Finite Group Databasebeta

← C2×#24918285 #36275013

Subgroups — C2×#24918285 #36275013

Order 21248.

2322 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581768C211yesmaximal, characteristic
2C2×C22⋊Q8×D83C211yesmaximal, characteristic
3#24918285C2116yesmaximal, direct product factor
4C2×#19128032C211yesmaximal, characteristic, complemented
5C2×#19128030C212yesmaximal, complemented
6C2×#19128029C211yesmaximal, characteristic, complemented
7C2×#19127958C212yesmaximal, complemented
8C2×#19127956C212yesmaximal, complemented
9C2×#19127857C211yesmaximal, characteristic, complemented
10C2×#19127855C212yesmaximal, complemented
11C2×#19127663C211yesmaximal, characteristic
12C2×#451×C83C211yesmaximal, characteristic, complemented
13C22×Q8×D83C2211yescharacteristic
14C23×C4×D83C2211yescharacteristic
15C22×#13050580C2212yescomplemented
16C22×#13050573C2212yes—
17C2×#14581772C2211yescharacteristic
18C2×#14581771C2211yescharacteristic
19C2×#14581770—21no—
20C2×#14581769—21no—
21C2×#14581768—21no—
22C2×#14581768—24no—
23C2×#14581768—21no—
24C2×#14581768C2218yes—
25C2×#14581768C2211yescharacteristic
26C2×#14581768C2212yes—
27C2×#14581768C2212yes—
28C22⋊Q8×D83—24no—
29C22⋊Q8×D83C2218yes—
30C22×C4⋊Dic83C2211yescharacteristic
31C22×Dic83⋊C4—21no—
32C2×C4⋊C4×D83—21no—
33C2×C4⋊C4×D83C2211yescharacteristic
34C22×(C2×D83)⋊C4—21no—
35C2×C22⋊C4×D83—21no—
36#19128032C2218yescomplemented
37#19128030C22116yescomplemented
38#19128029C2218yescomplemented
39#19127958C22116yescomplemented
40#19127956C22116yescomplemented
41#19127857C2218yescomplemented
42#19127855C22116yescomplemented
43C2×#14581724C2212yescomplemented
44C2×#14581723C2212yescomplemented
45C2×#14581717C2212yescomplemented
46C2×#14581716C2212yescomplemented
47C2×#14581716C2212yescomplemented
48#19127663C2218yes—
49C2×C22⋊(C83⋊C8)C2211yescharacteristic
50C2×(C2×D83)⋊C8C2212yes—
51C23×Q8×C83C2211yescharacteristic
52C22×Q16×C83C2212yescomplemented
53C2×C22⋊Q8×C83C2211yescharacteristic
54#451×C83C2218yescomplemented
55C2×#103×C83C2212yescomplemented
56C2×C22⋊C8×C83C2211yescharacteristic
57C24×D83D411yescharacteristic
58C22×Dic166—21no—
59C22×Dic166C2311yescharacteristic
60C2×Q8×D83—22no—
61C2×Q8×D83—44no—
62C2×Q8×D83C2314yes—
63C23×Dic83—21no—
64C23×Dic83D411yescharacteristic
65C22×C4×D83—21no—
66C22×C4×D83—21no—
67C22×C4×D83—44no—
68C22×C4×D83D411yescharacteristic
69C22×C4×D83D414yes—
70C22×C4×D83D411yescharacteristic
71C22×C4×D83C2311yescharacteristic
72C22×C4×D83C2311yescharacteristic
73C22×C4×D83C2314yes—
74C2×#13050580—44no—
75C2×#13050580C2318yescomplemented
