Finite Group Databasebeta

← #10968216

Subgroups — #10968216

Order 768.

2930 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#878C211yesmaximal, characteristic, complemented
2C22×#67⋊C4C211yesmaximal, characteristic
3C3×#2315C211yesmaximal, characteristic, complemented
4#82121C211yesmaximal, characteristic
5#82121C211yesmaximal, characteristic
6#82095C211yesmaximal, characteristic, complemented
7C2×#4942C211yesmaximal, characteristic, complemented
8#74655C212yesmaximal, complemented
9#74621C212yesmaximal, complemented
10#74589C212yesmaximal, complemented
11#74502C212yesmaximal, complemented
12#74486C212yesmaximal, complemented
13#74485C212yesmaximal, complemented
14#74457C212yesmaximal, complemented
15#74405C212yesmaximal, complemented
16#73943C214yesmaximal, complemented
17#73889C214yesmaximal, complemented
18#35010—31nomaximal, Sylow
19C23×#67C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C23×Dic6C2211yescharacteristic, complemented
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic, complemented
30C22×Dic3⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2211yescharacteristic, complemented
32C22×Dic3⋊C4C2211yescharacteristic, complemented
33C22×Dic3⋊C4C2212yescomplemented
34C22×C4×Dic3C2211yescharacteristic
35C2×#896C2214yescomplemented
36C2×#67⋊C4—28no—
37C2×#67⋊C4C2212yes—
38C2×#67⋊C4C2212yes—
39C2×#67⋊C4C2212yes—
40C2×#67⋊C4C2212yes—
41C2×#878—28no—
42C2×#878C2212yes—
43C2×#878C2212yes—
44C2×#878C2212yescomplemented
45C2×#878C2212yescomplemented
46C3×#385C2212yes—
47C3×#385C2212yes—
48C3×#385C2212yescomplemented
49C3×#385C2212yescomplemented
50C3×#380C2214yescomplemented
51#5213C2214yes—
52#5213C2212yes—
53#5213C2212yes—
54#5210C2212yes—
55#5210C2212yes—
56C2×C3⋊#95C2212yescomplemented
57#4994C2214yescomplemented
58#4993C2214yescomplemented
59#4989C2214yescomplemented
60#4983C2214yescomplemented
61#4980C2214yescomplemented
62#4979C2214yescomplemented
63#4976C2214yescomplemented
64#4958C2214yes—
65#4958C2212yes—
66#4958C2212yes—
67#4955C2212yes—
68#4955C2212yes—
69#4946C2212yescomplemented
70#4946C2212yescomplemented
71#4943C2212yes—
72#4943C2212yes—
73#4942C2212yes—
74#4942C2212yes—
75#4942C2214yescomplemented
76#4942C2212yescomplemented
77#4942C2212yescomplemented
78#4676C2214yescomplemented
79#4673C2214yescomplemented
80#4668C2214yescomplemented
81#4667C2214yescomplemented
82#4658C2214yescomplemented
83#4657C2214yescomplemented
84#4652C2214yescomplemented
85#4646C2214yescomplemented
86C22×C22⋊Q8—31no—
87C22×C4×D4—31no—
88#2855—32no—
89#2848—32no—
90#2627—32no—
91#2626—32no—
92#2579—32no—
93#2579—32no—
94#2564—34no—
95#2487—32no—
96#2417—34no—
97#2409—32no—
98#2315—31no—
99#2315D311yescharacteristic, complemented
100#2308—31no—
101#2308—31no—
102C2×#380—31no—
103C25×C3C2311yescharacteristic
