Finite Group Databasebeta

← #10845940

Subgroups — #10845940

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×#5114C211yesmaximal, characteristic, complemented
2C2×C8×#67C211yesmaximal, characteristic, complemented
3#82669C211yesmaximal, characteristic
4C2×#4762C211yesmaximal, characteristic, complemented
5C2×#4778C211yesmaximal, characteristic, complemented
6#73936C211yesmaximal, characteristic, complemented
7C3×#1893C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#70176C211yesmaximal, characteristic, complemented
10#70157C211yesmaximal, characteristic, complemented
11#69524C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68883C211yesmaximal, characteristic, complemented
14#68796C211yesmaximal, characteristic, complemented
15#68781C211yesmaximal, characteristic, complemented
16#25387—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×#940—21no—
20C2×#940C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C22×#204C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#887C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C3×#380C2211yescharacteristic
34#5223—21no—
35C2×#832C2211yescharacteristic
36C2×#830C2211yescharacteristic
37#5114—24no—
38C2×#821C2211yescharacteristic
39C8×#67—24no—
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#817C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×Dic3⋊C8C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45#4987C2211yescharacteristic
46#4975C2211yescharacteristic
47Dic3×C4⋊C4C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#808C2211yescharacteristic
52#4960—21no—
53#4957—21no—
54#4957—21no—
55#4948—21no—
56#4778—24no—
57#4762—24no—
58#4676—21no—
59#4647—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
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#2000—31no—
74#1957—31no—
75#1948—31no—
76#1893—31no—
77#1893D311yescharacteristic, complemented
78C4×#103—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67D411yescharacteristic
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×Dic6C2311yescharacteristic
91C22×C3×C8—22no—
92C22×C3×C8—22no—
93C22×C3×C8—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×#121—22no—
97C3×#121—41no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217D411yescharacteristic
106#940—22no—
107#940—22no—
108#940—44no—
109#938—22no—
110#938—41no—
111C2×#214—22no—
112C2×#214—22no—
113C2×#214—41no—
114#930—22no—
115#930—41no—
116C4×#67—22no—
117C4×#67—22no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126#924—22no—
127#924—41no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4D411yescharacteristic
133C2×C4×Dic3—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C2×#204—22no—
139C2×#204—22no—
140C2×#204—41no—
141C2×D3×C8—22no—
142C2×D3×C8—22no—
143C2×D3×C8—41no—
144#897—22no—
145#897—41no—
146#895—22no—
147#895—41no—
148#887—22no—
149#887—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×#95—21no—
153#832—41no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—22no—
157#821—22no—
158(C2×D3)⋊C8—22no—
159#817—22no—
160#816D414yescomplemented
161Dic3⋊C8D414yescomplemented
162C8×Dic3—22no—
163#810—22no—
164#809—22no—
165#809—41no—
166#808—22no—
167C22×SD16—31no—
168C22×SD16—31no—
169C23×C8—31no—
170C23×C8C2×D311yescharacteristic
171C2×#127—31no—
172C2×#127—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
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×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
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#380C2×D311yescharacteristic
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340C2×D311yescharacteristic
213#340C2×D311yescharacteristic
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C23×D3—21no—
217C23×D3C2×D411yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—42no—
225C2×C3×D4—42no—
226C2×C3×D4—81no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—22no—
239C2×#67—22no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—81no—
249C2×#67—81no—
250C2×#67—81no—
251C2×#67—81no—
252C2×#67SD1614yescomplemented
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—42no—
266C2×D12—42no—
267C2×D12—81no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6C2×D412yes—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—44no—
285C2×C3×C8C2×D412yes—
286C2×C3×C8C2×D412yes—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4#4112yes—
293C3×C22⋊C4—42no—
294C3×C22⋊C4—81no—
295#217—22no—
296#217—42no—
297#217—42no—
298#214—44no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—81no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—42no—
308C4⋊Dic3C2×D412yes—
309Dic3⋊C4—22no—
310Dic3⋊C4—42no—
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—21no—
323C2×C3⋊C8C2×D412yes—
324#204—44no—
325D3×C8—44no—
326C22×Q8—31no—
