Finite Group Databasebeta

← #10846065

Subgroups — #10846065

Order 768.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#435C211yesmaximal, characteristic, complemented
2C2×#5134C211yesmaximal, characteristic, complemented
3C2×#5115C211yesmaximal, characteristic, complemented
4#82417C211yesmaximal, characteristic, complemented
5#82377C211yesmaximal, characteristic, complemented
6C2×#4844C211yesmaximal, characteristic, complemented
7#71990C211yesmaximal, characteristic, complemented
8#71972C211yesmaximal, characteristic, complemented
9#70453C211yesmaximal, characteristic, complemented
10#69962C211yesmaximal, characteristic, complemented
11#69961C211yesmaximal, characteristic, complemented
12#69937C211yesmaximal, characteristic, complemented
13#69934C211yesmaximal, characteristic, complemented
14#69821C211yesmaximal, characteristic, complemented
15#69812C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C22×C3×M16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#938—21no—
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×D24C2211yescharacteristic
28C22×#204C2211yescharacteristic
29C2×#875C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C3×#435—24no—
32C2×C3×C4⋊C8C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C2×C3×C22⋊C8C2211yescharacteristic
35C2×C3×#97C2211yescharacteristic
36#5223—21no—
37#5212C2211yescharacteristic
38#5212C2211yescharacteristic
39#5134—24no—
40#5115—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#818C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C2×#816C2211yescharacteristic
51#4993—21no—
52#4987—21no—
53#4961—21no—
54#4961—21no—
55#4957—21no—
56#4957—21no—
57#4935C2211yescharacteristic
58C4×C4⋊Dic3C2211yescharacteristic
59#4844—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#468—31no—
65C2×#466—31no—
66C2×#463—31no—
67C2×#435D311yescharacteristic, complemented
68#2540—31no—
69#2537—31no—
70#2036—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1959—31no—
75#1947—31no—
76#1895—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×D4D411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×D12C2311yescharacteristic
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×Dic6C2311yescharacteristic
90C2×C3×M16—22no—
91C2×C3×M16—22no—
92C2×C3×M16—41no—
93C22×C3×C8—22no—
94C22×C3×C8—22no—
95C22×C3×C8—41no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4D411yescharacteristic
103C2×C3×C22⋊C4D411yescharacteristic
104C2×C3×C22⋊C4D411yescharacteristic
105C2×C3×C42C2311yescharacteristic
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110#938—44no—
111#930—22no—
112#930—22no—
113#930—22no—
114#930—22no—
115#930—41no—
116#930—41no—
117#930—41no—
118#930—41no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
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×C4⋊Dic3—21no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133#924—22no—
134#924—22no—
135#924—41no—
136#924—41no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×C4×Dic3—21no—
140C2×D24—22no—
141C2×D24—22no—
142C2×D24—41no—
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—41no—
146#875—22no—
147#875—22no—
148C4×D12—22no—
149C4×D12—22no—
150C3×C4⋊C8D414yescomplemented
151C3×C22⋊C8—22no—
152C3×C22⋊C8—22no—
153C3×#97—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—22no—
158#821—22no—
159#821—22no—
160#821—41no—
161#821D414yescomplemented
162#818—22no—
163#818—22no—
164#816—22no—
165#816—22no—
166#816—41no—
167C22×SD16—31no—
168C22×D8—31no—
169C22×M16C2×D311yescharacteristic
170C23×C8C2×D311yescharacteristic
171C2×#124—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×D4—31no—
180C2×C4×D4C2×D311yescharacteristic
181#468—64no—
182#466—64no—
183#463—64no—
184#435—24no—
185C2×#107—31no—
186C2×#107—31no—
187C2×C4⋊C8C2×D311yescharacteristic
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×C22⋊C8C2×D311yescharacteristic
198C2×#97C2×D311yescharacteristic
199#399—61no—
200#394—61no—
201#394—61no—
202#392—61no—
203#390—61no—
204#390—61no—
205#384—31no—
206#380—31no—
207#380—31no—
208#380—61no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C23×D3—21no—
217C23×D3—21no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—41no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
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×C4C2411yescharacteristic
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—81no—
247C2×#67—81no—
248C2×#67—81no—
249C2×#67—81no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12C2×D412yes—
268C2×C4×D3—42no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C3×M16—44no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—44no—
288C2×C3×C8C2×D412yes—
289C2×C3×C8C2×D412yes—
290C2×C3×C8C2×D412yes—
291C3×C4⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—22no—
294C3×C42C2×D412yes—
295C3×C42#4112yes—
296#217—42no—
297#217—42no—
298#217—42no—
299#217—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—42no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3—42no—
316C4⋊Dic3—81no—
317C4⋊Dic3C2×D412yes—
318C4⋊Dic3#4112yes—
319Dic3⋊C4—42no—
320Dic3⋊C4—42no—
321C4×Dic3—81no—
322D24—44no—
323#204—44no—
324C22×Q8—31no—
325C22×D4—31no—
326C22×D4—31no—
327C22×D4—61no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4D1211yescharacteristic
332C23×C4—61no—
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—121no—
338C2×D8—62no—
339C2×D8—62no—
340C2×D8—121no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—41no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—41no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C22×C8C22×D311yescharacteristic
