Finite Group Databasebeta

← #11142047

Subgroups — #11142047

Order 768.

1646 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2397C211yesmaximal, characteristic
2#82391C211yesmaximal, characteristic, complemented
3#82386C211yesmaximal, characteristic, complemented
4#82371C212yesmaximal, complemented
5#82369C212yesmaximal, complemented
6#82363C212yesmaximal, complemented
7#82354C212yesmaximal, complemented
8#82336C211yesmaximal, characteristic, complemented
9#82325C211yesmaximal, characteristic, complemented
10#78083C212yesmaximal, complemented
11#78070C212yesmaximal, complemented
12#78060C212yesmaximal, complemented
13#78059C212yesmaximal, complemented
14#76751C212yesmaximal, complemented
15#76734C212yesmaximal, complemented
16#76724C212yesmaximal, complemented
17#76689C212yesmaximal, complemented
18#73405C211yesmaximal, characteristic, complemented
19#73394C211yesmaximal, characteristic, complemented
20#41979—31nomaximal, Sylow
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×C3×C4×D4C2212yes—
24C2×C3×C4×D4C2212yes—
25C2×#935C2212yes—
26C2×#890C2212yes—
27C2×#879C2212yes—
28C2×#879C2212yes—
29C2×#870C2211yescharacteristic
30C3×#399C2212yes—
31C3×#399C2211yescharacteristic
32C3×#399C2211yescharacteristic
33C3×#392C2211yescharacteristic
34C3×#392C2212yes—
35C3×#392C2211yescharacteristic
36C3×#376C2211yescharacteristic
37#5222C2212yes—
38#5222C2212yes—
39#5222C2212yes—
40#5222C2212yes—
41#5222C2212yes—
42#5221C2212yes—
43#5221C2212yes—
44#5221C2212yes—
45#5221C2211yescharacteristic
46#5221C2211yescharacteristic
47#5220C2212yes—
48#5220C2212yes—
49#5212C2212yes—
50#5212C2211yescharacteristic
51#5211C2212yes—
52#5211C2211yescharacteristic
53#5210C2212yes—
54#5210C2212yes—
55#5210C2212yes—
56#5210C2212yes—
57C4×#217C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59#4985C2212yes—
60#4984C2212yes—
61#4984C2212yes—
62#4983C2212yes—
63#4983C2212yes—
64#4982C2212yes—
65#4981C2212yes—
66#4980C2212yes—
67#4978C2212yes—
68#4977C2211yescharacteristic
69#4976C2212yes—
70#4975C2211yescharacteristic
71#4953C2212yes—
72#4953C2212yes—
73#4952C2212yes—
74#4952C2212yes—
75#4951C2212yes—
76#4951C2212yes—
77#4951C2212yes—
78#4951C2212yes—
79#4951C2212yes—
80#4949C2212yes—
81#4949C2212yes—
82#4949C2212yes—
83#4948C2212yes—
84#4948C2212yes—
85#4948C2212yes—
86#4948C2212yes—
87#4948C2212yes—
88#4945C2212yes—
89#4944C2212yes—
90#4943C2212yes—
91#4942C2212yes—
92Dic3×C22⋊C4C2212yes—
93#4937C2211yescharacteristic
94C4×C4⋊Dic3C2211yescharacteristic
95#4933C2212yes—
96#4933C2212yes—
97#4932C2211yescharacteristic
98C4×Dic3⋊C4C2212yes—
99#4928C2212yes—
100#4661C2212yes—
101#4657C2212yes—
102#4654C2212yes—
103#4654C2212yes—
104#4653C2212yes—
105#4652C2212yes—
106#4649C2212yes—
107#4647C2212yes—
108#2829—32no—
109#2773—32no—
110#2752—32no—
111#2721—32no—
112#2705—32no—
113#2667—32no—
114#2664—32no—
115#2633—31no—
116#2606—31no—
117#2566—31no—
118#2554—32no—
119#2468—32no—
120#2466—32no—
121#2454—32no—