76C2×#13050573—44no—
77C2×#13050573C2318yes—
78C22×C83⋊C8C2312yes—
79#14581772—22no—
80#14581772C2314yes—
81#14581771—22no—
82#14581771C2314yes—
83#14581770—28no—
84#14581769—28no—
85#14581768—22no—
86#14581768—24no—
87#14581768—24no—
88#14581768—28no—
89#14581768—28no—
90#14581768C2318yes—
91#14581768C2314yes—
92#14581768C2318yes—
93C2×C4⋊Dic83—21no—
94C2×C4⋊Dic83—22no—
95C2×C4⋊Dic83—21no—
96C2×C4⋊Dic83C2311yescharacteristic
97C2×C4⋊Dic83C2312yes—
98C2×C4⋊Dic83C2314yes—
99C2×Dic83⋊C4—21no—
100C2×Dic83⋊C4—21no—
101C2×Dic83⋊C4—22no—
102C2×Dic83⋊C4—22no—
103C2×Dic83⋊C4—28no—
104C2×Dic83⋊C4—21no—
105C4⋊C4×D83—28no—
106C4⋊C4×D83—22no—
107C4⋊C4×D83C2314yes—
108C2×C22⋊Dic83—21no—
109C2×(C2×D83)⋊C4—21no—
110C2×(C2×D83)⋊C4—21no—
111C2×(C2×D83)⋊C4—22no—
112C2×(C2×D83)⋊C4—28no—
113C2×(C2×D83)⋊C4—22no—
114C22⋊C4×D83—28no—
115#14581724C2318yescomplemented
116#14581723C2318yescomplemented
117#14581717C2318yescomplemented
118#14581716C2318yescomplemented
119#14581716C2318yescomplemented
120C22⋊(C83⋊C8)C2314yes—
121(C2×D83)⋊C8C2318yes—
122C22×Q8×C83—22no—
123C22×Q8×C83—21no—
124C22×Q8×C83—44no—
125C22×Q8×C83C2311yescharacteristic
126C22×Q8×C83C2312yes—
127C22×Q8×C83C2314yes—
128C23×C4×C83—21no—
129C23×C4×C83C2311yescharacteristic
130C2×Q16×C83—44no—
131C2×Q16×C83C2318yescomplemented
132C22×C8×C83C2312yes—
133C22⋊Q8×C83—22no—
134C22⋊Q8×C83C2314yes—
135C2×C4⋊C4×C83—21no—
136C2×C4⋊C4×C83C2311yescharacteristic
137C2×C22⋊C4×C83—21no—
138#103×C83C2318yescomplemented
139C22⋊C8×C83C2314yes—
140C23×D83—24no—
141C23×D83—24no—
142C23×D83—42no—
143C23×D83C2×D411yescharacteristic
144C23×D83C2×D414yes—
145C23×D83C2×D411yescharacteristic
146C2×Dic166—24no—
147C2×Dic166—21no—
148C2×Dic166—24no—
149C2×Dic166—44no—
150C2×Dic166C2412yes—
151Q8×D83—48no—
152Q8×D83—48no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C22×Dic83—24no—
156C22×Dic83—22no—
157C22×Dic83—42no—
158C22×Dic83—44no—
159C22×Dic83C2×D411yescharacteristic
160C22×Dic83C2×D411yescharacteristic
161C22×Dic83C2×D414yes—
162C2×C4×D83—24no—
163C2×C4×D83—24no—
164C2×C4×D83—24no—
165C2×C4×D83—24no—
166C2×C4×D83—48no—
167C2×C4×D83—48no—
168C2×C4×D83—42no—
169C2×C4×D83—42no—
170C2×C4×D83—44no—
171C2×C4×D83—44no—
172C2×C4×D83C2×D412yes—
173C2×C4×D83C2×D412yes—
174C2×C4×D83C2×D414yes—
175C2×C4×D83C2×D414yes—
176C2×C4×D83C2412yes—
177C2×C4×D83C2412yes—
178#13050580—48no—
179#13050573—48no—
180C2×C83⋊C8—24no—
181C2×C83⋊C8C2414yes—
182C4⋊Dic83—24no—
183C4⋊Dic83—22no—
184C4⋊Dic83—21no—
185C4⋊Dic83—24no—
186C4⋊Dic83C2414yes—
187C4⋊Dic83C2412yes—
188Dic83⋊C4—24no—
189Dic83⋊C4—28no—
190Dic83⋊C4—28no—
