Finite Group Databasebeta

← #10827605

Subgroups — #10827605

Order 768.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5543C211yesmaximal, characteristic, complemented
2C2×#5133C211yesmaximal, characteristic, complemented
3#82402C211yesmaximal, characteristic
4C2×#4733C211yesmaximal, characteristic, complemented
5C3×#1870C211yesmaximal, characteristic, complemented
6#71989C211yesmaximal, characteristic, complemented
7#69964C211yesmaximal, characteristic, complemented
8#69962C211yesmaximal, characteristic, complemented
9#69932C211yesmaximal, characteristic, complemented
10#69930C211yesmaximal, characteristic, complemented
11#69924C211yesmaximal, characteristic, complemented
12#68689C211yesmaximal, characteristic, complemented
13#68686C211yesmaximal, characteristic, complemented
14#68685C211yesmaximal, characteristic, complemented
15#68678C211yesmaximal, characteristic, complemented
16#23981—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×D4×Dic3—21no—
21C2×#930C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C22×C4⋊Dic3C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×Dic12C2211yescharacteristic
28C22×#204C2211yescharacteristic
29#5543—24no—
30#5543—24no—
31C2×#890—21no—
32C2×#878—21no—
33C2×#878—21no—
34C2×#869C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5223—21no—
40#5212C2211yescharacteristic
41#5133—24no—
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#816C2211yescharacteristic
50#4989—21no—
51#4959—21no—
52#4956—21no—
53#4939C2211yescharacteristic
54#4929C2211yescharacteristic
55#4733—24no—
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#554—31no—
65C2×#452—31no—
66C2×#417—31no—
67#2407—31no—
68#2024—31no—
69#2023—31no—
70#2001—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1878—31no—
75#1874—31no—
76#1872—31no—
77#1870D311yescharacteristic, complemented
78#1823—31no—
79C22×C3×D4D411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C23×Dic3—21no—
85C23×Dic3—21no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—41no—
91C2×#235—41no—
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×Dic6—21no—
95C22×Dic6C2311yescharacteristic
96C22×Dic6C2311yescharacteristic
97C2×C3×M16—22no—
98C2×C3×M16—41no—
99C2×C3×M16—41no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C2×C3×C4⋊C4D411yescharacteristic
107C2×C3×C22⋊C4D411yescharacteristic
108C2×C3×C22⋊C4D411yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114D4×Dic3—28no—
115#930—22no—
116#930—41no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—22no—
126C2×C4⋊Dic3D414yescomplemented
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132#924—22no—
133#924—22no—
134#924—22no—
135#924—22no—
136#924—41no—
137#924D414yescomplemented
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×C4×Dic3—21no—
143C2×Dic12—22no—
144C2×Dic12—22no—
145C2×Dic12—41no—
146C2×#204—22no—
147C2×#204—22no—
148C2×#204—41no—
149#890—28no—
150#878—28no—
151#878—28no—
152#869—22no—
153#869—22no—
154C4×Dic6—22no—
155C4×Dic6—22no—
156C3×C22⋊C8—22no—
157C3×C22⋊C8—41no—
158C3×C22⋊C8—41no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—22no—
163#821—22no—
164#821—22no—
165#816—22no—
166#816—22no—
167#816—22no—
168#816—41no—
169#816—41no—
170C22×#41—31no—
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16C2×D311yescharacteristic
174#554—64no—
175#554—64no—
176C2×C4⋊Q8—31no—
177C2×#125—61no—
178C2×C22⋊Q8—31no—
179C2×C22⋊Q8—31no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—61no—
182C2×C22⋊Q8—61no—
183C2×#121—31no—
184C2×C4×Q8—31no—
185C2×C4×D4—61no—
186C2×C4×D4C2×D311yescharacteristic
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189#452—64no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8C2×D311yescharacteristic
200C2×C22⋊C8C2×D311yescharacteristic
201C2×C22⋊C8C2×D311yescharacteristic
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336C2×D311yescharacteristic
216#336C2×D311yescharacteristic
217C24×C3C2×D411yescharacteristic
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2411yescharacteristic