122#2419—32no—
123#2397D311yescharacteristic
124#2371—31no—
125#2353—31no—
126#2319—31no—
127C22×C3×D4C2311yescharacteristic
128C22×C3×D4C2312yes—
129C22×C3×D4C2311yescharacteristic
130C22×C3×D4C2312yes—
131C23×C3×C4C2311yescharacteristic
132C23×C3×C4C2311yescharacteristic
133C23×C3×C4C2312yes—
134C23×Dic3C2312yes—
135C3×C4×D4—24no—
136C3×C4×D4—24no—
137C3×C4×D4—44no—
138C3×C4×D4—44no—
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C4⋊C4C2312yes—
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C22⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4C2312yes—
145C2×C3×C22⋊C4C2311yescharacteristic
146C2×C3×C22⋊C4C2312yes—
147C2×C3×C22⋊C4C2312yes—
148C2×C3×C22⋊C4C2312yes—
149C2×C3×C22⋊C4C2312yes—
150C2×C3×C42C2312yes—
151C2×C3×C42C2311yescharacteristic
152C2×#217C2312yes—
153C2×#217C2312yes—
154C2×#217C2312yes—
155C2×#217C2312yes—
156C2×#217C2312yes—
157C2×#217C2312yes—
158C2×#217C2312yes—
159C2×#217C2312yes—
160C2×#217C2312yes—
161C2×#217C2312yes—
162C2×#217C2312yes—
163C2×#217C2312yes—
164C2×#217C2312yes—
165C2×#217C2312yes—
166C2×#217C2312yes—
167#935—44no—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2312yes—
171C2×C4⋊Dic3C2312yes—
172C2×C4⋊Dic3C2312yes—
173C2×C4⋊Dic3C2312yes—
174C2×C4⋊Dic3C2312yes—
175C2×C4⋊Dic3C2312yes—
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×Dic3⋊C4C2312yes—
188C2×C4×Dic3C2312yes—
189C2×C4×Dic3C2311yescharacteristic
190C2×C4×Dic3C2312yes—
191C2×C4×Dic3C2312yes—
192C2×C4×Dic3C2311yescharacteristic
193C2×C4×Dic3C2312yes—
194#890—44no—
195#879—44no—
196#879—44no—
197#870—24no—
198C3×#95C2312yes—
199C3×#95C2311yescharacteristic
200C3×#95C2311yescharacteristic
201C3⋊#95C2312yes—
202C3⋊#95C2312yes—
203C3⋊#95C2312yes—
204C3⋊#95C2312yes—
205C3⋊#95C2312yes—
206C3⋊#95C2312yes—
207C3⋊#95C2312yes—
208C3⋊#95C2312yes—
209C3⋊#95C2312yes—
210C3⋊#95C2311yescharacteristic
211C3⋊#95C2312yes—
212C3⋊#95C2311yescharacteristic
213C3⋊#95C2311yescharacteristic
214C3⋊#95C2311yescharacteristic
215C3⋊#95C2312yes—
216C3⋊#95C2312yes—
217C3⋊#95C2312yes—
218C3⋊#95C2312yes—
219C3⋊#95C2312yes—
220C3⋊#95C2312yes—
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C2×#126—32no—
224C2×#126—32no—
225C2×#125—32no—
226C2×#125—31no—
227C2×#123—32no—
228C2×C4×D4C2×D311yescharacteristic
229C2×C4×D4C2×D311yescharacteristic
230C2×C4×D4C2×D312yes—
231C2×C4×D4C2×D312yes—
232#400—32no—
233#399—32no—
234#399—32no—
235#399—32no—
236#399C2×D311yescharacteristic
237#399C2×D311yescharacteristic
238#399C2×D312yes—
239#398—32no—
240#398—32no—
241#398—32no—
242#398—32no—
243#398—32no—
244#398—32no—
245#397—32no—
246#397—32no—
247#397—32no—
248#397—32no—
249#396—32no—
250#396—32no—
251#396—32no—
252#396—32no—
253#396—32no—
254#394—32no—
255#394—32no—
256#394—32no—
257#394—32no—
258#394—32no—
259#392C2×D311yescharacteristic
260#392C2×D312yes—
261#392C2×D311yescharacteristic
262#390—31no—
263#390—31no—
264#390—32no—
265#390—32no—
266#390—32no—
267#389—32no—
268#389—32no—