191Dic83⋊C4—24no—
192Dic83⋊C4—24no—
193C22⋊Dic83—24no—
194(C2×D83)⋊C4—28no—
195(C2×D83)⋊C4—28no—
196(C2×D83)⋊C4—24no—
197(C2×D83)⋊C4—24no—
198C24×C83C2×D411yescharacteristic
199C2×Q8×C83—24no—
200C2×Q8×C83—22no—
201C2×Q8×C83—21no—
202C2×Q8×C83—24no—
203C2×Q8×C83—24no—
204C2×Q8×C83—24no—
205C2×Q8×C83—48no—
206C2×Q8×C83—44no—
207C2×Q8×C83—48no—
208C2×Q8×C83C2414yes—
209C2×Q8×C83C2412yes—
210C22×C4×C83—24no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—24no—
214C22×C4×C83—22no—
215C22×C4×C83—44no—
216C22×C4×C83C2×D412yes—
217C22×C4×C83C2×D411yescharacteristic
218C22×C4×C83C2412yes—
219C22×C4×C83C2411yescharacteristic
220Q16×C83—48no—
221C2×C8×C83—24no—
222C2×C8×C83C2414yes—
223C4⋊C4×C83—24no—
224C4⋊C4×C83—21no—
225C4⋊C4×C83C2412yes—
226C22⋊C4×C83—24no—
227C23×C83—22no—
228C23×C83—22no—
229C23×C83#13714yes—
230C23×C83C22×D412yes—
231C23×C83C22×D411yescharacteristic
232C22×D83—22no—
233C22×D83—22no—
234C22×D83—22no—
235C22×D83—22no—
236C22×D83—28no—
237C22×D83—22no—
238C22×D83—28no—
239C22×D83—44no—
240C22×D83—416no—
241C22×D83#13714yes—
242C22×D83C22×D412yes—
243C22×D83C22×D412yes—
244Q8×C83—24no—
245Q8×C83—24no—
246Q8×C83—24no—
247Q8×C83—48no—
248Q8×C83—44no—
249Q8×C83—42no—
250C2×C4×C83—22no—
251C2×C4×C83—24no—
252C2×C4×C83—24no—
253C2×C4×C83—22no—
254C2×C4×C83—22no—
255C2×C4×C83—24no—
256C2×C4×C83—48no—
257C2×C4×C83—44no—
258C2×C4×C83—42no—
259C2×C4×C83—42no—
260C2×C4×C83C22×D412yes—
261C2×C4×C83C22×D411yescharacteristic
262C2×C4×C83H(5,𝔽2)14yes—
263C2×C4×C83C2511yescharacteristic
264C2×Dic83—22no—
265C2×Dic83—22no—
266C2×Dic83—24no—
267C2×Dic83—22no—
268C2×Dic83—22no—
269C2×Dic83—44no—
270C2×Dic83—42no—
271C2×Dic83—42no—
272C2×Dic83—48no—
273C2×Dic83—44no—
274C2×Dic83C22×D412yes—
275C2×Dic83C22×D412yes—
276C4×D83—24no—
277C4×D83—24no—
278C4×D83—24no—
279C4×D83—24no—
280C4×D83—44no—
281C4×D83—44no—
282C4×D83—48no—
283C4×D83—48no—
284Dic166—24no—
285Dic166—48no—
286Dic166—42no—
287C8×C83—24no—
288C83⋊C8—24no—
289C22×C83—22no—
290C22×C83—28no—
291C22×C83—22no—
292C22×C83#53412yes—
293C22×C83C2×#13712yes—
294C22×C83C2×#13714yes—
295C22×C83C2×#13712yes—
296C22×C83C23×D411yescharacteristic
297C2×D83—22no—
298C2×D83—28no—
299C2×D83—22no—
300C2×D83—22no—
301C2×D83—22no—
302C2×D83—22no—
303C2×D83—416no—
304C2×D83—44no—
305C2×D83C2×#13714yes—
306C4×C83—22no—
307C4×C83—42no—
308C4×C83—44no—
309C4×C83—42no—
310C4×C83#53412yes—
311C4×C83C2×H(5,𝔽2)12yes—
312Dic83—22no—
313Dic83—22no—
314Dic83—42no—
315Dic83—42no—
316Dic83—44no—
317C2×#3195—831nomaximal, Sylow
318C2×C83—24no—
319C2×C83#319514yescomplemented
