Finite Group Databasebeta

← #32054584

Subgroups — #32054584

Order 18176.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986284C211yesmaximal, characteristic, complemented
2C22×#14556052C211yesmaximal, characteristic
3#22592042C211yesmaximal, characteristic
4#22589883C211yesmaximal, characteristic, complemented
5#22589721C211yesmaximal, characteristic, complemented
6#22589721C211yesmaximal, characteristic, complemented
7#22589481C211yesmaximal, characteristic, complemented
8#22588608C211yesmaximal, characteristic, complemented
9#22588608C211yesmaximal, characteristic, complemented
10#22588532C211yesmaximal, characteristic
11#22588520C211yesmaximal, characteristic
12#22588363C211yesmaximal, characteristic
13#22588345C211yesmaximal, characteristic, complemented
14#22588275C211yesmaximal, characteristic
15Q8×C22⋊C4×C71C211yesmaximal, characteristic
16C23×C71⋊C8C2211yescharacteristic
17C2×#14556128C2211yescharacteristic
18C2×#14556105—21no—
19C22×C4⋊Dic71C2211yescharacteristic
20#17986284—24no—
21C2×#14556059C2211yescharacteristic
22C2×#14556059C2211yescharacteristic
23C2×#14556059C2211yescharacteristic
24C2×#14556059C2211yescharacteristic
25C2×C4⋊(C71⋊C8)C2211yescharacteristic
26C2×C4⋊(C71⋊C8)C2211yescharacteristic
27C2×#14556052—24no—
28C2×#14556052C2211yescharacteristic
29C2×#14556052C2211yescharacteristic
30C2×#14556052C2211yescharacteristic
31C2×#14556052C2211yescharacteristic
32C2×#14556052C2211yescharacteristic
33C2×#14556052C2211yescharacteristic
34C2×#14556052C2211yescharacteristic
35C2×#14556052C2211yescharacteristic
36C2×C22⋊(C71⋊C8)C2211yescharacteristic
37#17985931—21no—
38#17985920—21no—
39#17985897C2211yescharacteristic
40#17985897C2211yescharacteristic
41#17985874—21no—
42#17985869C2211yescharacteristic
43#17985859C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985754C2211yescharacteristic
49#17985754C2211yescharacteristic
50C23×Q8×C71C2211yescharacteristic
51C2×C4×Q8×C71C2211yescharacteristic
52C2×C4×Q8×C71C2211yescharacteristic
53#391×C71—21no—
54#391×C71—21no—
55#391×C71C2211yescharacteristic
56#391×C71C2211yescharacteristic
57#380×C71—21no—
58#380×C71C2211yescharacteristic
59C4×C22⋊C4×C71—21no—
60C4×C22⋊C4×C71C2211yescharacteristic
61C22×Dic142—21no—
62C23×Dic71—21no—
63C22×C71⋊C8—22no—
64C22×C71⋊C8—22no—
65C22×C71⋊C8—41no—
66C22×C71⋊C8C2311yescharacteristic
67C22×C71⋊C8C2311yescharacteristic
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70#14556128—22no—
71#14556128—41no—
72#14556105—44no—
73C2×C4⋊Dic71—22no—
74C2×C4⋊Dic71—21no—
75C2×C4⋊Dic71—21no—
76C2×C4⋊Dic71—21no—
77C2×C4⋊Dic71—21no—
78C2×C4⋊Dic71—41no—
79C2×C4⋊Dic71C2311yescharacteristic
80C2×C4⋊Dic71C2311yescharacteristic
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C4⋊Dic71C2311yescharacteristic
83C2×Dic71⋊C4—21no—
84C2×Dic71⋊C4—21no—
85C2×C22⋊Dic71—21no—
86#14556059—22no—
87#14556059—22no—
88#14556059—41no—
89#14556059—41no—
90C4⋊(C71⋊C8)—22no—
91C4⋊(C71⋊C8)—41no—
92#14556052—22no—
