Finite Group Databasebeta

← #10845934

Subgroups — #10845934

Order 768.

1154 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5171C211yesmaximal, characteristic, complemented
2C2×#5163C211yesmaximal, characteristic, complemented
3#82778C211yesmaximal, characteristic, complemented
4C2×#5048C211yesmaximal, characteristic, complemented
5#82669C211yesmaximal, characteristic
6C2×#67⋊C8C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#71681C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10Dic3×#103C211yesmaximal, characteristic, complemented
11#70207C211yesmaximal, characteristic, complemented
12#70157C211yesmaximal, characteristic, complemented
13#69935C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68796C211yesmaximal, characteristic, complemented
16#25387—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#940—21no—
24C2×#940C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C2×#835C2211yescharacteristic
35#5223—21no—
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38#5212C2211yescharacteristic
39#5171—24no—
40#5163—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#817C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic
46C2×C8×Dic3C2211yescharacteristic
47#5048—24no—
48#4994—21no—
49#4987C2211yescharacteristic
50#4976—21no—
51#4975C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4960—21no—
56#4957—21no—
57#4957—21no—
58#4948—21no—
59#67⋊C8—24no—
60C3×#340C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#465—31no—
65C2×#465—31no—
66C2×#460—31no—
67C2×C8×D4—31no—
68#2541—31no—
69#2538—31no—
70#2034—31no—
71#2034—31no—
72#2000—31no—
73#2000D311yescharacteristic, complemented
74#1957—31no—
75#1948—31no—
76#1893—31no—
77#1893—31no—
78C4×#103—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×#67D411yescharacteristic
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—41no—
98C3×#121—22no—
99C3×#121—41no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217D411yescharacteristic
108#946—22no—
109#946—41no—
110Q8×Dic3—22no—
111Q8×Dic3—22no—
112C2×#215—22no—
113C2×#215—22no—
114C2×#215—41no—
115#940—22no—
116#940—22no—
117#940—44no—
118#938—22no—
119#938—41no—
120#930—22no—
121#930—41no—
122C4×#67—22no—
123C4×#67—22no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4D411yescharacteristic
137C2×C4×Dic3—21no—
138C2×C4×Dic3—21no—
139C2×C4×Dic3C2311yescharacteristic
140C22×C3⋊C8—22no—
141C22×C3⋊C8—22no—
142C22×C3⋊C8—41no—
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D3×C8—22no—
146C2×D3×C8—22no—
147C2×D3×C8—41no—
148#895—22no—
149#895—41no—
150C3×#103—22no—
151C3×#102—41no—
152C3×C22⋊C8—22no—
153#835D414yescomplemented
154#832—22no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821—41no—
161(C2×D3)⋊C8—22no—
162#817—22no—
163Dic3⋊C8D414yescomplemented
164C8×Dic3—22no—
165#809—22no—
166#808—22no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169C23×C8—31no—
170C23×C8—31no—
171C2×#127—31no—
172C2×#127—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181#465—64no—
182#465—64no—
183#460—64no—
184C8×D4—64no—
185C2×#106—31no—
186C2×#106—31no—
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8C2×D311yescharacteristic
198C2×C4×C8—31no—
199#396—61no—
200#396—61no—
201#392—61no—
202#392—61no—
203#390—61no—
204#390—61no—
205#389—61no—
206#384—31no—
207#380—31no—
208#380—31no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C23×D3—21no—
217C23×D3C2×D411yescharacteristic
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—81no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×#67—22no—
245C2×#67—22no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—81no—
255C2×#67—81no—
256C2×#67—81no—
257C2×#67—81no—
