3C2311yescharacteristic
197C2×C4×Dic3C2311yescharacteristic
198#897—28no—
199#897—28no—
200#896—28no—
201#893Q818yescomplemented
202#892—28no—
203#892—28no—
204#890—28no—
205#890—28no—
206#888—24no—
207#887—28no—
208#887—28no—
209C42×D3—28no—
210#869—28no—
211C3×#95C2312yes—
212C3×#95C2312yes—
213C3×#95C2312yes—
214C3×#95C2312yes—
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—
233#533—616no—
234C2×C4⋊Q8—31no—
235C2×C4⋊Q8—32no—
236C2×C4⋊Q8C2×D312yes—
237C2×#125—32no—
238C2×#125—32no—
239C2×C22⋊Q8—32no—
240C2×C22⋊Q8—32no—
241C2×C22⋊Q8—32no—
242C2×C22⋊Q8—32no—
243C2×C22⋊Q8—32no—
244C2×C4×Q8—31no—
245C2×C4×Q8—32no—
246C2×C4×Q8—32no—
247C2×C4×Q8—32no—
248C2×C4×D4—31no—
249C2×#117—32no—
250C2×#117—32no—
251C22×C42—32no—
252#400—32no—
253#400—32no—
254#399—32no—
255#399—32no—
256#398—32no—
257#398—32no—
258#398—32no—
259#398—32no—
260#398—32no—
261#398—32no—
262#398—32no—
263#398C2×D312yes—
264#396—32no—
265#396—32no—
266#396—32no—
267#396—32no—
268#395—32no—
269#395—32no—
270#395—32no—
271#395—32no—
272#395C2×D312yes—
273#395C2×D312yes—
274#393—32no—
275#393—32no—
276#391—31no—
277#391—32no—
278#391—32no—
279#391C2×D311yescharacteristic
280#390—31no—
281#390—31no—
282#389—32no—
283#389—31no—
284#389—31no—
285#389—31no—
286#389—31no—
287#389—32no—
288#389C2×D311yescharacteristic
289#389C2×D311yescharacteristic
290#388—32no—
291#388—32no—
292#388—32no—
293#388—32no—
294#387—32no—
295#387—32no—
296#387—32no—
297#387—32no—
298#387C2×D312yes—
299#387C2×D312yes—
300#386—32no—
301#386—32no—
302#385—32no—
303#385—32no—
304#385—32no—
305#385—32no—
306#384—31no—
307#380—32no—
308C4×C4⋊C4—31no—
309C4×C4⋊C4—31no—
310C4×C4⋊C4—32no—
311C4×C4⋊C4—31no—
312C4×C4⋊C4—31no—
313C4×C4⋊C4—32no—
314C4×C4⋊C4—32no—
315C4×C4⋊C4—32no—
316C4×C22⋊C4—32no—
317C4×C22⋊C4—32no—
318C4×C22⋊C4—32no—
319#376—32no—
320C43—31no—
321C23×D3C2412yes—
322C2×C3×Q8—24no—
323C2×C3×Q8—41no—
324C2×C3×Q8—41no—
325C2×C3×Q8—42no—
326C2×C3×Q8—42no—
327C2×C3×Q8C2×D414yes—
328C22×C3×C4C2412yes—
329C22×C3×C4C2412yes—
330C22×C3×C4C2412yes—
331C22×C3×C4C2412yes—
332C22×C3×C4C2411yescharacteristic
333C22×C3×C4C2411yescharacteristic
334C22×C3×C4C2412yes—
335C22×C3×C4C2412yes—
336C22×C3×C4C2411yescharacteristic
337C22×Dic3C2411yescharacteristic
338C22×Dic3C2412yes—
339C22×Dic3C2412yes—
340C22×Dic3C2412yes—
341C22×Dic3C2412yes—
342C22×Dic3C2411yescharacteristic
343C22×Dic3C2412yes—
344C22×Dic3C2411yescharacteristic
345C22×Dic3C2411yescharacteristic
346C2×D12—41no—
347C2×D12—41no—
348C2×D12C2×Q814yes—
349C2×C4×D3—24no—
350C2×C4×D3—24no—
351C2×C4×D3—24no—
352C2×C4×D3—24no—
353C2×C4×D3—24no—
354C2×C4×D3—42no—
355C2×C4×D3—42no—
356C2×C4×D3—42no—
357C2×C4×D3C2×Q818yes—
358C2×Dic6—24no—
359C2×Dic6—24no—
360C2×Dic6—24no—
361C2×Dic6—24no—
362C2×Dic6—42no—
363C2×Dic6—42no—