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—81no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—24no—
252C22×Dic3—24no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—81no—
256C22×Dic3—81no—
257C22×Dic3—81no—
258C22×Dic3—81no—
259#235—28no—
260#235—44no—
261#235—44no—
262#235—44no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12#4112yes—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×C4×D3—42no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—24no—
283C2×Dic6—81no—
284C2×Dic6—81no—
285C2×Dic6C2×D412yes—
286C2×Dic6#4112yes—
287C3×M16—44no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C3×C4⋊C4—22no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—22no—
303C3×C42—21no—
304C3×C42—21no—
305#217—24no—
306#217—24no—
307#217—42no—
308#217—81no—
309(C2×D3)⋊C4—42no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—81no—
312C4⋊Dic3—24no—
313C4⋊Dic3—24no—
314C4⋊Dic3—24no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3C2×D412yes—
323C4⋊Dic3C2×D412yes—
324C4⋊Dic3C2×D412yes—
325Dic3⋊C4—24no—
326Dic3⋊C4—24no—
327Dic3⋊C4—24no—
328Dic3⋊C4—42no—
329C4×Dic3—24no—
330Dic12—44no—
331#204—44no—
332C2×#41—62no—
333C2×#41—62no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—121no—
337C2×#41—121no—
338C22×Q8—31no—
339C22×Q8—31no—
340C22×Q8—61no—
341C22×D4—31no—
342C22×D4—61no—
343C22×D4—61no—
344C22×D4D1211yescharacteristic
345C23×C4—61no—
346C23×C4—61no—
347C23×C4—61no—
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C2×Q16—62no—
351C2×Q16—62no—
352C2×Q16—121no—
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×M16—22no—
357C2×M16—41no—
358C2×M16—41no—
359C22×C8C22×D311yescharacteristic
360C22×C8C22×D311yescharacteristic
361C22×C8C22×D311yescharacteristic
362C22×C8C22×D311yescharacteristic
363C4⋊Q8—62no—
364C4⋊Q8—62no—
365#125—68no—
366C22⋊Q8—34no—
367C22⋊Q8—68no—
368C22⋊Q8—68no—
369C22⋊Q8—62no—
370C22⋊Q8—62no—
371C22⋊Q8—62no—
372C22⋊Q8—62no—
373C22⋊Q8—121no—
374#121—62no—
375#121—121no—
376C4×Q8—62no—
377C4×Q8—62no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—68no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—62no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4D1211yescharacteristic
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4D1211yescharacteristic
406C2×C22⋊C4D1211yescharacteristic
407C2×C42—61no—
408C2×C42C22×D311yescharacteristic
409#103—62no—
410#103—62no—
411#103—62no—
412#103—121no—
413#103—121no—
414#102—62no—
415#102—62no—
416#102—62no—
417C22⋊C8—22no—
418C22⋊C8—41no—
419C22⋊C8—41no—
420#95—61no—
421#95—61no—
422#95—61no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3#12012yes—
436C23×C3#13712yes—
437C23×C3C22×D411yescharacteristic
438C22×D3—22no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C3×D4—28no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4#12012yes—
465C2×C3×C4#13712yes—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472#67—48no—
473#67—84no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
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—41no—
494C2×Dic3—41no—
495C2×Dic3—84no—
496C2×Dic3—84no—
497D12—22no—
498D12—22no—
499D12—41no—
500D12—41no—
501C4×D3—48no—
502Dic6—22no—
503Dic6—22no—
504Dic6—22no—
505Dic6—22no—
506Dic6—41no—
507Dic6—41no—
508Dic6—41no—
509Dic6—41no—
510Dic6—84no—
511C3×C8—41no—
512C3×C8—41no—
513C3×C8—41no—
514C3×C8—41no—
515C24—61no—
516C24C2×D1211yescharacteristic
517C24C2×D1211yescharacteristic
518#41—68no—
519#41—124no—
520#41—124no—
521#41—124no—
522C2×Q8—32no—
523C2×Q8—32no—
524C2×Q8—64no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×Q8—61no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—241no—
536C2×Q8—241no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—32no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—241no—
552C22×C4—21no—
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—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—122no—
572C22×C4—122no—
573C22×C4—122no—
574C22×C4—241no—
575C22×C4—241no—
576C22×C4—241no—
