Finite Group Databasebeta

← C22×#5647 #11702065

Subgroups — C22×#5647 #11702065

Order 768.

8102 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#946C211yesmaximal, characteristic, complemented
3C22×#947C211yesmaximal, characteristic, complemented
4C22×#929C211yesmaximal, characteristic, complemented
5C22×#930C211yesmaximal, characteristic, complemented
6C2×#5647C2148yesmaximal, direct product factor
7C22×#894C211yesmaximal, characteristic, complemented
8C22×#894C211yesmaximal, characteristic, complemented
9C22×#896C211yesmaximal, characteristic, complemented
10C22×#897C211yesmaximal, characteristic, complemented
11C22×#895C211yesmaximal, characteristic, complemented
12C22×#889C211yesmaximal, characteristic, complemented
13C22×#883C211yesmaximal, characteristic, complemented
14C22×#884C211yesmaximal, characteristic, complemented
15C22×#884C211yesmaximal, characteristic, complemented
16C22×#885C211yesmaximal, characteristic, complemented
17C22×#562—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×D12C2211yescharacteristic
24C23×D12C2211yescharacteristic
25C23×D12C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C23×C4×D3C2211yescharacteristic
28C23×C4×D3C2211yescharacteristic
29C23×Dic6C2211yescharacteristic
30C2×C3×C22⋊Q8C22124yescomplemented
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C2×#947C22124yescomplemented
38C2×#946C22124yescomplemented
39C2×#930C22124yescomplemented
40C2×#929C22124yescomplemented
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×(C2×D3)⋊C4C2211yescharacteristic
48C22×(C2×D3)⋊C4C2211yescharacteristic
49C22×(C2×D3)⋊C4C2211yescharacteristic
50C22×C4⋊Dic3C2211yescharacteristic
51C22×C4⋊Dic3C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C22×Dic3⋊C4C2211yescharacteristic
54C22×Dic3⋊C4C2211yescharacteristic
55C22×Dic3⋊C4C2211yescharacteristic
56C22×Dic3⋊C4C2211yescharacteristic
57C22×C4×Dic3C2211yescharacteristic
58#5647C221256yesdirect product factor
59C2×#897C22124yescomplemented
60C2×#896C22124yescomplemented
61C2×#895C22124yescomplemented
62C2×#894C22124yescomplemented
63C2×#894C22124yescomplemented
64C2×#889C22124yescomplemented
65C2×#885C22124yescomplemented
66C2×#884C22124yescomplemented
67C2×#884C22124yescomplemented
68C2×#883C22124yescomplemented
69C2×#562—348no—
70C22×#125—31no—
71C22×#124—31no—
72C22×#124—31no—
73C22×#123—31no—
74C22×#123—31no—
75C22×#123—31no—
76C22×#123—31no—
77C22×C22⋊Q8—31no—
78C22×C22⋊Q8—31no—
79C22×C22⋊Q8—31no—
80C22×C22⋊Q8D311yescharacteristic, complemented
81C22×#121—31no—
82C22×#121—31no—
83C22×#121—31no—
84C22×#121—31no—
85C25×C3C2311yescharacteristic
86C24×D3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C22×C3×Q8—44no—
90C22×C3×Q8C23112yes—
91C23×C3×C4—44no—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C23112yes—
99C22×#67—44no—
100C22×#67—44no—
101C22×#67—44no—
102C22×#67C23112yes—
103C22×#67C23112yes—
104C22×#67C23112yes—