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—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—62no—
342C2×SD16—121no—
343C2×SD16—121no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—41no—
349C22×C8—62no—
350C22×C8—62no—
351C22×C8—121no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#127—62no—
355#127—62no—
356#127—124no—
357C22⋊Q8—62no—
358C22⋊Q8—62no—
359C22⋊Q8—121no—
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—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4C22×D311yescharacteristic
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—34no—
401#103—62no—
402#102—22no—
403#102—22no—
404#102—62no—
405#102—62no—
406#102—121no—
407#102—121no—
408C22⋊C8—62no—
409C22⋊C8—62no—
410C4×C8—62no—
411#95—21no—
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×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—84no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
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×C4C22×D411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470#67—28no—
471#67—84no—
472#67—84no—
473#67—84no—
474#67—84no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3#12112yes—
490C2×Dic3#12112yes—
491C2×Dic3C2×SD1612yes—
492C2×Dic3#13512yes—
493D12—41no—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—84no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501C4×D3—41no—
502Dic6—22no—
503Dic6—22no—
504Dic6—41no—
505Dic6—41no—
506C3×C8—22no—
507C3×C8—22no—
508C3⋊C8—22no—
509C3⋊C8—41no—
510C24—21no—
511C24—31no—
512C24—61no—
513C24D3×D411yescharacteristic
514C2×Q8—32no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—61no—
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—124no—
577SD16—124no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—32no—
583C2×C8—44no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8—61no—
589C2×C8—124no—
590C2×C8D3×D412yes—
591C2×C8D3×D412yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—32no—
598C4⋊C4—62no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—122no—
603C4⋊C4—122no—
604C4⋊C4—122no—
605C4⋊C4—122no—
606C4⋊C4—241no—
607C4⋊C4#23512yes—
608C22⋊C4—42no—
609C22⋊C4—62no—
610C22⋊C4—62no—
611C22⋊C4—81no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C22⋊C4—122no—
615C22⋊C4—122no—
616C22⋊C4—122no—
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—81no—
660C3×C4—81no—
661C3×C4#53211yescharacteristic
662C3×C4#54011yescharacteristic
663C3×C4D4211yescharacteristic
664C3×C4#55011yescharacteristic
665Dic3—22no—
666Dic3—42no—
667Dic3—41no—
668Dic3—42no—
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—62no—
701Q8—62no—
702Q8—121no—
703Q8—121no—
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—21no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—41no—
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—61no—
742C2×C4—61no—
743C2×C4—62no—
744C2×C4—61no—
745C2×C4—62no—
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×#23511yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×D3×D411yescharacteristic
760C2×C4#100411yescharacteristic
761C2×C4D3×#4111yescharacteristic
762C2×C4#100911yescharacteristic
763C8—22no—
764C8—22no—
765C8—62no—
766C8—121no—
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#549011yescharacteristic
807C22D3×#12111yescharacteristic
808C22#560911yescharacteristic
809C22#575711yescharacteristic
810C22C2×D3×SD1611yescharacteristic
811C22D3×#13511yescharacteristic
812C22#577011yescharacteristic
813C4—34no—
814C4—42no—
815C4—41no—
816C4—62no—
817C4—81no—
818C4—81no—
819C4—122no—
820C4—121no—
821C4—122no—
822C4—241no—
823C4#554811yescharacteristic
824C4#555311yescharacteristic
825C4#559011yescharacteristic
826C4#566311yescharacteristic
827C3#2538711yescharacteristic, complemented, Sylow
828C2—42no—
829C2—122no—
830C2—161no—
831C2—481no—
832C2#7469811yescharacteristic
833C2#7875811yescharacteristic
834C2#7885111yescharacteristic
835C2D3×#46511yescharacteristic
836C2#8067611yescharacteristic
837C2#8071811yescharacteristic
838C2#8073511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1893C2
socleC23×C3C22×D4
prime radical#82669C2
hypercenter#1893D3
hypocenterC3#25387
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
1. C2×#5114C2semidirect
2. C2×C8×#67C2semidirect
4. C2×#4762C2semidirect
5. C2×#4778C2semidirect
6. #73936C2semidirect
7. C3×#1893C2semidirect
8. #71685C2semidirect
9. #70176C2semidirect
10. #70157C2semidirect
11. #69524C2semidirect
12. #68887C2semidirect
13. #68883C2semidirect
14. #68796C2semidirect
15. #68781C2semidirect
77. #1893D3semidirect
160. #816D4semidirect
161. Dic3⋊C8D4semidirect
252. 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×#51142
C2×C8×#672
#826692
C2×#47622
C2×#47782
#739362
C3×#18932
#716852
#701762
#701572
#695242
#688872
#688832
#687962
#687812
#253873