Finite Group Databasebeta

← C2×#22601281 #32877975

Subgroups — C2×#22601281 #32877975

Order 18176.

1822 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×#17986725C211yesmaximal, characteristic, complemented
2C2×#17986708C211yesmaximal, characteristic
3#22601281C2116yesmaximal, direct product factor
4C2×#17986406C211yesmaximal, characteristic, complemented
5C2×#17986406C211yesmaximal, characteristic, complemented
6C2×#17986401C211yesmaximal, characteristic, complemented
7C2×#17986306C211yesmaximal, characteristic, complemented
8C2×#17986304C211yesmaximal, characteristic, complemented
9C2×#17986282C211yesmaximal, characteristic, complemented
10C2×#17986301C211yesmaximal, characteristic
11C2×#17986299C211yesmaximal, characteristic
12C2×#17986287C211yesmaximal, characteristic
13C2×#17986129C211yesmaximal, characteristic, complemented
14C2×#17986100C211yesmaximal, characteristic
15C2×#17986100C211yesmaximal, characteristic
16C2×C4×SD16×C71C211yesmaximal, characteristic
17#17986725—24no—
18#17986725C2218yescomplemented
19#17986708—24no—
20#17986708C2218yes—
21C2×#14556127—21no—
22C2×#14556127C2211yescharacteristic
23C2×#14556127C2211yescharacteristic
24C2×#14556120—21no—
25C2×#14556120C2211yescharacteristic
26C2×#14556120C2211yescharacteristic
27C2×#14556119—21no—
28C2×#14556119C2211yescharacteristic
29C2×#14556119C2211yescharacteristic
30C2×#14556107—21no—
31C2×#14556105—21no—
32C2×#14556105—21no—
33C2×Q8×Dic71C2211yescharacteristic
34C2×Q8×Dic71C2211yescharacteristic
35C2×C4×Dic142—21no—
36C2×C4×Dic142C2211yescharacteristic
37C2×D4×Dic71C2211yescharacteristic
38C2×D4×Dic71C2211yescharacteristic
39C22×Dic71⋊C4—21no—
40#17986406C2218yescomplemented
41#17986406C2218yescomplemented
42#17986401C2218yescomplemented
43#17986306C2218yescomplemented
44#17986304C2218yescomplemented
45#17986301C2218yes—
46#17986299C2218yes—
47#17986287C2218yes—
48#17986282C2218yescomplemented
49#17986129C2218yescomplemented
50#17986100C2218yes—
51#17986100C2218yes—
52C2×#14556062C2211yescharacteristic
53C2×#14556062C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58C2×#14556059C2211yescharacteristic
59C2×#14556059C2211yescharacteristic
60C2×C4⋊(C71⋊C8)C2211yescharacteristic
61C2×Dic71⋊C8C2211yescharacteristic
62C2×Dic71⋊C8C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556052C2211yescharacteristic
65C2×#14556049C2211yescharacteristic
66C2×#14556049C2211yescharacteristic
67C2×#14556038C2211yescharacteristic
68C2×#14556038C2211yescharacteristic
69C22×SD16×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72C4×SD16×C71C2218yes—
73C2×#106×C71C2211yescharacteristic
74C2×#103×C71C2211yescharacteristic
75C2×#102×C71C2211yescharacteristic
76C2×C4×C8×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142D411yescharacteristic
80C23×Dic71—21no—
81C23×Dic71—21no—
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84#14556127—28no—
85#14556127—22no—
86#14556127—22no—
87#14556127C2314yes—
88#14556127C2314yes—
89#14556120—28no—
90#14556120—22no—
91#14556120—22no—
92#14556120C2314yes—
93#14556120C2314yes—
94#14556119—28no—
95#14556119—22no—
96#14556119—22no—
97#14556119C2314yes—
98#14556119C2314yes—
99#14556107—28no—
100#14556105—28no—
101#14556105—28no—
102Q8×Dic71—22no—
103Q8×Dic71—22no—
104Q8×Dic71C2314yes—
105Q8×Dic71C2314yes—
106C4×Dic142—28no—
107C4×Dic142D414yes—
108C4×Dic142C2314yes—
109D4×Dic71—22no—
110D4×Dic71—22no—
111D4×Dic71C2314yes—
112D4×Dic71C2314yes—
113C2×C4⋊Dic71—21no—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71D411yescharacteristic
118C2×C4⋊Dic71C2311yescharacteristic
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×Dic71⋊C4—21no—
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—28no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4D411yescharacteristic