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C22×D12—44no—
111C22×D12—44no—
112C22×D12—44no—
113C22×D12C23112yes—
114C22×D12C23112yes—
115C22×D12C23112yes—
116C22×C4×D3—44no—
117C22×C4×D3—44no—
118C22×C4×D3—44no—
119C22×C4×D3C23112yes—
120C22×C4×D3C23112yes—
121C22×C4×D3C23112yes—
122C22×Dic6—44no—
123C22×Dic6C23112yes—
124C3×C22⋊Q8C23164yescomplemented
125C2×C3×C4⋊C4C23112yes—
126C2×C3×C4⋊C4C23112yes—
127C2×C3×C4⋊C4C23112yes—
128C2×C3×C22⋊C4C23112yes—
129C2×C3×C22⋊C4C23112yes—
130C2×#217C23112yes—
131#947C23164yescomplemented
132#946C23164yescomplemented
133#930C23164yescomplemented
134#929C23164yescomplemented
135C2×(C2×D3)⋊C4C23112yes—
136C2×(C2×D3)⋊C4C23112yes—
137C2×(C2×D3)⋊C4C23112yes—
138C2×(C2×D3)⋊C4C23112yes—
139C2×(C2×D3)⋊C4C23112yes—
140C2×(C2×D3)⋊C4C23112yes—
141C2×(C2×D3)⋊C4C23112yes—
142C2×(C2×D3)⋊C4C23112yes—
143C2×(C2×D3)⋊C4C23112yes—
144C2×C4⋊Dic3C23112yes—
145C2×C4⋊Dic3C23112yes—
146C2×Dic3⋊C4C23112yes—
147C2×Dic3⋊C4C23112yes—
148C2×Dic3⋊C4C23112yes—
149C2×Dic3⋊C4C23112yes—
150C2×Dic3⋊C4C23112yes—
151C2×C4×Dic3C23112yes—
152#897C23164yescomplemented
153#896C23164yescomplemented
154#895C23164yescomplemented
155#894C23164yescomplemented
156#894C23164yescomplemented
157#889C23164yescomplemented
158#885C23164yescomplemented
159#884C23164yescomplemented
160#884C23164yescomplemented
161#883C23164yescomplemented
162C23×Q8—31no—
163C23×Q8C2×D311yescharacteristic
164C23×D4—31no—
165C23×D4—31no—
166C23×D4—31no—
167C23×D4—31no—
168C23×D4—31no—
169C23×D4—31no—
170C24×C4—31no—
171C24×C4—31no—
172C24×C4—31no—
173C24×C4C2×D311yescharacteristic
174#562—3256no—
175C2×#125—324no—
176C2×#124—324no—
177C2×#124—324no—
178C2×#123—324no—
179C2×#123—324no—
180C2×#123—324no—
181C2×#123—324no—
182C2×C22⋊Q8—324no—
183C2×C22⋊Q8—324no—
184C2×C22⋊Q8—324no—
185C2×C22⋊Q8C2×D3124yescomplemented
186C2×#121—324no—
187C2×#121—324no—
188C2×#121—324no—
189C2×#121—324no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4C2×D311yescharacteristic
198C22×C4⋊C4C2×D311yescharacteristic
199C22×C4⋊C4C2×D311yescharacteristic
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C42—31no—
213C24×C3—24no—
214C24×C3—24no—
215C24×C3—24no—
216C24×C3C2416yes—
217C24×C3C2411yescharacteristic
218C23×D3—24no—
219C23×D3—24no—
220C23×D3—24no—
221C23×D3—24no—
222C23×D3—24no—
223C23×D3—24no—
224C23×D3—24no—
225C23×D3—24no—
226C23×D3—24no—
227C23×D3C2416yes—
228C23×D3C2416yes—
229C23×D3C2416yes—
230C2×C3×Q8—424no—
231C2×C3×Q8C24116yes—
232C22×C3×C4—24no—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C22×C3×C4—24no—
236C22×C3×C4—24no—
237C22×C3×C4—24no—
238C22×C3×C4—424no—
239C22×C3×C4C2416yes—
240C22×C3×C4C2416yes—
241C22×C3×C4C2416yes—
242C22×C3×C4C2416yes—
243C22×C3×C4C2416yes—
244C22×C3×C4C2416yes—
245C22×C3×C4C24116yes—
246C2×#67—424no—
247C2×#67—424no—
248C2×#67—424no—
249C2×#67C24116yes—
250C2×#67C24116yes—
251C2×#67C24116yes—
252C22×Dic3—24no—
253C22×Dic3—24no—
254C22×Dic3—24no—
255C22×Dic3—24no—
256C22×Dic3—24no—