258C2×#67SD1614yescomplemented
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12—81no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C3×SD16—44no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8C2×D412yes—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—42no—
291C3×C4⋊C4#4112yes—
292C3×C22⋊C4—42no—
293C3×C22⋊C4—42no—
294#217—22no—
295#217—42no—
296#217—81no—
297#215—44no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—81no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—42no—
309C4⋊Dic3C2×D412yes—
310Dic3⋊C4—22no—
311Dic3⋊C4—42no—
312Dic3⋊C4—42no—
313Dic3⋊C4—81no—
314C4×Dic3—42no—
315C4×Dic3—42no—
316C4×Dic3C2×D412yes—
317C4×Dic3#4112yes—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—44no—
323C2×C3⋊C8C2×D412yes—
324C2×C3⋊C8C2×D412yes—
325D3×C8—44no—
326C22×Q8C22×D311yescharacteristic
327C22×D4—21no—
328C22×D4—31no—
329C22×D4—31no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4—61no—
333C22×D4—61no—
334C22×D4—61no—
335C22×D4C22×D311yescharacteristic
336C23×C4—31no—
337C23×C4C22×D311yescharacteristic
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—41no—
341C2×SD16—62no—
342C2×SD16—62no—
343C2×SD16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—62no—
347C22×C8—62no—
348C22×C8—62no—
349C22×C8—62no—
350C22×C8—121no—
351C22×C8—121no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#127—62no—
355#127—62no—
356#127—124no—
357C22⋊Q8—22no—
358C22⋊Q8—41no—
359C22⋊Q8—62no—
360C22⋊Q8—121no—
361#121—22no—
362#121—41no—
363#121—62no—
364#121—62no—
365#121—62no—
366#121—121no—
367#121—121no—
368#121—121no—
369C4×Q8—62no—
370C4×Q8—62no—
371C4×D4—62no—
372C4×D4—62no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C42—31no—
395C2×C42—61no—
396C2×C42—61no—
397#106—62no—
398#106—62no—
399C4⋊C8—34no—
400#103—22no—
401#103—34no—
402#102—41no—
403#102—62no—
404#102—62no—
405#102—62no—
406#102—62no—
407#102—121no—
408C22⋊C8—22no—
409C22⋊C8—62no—
410C4×C8—62no—
411#95—61no—
412#95—61no—
413#95—61no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3C2×SD1612yes—
428C23×C3C22×D411yescharacteristic
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3C2×SD1612yes—
443C3×Q8—22no—
444C3×Q8—22no—
445C3×Q8—41no—
446C3×Q8—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—84no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473C2×C3×C4H(5,𝔽2)11yescharacteristic
474#67—28no—
475#67—84no—
476#67—84no—
477#67—84no—
478#67—84no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3#12112yes—
494C2×Dic3#12112yes—
495C2×Dic3C2×SD1612yes—
496C2×Dic3#13512yes—
497D12—41no—
498D12—41no—
499D12—41no—
500D12—41no—
501D12—84no—
502C4×D3—41no—
503C4×D3—41no—
504C4×D3—41no—
505C4×D3—41no—
506C3×C8—22no—
507C3×C8—41no—
508C3⋊C8—22no—
509C3⋊C8—22no—
510C24—21no—
511C24—31no—
512C24—61no—
513C24D3×D411yescharacteristic
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8D3×D412yes—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—34no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—62no—
530C2×D4—62no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—81no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—241no—
549C2×D4—241no—
550C2×D4—241no—
551C2×D4—241no—
552C2×D4—241no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4D3×D411yescharacteristic
575C22×C4C23×D311yescharacteristic
576SD16—44no—
577SD16—124no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—32no—
584C2×C8—32no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8—61no—
589C2×C8—124no—
590C2×C8—124no—
591C2×C8D3×D412yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—32no—
596C4⋊C4—42no—
597C4⋊C4—62no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—122no—
604C4⋊C4—122no—
605C4⋊C4—122no—