269#389—32no—
270#389—32no—
271#389—32no—
272#388—32no—
273#388—32no—
274#388—32no—
275#388—32no—
276#388—32no—
277#388—32no—
278#388—32no—
279#387—32no—
280#387—32no—
281#387—32no—
282#387—32no—
283#387—32no—
284#387—32no—
285#387—32no—
286#387—32no—
287#386—32no—
288#386—32no—
289#385—32no—
290#385—32no—
291#385—32no—
292#385—32no—
293#384—31no—
294#383—31no—
295#382—31no—
296#381—32no—
297#381—31no—
298#381—32no—
299#380—32no—
300#380—31no—
301#380—32no—
302C4×C4⋊C4—31no—
303C4×C4⋊C4—32no—
304C4×C4⋊C4—32no—
305C4×C22⋊C4—31no—
306C4×C22⋊C4—32no—
307#376—31no—
308#376C2×D311yescharacteristic
309C2×#95—31no—
310C24×C3C2411yescharacteristic
311C24×C3C2412yes—
312C24×C3C2411yescharacteristic
313C2×C3×D4—22no—
314C2×C3×D4—24no—
315C2×C3×D4—22no—
316C2×C3×D4—22no—
317C2×C3×D4—24no—
318C2×C3×D4—42no—
319C2×C3×D4—41no—
320C2×C3×D4—42no—
321C2×C3×D4—42no—
322C2×C3×D4—42no—
323C2×C3×D4—42no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—24no—
327C22×C3×C4—42no—
328C22×C3×C4—42no—
329C22×C3×C4—42no—
330C22×C3×C4—42no—
331C22×C3×C4C2412yes—
332C22×C3×C4C2411yescharacteristic
333C22×C3×C4C2412yes—
334C22×C3×C4C2411yescharacteristic
335C22×C3×C4C2411yescharacteristic
336C22×C3×C4C2411yescharacteristic
337C22×C3×C4C2411yescharacteristic
338C22×C3×C4C2412yes—
339C22×Dic3—24no—
340C22×Dic3—42no—
341C22×Dic3—42no—
342C22×Dic3C2412yes—
343C22×Dic3C2412yes—
344C22×Dic3C2412yes—
345C22×Dic3C2412yes—
346C22×Dic3C2412yes—
347C22×Dic3C2412yes—
348C22×Dic3C2412yes—
349C22×Dic3C2412yes—
350C3×C4⋊C4—22no—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—24no—
353C3×C4⋊C4—42no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—24no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—24no—
359C3×C22⋊C4—42no—
360C3×C22⋊C4—42no—
361C3×C42—24no—
362C3×C42#4114yes—
363#217—42no—
364#217—42no—
365#217—42no—
366#217—42no—
367#217—42no—
368#217—42no—
369#217—42no—
370#217—42no—
371#217—42no—
372#217—42no—
373#217—42no—
374#217—42no—
375#217—42no—
376#217—42no—
377#217—42no—
378C4⋊Dic3—22no—
379C4⋊Dic3—22no—
380C4⋊Dic3—24no—
381C4⋊Dic3—42no—
382C4⋊Dic3—42no—
383C4⋊Dic3—42no—
384C4⋊Dic3—42no—
385C4⋊Dic3—42no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4—42no—
391Dic3⋊C4—42no—
392Dic3⋊C4—42no—
393Dic3⋊C4—42no—
394Dic3⋊C4—42no—
395Dic3⋊C4—42no—
396Dic3⋊C4—42no—
397Dic3⋊C4—42no—
398C4×Dic3—24no—
399C4×Dic3—42no—
400C4×Dic3—42no—
401C4×Dic3—42no—
402C4×Dic3—41no—
403C4×Dic3—41no—
404C22×D4C22×D312yes—
405C22×D4C22×D311yescharacteristic
406C22×D4C22×D311yescharacteristic
407C22×D4C22×D312yes—
408C23×C4—32no—
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D312yes—
412#126—124no—
413#126—124no—
414#125—64no—
415#125—124no—
416#123—124no—
417C4×D4—24no—
418C4×D4—24no—
419C4×D4—44no—
420C4×D4—44no—
421C2×C4⋊C4—32no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—32no—
429C2×C4⋊C4—32no—
430C2×C4⋊C4—32no—
431C2×C4⋊C4—32no—
432C2×C4⋊C4—32no—
433C2×C4⋊C4—32no—
434C2×C4⋊C4—32no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—32no—