320C2×C83C2×#53411yescharacteristic
321C2×C83C22×#13711yescharacteristic
322C2×C83C22×#13711yescharacteristic
323D83—24no—
324D83—42no—
325C22×C22⋊Q8—831no—
326C22×C22⋊Q8—831no—
327#3195—8316no—
328C2×#483—832no—
329C2×#483—831no—
330C2×#483—831no—
331C2×#470—832no—
332C2×#470—832no—
333C2×#451—831no—
334C2×#451—832no—
335C2×#451D8311yescharacteristic, complemented
336C2×#407—831no—
337C83C2×#319511yescharacteristic, complemented, Sylow
338C23×Q8—831no—
339C23×Q8C2×D8311yescharacteristic
340C24×C4—831no—
341C22×Q16—832no—
342C22×Q16C2×D8312yescomplemented
343C22×M16—832no—
344C2×C22⋊Q8—832no—
345C2×C22⋊Q8—838no—
346C2×C22⋊Q8—832no—
347C2×C22⋊Q8—831no—
348C2×C22⋊Q8—831no—
349C2×C22⋊Q8—838no—
350C2×C22⋊Q8—831no—
351C2×C22⋊Q8—1661no—
352C2×C22⋊Q8—1661no—
353C2×C22⋊Q8—1664no—
354C2×C22⋊Q8—1661no—
355C2×C22⋊Q8—1664no—
356C2×C22⋊Q8—1661no—
357C2×C22⋊Q8C2×D8311yescharacteristic
358C22×C4⋊C4—831no—
359C22×C4⋊C4—831no—
360C22×C4⋊C4—1661no—
361C22×C4⋊C4—1661no—
362C22×C22⋊C4—1661no—
363C22×C22⋊C4—1661no—
364#483—838no—
365#483—8316no—
366#483—838no—
367#470—8316no—
368#470—8316no—
369#451—838no—
370#451—8316no—
371#451C2×D8318yescomplemented
372C2×#106—832no—
373C2×#106—832no—
374C2×#103—832no—
375C2×#103—832no—
376C2×#103—832no—
377C2×#103C2×D8312yescomplemented
378#407—838no—
379C2×C22⋊C8—831no—
380C2×C22⋊C8—832no—
381C2×C22⋊C8C2×D8311yescharacteristic
382C25—831no—
383C22×Q8—22no—
384C22×Q8—21no—
385C22×Q8—44no—
386C22×Q8—3324no—
387C22×Q8—834no—
388C22×Q8—831no—
389C22×Q8—1661no—
390C22×Q8—1662no—
391C22×Q8C22×D8312yes—
392C22×Q8C22×D8311yescharacteristic
393C22×Q8C22×D8314yes—
394C23×C4—21no—
395C23×C4—3324no—
396C23×C4—831no—
397C23×C4—831no—
398C23×C4—831no—
399C23×C4—834no—
400C23×C4—834no—
401C23×C4—831no—
402C23×C4—831no—
403C23×C4—1661no—
404C23×C4—1661no—
405C23×C4—1661no—
406C23×C4C22×D8311yescharacteristic
407C2×Q16—44no—
408C2×Q16—3324no—
409C2×Q16—838no—
410C2×Q16C22×D8318yescomplemented
411C2×M16—3324no—
412C2×M16—838no—
413C22×C8—832no—
414C22×C8C22×D8312yes—
415C22⋊Q8—22no—
416C22⋊Q8—838no—
417C22⋊Q8—834no—
418C22⋊Q8—838no—
419C22⋊Q8—834no—
420C22⋊Q8—834no—
421C22⋊Q8—1668no—
422C22⋊Q8—1668no—
423C22⋊Q8—1662no—
424C22⋊Q8—1668no—
425C22⋊Q8—1668no—
426C22⋊Q8—1664no—
427C22⋊Q8—1662no—
428C22⋊Q8—1664no—
429C22⋊Q8—1662no—
430C22⋊Q8C22×D8314yes—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—832no—
433C2×C4⋊C4—831no—
434C2×C4⋊C4—834no—
435C2×C4⋊C4—834no—
436C2×C4⋊C4—1662no—
437C2×C4⋊C4—1668no—
438C2×C4⋊C4—1661no—
439C2×C4⋊C4—1668no—
440C2×C4⋊C4—1661no—
441C2×C4⋊C4—1662no—
442C2×C4⋊C4—1662no—
443C2×C4⋊C4—1661no—