93#14556052—22no—
94#14556052—22no—
95#14556052—22no—
96#14556052—22no—
97#14556052—41no—
98#14556052—41no—
99#14556052D414yes—
100C22⋊(C71⋊C8)—22no—
101C71⋊#95—21no—
102C71⋊#95—21no—
103C71⋊#95—21no—
104C22×Q8×C71—21no—
105C22×Q8×C71—22no—
106C22×Q8×C71—22no—
107C22×Q8×C71—22no—
108C22×Q8×C71—41no—
109C22×Q8×C71—41no—
110C22×Q8×C71Q814yescomplemented
111C22×Q8×C71C2311yescharacteristic
112C22×Q8×C71C2311yescharacteristic
113C23×C4×C71—21no—
114C23×C4×C71C2311yescharacteristic
115C4×Q8×C71—22no—
116C4×Q8×C71—22no—
117C4×Q8×C71—41no—
118C4×Q8×C71—41no—
119C2×C4⋊C4×C71—21no—
120C2×C4⋊C4×C71—21no—
121C2×C4⋊C4×C71C2311yescharacteristic
122C2×C4⋊C4×C71C2311yescharacteristic
123C2×C22⋊C4×C71—21no—
124C2×C22⋊C4×C71D411yescharacteristic
125C2×C22⋊C4×C71D411yescharacteristic
126C2×C42×C71—21no—
127C2×C42×C71—21no—
128C2×C42×C71C2311yescharacteristic
129C2×C42×C71C2311yescharacteristic
130#95×C71—21no—
131#95×C71—21no—
132#95×C71—21no—
133#95×C71—21no—
134#95×C71—21no—
135#95×C71D411yescharacteristic
136#95×C71D411yescharacteristic
137C2×Dic142—42no—
138C2×Dic142—42no—
139C2×Dic142—81no—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—42no—
145C22×Dic71—42no—
146C22×Dic71—81no—
147C2×C71⋊C8—21no—
148C2×C71⋊C8—21no—
149C2×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—44no—
159C2×C71⋊C8C2×D412yes—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—42no—
168C4⋊Dic71—42no—
169C4⋊Dic71—42no—
170C4⋊Dic71—81no—
171C4⋊Dic71C2×D412yes—
172Dic71⋊C4—42no—
173Dic71⋊C4—42no—
174C22⋊Dic71—42no—
175C24×C71C2×D411yescharacteristic
176C2×Q8×C71—24no—
177C2×Q8×C71—21no—
178C2×Q8×C71—21no—
179C2×Q8×C71—21no—
180C2×Q8×C71—21no—
181C2×Q8×C71—28no—
182C2×Q8×C71—21no—
183C2×Q8×C71—21no—
184C2×Q8×C71—21no—
185C2×Q8×C71—21no—
186C2×Q8×C71—42no—
187C2×Q8×C71—42no—
188C2×Q8×C71—44no—
189C2×Q8×C71—44no—
190C2×Q8×C71—44no—
191C2×Q8×C71C2×D412yes—
192C2×Q8×C71C2×Q812yes—
193C2×Q8×C71C2×Q812yes—
194C2×Q8×C71#4112yes—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—24no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—42no—
205C22×C4×C71—42no—
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71C2×D411yescharacteristic
210C22×C4×C71C2×D411yescharacteristic
211C22×C4×C71C2×Q812yes—
212C22×C4×C71#4112yes—
213C22×C4×C71C2411yescharacteristic
214C4⋊C4×C71—21no—
215C4⋊C4×C71—21no—
216C4⋊C4×C71—21no—
217C4⋊C4×C71—21no—
218C4⋊C4×C71—42no—
219C4⋊C4×C71—42no—
220C22⋊C4×C71—22no—
221C22⋊C4×C71—42no—
222C22⋊C4×C71SD1614yes—
223C42×C71—21no—
224C42×C71—21no—
225C42×C71—21no—
226C42×C71—21no—
227C42×C71—42no—
228C42×C71—42no—
229C23×C71—21no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71C22⋊Q812yes—
234C23×C71C2×SD1612yes—
235C23×C71#13712yes—
236C23×C71C22×D411yescharacteristic
237Q8×C71—22no—
238Q8×C71—22no—
239Q8×C71—22no—
240Q8×C71—22no—
241Q8×C71—22no—
242Q8×C71—48no—
243Q8×C71—41no—
244Q8×C71—41no—
245Q8×C71C22⋊Q814yescomplemented
246C2×C4×C71—22no—
247C2×C4×C71—21no—