104C24×D3C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2312yes—
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C22×#67—24no—
111C22×#67—24no—
112C22×#67Q818yescomplemented
113C22×#67C2312yes—
114C22×#67C2312yes—
115C23×Dic3—44no—
116C23×Dic3D418yes—
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2312yes—
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C22×C4×D3—24no—
128C22×C4×D3—44no—
129C22×C4×D3C2312yes—
130C22×C4×D3C2312yes—
131C22×Dic6—24no—
132C22×Dic6—44no—
133C22×Dic6C2312yes—
134C22×Dic6C2312yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C4⋊C4C2314yes—
137C2×C3×C22⋊C4—24no—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4C2312yes—
141C2×C3×C22⋊C4C2312yes—
142C2×C3×C22⋊C4C2312yes—
143C2×C3×C22⋊C4C2312yes—
144C2×C3×C22⋊C4C2312yes—
145C2×C3×C22⋊C4C2312yes—
146C2×#217—24no—
147C2×#217—24no—
148C2×#217C2312yes—
149C2×#217C2312yes—
150C2×#217C2312yes—
151C2×#217C2312yes—
152C2×(C2×D3)⋊C4—24no—
153C2×(C2×D3)⋊C4C2312yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×C4⋊Dic3—24no—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2312yes—
162C2×Dic3⋊C4—24no—
163C2×Dic3⋊C4—24no—
164C2×Dic3⋊C4—24no—
165C2×Dic3⋊C4—44no—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2312yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2312yes—
170C2×Dic3⋊C4C2312yes—
171C2×Dic3⋊C4C2312yes—
172C2×Dic3⋊C4C2312yes—
173C2×Dic3⋊C4C2314yes—
174C2×Dic3⋊C4C2314yes—
175C2×Dic3⋊C4C2314yes—
176C2×C4×Dic3—24no—
177C2×C4×Dic3C2312yes—
178C2×C4×Dic3C2312yes—
179#896—48no—
180#67⋊C4—28no—
181#67⋊C4—28no—
182#67⋊C4—28no—
183#67⋊C4—28no—
184#878—28no—
185#878—28no—
186#878—28no—
187#878—28no—
188C3×#95C2314yes—
189C3×#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C3⋊#95C2314yes—
195C3⋊#95C2314yes—
196C3⋊#95C2314yes—
197C3⋊#95C2314yes—
198C23×Q8—31no—
199C23×D4—31no—
200C24×C4—31no—
201C24×C4—31no—
202C2×C22⋊Q8—34no—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8—32no—
207C2×C22⋊Q8—68no—
208C2×C4×D4—32no—
209C2×C4×D4—32no—
210C2×C4×D4—32no—
211C2×C4×D4—32no—
212C2×C4×D4—68no—
213C22×C4⋊C4—31no—
214C22×C4⋊C4—31no—
215C22×C4⋊C4—31no—
216C22×C4⋊C4—31no—
217C22×C4⋊C4—32no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4C2×D311yescharacteristic
222C22×C22⋊C4C2×D311yescharacteristic
223C22×C22⋊C4C2×D311yescharacteristic
224C22×C42—31no—
225#400—34no—
226#399—34no—
227#398—34no—
228#398—34no—
229#396—34no—
230#396—34no—
231#395—34no—
232#393—34no—
233#391—34no—
234#389—34no—
235#387—34no—
236#387—34no—
237#386—34no—
238#386—32no—
239#386—32no—
240#386—34no—
241#386—32no—
242#386—32no—
243#385—32no—
244#385—32no—
245#385—34no—
246#385—32no—
247#385—32no—
248#385—34no—
249#385C2×D312yes—
250#385C2×D312yes—
251#385C2×D312yescomplemented
252#385C2×D312yescomplemented
253#381—32no—
254#381—32no—
255#380—34no—
256#380—32no—
257#380—32no—
258#380—32no—