444C2×C4⋊C4—1662no—
445C2×C4⋊C4—1661no—
446C2×C4⋊C4—1661no—
447C2×C4⋊C4C22×D8311yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—1668no—
450C2×C22⋊C4—1668no—
451C2×C22⋊C4—1661no—
452C2×C22⋊C4—1661no—
453C2×C22⋊C4—1662no—
454C2×C22⋊C4—1662no—
455C2×C22⋊C4—1661no—
456#106—838no—
457#106—838no—
458#103—838no—
459#103—838no—
460#103—838no—
461#103C22×D8318yescomplemented
462C22⋊C8—834no—
463C22⋊C8—838no—
464C22⋊C8C22×D8314yes—
465C24—3322no—
466C24—834no—
467C24—831no—
468C24—831no—
469C24—1664no—
470C24—1664no—
471C24D4×D8311yescharacteristic
472C2×Q8—21no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—48no—
479C2×Q8—44no—
480C2×Q8—48no—
481C2×Q8—3324no—
482C2×Q8—3328no—
483C2×Q8—3328no—
484C2×Q8—832no—
485C2×Q8—1664no—
486C2×Q8—1664no—
487C2×Q8—1661no—
488C2×Q8C23×D8312yes—
489C2×Q8C23×D8314yes—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—44no—
496C22×C4—3322no—
497C22×C4—3322no—
498C22×C4—3328no—
499C22×C4—3328no—
500C22×C4—3324no—
501C22×C4—3324no—
502C22×C4—3324no—
503C22×C4—3322no—
504C22×C4—834no—
505C22×C4—834no—
506C22×C4—834no—
507C22×C4—831no—
508C22×C4—831no—
509C22×C4—832no—
510C22×C4—832no—
511C22×C4—832no—
512C22×C4—832no—
513C22×C4—1664no—
514C22×C4—1664no—
515C22×C4—1664no—
516C22×C4—1661no—
517C22×C4—1662no—
518C22×C4—1661no—
519C22×C4—1664no—
520C22×C4—1664no—
521C22×C4D4×D8312yes—
522C22×C4D4×D8311yescharacteristic
523C22×C4C23×D8312yes—
524C22×C4C23×D8311yescharacteristic
525Q16—48no—
526Q16—3328no—
527M16—3328no—
528C2×C8—24no—
529C2×C8—834no—
530C2×C8—1664no—
531C2×C8C23×D8314yes—
532C4⋊C4—24no—
533C4⋊C4—21no—
534C4⋊C4—832no—
535C4⋊C4—834no—
536C4⋊C4—1664no—
537C4⋊C4—1664no—
538C4⋊C4—1668no—
539C4⋊C4—1668no—
540C4⋊C4—1664no—
541C4⋊C4—1664no—
542C4⋊C4—1661no—
543C4⋊C4—1662no—
544C4⋊C4—1664no—
545C4⋊C4C23×D8312yes—
546C22⋊C4—24no—
547C22⋊C4—1664no—
548C22⋊C4—1664no—
549C22⋊C4—1668no—
550C22⋊C4—1668no—
551C22⋊C4—1664no—
552C23—22no—
553C23—22no—
554C23—33216no—
555C23—3324no—
556C23—834no—
557C23—832no—
558C23—832no—
559C23—1668no—
560C23—1662no—
561C23—1668no—
562C23—1662no—
563C23—1662no—
564C23—1662no—
565C23—1662no—
566C23#1458182414yes—
567C23C2×D4×D8312yes—
568C23C2×D4×D8311yescharacteristic
569Q8—24no—
570Q8—24no—
571Q8—24no—
572Q8—48no—
573Q8—44no—
574Q8—42no—
575Q8—3328no—
576Q8—3322no—
577Q8—1664no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—48no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—42no—
588C2×C4—3324no—
589C2×C4—3324no—
590C2×C4—3328no—
591C2×C4—3328no—
592C2×C4—3322no—
593C2×C4—3328no—
594C2×C4—3324no—
595C2×C4—3322no—
596C2×C4—3324no—
597C2×C4—832no—