248C2×C4×C71—22no—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—22no—
252C2×C4×C71—21no—
253C2×C4×C71—21no—
254C2×C4×C71—21no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—22no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—48no—
267C2×C4×C71—41no—
268C2×C4×C71—41no—
269C2×C4×C71—41no—
270C2×C4×C71—41no—
271C2×C4×C71—41no—
272C2×C4×C71—41no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71C22⋊Q812yes—
276C2×C4×C71C2×SD1612yes—
277C2×C4×C71C2×SD1612yes—
278C2×C4×C71C22×D411yescharacteristic
279C2×C4×C71C22×Q811yescharacteristic
280C2×C4×C71C2×#4111yescharacteristic
281C2×C4×C71C2×#4111yescharacteristic
282C2×C4×C71H(5,𝔽2)11yescharacteristic
283C2×C4×C71H(5,𝔽2)11yescharacteristic
284C2×Dic71—22no—
285C2×Dic71—41no—
286C2×Dic71—41no—
287C2×Dic71—41no—
288C2×Dic71—41no—
289C2×Dic71—41no—
290C2×Dic71—41no—
291C2×Dic71—41no—
292C2×Dic71—41no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—84no—
297Dic142—84no—
298C71⋊C8—22no—
299C71⋊C8—41no—
300C71⋊C8—41no—
301C71⋊C8—41no—
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—22no—
306C22×C71—22no—
307C22×C71—22no—
308C22×C71#47514yescomplemented
309C22×C71C2×C22⋊Q811yescharacteristic
310C22×C71D4211yescharacteristic
311C22×C71#54611yescharacteristic
312C22×C71C22×SD1611yescharacteristic
313C22×C71C2×#13711yescharacteristic
314C22×C71#57711yescharacteristic
315C22×C71#57811yescharacteristic
316C4×C71—22no—
317C4×C71—24no—
318C4×C71—22no—
319C4×C71—22no—
320C4×C71—42no—
321C4×C71—41no—
322C4×C71—41no—
323C4×C71—81no—
324C4×C71—81no—
325C4×C71C2×C22⋊Q811yescharacteristic
326C4×C71#54311yescharacteristic
327C4×C71#54611yescharacteristic
328C4×C71#55111yescharacteristic
329Dic71—42no—
330Dic71—81no—
331Dic71—81no—
332Dic71—81no—
333#25955—711nomaximal, Sylow
334C2×C71—24no—
335C2×C71#243711yescharacteristic
336C2×C71C2×#47511yescharacteristic
337C2×C71#308211yescharacteristic
338C2×C71#327011yescharacteristic
339C2×C71D4×SD1611yescharacteristic
340C2×C71#329811yescharacteristic
341C2×C71#331611yescharacteristic
342C2×#475—711no—
343C22×#103—711no—
344#2440—711no—
345Q8×C22⋊C4D7111yescharacteristic
346#2096—711no—
347#2066—711no—
348#2066—711no—
349#2024—711no—
350#1865—711no—
351#1865—711no—
352#1853—711no—
353#1850—711no—
354#1807—711no—
355#1803—711no—
356#1787—711no—
357C71#2595511yescharacteristic, complemented, Sylow
358C23×Q8C2×D7111yescharacteristic
359C23×C8—711no—
360C2×C4⋊Q8—711no—
361C2×C22⋊Q8—1421no—
362C2×C4×Q8C2×D7111yescharacteristic
363C2×C4×Q8C2×D7111yescharacteristic
364C22×C4⋊C4—711no—
365#475—1424no—
366C2×#106—711no—
367C2×#106—711no—
368C2×#106—711no—
369C2×#106—711no—
370C2×C4⋊C8—711no—
371C2×C4⋊C8—711no—
372C2×#103—711no—
373C2×#103—711no—
374C2×#103—711no—
375C2×#103—711no—
376C2×#103—711no—
377C2×#103—711no—
378C2×#103—711no—
379C2×#103—711no—
380C2×#103—1424no—
381C2×C22⋊C8—711no—
382#398—1421no—
383#395—1421no—
384#391—21no—
385#391—21no—
386#391C2×D7111yescharacteristic
387#391C2×D7111yescharacteristic