364C3×C4⋊C4—24no—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—24no—
368C3×C4⋊C4—41no—
369C3×C4⋊C4—41no—
370C3×C4⋊C4—41no—
371C3×C4⋊C4—42no—
372C3×C4⋊C4C2×Q814yes—
373C3×C4⋊C4#4114yes—
374C3×C42—24no—
375C3×C42—41no—
376(C2×D3)⋊C4—24no—
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—42no—
383(C2×D3)⋊C4—42no—
384(C2×D3)⋊C4—42no—
385(C2×D3)⋊C4—42no—
386(C2×D3)⋊C4C2×Q818yes—
387C4⋊Dic3—24no—
388C4⋊Dic3—22no—
389C4⋊Dic3—24no—
390C4⋊Dic3—24no—
391C4⋊Dic3—24no—
392C4⋊Dic3—24no—
393C4⋊Dic3—41no—
394C4⋊Dic3—41no—
395C4⋊Dic3—41no—
396C4⋊Dic3—42no—
397C4⋊Dic3C2×D418yes—
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—42no—
407Dic3⋊C4—42no—
408Dic3⋊C4—42no—
409C4×Dic3—22no—
410C4×Dic3—24no—
411C4×Dic3—24no—
412C4×Dic3—24no—
413C4×Dic3—24no—
414C4×Dic3—22no—
415C4×Dic3—24no—
416C4×Dic3—41no—
417C4×Dic3—41no—
418C4×Dic3C2×D418yes—
419C4×Dic3C2×D414yes—
420C4×Dic3C2×Q814yes—
421C22×Q8—32no—
422C22×Q8—32no—
423C22×Q8C22×D312yes—
424C22×Q8C22×D311yescharacteristic
425C22×D4—31no—
426C23×C4—32no—
427C23×C4—32no—
428C23×C4—32no—
429C4⋊Q8—28no—
430C4⋊Q8—68no—
431C4⋊Q8—64no—
432#125—68no—
433#125—68no—
434C22⋊Q8—68no—
435C22⋊Q8—68no—
436C22⋊Q8—68no—
437C22⋊Q8—68no—
438C22⋊Q8—68no—
439C4×Q8—38no—
440C4×Q8—68no—
441C4×Q8—68no—
442C4×Q8—68no—
443C4×D4—38no—
444#117—68no—
445#117—68no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—32no—
448C2×C4⋊C4—32no—
449C2×C4⋊C4—32no—
450C2×C4⋊C4—32no—
451C2×C4⋊C4—32no—
452C2×C4⋊C4—32no—
453C2×C4⋊C4—32no—
454C2×C4⋊C4—32no—
455C2×C4⋊C4—32no—
456C2×C4⋊C4—32no—
457C2×C4⋊C4—32no—
458C2×C4⋊C4—32no—
459C2×C4⋊C4—32no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—32no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—32no—
464C2×C4⋊C4—32no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—32no—
468C2×C4⋊C4C22×D312yes—
469C2×C4⋊C4C22×D312yes—
470C2×C4⋊C4C22×D312yes—
471C2×C4⋊C4C22×D312yes—
472C2×C4⋊C4C22×D311yescharacteristic
473C2×C4⋊C4C22×D311yescharacteristic
474C2×C4⋊C4C22×D311yescharacteristic
475C2×C4⋊C4C22×D312yes—
476C2×C4⋊C4C22×D311yescharacteristic
477C2×C4⋊C4C22×D311yescharacteristic
478C2×C22⋊C4—32no—
479C2×C22⋊C4—32no—
480C2×C22⋊C4—32no—
481C2×C22⋊C4—32no—
482C2×C22⋊C4—32no—
483C2×C22⋊C4—32no—
484C2×C22⋊C4—32no—
485C2×C22⋊C4—32no—
486C2×C22⋊C4—32no—
487C2×C22⋊C4—32no—
488C2×C22⋊C4—32no—
489C2×C42—31no—
490C2×C42—32no—
491C2×C42—31no—
492C2×C42—32no—
493C2×C42—32no—
494C2×C42—32no—
495C2×C42—32no—
496C2×C42—31no—
497C2×C42—31no—
498C2×C42—32no—
499C2×C42—31no—
500C2×C42—31no—
501C2×C42—68no—
502C2×C42C22×D312yes—
503C2×C42C22×D311yescharacteristic
504#95—32no—
505#95—32no—
506#95—32no—
507#95—32no—
508#95—32no—
509#95—32no—
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#95C22×D312yes—
520#95C22×D312yes—
521#95C22×D312yes—
522#95C22×D312yes—
523#95C22×D312yes—
524#95C22×D312yes—
525#95C22×D312yes—