598C2×C4—832no—
599C2×C4—1662no—
600C2×C4—1664no—
601C2×C4—1662no—
602C2×C4—1662no—
603C2×C4—1662no—
604C2×C4—1664no—
605C2×C4—1664no—
606C2×C4—1664no—
607C2×C4—1664no—
608C2×C4C2×D4×D8312yes—
609C2×C4C2×D4×D8311yescharacteristic
610C2×C4#1458183714yes—
611C2×C4C24×D8311yescharacteristic
612C8—24no—
613C8—1664no—
614C22—28no—
615C22—22no—
616C22—22no—
617C22—33216no—
618C22—3324no—
619C22—834no—
620C22—1662no—
621C22—1662no—
622C22—1662no—
623C22—1668no—
624C22—1662no—
625C22—1662no—
626C22#1912826112yes—
627C22#137×D8312yes—
628C22C2×#1458182414yes—
629C22C2×#1458182412yes—
630C22C22×D4×D8311yescharacteristic
631C4—22no—
632C4—42no—
633C4—44no—
634C4—42no—
635C4—3322no—
636C4—3324no—
637C4—3322no—
638C4—1662no—
639C4—1662no—
640C4#1912826112yes—
641C4C2×#1458183712yes—
642C2—24no—
643C2—3322no—
644C2—1664no—
645C2#2491828514yesdirect product factor
646C2C2×#1912826111yescharacteristic
647C2C2×#137×D8311yescharacteristic
648C2C22×#1458182411yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#451×C83C2
socleC23×C83C22×D4
prime radicalC24×D83D4
hypercenterC2×#451D83
hypocenterC83C2×#3195
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #24918285C2direct (N × H)
4. C2×#19128032C2semidirect
5. C2×#19128030C2semidirect
6. C2×#19128029C2semidirect
7. C2×#19127958C2semidirect
8. C2×#19127956C2semidirect
9. C2×#19127857C2semidirect
10. C2×#19127855C2semidirect
12. C2×#451×C83C2semidirect
15. C22×#13050580C22semidirect
36. #19128032C22semidirect
37. #19128030C22semidirect
38. #19128029C22semidirect
39. #19127958C22semidirect
40. #19127956C22semidirect
41. #19127857C22semidirect
42. #19127855C22semidirect
43. C2×#14581724C22semidirect
44. C2×#14581723C22semidirect
45. C2×#14581717C22semidirect
46. C2×#14581716C22semidirect
47. C2×#14581716C22semidirect
52. C22×Q16×C83C22semidirect
54. #451×C83C22semidirect
55. C2×#103×C83C22semidirect
75. C2×#13050580C23semidirect
115. #14581724C23semidirect
116. #14581723C23semidirect
117. #14581717C23semidirect
118. #14581716C23semidirect
119. #14581716C23semidirect
131. C2×Q16×C83C23semidirect
138. #103×C83C23semidirect
319. C2×C83#3195semidirect
335. C2×#451D83semidirect
337. C83C2×#3195semidirect
342. C22×Q16C2×D83semidirect
371. #451C2×D83semidirect
377. C2×#103C2×D83semidirect
410. C2×Q16C22×D83semidirect
461. #103C22×D83semidirect
645. C2#24918285direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817682
C2×C22⋊Q8×D832
#249182852
C2×#191280322
C2×#191280302
C2×#191280292
C2×#191279582
C2×#191279562
C2×#191278572
C2×#191278552
C2×#191276632
C2×#451×C832
C2×#319583