259#380—32no—
260#380—34no—
261#380C2×D314yescomplemented
262#379—32no—
263#379—32no—
264C2×#95—32no—
265C24×C3—42no—
266C24×C3—42no—
267C24×C3C2×D414yes—
268C24×C3C2×Q814yes—
269C24×C3#4114yes—
270C24×C3C2411yescharacteristic
271C24×C3C2411yescharacteristic
272C24×C3C2411yescharacteristic
273C23×D3—22no—
274C23×D3—22no—
275C23×D3—42no—
276C23×D3—42no—
277C23×D3C2×Q814yescomplemented
278C23×D3C2412yes—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—24no—
284C22×C3×C4—42no—
285C22×C3×C4—42no—
286C22×C3×C4—42no—
287C22×C3×C4—42no—
288C22×C3×C4—42no—
289C22×C3×C4—42no—
290C22×C3×C4C2414yes—
291C22×C3×C4C2412yes—
292C22×C3×C4C2412yes—
293C22×C3×C4C2412yes—
294C22×C3×C4C2412yes—
295C2×#67—232no—
296C2×#67—24no—
297C2×#67—24no—
298C2×#67—24no—
299C2×#67—24no—
300C2×#67C2×Q818yes—
301C2×#67C2×Q818yescomplemented
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—24no—
305C22×Dic3—24no—
306C22×Dic3—24no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—24no—
310C22×Dic3—416no—
311C22×Dic3—42no—
312C22×Dic3—42no—
313C22×Dic3—42no—
314C22×Dic3—42no—
315C22×Dic3—42no—
316C22×Dic3—42no—
317C22×Dic3—42no—
318C22×Dic3C2×D414yes—
319C22×Dic3C2×D414yes—
320C22×Dic3C2×D414yes—
321C22×Dic3C2×D414yes—
322C22×Dic3C2×D414yes—
323C22×Dic3C2×D414yes—
324C22×Dic3C2×Q814yescomplemented
325C22×Dic3C2414yes—
326C22×Dic3C2412yes—
327C22×Dic3C2412yes—
328C22×Dic3C2411yescharacteristic
329C22×Dic3C2411yescharacteristic
330C22×Dic3C2411yescharacteristic
331C22×Dic3C2412yes—
332C22×Dic3C2411yescharacteristic
333C2×C4×D3—24no—
334C2×C4×D3—24no—
335C2×C4×D3—28no—
336C2×C4×D3—44no—
337C2×C4×D3—416no—
338C2×Dic6—24no—
339C2×Dic6—24no—
340C2×Dic6—28no—
341C2×Dic6—44no—
342C2×Dic6—416no—
343C3×C4⋊C4—44no—
344C3×C4⋊C4—44no—
345C3×C22⋊C4—24no—
346C3×C22⋊C4—24no—
347C3×C22⋊C4—24no—
348C3×C22⋊C4—24no—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351#217—24no—
352#217—24no—
353#217—24no—
354#217—24no—
355(C2×D3)⋊C4—24no—
356(C2×D3)⋊C4—24no—
357(C2×D3)⋊C4—44no—
358(C2×D3)⋊C4—44no—
359(C2×D3)⋊C4—44no—
360(C2×D3)⋊C4—44no—
361C4⋊Dic3—24no—
362C4⋊Dic3—24no—
363Dic3⋊C4—24no—
364Dic3⋊C4—24no—
365Dic3⋊C4—24no—
366Dic3⋊C4—24no—
367Dic3⋊C4—24no—
368Dic3⋊C4—24no—
369Dic3⋊C4—28no—
370Dic3⋊C4—44no—
371Dic3⋊C4—44no—
372Dic3⋊C4—44no—
373C4×Dic3—24no—
374C4×Dic3—24no—
375C25—31no—
376C25C22×D311yescharacteristic
377C22×Q8—32no—
378C22×Q8—32no—
379C22×Q8—64no—
380C22×Q8—124no—
381C22×D4—38no—
382C22×D4—32no—
383C22×D4—32no—
384C22×D4—64no—
385C22×D4—64no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—38no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—32no—
397C23×C4—32no—
398C23×C4—32no—
399C23×C4—64no—
400C23×C4—124no—
401C23×C4—124no—
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D312yes—
407C22⋊Q8—68no—
408C22⋊Q8—68no—
409C22⋊Q8—68no—
410C22⋊Q8—68no—