526C23×C3C2511yescharacteristic
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3C22×Q814yes—
534C3×Q8—44no—
535C3×Q8—48no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—21no—
539C2×C3×C4—22no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—22no—
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×C4C22×D412yes—
558C2×C3×C4C22×D414yes—
559C2×C3×C4C22×Q812yes—
560C2×C3×C4C22×Q814yes—
561C2×C3×C4C2×#4112yes—
562C2×C3×C4C2×#4114yes—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—22no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
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—
590D12—44no—
591C4×D3—216no—
592C4×D3—48no—
593C4×D3—48no—
594Dic6—48no—
595Dic6—48no—
596C24—32no—
597C2×Q8—24no—
598C2×Q8—41no—
599C2×Q8—41no—
600C2×Q8—42no—
601C2×Q8—42no—
602C2×Q8—64no—
603C2×Q8—64no—
604C2×Q8—64no—
605C2×Q8—64no—
606C2×Q8—122no—
607C2×Q8—122no—
608C2×Q8D3×D414yes—
609C2×D4—34no—
610C2×D4—121no—
611C2×D4—121no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—32no—
616C22×C4—38no—
617C22×C4—31no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—64no—
623C22×C4—64no—
624C22×C4—64no—
625C22×C4—64no—
626C22×C4—64no—
627C22×C4—122no—
628C22×C4—122no—
629C22×C4—122no—
630C22×C4C23×D312yes—
631C22×C4C23×D312yes—
632C22×C4C23×D312yes—
633C22×C4C23×D312yes—
634C22×C4C23×D311yescharacteristic
635C22×C4C23×D311yescharacteristic
636C22×C4C23×D312yes—
637C22×C4C23×D312yes—
638C22×C4C23×D311yescharacteristic
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—34no—
644C4⋊C4—38no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—42no—
649C4⋊C4—64no—
650C4⋊C4—64no—
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—62no—
662C4⋊C4—122no—
663C4⋊C4—122no—
664C4⋊C4—122no—
665C4⋊C4—121no—
666C4⋊C4—121no—
667C4⋊C4—121no—
668C4⋊C4—122no—
669C4⋊C4D3×Q814yes—
670C4⋊C4#23914yes—
671C22⋊C4—38no—
672C22⋊C4—64no—
673C22⋊C4—64no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—64no—
677C22⋊C4—64no—
678C22⋊C4—122no—
679C22⋊C4—122no—
680C22⋊C4—122no—
681C22⋊C4—122no—
682C42—24no—
683C42—38no—
684C42—34no—
685C42—34no—
686C42—41no—
687C42—64no—
688C42—64no—
689C42—64no—
690C42—64no—
691C42—62no—
692C42—64no—
693C42—62no—
694C42—121no—
695C42—121no—
696C22×C3C23×D411yescharacteristic
697C22×C3C23×Q811yescharacteristic
698C22×C3C22×#4111yescharacteristic
699C22×C3C2×2−1+411yescharacteristic
700C22×C3#58511yescharacteristic
701C22×C3#58511yescharacteristic
702C22×C3#58511yescharacteristic
703C2×D3—24no—
704C2×D3—24no—
705C2×D3—24no—
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C3×C4—24no—
711C3×C4—22no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—24no—
715C3×C4—24no—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—42no—
719Dic3—22no—
720Dic3—24no—
721Dic3—22no—
722Dic3—42no—
723Dic3—42no—
724Dic3—42no—
725Dic3—42no—