388#389—711no—
389#389—711no—
390#385—1421no—
391#384—711no—
392#380—21no—
393#380—711no—
394#380C2×D7111yescharacteristic
395C4×C22⋊C4—21no—
396C4×C22⋊C4C2×D7111yescharacteristic
397#340—711no—
398#340—711no—
399#340—711no—
400#340—711no—
401#336—711no—
402#336—711no—
403C22×Q8—21no—
404C22×Q8—22no—
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—41no—
408C22×Q8—41no—
409C22×Q8—1421no—
410C22×Q8Dic14214yescomplemented
411C22×Q8C22×D7111yescharacteristic
412C22×Q8C22×D7111yescharacteristic
413C23×C4—21no—
414C23×C4—1421no—
415C23×C4C22×D7111yescharacteristic
416C22×C8—2841no—
417C22×C8—711no—
418C22×C8—711no—
419C22×C8—711no—
420C22×C8—711no—
421C22×C8—1422no—
422C22×C8—1422no—
423C4⋊Q8—2841no—
424C4⋊Q8—1422no—
425C22⋊Q8—2844no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—41no—
429C4×Q8—41no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—2841no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C4⋊C4—711no—
436C2×C4⋊C4—711no—
437C2×C4⋊C4—1421no—
438C2×C4⋊C4—1421no—
439C2×C4⋊C4—1421no—
440C2×C4⋊C4—1421no—
441C2×C4⋊C4—1421no—
442C2×C4⋊C4—1422no—
443C2×C4⋊C4—1421no—
444C2×C4⋊C4C22×D7111yescharacteristic
445C2×C4⋊C4C22×D7111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—1421no—
448C2×C22⋊C4C22⋊D7111yescharacteristic
449C2×C22⋊C4C22⋊D7111yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C22×D7111yescharacteristic
453C2×C42C22×D7111yescharacteristic
454#106—2841no—
455#106—2841no—
456#106—1422no—
457#106—1422no—
458C4⋊C8—2841no—
459C4⋊C8—1422no—
460#103—2841no—
461#103—2841no—
462#103—714no—
463#103—1422no—
464#103—1422no—
465#103—1422no—
466#103—1422no—
467#103—1422no—
468C22⋊C8—1422no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—1421no—
475#95—1421no—
476#95—1421no—
477#95C22⋊D7111yescharacteristic
478#95C22⋊D7111yescharacteristic
479C24C2×C22⋊D7111yescharacteristic
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—24no—
485C2×Q8—28no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—2842no—
496C2×Q8—2842no—
497C2×Q8—5681no—
498C2×Q8D4×D7112yes—
499C2×Q8C2×Dic14212yes—
500C2×Q8C2×Dic14212yes—
501C2×Q8#1176586412yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—2842no—
514C22×C4—2842no—
515C22×C4—5681no—
516C22×C4—1421no—
517C22×C4—1421no—
518C22×C4—1421no—
519C22×C4—1421no—
520C22×C4C2×C22⋊D7111yescharacteristic
521C22×C4C2×C22⋊D7111yescharacteristic
522C22×C4C2×C22⋊D7111yescharacteristic
523C22×C4C2×C22⋊D7111yescharacteristic
524C22×C4C2×C22⋊D7111yescharacteristic
525C22×C4C2×Dic14212yes—
526C22×C4#1176586512yes—
527C22×C4C23×D7111yescharacteristic
528C2×C8—2844no—
529C2×C8—712no—
530C2×C8—1421no—
531C2×C8—1421no—
532C2×C8—1421no—
533C2×C8—1421no—
534C2×C8—1421no—
535C2×C8—1421no—
536C2×C8—1421no—
537C2×C8—1421no—
538C2×C8—1421no—
539C2×C8—1421no—
540C2×C8—1421no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—2842no—
548C4⋊C4—2842no—
549C4⋊C4—2842no—
550C4⋊C4—2842no—
551C4⋊C4—2842no—
552C4⋊C4—5681no—
553C4⋊C4—712no—