411C22⋊Q8—128no—
412C4×D4—68no—
413C4×D4—68no—
414C4×D4—68no—
415C4×D4—68no—
416C2×C4⋊C4—32no—
417C2×C4⋊C4—32no—
418C2×C4⋊C4—32no—
419C2×C4⋊C4—32no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—32no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—34no—
425C2×C4⋊C4—34no—
426C2×C4⋊C4—34no—
427C2×C4⋊C4—34no—
428C2×C4⋊C4—64no—
429C2×C4⋊C4—64no—
430C2×C4⋊C4—64no—
431C2×C4⋊C4—64no—
432C2×C4⋊C4—124no—
433C2×C4⋊C4C22×D314yes—
434C2×C4⋊C4C22×D314yes—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—32no—
442C2×C22⋊C4—32no—
443C2×C22⋊C4—32no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—64no—
449C2×C22⋊C4—64no—
450C2×C22⋊C4—64no—
451C2×C22⋊C4C22×D312yes—
452C2×C22⋊C4C22×D312yes—
453C2×C22⋊C4C22×D312yes—
454C2×C22⋊C4C22×D312yes—
455C2×C22⋊C4C22×D312yes—
456C2×C22⋊C4C22×D312yes—
457C2×C42—32no—
458C2×C42—32no—
459C2×C42—64no—
460#95—34no—
461#95—34no—
462#95—34no—
463#95—34no—
464#95—34no—
465#95—34no—
466#95—34no—
467#95—34no—
468#95C22×D314yes—
469#95C22×D314yes—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—44no—
477C23×C3—44no—
478C23×C3—48no—
479C23×C3—48no—
480C23×C3C22⋊Q8116yescomplemented
481C23×C3C22×D412yes—
482C23×C3C22×D412yes—
483C23×C3C22×D412yes—
484C23×C3C22×Q812yes—
485C23×C3C22×Q812yes—
486C23×C3C22×Q812yes—
487C23×C3C2×#4112yes—
488C23×C3C2×#4112yes—
489C23×C3C2×#4112yes—
490C23×C3C2511yescharacteristic
491C22×D3—28no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—24no—
495C22×D3—24no—
496C22×D3—48no—
497C22×D3—44no—
498C22×D3—44no—
499C22×D3—48no—
500C22×D3C22×Q814yes—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—24no—
506C2×C3×C4—24no—
507C2×C3×C4—24no—
508C2×C3×C4—24no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—24no—
512C2×C3×C4—44no—
513C2×C3×C4—44no—
514C2×C3×C4—44no—
515C2×C3×C4—44no—
516C2×C3×C4—84no—
517#67—216no—
518#67—216no—
519C2×Dic3—28no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—28no—
526C2×Dic3—28no—
527C2×Dic3—28no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—24no—
531C2×Dic3—24no—
532C2×Dic3—24no—
533C2×Dic3—24no—
534C2×Dic3—24no—
535C2×Dic3—44no—
536C2×Dic3—44no—
537C2×Dic3—44no—
538C2×Dic3—44no—
539C2×Dic3—44no—
540C2×Dic3—84no—
541C2×Dic3C22×D412yes—
542C2×Dic3C22×D412yes—
543C2×Dic3C22×D412yes—
544C2×Dic3C22×D412yes—
545C2×Dic3C22×Q814yes—
546C2×Dic3H(5,𝔽2)14yes—
547C4×D3—48no—
548C4×D3—48no—
549Dic6—48no—
550Dic6—48no—
551C24—32no—
552C24—34no—
553C24—42no—
554C24—42no—
555C24—62no—
556C24—62no—
557C24—122no—
558C24—122no—
559C24#23514yes—
560C24D3×D414yes—
561C24D3×Q814yes—
562C24C23×D311yescharacteristic
563C24C23×D311yescharacteristic
564C24C23×D311yescharacteristic
565C2×Q8—64no—
566C2×Q8—64no—
567C2×Q8—68no—
568C2×Q8—124no—
569C2×Q8—1216no—
570C2×D4—38no—
571C2×D4—38no—
572C2×D4—632no—
573C2×D4—64no—
574C2×D4—64no—
575C2×D4—64no—