257C22×Dic3C2416yes—
258C22×Dic3C2416yes—
259C22×Dic3C2416yes—
260C22×Dic3C2416yes—
261C22×Dic3C2416yes—
262C2×D12—424no—
263C2×D12—424no—
264C2×D12—424no—
265C2×D12C24116yes—
266C2×D12C24116yes—
267C2×D12C24116yes—
268C2×C4×D3—424no—
269C2×C4×D3—424no—
270C2×C4×D3—424no—
271C2×C4×D3C24116yes—
272C2×C4×D3C24116yes—
273C2×C4×D3C24116yes—
274C2×Dic6—424no—
275C2×Dic6C24116yes—
276C3×C4⋊C4C24116yes—
277C3×C4⋊C4C24116yes—
278C3×C4⋊C4C24116yes—
279C3×C22⋊C4C24116yes—
280C3×C22⋊C4C24116yes—
281#217C24116yes—
282(C2×D3)⋊C4C24116yes—
283(C2×D3)⋊C4C24116yes—
284(C2×D3)⋊C4C24116yes—
285(C2×D3)⋊C4C24116yes—
286(C2×D3)⋊C4C24116yes—
287(C2×D3)⋊C4C24116yes—
288(C2×D3)⋊C4C24116yes—
289(C2×D3)⋊C4C24116yes—
290(C2×D3)⋊C4C24116yes—
291C4⋊Dic3C24116yes—
292C4⋊Dic3C24116yes—
293Dic3⋊C4C24116yes—
294Dic3⋊C4C24116yes—
295Dic3⋊C4C24116yes—
296Dic3⋊C4C24116yes—
297Dic3⋊C4C24116yes—
298C4×Dic3C24116yes—
299C25—31no—
300C25—31no—
301C25—31no—
302C25C22×D311yescharacteristic
303C22×Q8—312no—
304C22×Q8—44no—
305C22×Q8—124no—
306C22×Q8C22×D3112yes—
307C22×D4—312no—
308C22×D4—312no—
309C22×D4—312no—
310C22×D4—312no—
311C22×D4—312no—
312C22×D4—312no—
313C22×D4—124no—
314C22×D4—124no—
315C22×D4—124no—
316C22×D4—124no—
317C22×D4—124no—
318C22×D4—124no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—312no—
325C23×C4—312no—
326C23×C4—312no—
327C23×C4—44no—
328C23×C4—124no—
329C23×C4—124no—
330C23×C4—124no—
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337C23×C4C22×D3112yes—
338#125—364no—
339#124—364no—
340#124—364no—
341#123—364no—
342#123—364no—
343#123—364no—
344#123—364no—
345C22⋊Q8—364no—
346C22⋊Q8—364no—
347C22⋊Q8—364no—
348C22⋊Q8C22×D3164yescomplemented
349#121—364no—
350#121—364no—
351#121—364no—
352#121—364no—
353C2×C4⋊C4—312no—
354C2×C4⋊C4—312no—
355C2×C4⋊C4—312no—
356C2×C4⋊C4—312no—
357C2×C4⋊C4—312no—
358C2×C4⋊C4—312no—
359C2×C4⋊C4—312no—
360C2×C4⋊C4C22×D3112yes—
361C2×C4⋊C4C22×D3112yes—
362C2×C4⋊C4C22×D3112yes—
363C2×C22⋊C4—312no—
364C2×C22⋊C4—312no—
365C2×C22⋊C4—312no—
366C2×C22⋊C4—312no—
367C2×C22⋊C4—312no—
368C2×C22⋊C4—312no—
369C2×C22⋊C4—312no—
370C2×C22⋊C4—312no—
371C2×C22⋊C4—312no—
372C2×C22⋊C4—312no—
373C2×C22⋊C4C22×D3112yes—
374C2×C22⋊C4C22×D3112yes—
375C2×C42—312no—
376C23×C3—212no—
377C23×C3—212no—
378C23×C3—212no—
379C23×C3—416no—
380C23×C3H(5,𝔽2)14yes—
381C23×C3H(5,𝔽2)14yes—
382C23×C32−1+414yes—
383C23×C3C2514yes—
384C23×C3C2513yes—
385C22×D3—212no—
386C22×D3—212no—
387C22×D3—212no—
388C22×D3—212no—
389C22×D3—212no—
390C22×D3—212no—
391C22×D3—212no—
392C22×D3—212no—
393C22×D3—212no—
394C22×D3—416no—
395C22×D3—416no—
396C22×D3—416no—
397C22×D3C2514yes—
398C22×D3C2514yes—
399C22×D3C2514yes—
400C3×Q8—416no—
401C2×C3×C4—212no—
402C2×C3×C4—212no—
403C2×C3×C4—212no—
404C2×C3×C4—212no—
405C2×C3×C4—212no—
406C2×C3×C4—212no—
407C2×C3×C4—416no—
408C2×C3×C4C2514yes—
409C2×C3×C4C2514yes—
410C2×C3×C4C2514yes—
411C2×C3×C4C2514yes—
412C2×C3×C4C2514yes—
413C2×C3×C4C2514yes—