577C22×C4—241no—
578C22×C4C2×D1211yescharacteristic
579C22×C4C2×D1211yescharacteristic
580C22×C4C2×D1211yescharacteristic
581C22×C4C2×D1211yescharacteristic
582C22×C4D3×D412yes—
583C22×C4D3×D412yes—
584C22×C4C23×D311yescharacteristic
585Q16—124no—
586SD16—124no—
587M16—44no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C4⋊C4—22no—
601C4⋊C4—32no—
602C4⋊C4—32no—
603C4⋊C4—32no—
604C4⋊C4—64no—
605C4⋊C4—64no—
606C4⋊C4—64no—
607C4⋊C4—64no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—122no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—64no—
621C22⋊C4—64no—
622C22⋊C4—122no—
623C22⋊C4—122no—
624C22⋊C4—122no—
625C22⋊C4—241no—
626C22⋊C4—241no—
627C42—21no—
628C42—21no—
629C42—64no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3C2×#12011yescharacteristic
645C22×C3#54611yescharacteristic
646C22×C3#54611yescharacteristic
647C22×C3C2×#13711yescharacteristic
648C22×C3C2×#13711yescharacteristic
649C22×C3#57611yescharacteristic
650C22×C3#57711yescharacteristic
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4#52511yescharacteristic
663C3×C4#53511yescharacteristic
664C3×C4#54611yescharacteristic
665C3×C4#54611yescharacteristic
666Dic3—42no—
667Dic3—42no—
668Dic3—42no—
669Dic3—42no—
670Dic3—42no—
671Dic3—81no—
672Dic3—81no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—62no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23#88212yes—
693C23#90912yes—
694C23C22×D1211yescharacteristic
695Q8—62no—
696Q8—62no—
697Q8—62no—
698Q8—62no—
699Q8—121no—
700Q8—121no—
701Q8—121no—
702Q8—121no—
703Q8—244no—
704D4—28no—
705D4—62no—
706D4—62no—
707D4—128no—
708D4—121no—
709D4—121no—
710D4—244no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—128no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—244no—
752C2×C4—244no—
753C2×C4#88212yes—
754C2×C4#90912yes—
755C2×C4C2×D3×D411yescharacteristic
756C2×C4C2×D3×D411yescharacteristic
757C2×C4#100411yescharacteristic
758C2×C4#100411yescharacteristic
759C2×C4D3×#4111yescharacteristic
760C2×C4D3×#4111yescharacteristic
761C8—41no—
762C8—41no—
763C8—41no—
764C8—41no—
765C2×C3—42no—
766C2×C3—42no—
767C2×C3#240411yescharacteristic
768C2×C3#300411yescharacteristic
769C2×C3#301211yescharacteristic
770C2×C3#331411yescharacteristic
771C2×C3#331611yescharacteristic
772C2×C3#333111yescharacteristic
773C2×C3#333311yescharacteristic
774D3—82no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22C2×#88211yescharacteristic
797C22#555411yescharacteristic
798C22#555411yescharacteristic
799C22C2×#90911yescharacteristic
800C22C2×#90911yescharacteristic
801C22#575111yescharacteristic
802C22#575211yescharacteristic
803C4—22no—
804C4—22no—
805C4—41no—
806C4—41no—
807C4—122no—
808C4—122no—
809C4—122no—
810C4—122no—
811C4—122no—
812C4—241no—
813C4—241no—
814C4#559211yescharacteristic
815C4#561011yescharacteristic
816C4#561011yescharacteristic
817C4#565611yescharacteristic
818C3#2398111yescharacteristic, complemented, Sylow
819C2—42no—
820C2—42no—
821C2—242no—
822C2#7488511yescharacteristic
823C2#7864511yescharacteristic
824C2#7867211yescharacteristic
825C2#7950311yescharacteristic
826C2#7951311yescharacteristic
827C2#7955811yescharacteristic
828C2#7956611yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1870C2
socleC23×C3C22×D4
prime radical#82402C2
hypercenter#1870D3
hypocenterC3#23981
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#5543C2semidirect
2. C2×#5133C2semidirect
4. C2×#4733C2semidirect
5. C3×#1870C2semidirect
6. #71989C2semidirect
7. #69964C2semidirect
8. #69962C2semidirect
9. #69932C2semidirect
10. #69930C2semidirect
11. #69924C2semidirect
12. #68689C2semidirect
13. #68686C2semidirect
14. #68685C2semidirect
15. #68678C2semidirect
77. #1870D3semidirect
126. C2×C4⋊Dic3D4semidirect
137. #924D4semidirect
818. C3#23981semidirect

Maximal subgroups

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

subgroupindex
C2×#55432
C2×#51332
#824022
C2×#47332
C3×#18702
#719892
#699642
#699622
#699322
#699302
#699242
#686892
#686862
#686852
#686782
#239813