350C22×C8C22×D311yescharacteristic
351#124—62no—
352#124—62no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—62no—
358#121—62no—
359#121—62no—
360#121—62no—
361#121—121no—
362#121—121no—
363#121—121no—
364#121—121no—
365#121—124no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—62no—
369C4×D4—62no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4D1211yescharacteristic
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4D1211yescharacteristic
392C2×C22⋊C4D1211yescharacteristic
393C2×C42—61no—
394C2×C42C22×D311yescharacteristic
395#107—62no—
396#107—62no—
397C4⋊C8#6714yescomplemented
398#103—62no—
399#103—62no—
400#103—121no—
401#102—34no—
402#102—62no—
403#102—62no—
404#102—62no—
405#102—121no—
406C22⋊C8—22no—
407C22⋊C8—22no—
408#97—22no—
409#95—61no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3AGL(1,ℤ/8)12yes—
426C23×C3C22×D411yescharacteristic
427C22×D3—22no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C3×D4—44no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
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#12112yes—
461C2×C3×C4#12112yes—
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468#67—84no—
469#67—84no—
470#67—84no—
471#67—84no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
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—
490D12—22no—
491D12—22no—
492D12—41no—
493D12—41no—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—41no—
498C4×D3—84no—
499Dic6—41no—
500Dic6—41no—
501Dic6—41no—
502Dic6—41no—
503C3×C8—22no—
504C3×C8—22no—
505C3×C8—22no—
506C3×C8—41no—
507C24—61no—
508C24—61no—
509C24C2×D1211yescharacteristic
510C24C2×D1211yescharacteristic
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—32no—
520C2×D4—41no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—241no—
541C2×D4—241no—
542C2×D4—241no—
543C2×D4—241no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—122no—
565C22×C4C2×D1211yescharacteristic
566C22×C4C2×D1211yescharacteristic
567C22×C4C2×D1211yescharacteristic
568C22×C4C2×D1211yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—124no—
571D8—124no—
572M16—44no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—44no—
583C2×C8D3×D412yes—
584C2×C8C2×#6712yes—
585C2×C8C2×#6712yes—
586C4⋊C4—22no—
587C4⋊C4—32no—
588C4⋊C4—32no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4—122no—
600C4⋊C4—241no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—241no—
615C42#23512yes—
616C42C2×#6712yes—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3C2×#12111yescharacteristic
632C22×C3D4211yescharacteristic
633C22×C3#54611yescharacteristic
634C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
635C22×C3#57511yescharacteristic
636C22×C3#57611yescharacteristic
637C22×C3#57811yescharacteristic
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4#53211yescharacteristic
657C3×C4#54011yescharacteristic
658C3×C4D4211yescharacteristic
659C3×C4#55011yescharacteristic
660Dic3—42no—
661Dic3—42no—
662Dic3—81no—
663Dic3—81no—
664Dic3—81no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—62no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23#90812yes—
694C23C22×D1211yescharacteristic
695Q8—121no—
696Q8—121no—
697Q8—121no—
698Q8—121no—
699D4—44no—
700D4—62no—
701D4—62no—
702D4—121no—
703D4—121no—
704D4—121no—
705D4—121no—
706D4—121no—
707D4—121no—
708D4—244no—
709D4—244no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
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—244no—
749C2×C4#93012yes—
750C2×C4#93012yes—
751C2×C4C2×#23511yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4#100411yescharacteristic
754C2×C4D3×#4111yescharacteristic
755C2×C4#100911yescharacteristic
756C2×C4C22×#6711yescharacteristic
757C8—22no—
758C8—22no—
759C8—22no—
760C8—41no—
761C2×C3—42no—
762C2×C3—81no—
763C2×C3#242811yescharacteristic
764C2×C3#305511yescharacteristic
765C2×C3#306111yescharacteristic
766C2×C3#326411yescharacteristic
767C2×C3#326911yescharacteristic
768C2×C3#330811yescharacteristic
769C2×C3#331911yescharacteristic
770D3—82no—
771D3—161no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22D4×D1211yescharacteristic
801C22#555411yescharacteristic
802C22C2×#90811yescharacteristic
803C22#574811yescharacteristic
804C22#575211yescharacteristic
805C22#575311yescharacteristic
806C22C2×#93011yescharacteristic
807C4—22no—
808C4—22no—
809C4—41no—
810C4—41no—
811C4—122no—
812C4—122no—
813C4—241no—
814C4—241no—
815C4—241no—
816C4—241no—
817C4#554811yescharacteristic
818C4#556211yescharacteristic
819C4D4×#6711yescharacteristic
820C4#583411yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—42no—
823C2—81no—
824C2—242no—
825C2—481no—
826C2#7949311yescharacteristic
827C2#7949811yescharacteristic
828C2#7950611yescharacteristic
829C2#7950911yescharacteristic
830C2#8240911yescharacteristic
831C2#8377211yescharacteristic
832C2#8380111yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#435C2
socleC23×C3C22×D4
hypercenterC2×#435D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×C3×#435C2semidirect
2. C2×#5134C2semidirect
3. C2×#5115C2semidirect
4. #82417C2semidirect
5. #82377C2semidirect
6. C2×#4844C2semidirect
7. #71990C2semidirect
8. #71972C2semidirect
9. #70453C2semidirect
10. #69962C2semidirect
11. #69961C2semidirect
12. #69937C2semidirect
13. #69934C2semidirect
14. #69821C2semidirect
15. #69812C2semidirect
67. C2×#435D3semidirect
150. C3×C4⋊C8D4semidirect
161. #821D4semidirect
397. C4⋊C8#67semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4352
C2×#51342
C2×#51152
#824172
#823772
C2×#48442
#719902
#719722
#704532
#699622
#699612
#699372
#699342
#698212
#698122
#253973