437C2×C4⋊C4—32no—
438C2×C4⋊C4—32no—
439C2×C4⋊C4—32no—
440C2×C4⋊C4—32no—
441C2×C4⋊C4C22×D312yes—
442C2×C4⋊C4C22×D311yescharacteristic
443C2×C4⋊C4C22×D311yescharacteristic
444C2×C4⋊C4C22×D312yes—
445C2×C22⋊C4—32no—
446C2×C22⋊C4—32no—
447C2×C22⋊C4—32no—
448C2×C22⋊C4—32no—
449C2×C22⋊C4—32no—
450C2×C22⋊C4—32no—
451C2×C22⋊C4—32no—
452C2×C22⋊C4—32no—
453C2×C22⋊C4—32no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—32no—
456C2×C22⋊C4—32no—
457C2×C22⋊C4—32no—
458C2×C22⋊C4—32no—
459C2×C22⋊C4—32no—
460C2×C22⋊C4C22×D312yes—
461C2×C22⋊C4C22×D312yes—
462C2×C22⋊C4C22×D311yescharacteristic
463C2×C22⋊C4C22×D311yescharacteristic
464C2×C22⋊C4C22×D312yes—
465C2×C22⋊C4C22×D312yes—
466C2×C22⋊C4C22×D312yes—
467C2×C42—32no—
468C2×C42—32no—
469C2×C42—32no—
470C2×C42—32no—
471C2×C42—31no—
472C2×C42—31no—
473C2×C42C22×D312yes—
474C2×C42C22×D311yescharacteristic
475#95—31no—
476#95—31no—
477#95—32no—
478#95—31no—
479#95—32no—
480#95—31no—
481#95—32no—
482#95—32no—
483#95—32no—
484#95—32no—
485#95—32no—
486#95—32no—
487#95—32no—
488#95—32no—
489#95—32no—
490#95—32no—
491#95—32no—
492#95—32no—
493#95—32no—
494#95—32no—
495#95—32no—
496#95—32no—
497#95C22×D311yescharacteristic
498#95C22×D312yes—
499#95C22×D311yescharacteristic
500C23×C3—21no—
501C23×C3—22no—
502C23×C3—21no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—21no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—21no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—21no—
516C23×C32−1+412yes—
517C23×C3C2511yescharacteristic
518C3×D4—44no—
519C3×D4—48no—
520C3×D4—44no—
521C3×D4—48no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—22no—
530C2×C3×C4—21no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—82no—
539C2×C3×C4—82no—
540C2×C3×C4—84no—
541C2×C3×C4C2×#4112yes—
542C2×C3×C4C2×#4112yes—
543C2×C3×C4C2×#4112yes—
544C2×C3×C4H(5,𝔽2)14yes—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—84no—
570C24C23×D311yescharacteristic
571C24C23×D312yes—
572C24C23×D311yescharacteristic
573C2×D4—24no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—24no—
578C2×D4—42no—
579C2×D4—41no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—64no—
600C22×C4—122no—
601C22×C4—122no—
602C22×C4C23×D312yes—
603C22×C4C23×D311yescharacteristic
604C22×C4C23×D312yes—
605C22×C4C23×D311yescharacteristic
606C22×C4C23×D311yescharacteristic
607C22×C4C23×D311yescharacteristic
608C22×C4C23×D311yescharacteristic
609C22×C4C23×D312yes—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—42no—
614C4⋊C4—64no—
615C4⋊C4—64no—
616C4⋊C4—62no—
617C4⋊C4—62no—
618C4⋊C4—64no—
619C4⋊C4—64no—
620C4⋊C4—64no—
621C4⋊C4—122no—
622C4⋊C4—122no—
623C4⋊C4—122no—
624C4⋊C4—122no—
625C4⋊C4—122no—
626C4⋊C4—122no—
627C4⋊C4—122no—
628C4⋊C4—122no—
629C4⋊C4—122no—
630C4⋊C4—122no—
631C4⋊C4—122no—
632C4⋊C4—122no—
633C4⋊C4—122no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—122no—
642C22⋊C4—122no—
643C22⋊C4—122no—
644C22⋊C4—122no—
645C22⋊C4—122no—