414#67—416no—
415#67—416no—
416#67—416no—
417C2×Dic3—212no—
418C2×Dic3—212no—
419C2×Dic3—212no—
420C2×Dic3—212no—
421C2×Dic3—212no—
422C2×Dic3C2514yes—
423C2×Dic3C2514yes—
424C2×Dic3C2514yes—
425C2×Dic3C2514yes—
426C2×Dic3C2514yes—
427D12—416no—
428D12—416no—
429D12—416no—
430C4×D3—416no—
431C4×D3—416no—
432C4×D3—416no—
433Dic6—416no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—36no—
438C24—36no—
439C24—36no—
440C24—64no—
441C24—64no—
442C24—64no—
443C24—64no—
444C24—64no—
445C24—64no—
446C24—64no—
447C24—64no—
448C24—64no—
449C24C23×D316yes—
450C24C23×D311yescharacteristic
451C2×Q8—316no—
452C2×Q8—424no—
453C2×Q8—1224no—
454C2×Q8C23×D3116yes—
455C2×D4—316no—
456C2×D4—316no—
457C2×D4—316no—
458C2×D4—316no—
459C2×D4—316no—
460C2×D4—316no—
461C2×D4—1224no—
462C2×D4—1224no—
463C2×D4—1224no—
464C2×D4—1224no—
465C2×D4—1224no—
466C2×D4—1224no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—36no—
474C22×C4—36no—
475C22×C4—36no—
476C22×C4—36no—
477C22×C4—36no—
478C22×C4—316no—
479C22×C4—316no—
480C22×C4—316no—
481C22×C4—424no—
482C22×C4—64no—
483C22×C4—64no—
484C22×C4—64no—
485C22×C4—64no—
486C22×C4—64no—
487C22×C4—1224no—
488C22×C4—1224no—
489C22×C4—1224no—
490C22×C4C23×D316yes—
491C22×C4C23×D316yes—
492C22×C4C23×D316yes—
493C22×C4C23×D316yes—
494C22×C4C23×D316yes—
495C22×C4C23×D316yes—
496C22×C4C23×D3116yes—
497C4⋊C4—316no—
498C4⋊C4—316no—
499C4⋊C4—316no—
500C4⋊C4—316no—
501C4⋊C4—316no—
502C4⋊C4—316no—
503C4⋊C4—316no—
504C4⋊C4C23×D3116yes—
505C4⋊C4C23×D3116yes—
506C4⋊C4C23×D3116yes—
507C22⋊C4—316no—
508C22⋊C4—316no—
509C22⋊C4—316no—
510C22⋊C4—316no—
511C22⋊C4—316no—
512C22⋊C4—316no—
513C22⋊C4—316no—
514C22⋊C4—316no—
515C22⋊C4—316no—
516C22⋊C4—316no—
517C22⋊C4C23×D3116yes—
518C22⋊C4C23×D3116yes—
519C42—316no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—24no—
523C22×C3—424no—
524C22×C3#562116yescomplemented
525C22×C3C2×H(5,𝔽2)16yes—
526C22×C3C2×H(5,𝔽2)16yes—
527C22×C3C2×2−1+416yes—
528C22×C3C2611yescharacteristic
529C2×D3—24no—
530C2×D3—24no—
531C2×D3—24no—
532C2×D3—24no—
533C2×D3—24no—
534C2×D3—24no—
535C2×D3—24no—
536C2×D3—24no—
537C2×D3—24no—
538C2×D3—424no—
539C2×D3—424no—
540C2×D3—424no—
541C3×C4—24no—
542C3×C4—24no—
543C3×C4—24no—
544C3×C4—24no—
545C3×C4—24no—
546C3×C4—24no—
547Dic3—24no—
548Dic3—24no—
549Dic3—24no—
550Dic3—24no—
551Dic3—24no—
552C23—212no—
553C23—212no—
554C23—212no—
555C23—34no—
556C23—34no—
557C23—34no—
558C23—416no—
559C23—612no—
560C23—612no—
561C23—612no—
562C23—612no—
563C23—612no—
564C23—612no—
565C23—612no—
566C23—612no—
567C23—612no—
568C23—1216no—
569C23—1216no—
570C23—1216no—
571C23#100414yes—
572C23#100714yes—
573C23#100914yes—
574C23C24×D314yes—
575C23C24×D313yes—
576Q8—416no—
577Q8—1216no—
578D4—1216no—
579D4—1216no—
580D4—1216no—
581D4—1216no—
582D4—1216no—
583D4—1216no—
584C2×C4—212no—
585C2×C4—212no—
586C2×C4—212no—
587C2×C4—212no—
588C2×C4—212no—
589C2×C4—212no—
590C2×C4—34no—
591C2×C4—34no—
592C2×C4—34no—