576C2×D4—64no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—31no—
583C22×C4—34no—
584C22×C4—34no—
585C22×C4—34no—
586C22×C4—34no—
587C22×C4—32no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—34no—
592C22×C4—34no—
593C22×C4—34no—
594C22×C4—34no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4—68no—
606C22×C4—64no—
607C22×C4—64no—
608C22×C4—64no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—64no—
614C22×C4—124no—
615C22×C4—1216no—
616C22×C4—1216no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4—122no—
622C22×C4—122no—
623C22×C4—122no—
624C22×C4C23×D314yes—
625C22×C4C23×D312yes—
626C22×C4C23×D312yes—
627C22×C4C23×D312yes—
628C22×C4C23×D312yes—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—64no—
632C4⋊C4—64no—
633C4⋊C4—64no—
634C4⋊C4—64no—
635C4⋊C4—64no—
636C4⋊C4—64no—
637C4⋊C4—64no—
638C4⋊C4—64no—
639C4⋊C4—68no—
640C4⋊C4—124no—
641C4⋊C4—124no—
642C4⋊C4—124no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—64no—
650C22⋊C4—64no—
651C22⋊C4—64no—
652C22⋊C4—64no—
653C22⋊C4—64no—
654C22⋊C4—64no—
655C22⋊C4—124no—
656C22⋊C4—124no—
657C22⋊C4—124no—
658C22⋊C4—124no—
659C42—64no—
660C42—64no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—24no—
668C22×C3—24no—
669C22×C3—24no—
670C22×C3—24no—
671C22×C3—24no—
672C22×C3—24no—
673C22×C3—416no—
674C22×C3C2×C22⋊Q814yes—
675C22×C3C2×C22⋊Q814yes—
676C22×C3C2×C22⋊Q814yes—
677C22×C3C23×D411yescharacteristic
678C22×C3C23×Q811yescharacteristic
679C22×C3C22×#4111yescharacteristic
680C22×C3C2×H(5,𝔽2)12yes—
681C22×C3#58512yes—
682C2×D3—24no—
683C2×D3—28no—
684C2×D3—416no—
685C2×D3—42no—
686C2×D3—42no—
687C2×D3—44no—
688C3×C4—42no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4—44no—
693Dic3—24no—
694Dic3—22no—
695Dic3—22no—
696Dic3—22no—
697Dic3—42no—
698Dic3—42no—
699Dic3—44no—
700Dic3#53414yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—34no—
708C23—44no—
709C23—48no—
710C23—44no—
711C23—48no—
712C23—62no—
713C23—62no—
714C23—64no—
715C23—64no—
716C23—68no—
717C23—128no—
718C23—124no—
719C23—124no—
720C23—128no—
721C23#896116yescomplemented
722C23C2×#23512yes—
723C23C2×#23512yes—
724C23C2×#23512yes—
725C23C2×D3×D412yes—
726C23C2×D3×D412yes—
727C23C2×D3×D412yes—
728C23C2×D3×Q812yes—
729C23C2×D3×Q812yes—
730C23C2×D3×Q812yes—
731C23C24×D311yescharacteristic
732Q8—128no—
733Q8—128no—
734D4—616no—
735D4—616no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—32no—
748C2×C4—34no—
749C2×C4—32no—
750C2×C4—32no—
751C2×C4—32no—
752C2×C4—34no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—68no—
758C2×C4—68no—
759C2×C4—68no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—68no—
766C2×C4—64no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—64no—
770C2×C4—64no—
771C2×C4—64no—
772C2×C4—64no—
773C2×C4—84no—
774C2×C4—128no—
775C2×C4—128no—
776C2×C4—124no—
777C2×C4—124no—
