Finite Group Databasebeta

← #10847382

Subgroups — #10847382

Order 768.

1474 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5596C211yesmaximal, characteristic, complemented
2C2×#5115C211yesmaximal, characteristic, complemented
3C2×#5038C211yesmaximal, characteristic, complemented
4#73999C211yesmaximal, characteristic, complemented
5C3×#1893C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7#70209C211yesmaximal, characteristic, complemented
8#70177C211yesmaximal, characteristic, complemented
9#70172C211yesmaximal, characteristic, complemented
10#70168C211yesmaximal, characteristic, complemented
11#69515C211yesmaximal, characteristic, complemented
12#68898C211yesmaximal, characteristic, complemented
13#68897C211yesmaximal, characteristic, complemented
14#68894C211yesmaximal, characteristic, complemented
15#68826C211yesmaximal, characteristic, complemented
16#25496—31nomaximal, Sylow
17C22×#237—21no—
18C23×C3×C8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#940C2211yescharacteristic
21C2×#939—21no—
22C2×D4×Dic3C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C23×C3⋊C8C2211yescharacteristic
28C22×D24C2211yescharacteristic
29#5596—24no—
30#5596—24no—
31C2×#893C2211yescharacteristic
32C2×#888C2211yescharacteristic
33C2×#886—21no—
34C2×#885—21no—
35C2×#67⋊C4—21no—
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5115—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#818C2211yescharacteristic
44#5038—24no—
45#4988C2211yescharacteristic
46#4988C2211yescharacteristic
47#4984C2211yescharacteristic
48#4984C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4958—21no—
54#4670—21no—
55#4670—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#532—31no—
65C2×#466—31no—
66C2×#466—31no—
67#2854—31no—
68#2057—31no—
69#2041—31no—
70#2023—31no—
71#2011—31no—
72#1893—31no—
73#1893D311yescharacteristic, complemented
74#1879—31no—
75#1879—31no—
76#1862—31no—
77#1862—31no—
78C2×#336—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C23×Dic3D411yescharacteristic
88C23×Dic3D411yescharacteristic
89C2×#237—28no—
90C2×#237—44no—
91C2×#237—44no—
92C22×D12C2311yescharacteristic
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×Dic6—21no—
96C22×C3×C8—22no—
97C22×C3×C8—22no—
98C22×C3×C8—41no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#121—22no—
102C3×#121D414yes—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×#217—21no—
109#940—22no—
110#940—22no—
111#939—28no—
112D4×Dic3—22no—
113D4×Dic3—22no—
114C2×#213—22no—
115C2×#213—22no—
116C2×#213—41no—
117#930—22no—
118#930—22no—
119#930—22no—
120#930D414yes—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×Dic3⋊C4—21no—
133C2×C4×Dic3—22no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3C2311yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—41no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C2×D24—22no—
145C2×D24—22no—
146C2×D24—41no—
147#893—22no—
148#893—22no—
149#888—22no—
150#888—22no—
151#886—44no—
152#885—28no—
153#67⋊C4—28no—
154C3×#102—22no—
155C3×#102—41no—
156C3×#95—21no—
157#832—22no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#821—22no—
161#821—22no—
162#818—22no—
163#809—22no—
164#809—22no—
165#809—41no—
166#807—22no—
167C22×#41—61no—
168C22×D8—31no—
169C22×D8—31no—
170C23×C8—31no—
171C23×C8C2×D311yescharacteristic
172#532—64no—
173#532—64no—
174C2×C4⋊Q8—31no—
175C2×#127—31no—
176C2×#124—61no—
177C2×#123—61no—
178C2×#121—31no—
179C2×#121—31no—
180C2×#121—61no—
181C2×#121C2×D311yescharacteristic
182C2×C4×D4—31no—
183C2×C4×D4—31no—
184C2×C4×D4—61no—
185C22×C42—31no—
186#466—64no—
187#466—64no—
188C2×#107—31no—
189C2×#107—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102C2×D311yescharacteristic
197C2×#102C2×D311yescharacteristic
198#390—31no—
199#390—31no—
200#389—31no—
201#389—31no—
202#388—61no—
203#388—61no—
204#386—61no—
205#380C2×D311yescharacteristic
206#340—31no—
207#340—31no—
208#340C2×D311yescharacteristic
209#340C2×D311yescharacteristic
210#336—31no—
211#336—31no—
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C23×D3—21no—
217C23×D3—21no—
218C2×C3×D4—24no—
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×D4C2×D412yes—
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×C4C2×D412yes—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D412yes—
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—24no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—24no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—22no—