554C4⋊C4—1421no—
555C4⋊C4—1421no—
556C4⋊C4—1421no—
557C4⋊C4—1421no—
558C4⋊C4—1421no—
559C4⋊C4—1421no—
560C4⋊C4—1421no—
561C22⋊C4—22no—
562C22⋊C4—42no—
563C22⋊C4—2842no—
564C22⋊C4#1176585214yes—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—42no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23#1455610712yes—
576C23C2×#1176585212yes—
577C23#1455615812yes—
578C23C22×C22⋊D7111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—48no—
585Q8—41no—
586Q8—41no—
587Q8—5684no—
588Q8#1455610514yescomplemented
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—48no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—2841no—
619C2×C4—2841no—
620C2×C4—2841no—
621C2×C4—2841no—
622C2×C4—2841no—
623C2×C4—2841no—
624C2×C4—2841no—
625C2×C4—2841no—
626C2×C4—2841no—
627C2×C4—2841no—
628C2×C4—2841no—
629C2×C4—5684no—
630C2×C4—1422no—
631C2×C4#1455610712yes—
632C2×C4C2×#1176585212yes—
633C2×C4C2×#1176585212yes—
634C2×C4C2×D4×D7111yescharacteristic
635C2×C4C22×Dic14211yescharacteristic
636C2×C4C2×#1176586411yescharacteristic
637C2×C4C2×#1176586511yescharacteristic
638C2×C4#1455617311yescharacteristic
639C2×C4#1455617311yescharacteristic
640C8—2841no—
641C8—2841no—
642C8—2841no—
643C8—1422no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22#1798628414yescomplemented
651C22C2×#1455610711yescharacteristic
652C22D4×C22⋊D7111yescharacteristic
653C22#1798664311yescharacteristic
654C22C22×#1176585211yescharacteristic
655C22C2×#1455615811yescharacteristic
656C22#1798680711yescharacteristic
657C22#1798681411yescharacteristic
658C4—22no—
659C4—24no—
660C4—22no—
661C4—22no—
662C4—42no—
663C4—41no—
664C4—41no—
665C4—81no—
666C4—81no—
667C4—2842no—
668C4—5681no—
669C4—5681no—
670C4—5681no—
671C4C2×#1455610511yescharacteristic
672C4#1798662511yescharacteristic
673C4#1798663911yescharacteristic
674C4#1798667511yescharacteristic
675C2—24no—
676C2#2259200111yescharacteristic
677C2C2×#1798628411yescharacteristic
678C2#2259818211yescharacteristic
679C2#2259990611yescharacteristic
680C2D4×#1176585211yescharacteristic
681C2#2260020511yescharacteristic
682C2#2260045111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
FittingQ8×C22⋊C4×C71C2
socleC23×C71C22×D4
prime radicalC24×C71C2×D4
hypercenterQ8×C22⋊C4D71
hypocenterC71#25955
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#17986284C2semidirect
4. #22589883C2semidirect
5. #22589721C2semidirect
6. #22589721C2semidirect
7. #22589481C2semidirect
8. #22588608C2semidirect
9. #22588608C2semidirect
13. #22588345C2semidirect
110. C22×Q8×C71Q8semidirect
245. Q8×C71C22⋊Q8semidirect
308. C22×C71#475semidirect
357. C71#25955semidirect
410. C22×Q8Dic142semidirect
588. Q8#14556105semidirect
650. C22#17986284semidirect

Maximal subgroups

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

subgroupindex
C2×#179862842
C22×#145560522
#225920422
#225898832
#225897212
#225894812
#225886082
#225885322
#225885202
#225883632
#225883452
#225882752
Q8×C22⋊C4×C712
#2595571