778C2×C4—124no—
779C2×C4—124no—
780C2×C4—124no—
781C2×C4—244no—
782C2×C3—24no—
783C2×C3—24no—
784C2×C3—24no—
785C2×C3C22×C22⋊Q811yescharacteristic
786C2×C3C2×#53411yescharacteristic
787C2×C3#344911yescharacteristic
788C2×C3#350112yes—
789C2×C3#350512yes—
790D3—44no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—416no—
804C22—68no—
805C22—64no—
806C22—1216no—
807C22—122no—
808C22—122no—
809C22—124no—
810C22C2×#89614yes—
811C22C2×#89614yes—
812C22C2×#89614yes—
813C22C22×#23511yescharacteristic
814C22C22×D3×D411yescharacteristic
815C22C22×D3×Q811yescharacteristic
816C22D3×H(5,𝔽2)12yes—
817C22#596612yes—
818C4—34no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—44no—
824C4—62no—
825C4—62no—
826C4—62no—
827C4—64no—
828C4—122no—
829C4—122no—
830C4—124no—
831C3#3501011yescharacteristic, complemented, Sylow
832C2—24no—
833C2—24no—
834C2—24no—
835C2—124no—
836C2C22×#89611yescharacteristic
837C2#8586112yes—
838C2#8629411yescharacteristic
839C2D3×#53411yescharacteristic
840C2#8657412yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2315C2
prime radicalC23×#67C22
hypercenter#2315D3
hypocenterC3#35010
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
1. C22×#878C2semidirect
3. C3×#2315C2semidirect
6. #82095C2semidirect
7. C2×#4942C2semidirect
8. #74655C2semidirect
9. #74621C2semidirect
10. #74589C2semidirect
11. #74502C2semidirect
12. #74486C2semidirect
13. #74485C2semidirect
14. #74457C2semidirect
15. #74405C2semidirect
16. #73943C2semidirect
17. #73889C2semidirect
22. C23×Dic6C22semidirect
29. C22×C4⋊Dic3C22semidirect
31. C22×Dic3⋊C4C22semidirect
32. C22×Dic3⋊C4C22semidirect
33. C22×Dic3⋊C4C22semidirect
35. C2×#896C22semidirect
44. C2×#878C22semidirect
45. C2×#878C22semidirect
48. C3×#385C22semidirect
49. C3×#385C22semidirect
50. C3×#380C22semidirect
56. C2×C3⋊#95C22semidirect
57. #4994C22semidirect
58. #4993C22semidirect
59. #4989C22semidirect
60. #4983C22semidirect
61. #4980C22semidirect
62. #4979C22semidirect
63. #4976C22semidirect
69. #4946C22semidirect
70. #4946C22semidirect
75. #4942C22semidirect
76. #4942C22semidirect
77. #4942C22semidirect
78. #4676C22semidirect
79. #4673C22semidirect
80. #4668C22semidirect
81. #4667C22semidirect
82. #4658C22semidirect
83. #4657C22semidirect
84. #4652C22semidirect
85. #4646C22semidirect
99. #2315D3semidirect
112. C22×#67Q8semidirect
251. #385C2×D3semidirect
252. #385C2×D3semidirect
261. #380C2×D3semidirect
277. C23×D3C2×Q8semidirect
301. C2×#67C2×Q8semidirect
324. C22×Dic3C2×Q8semidirect
480. C23×C3C22⋊Q8semidirect
721. C23#896semidirect
831. C3#35010semidirect

Maximal subgroups

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

subgroupindex
C22×#8782
C22×#67⋊C42
C3×#23152
#821212
#820952
C2×#49422
#746552
#746212
#745892
#745022
#744862
#744852
#744572
#744052
#739432
#738892
#350103