726Dic3—41no—
727Dic3D4×Q814yes—
728C23—34no—
729C23—62no—
730C23—62no—
731C23—62no—
732C23—62no—
733C23—62no—
734C23—62no—
735C23C24×D311yescharacteristic
736Q8—44no—
737Q8—48no—
738Q8—128no—
739Q8—128no—
740D4—124no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
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—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—34no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—616no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—62no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—61no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—128no—
791C2×C4—128no—
792C2×C4C2×D3×D414yes—
793C2×C4C2×D3×D412yes—
794C2×C4C2×D3×Q812yes—
795C2×C4C2×D3×Q814yes—
796C2×C4C2×#23912yes—
797C2×C4C2×#23914yes—
798C2×C3#344911yescharacteristic
799C2×C3#345811yescharacteristic
800C2×C3#346111yescharacteristic
801C2×C3C2×D4×Q811yescharacteristic
802C2×C3D4×#4111yescharacteristic
803C2×C3Q8×#4111yescharacteristic
804C2×C3#353111yescharacteristic
805D3—44no—
806C22—64no—
807C22—64no—
808C22—64no—
809C22—122no—
810C22—122no—
811C22—122no—
812C22—122no—
813C22C22×D3×D411yescharacteristic
814C22C22×D3×Q811yescharacteristic
815C22C22×#23911yescharacteristic
816C22#596611yescharacteristic
817C22#596611yescharacteristic
818C22D3×2−1+411yescharacteristic
819C22#596811yescharacteristic
820C4—24no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—24no—
825C4—24no—
826C4—34no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—64no—
831C4—62no—
832C4—62no—
833C4—122no—
834C4—122no—
835C4—121no—
836C4—122no—
837C4—122no—
838C3#5216211yescharacteristic, complemented, Sylow
839C2—124no—
840C2#8629411yescharacteristic
841C2#8658111yescharacteristic
842C2#8658311yescharacteristic
843C2D4×#23911yescharacteristic
844C2D3×D4×Q811yescharacteristic
845C2Q8×#23911yescharacteristic
846C2#8711611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2734C2
prime radicalC22×D12C23
hypercenter#2734D3
hypocenterC3#52162
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2734

Complements

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

NH ≅ G/Ntype
1. C2×#5728C2semidirect
2. C3×#2734C2semidirect
3. #83267C2semidirect
4. #77852C2semidirect
5. #77739C2semidirect
6. #77220C2semidirect
8. #77171C2semidirect
9. #77170C2semidirect
11. #76477C2semidirect
13. #76128C2semidirect
14. #75967C2semidirect
16. #75390C2semidirect
17. #75158C2semidirect
18. #74941C2semidirect
110. #2734D3semidirect
152. Q8×Dic3D4semidirect
201. #893Q8semidirect
838. C3#52162semidirect

Maximal subgroups

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

subgroupindex
C2×#57282
C3×#27342
#832672
#778522
#777392
#772202
#772152
#771712
#771702
#766562
#764772
#762612
#761282
#759672
#759612
#753902
#751582
#749412
#749372
#521623