256C22×Dic3—21no—
257C22×Dic3—41no—
258C22×Dic3—42no—
259C22×Dic3—42no—
260C22×Dic3D814yescomplemented
261C22×Dic3C2×D411yescharacteristic
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265#237—432no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12C2×D412yes—
278C2×C4×D3—24no—
279C2×C4×D3—42no—
280C2×C4×D3—42no—
281C2×Dic6—24no—
282C2×Dic6—42no—
283C2×Dic6—42no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—44no—
290C2×C3×C8#4112yescomplemented
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4C2×D412yes—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—42no—
299#217—24no—
300#213—44no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—42no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—42no—
312C4⋊Dic3—42no—
313C4⋊Dic3C2×D412yes—
314Dic3⋊C4—24no—
315C4×Dic3—22no—
316C4×Dic3—22no—
317C4×Dic3—21no—
318C4×Dic3—21no—
319C4×Dic3—21no—
320C4×Dic3—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—44no—
327C2×C3⋊C8#4112yescomplemented
328D24—44no—
329C2×#41—68no—
330C2×#41—124no—
331C2×#41—124no—
332C22×Q8—61no—
333C22×D4—21no—
334C22×D4—31no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4—61no—
340C22×D4C22×D311yescharacteristic
341C23×C4—31no—
342C23×C4—31no—
343C23×C4—61no—
344C23×C4—61no—
345C23×C4C22×D311yescharacteristic
346C2×D8—62no—
347C2×D8—62no—
348C2×D8—62no—
349C2×D8—62no—
350C2×D8—121no—
351C2×D8—121no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—31no—
355C22×C8—31no—
356C22×C8—41no—
357C22×C8—62no—
358C22×C8—62no—
359C22×C8—121no—
360C22×C8C22×D311yescharacteristic
361C22×C8C22×D311yescharacteristic
362C4⋊Q8—62no—
363C4⋊Q8—62no—
364#127—62no—
365#127—62no—
366#124—68no—
367#123—124no—
368#121—22no—
369#121—34no—
370#121—68no—
371#121—62no—
372#121—62no—
373#121—62no—
374#121D1214yes—
375C4×D4—68no—
376C4×D4—62no—
377C4×D4—62no—
378C4×D4—62no—
379C4×D4—62no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4C22×D311yescharacteristic
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C42—31no—
399C2×C42—31no—
400C2×C42—31no—
401C2×C42—31no—
402C2×C42—62no—
403C2×C42—62no—
404#107—62no—
405#107—62no—
406#102—22no—
407#102—41no—
408#102—62no—
409#102—62no—
410#102—62no—
411#102—62no—
412#102—62no—
413#102—121no—
414#95—21no—
415#95—61no—
416#95—61no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—22no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3#12012yes—
429C23×C3C2×D812yes—
430C23×C3AGL(1,ℤ/8)12yes—
431C23×C3C22×D411yescharacteristic
432C22×D3—22no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—48no—
449C3×D4—41no—
450C3×D4—41no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
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#12012yes—
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472C2×C3×C42−1+411yescharacteristic
473#67—48no—
474#67—48no—
475#67—48no—
476#67—84no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—28no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—44no—
489C2×Dic3—48no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3C2×D812yes—
496C2×Dic3C2×D812yes—
497C2×Dic3#13512yes—
498D12—22no—
499D12—22no—
500D12—41no—
501D12—41no—
502D12—41no—
503D12—41no—
504D12—41no—
505D12—41no—
506C4×D3—48no—
507Dic6—48no—
508C3×C8—22no—
509C3×C8—41no—
510C3⋊C8—22no—
511C3⋊C8—41no—
512C24—21no—
513C24—61no—
514C24—61no—
515C24D3×D411yescharacteristic
516#41—1232no—
517C2×Q8—64no—
518C2×Q8—122no—
519C2×Q8—122no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—32no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—64no—
530C2×D4—64no—
531C2×D4—64no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4—61no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—122no—
551C2×D4—122no—
552C2×D4C2×D1212yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—34no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—64no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—64no—
570C22×C4—62no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—122no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—121no—
577C22×C4—122no—
578C22×C4C2×D1212yes—
579C22×C4D3×D411yescharacteristic
580C22×C4D3×D412yes—
581C22×C4C23×D311yescharacteristic
582D8—124no—
583D8—124no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—32no—
590C2×C8—44no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—61no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—124no—
597C2×C8#23712yescomplemented