646C22⋊C4—122no—
647C22⋊C4—122no—
648C22⋊C4—122no—
649C22⋊C4—122no—
650C22⋊C4—122no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—122no—
656C42—24no—
657C42—64no—
658C42—122no—
659C42—121no—
660C42—121no—
661C42—122no—
662C42—122no—
663C42#23714yes—
664C22×C3—22no—
665C22×C3—24no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—42no—
673C22×C3—41no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3C22×#4111yescharacteristic
682C22×C3C2×H(5,𝔽2)12yes—
683C22×C3C2×2−1+411yescharacteristic
684C22×C3#58512yes—
685C22×C3#58511yescharacteristic
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—24no—
690C3×C4—41no—
691C3×C4—42no—
692C3×C4—41no—
693C3×C4—42no—
694Dic3—42no—
695Dic3—42no—
696Dic3—42no—
697Dic3—42no—
698Dic3—42no—
699Dic3—42no—
700Dic3—42no—
701Dic3—42no—
702C23—21no—
703C23—22no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—21no—
718C23#101012yes—
719C23C24×D311yescharacteristic
720D4—44no—
721D4—48no—
722D4—44no—
723D4—48no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—82no—
765C2×C4—82no—
766C2×C4—84no—
767C2×C4—244no—
768C2×C4C2×#23712yes—
769C2×C4C2×#23712yes—
770C2×C4C2×#23712yes—
771C2×C4#100414yes—
772C2×C3—42no—
773C2×C3—82no—
774C2×C3—81no—
775C2×C3#345511yescharacteristic
776C2×C3#349511yescharacteristic
777C2×C3#350811yescharacteristic
778C2×C3#353512yes—
779C2×C3#353912yes—
780C22—22no—
781C22—24no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—41no—
796C22—42no—
797C22C22×#23711yescharacteristic
798C22C2×#100412yes—
799C22C2×#101011yescharacteristic
800C22#596412yes—
801C22#596411yescharacteristic
802C4—22no—
803C4—22no—
804C4—24no—
805C4—22no—
806C4—42no—
807C4—41no—
808C4—42no—
809C4—41no—
810C4—122no—
811C4—122no—
812C4—122no—
813C4—122no—
814C4—122no—
815C4—122no—
816C4—122no—
817C4—122no—
818C3#4197911yescharacteristic, complemented, Sylow
819C2—42no—
820C2—82no—
821C2—81no—
822C2#8601911yescharacteristic
823C2#8602811yescharacteristic
824C2#8603012yes—
825C2#8605412yes—
826C2#8619011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
Fitting, prime radicalC3×#2397C2
hypercenter#2397D3
hypocenterC3#41979
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2397

Complements

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

NH ≅ G/Ntype
2. #82391C2semidirect
3. #82386C2semidirect
4. #82371C2semidirect
5. #82369C2semidirect
6. #82363C2semidirect
7. #82354C2semidirect
8. #82336C2semidirect
9. #82325C2semidirect
10. #78083C2semidirect
11. #78070C2semidirect
12. #78060C2semidirect
13. #78059C2semidirect
14. #76751C2semidirect
15. #76734C2semidirect
16. #76724C2semidirect
17. #76689C2semidirect
18. #73405C2semidirect
19. #73394C2semidirect
818. C3#41979semidirect

Maximal subgroups

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

subgroupindex
C3×#23972
#823912
#823862
#823712
#823692
#823632
#823542
#823362
#823252
#780832
#780702
#780602
#780592
#767512
#767342
#767242
#766892
#734052
#733942
#419793