593C2×C4—34no—
594C2×C4—34no—
595C2×C4—416no—
596C2×C4—612no—
597C2×C4—612no—
598C2×C4—612no—
599C2×C4—612no—
600C2×C4—612no—
601C2×C4—1216no—
602C2×C4—1216no—
603C2×C4—1216no—
604C2×C4C24×D314yes—
605C2×C4C24×D314yes—
606C2×C4C24×D314yes—
607C2×C4C24×D314yes—
608C2×C4C24×D314yes—
609C2×C4C24×D314yes—
610C2×C3—44no—
611C2×C3C2×#562112yescomplemented
612C2×C3C22×H(5,𝔽2)11yescharacteristic
613C2×C3C22×H(5,𝔽2)11yescharacteristic
614C2×C3C22×2−1+411yescharacteristic
615D3—44no—
616D3—44no—
617D3—44no—
618C22—24no—
619C22—24no—
620C22—24no—
621C22—424no—
622C22—64no—
623C22—64no—
624C22—64no—
625C22—64no—
626C22—64no—
627C22—64no—
628C22—64no—
629C22—64no—
630C22—64no—
631C22—1224no—
632C22—1224no—
633C22—1224no—
634C22#5647116yesdirect product factor
635C22C2×#100416yes—
636C22C2×#100716yes—
637C22C2×#100916yes—
638C22C25×D311yescharacteristic
639C4—24no—
640C4—24no—
641C4—24no—
642C4—24no—
643C4—24no—
644C4—24no—
645C4—64no—
646C4—64no—
647C4—64no—
648C4—64no—
649C4—64no—
650C3C22×#56211yescharacteristic, complemented, Sylow
651C2—44no—
652C2—124no—
653C2—124no—
654C2—124no—
655C2C2×#5647112yesdirect product factor
656C2C22×#100411yescharacteristic
657C2C22×#100711yescharacteristic
658C2C22×#100911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC22×C3×C22⋊Q8C2
socleC24×C3C24
hypercenterC22×C22⋊Q8D3
hypocenterC3C22×#562
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C22×#946C2semidirect
3. C22×#947C2semidirect
4. C22×#929C2semidirect
5. C22×#930C2semidirect
6. C2×#5647C2direct (N × H)
7. C22×#894C2semidirect
8. C22×#894C2semidirect
9. C22×#896C2semidirect
10. C22×#897C2semidirect
11. C22×#895C2semidirect
12. C22×#889C2semidirect
13. C22×#883C2semidirect
14. C22×#884C2semidirect
15. C22×#884C2semidirect
16. C22×#885C2semidirect
30. C2×C3×C22⋊Q8C22semidirect
37. C2×#947C22semidirect
38. C2×#946C22semidirect
39. C2×#930C22semidirect
40. C2×#929C22semidirect
58. #5647C22direct (N × H)
59. C2×#897C22semidirect
60. C2×#896C22semidirect
61. C2×#895C22semidirect
62. C2×#894C22semidirect
63. C2×#894C22semidirect
64. C2×#889C22semidirect
65. C2×#885C22semidirect
66. C2×#884C22semidirect
67. C2×#884C22semidirect
68. C2×#883C22semidirect
80. C22×C22⋊Q8D3semidirect
124. C3×C22⋊Q8C23semidirect
131. #947C23semidirect
132. #946C23semidirect
133. #930C23semidirect
134. #929C23semidirect
152. #897C23semidirect
153. #896C23semidirect
154. #895C23semidirect
155. #894C23semidirect
156. #894C23semidirect
157. #889C23semidirect
158. #885C23semidirect
159. #884C23semidirect
160. #884C23semidirect
161. #883C23semidirect
185. C2×C22⋊Q8C2×D3semidirect
348. C22⋊Q8C22×D3semidirect
524. C22×C3#562semidirect
611. C2×C3C2×#562semidirect
634. C22#5647direct (N × H)
650. C3C22×#562semidirect
655. C2C2×#5647direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×#9462
C22×#9472
C22×#9292
C22×#9302
C2×#56472
C22×#8942
C22×#8962
C22×#8972
C22×#8952
C22×#8892
C22×#8832
C22×#8842
C22×#8852
C22×#5623