606C4⋊C4—241no—
607C4⋊C4#23712yes—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—62no—
611C22⋊C4—62no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C22⋊C4—122no—
615C22⋊C4—122no—
616C22⋊C4—241no—
617C22⋊C4—241no—
618C42—32no—
619C42—32no—
620C42—122no—
621C42—122no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3C2×#12111yescharacteristic
637C22×C3D4211yescharacteristic
638C22×C3#54611yescharacteristic
639C22×C3C22×SD1611yescharacteristic
640C22×C3C2×#13511yescharacteristic
641C22×C3#57611yescharacteristic
642C22×C3#57711yescharacteristic
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—81no—
651C2×D3—81no—
652C2×D3—81no—
653C2×D3—81no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C3×C4—41no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—81no—
661C3×C4#53211yescharacteristic
662C3×C4#54011yescharacteristic
663C3×C4D4211yescharacteristic
664C3×C4#55011yescharacteristic
665Dic3—22no—
666Dic3—41no—
667Dic3—42no—
668Dic3—81no—
669Dic3—81no—
670Dic3#46514yescomplemented
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—32no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23D3×SD1612yes—
699C23C2×D3×D411yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—68no—
709D4—84no—
710D4—121no—
711D4—121no—
712D4—121no—
713D4—121no—
714D4—244no—
715D4—244no—
716D4—244no—
717D4—244no—
718D4—244no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—62no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×#23711yescharacteristic
760C2×C4#100411yescharacteristic
761C2×C4#100411yescharacteristic
762C2×C4D3×#4111yescharacteristic
763C8—22no—
764C8—41no—
765C8—62no—
766C8—62no—
767C2×C3—42no—
768C2×C3—161no—
769C2×C3#242811yescharacteristic
770C2×C3C2×#46511yescharacteristic
771C2×C3#306211yescharacteristic
772C2×C3D4×SD1611yescharacteristic
773C2×C3#328711yescharacteristic
774C2×C3#329511yescharacteristic
775C2×C3#330411yescharacteristic
776D3—42no—
777D3—161no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22—241no—
803C22—241no—
804C22—241no—
805C22—241no—
806C22#559011yescharacteristic
807C22#559111yescharacteristic
808C22D3×#12111yescharacteristic
809C22C2×D3×SD1611yescharacteristic
810C22D3×#13511yescharacteristic
811C22#577411yescharacteristic
812C22#577811yescharacteristic
813C4—34no—
814C4—42no—
815C4—41no—
816C4—42no—
817C4—62no—
818C4—81no—
819C4—121no—
820C4—122no—
821C4—241no—
822C4—241no—
823C4#559011yescharacteristic
824C4#559611yescharacteristic
825C4#561511yescharacteristic
826C4#571811yescharacteristic
827C3#2538711yescharacteristic, complemented, Sylow
828C2—42no—
829C2—122no—
830C2—161no—
831C2—481no—
832C2#7667111yescharacteristic
833C2#8006311yescharacteristic
834C2#8013111yescharacteristic
835C2#8015811yescharacteristic
836C2#8024911yescharacteristic
837C2D3×#46511yescharacteristic
838C2#8080911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radical#82669C2
hypercenter#2000D3
hypocenterC3#25387
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5171C2semidirect
2. C2×#5163C2semidirect
3. #82778C2semidirect
4. C2×#5048C2semidirect
6. C2×#67⋊C8C2semidirect
7. C3×#2000C2semidirect
8. #71681C2semidirect
9. #70272C2semidirect
10. Dic3×#103C2semidirect
11. #70207C2semidirect
12. #70157C2semidirect
13. #69935C2semidirect
14. #68883C2semidirect
15. #68796C2semidirect
73. #2000D3semidirect
153. #835D4semidirect
163. Dic3⋊C8D4semidirect
258. C2×#67SD16semidirect
670. Dic3#465semidirect
827. C3#25387semidirect

Maximal subgroups

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

subgroupindex
C2×#51712
C2×#51632
#827782
C2×#50482
#826692
C2×#67⋊C82
C3×#20002
#716812
#702722
Dic3×#1032
#702072
#701572
#699352
#688832
#687962
#253873