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—32no—
604C4⋊C4—64no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—122no—
609C4⋊C4—122no—
610C4⋊C4C2×D1212yes—
611C22⋊C4—24no—
612C22⋊C4—42no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—122no—
617C22⋊C4—122no—
618C22⋊C4—122no—
619C22⋊C4—122no—
620C22⋊C4—122no—
621C42—62no—
622C42—62no—
623C42—61no—
624C42—61no—
625C42—61no—
626C42—61no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3#44714yes—
641C22×C3C2×#12011yescharacteristic
642C22×C3#53211yescharacteristic
643C22×C3#53711yescharacteristic
644C22×C3C22×D811yescharacteristic
645C22×C3C2×#13511yescharacteristic
646C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
647C22×C3#57511yescharacteristic
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—81no—
652C2×D3—81no—
653C2×D3—81no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3—81no—
658C2×D3—81no—
659C2×D3—81no—
660C2×D3—81no—
661C2×D3—81no—
662C3×C4—22no—
663C3×C4—42no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4#54611yescharacteristic
667C3×C4#54611yescharacteristic
668C3×C4#54711yescharacteristic
669C3×C4#54711yescharacteristic
670Dic3—22no—
671Dic3—22no—
672Dic3—22no—
673Dic3—42no—
674Dic3—41no—
675Dic3—81no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—62no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23—121no—
696C23—121no—
697C23—121no—
698C23—121no—
699C23—121no—
700C23—121no—
701C23#88212yes—
702C23D3×D812yes—
703C23#91412yes—
704C23C2×D3×D411yescharacteristic
705Q8—128no—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—41no—
710D4—41no—
711D4—62no—
712D4—62no—
713D4—128no—
714D4—128no—
715D4—128no—
716D4—121no—
717D4—121no—
718D4—121no—
719D4—121no—
720D4—121no—
721D4—121no—
722D4—244no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—68no—
748C2×C4—61no—
749C2×C4—62no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—128no—
753C2×C4—124no—
754C2×C4—128no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4#88212yes—
761C2×C4C22×D1211yescharacteristic
762C2×C4C2×D3×D411yescharacteristic
763C2×C4C2×#23711yescharacteristic
764C2×C4#100411yescharacteristic
765C2×C4D3×#4111yescharacteristic
766C2×C4#101011yescharacteristic
767C8—22no—
768C8—41no—
769C8—62no—
770C8—121no—
771C2×C3—24no—
772C2×C3—82no—
773C2×C3#243011yescharacteristic
774C2×C3C2×#44711yescharacteristic
775C2×C3#300211yescharacteristic
776C2×C3#316911yescharacteristic
777C2×C3#318011yescharacteristic
778C2×C3#324511yescharacteristic
779C2×C3#324711yescharacteristic
780D3—82no—
781D3—161no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22—241no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22—241no—
803C22—241no—
804C22—241no—
805C22—241no—
806C22—241no—
807C22—241no—
808C22—241no—
809C22#477314yes—
810C22C2×#88211yescharacteristic
811C22#559611yescharacteristic
812C22#559711yescharacteristic
813C22C2×D3×D811yescharacteristic
814C22C2×#91411yescharacteristic
815C22D3×#13511yescharacteristic
816C22#576811yescharacteristic
817C4—22no—
818C4—42no—
819C4—62no—
820C4—62no—
821C4—62no—
822C4—81no—
823C4—81no—
824C4—122no—
825C4—121no—
826C4—241no—
827C4#555411yescharacteristic
828C4#555511yescharacteristic
829C4#559111yescharacteristic
830C4#565511yescharacteristic
831C3#2549611yescharacteristic, complemented, Sylow
832C2—24no—
833C2—82no—
834C2—242no—
835C2—481no—
836C2#7469911yescharacteristic
837C2C2×#477311yescharacteristic
838C2#7883311yescharacteristic
839C2#8063811yescharacteristic
840C2#8064111yescharacteristic
841C2#8069711yescharacteristic
842C2#8070211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1893C2
socleC23×C3C22×D4
hypercenter#1893D3
hypocenterC3#25496
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×#5596C2semidirect
2. C2×#5115C2semidirect
3. C2×#5038C2semidirect
4. #73999C2semidirect
5. C3×#1893C2semidirect
6. C2×#4550C2semidirect
7. #70209C2semidirect
8. #70177C2semidirect
9. #70172C2semidirect
10. #70168C2semidirect
11. #69515C2semidirect
12. #68898C2semidirect
13. #68897C2semidirect
14. #68894C2semidirect
15. #68826C2semidirect
73. #1893D3semidirect
260. C22×Dic3D8semidirect
290. C2×C3×C8#41semidirect
327. C2×C3⋊C8#41semidirect
597. C2×C8#237semidirect
831. C3#25496semidirect

Maximal subgroups

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

subgroupindex
C2×#55962
C2×#51152
C2×#50382
#739992
C3×#18932
C2×#45502
#702092
#701772
#701722
#701682
#695152
#688982
#688972
#688942
#688262
#254963