132C2×Dic71⋊C4D411yescharacteristic
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71—21no—
135C2×C4×Dic71—21no—
136C2×C4×Dic71—21no—
137C2×C4×Dic71C2311yescharacteristic
138C2×C4×Dic71C2311yescharacteristic
139#14556062C2314yes—
140#14556062C2314yes—
141#14556061C2314yes—
142#14556061C2314yes—
143#14556060C2314yes—
144#14556060C2314yes—
145#14556059C2314yes—
146#14556059C2314yes—
147C4⋊(C71⋊C8)C2314yes—
148Dic71⋊C8C2314yes—
149Dic71⋊C8C2314yes—
150#14556052C2314yes—
151#14556052C2314yes—
152#14556049C2314yes—
153#14556049C2314yes—
154#14556038C2314yes—
155#14556038C2314yes—
156C22×Q8×C71C2311yescharacteristic
157C22×D4×C71C2311yescharacteristic
158C23×C4×C71—21no—
159C2×SD16×C71Q818yescomplemented
160C2×SD16×C71C2314yes—
161C22×C8×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163C4×Q8×C71—22no—
164C4×Q8×C71C2314yes—
165C4×D4×C71—22no—
166C4×D4×C71C2314yes—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C22⋊C4×C71—21no—
171C2×C42×C71—21no—
172C2×C42×C71C2311yescharacteristic
173#106×C71C2314yes—
174#103×C71C2314yes—
175#102×C71C2314yes—
176C4×C8×C71C2314yes—
177C2×Dic142—24no—
178C2×Dic142—24no—
179C2×Dic142—42no—
180C2×Dic142—44no—
181C2×Dic142—82no—
182C2×Dic142C2×D414yes—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—24no—
188C22×Dic71—24no—
189C22×Dic71—44no—
190C22×Dic71—82no—
191C22×Dic71C2×D411yescharacteristic
192C22×Dic71C2×D411yescharacteristic
193C22×Dic71C2×D411yescharacteristic
194C22×Dic71C2×D411yescharacteristic
195C2×C71⋊C8—22no—
196C2×C71⋊C8—22no—
197C2×C71⋊C8C2412yes—
198C2×C71⋊C8C2412yes—
199C4⋊Dic71—21no—
200C4⋊Dic71—21no—
201C4⋊Dic71—21no—
202C4⋊Dic71—21no—
203C4⋊Dic71—24no—
204C4⋊Dic71—24no—
205C4⋊Dic71—24no—
206C4⋊Dic71—24no—
207C4⋊Dic71C2×D414yes—
208C4⋊Dic71C2412yes—
209C4⋊Dic71C2412yes—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212Dic71⋊C4—24no—
213Dic71⋊C4—24no—
214Dic71⋊C4—24no—
215Dic71⋊C4—24no—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220Dic71⋊C4C2×D414yes—
221Dic71⋊C4C2×D414yes—
222C22⋊Dic71—24no—
223C22⋊Dic71—24no—
224C4×Dic71—24no—
225C4×Dic71—24no—
226C4×Dic71C2×D412yes—
227C4×Dic71C2×D412yes—
228C4×Dic71C2412yes—
229C4×Dic71C2412yes—
230C24×C71—21no—
231C2×Q8×C71—21no—
232C2×Q8×C71—22no—
233C2×Q8×C71C2×Q814yes—
234C2×Q8×C71C2412yes—
235C2×D4×C71—21no—
236C2×D4×C71—22no—
237C2×D4×C71C2×Q814yes—
238C2×D4×C71C2412yes—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—24no—
243C22×C4×C71—82no—
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2411yescharacteristic
247SD16×C71C2×Q8116yescomplemented
248C2×C8×C71—22no—
249C2×C8×C71C2×Q814yes—
250C2×C8×C71C2412yes—
251C2×C8×C71C2412yes—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71C2412yes—
256C4⋊C4×C71C2412yes—
257C22⋊C4×C71—24no—
258C42×C71—24no—
259C42×C71C2×D412yes—
260C42×C71C2412yes—
261C23×C71—24no—
262C23×C71—22no—
263C23×C71—42no—
264C23×C71—42no—
265C23×C71C22×D411yescharacteristic
266Q8×C71—24no—
267Q8×C71—22no—
268Q8×C71C22×Q814yes—
269D4×C71—24no—
270D4×C71—22no—
271D4×C71C22×Q814yes—
272C2×C4×C71—24no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—42no—
279C2×C4×C71—42no—
280C2×C4×C71—84no—
281C2×C4×C71C22×D412yes—
282C2×C4×C71C22×D412yes—
283C2×C4×C71C22×D411yescharacteristic
284C2×C4×C71C22×Q812yes—
285C2×C4×C712−1+412yes—
286C2×C4×C71C2511yescharacteristic
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—48no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71—42no—
299C2×Dic71—42no—
300C2×Dic71—84no—
301C2×Dic71C22×D412yes—
302C2×Dic71C22×D412yes—
303C2×Dic71C22×D412yes—
304C2×Dic71C22×D412yes—
305Dic142—44no—
306Dic142—48no—
307Dic142—84no—
308C8×C71—22no—
309C8×C71C22×Q814yes—
310C71⋊C8—22no—
311C71⋊C8—22no—
312C22×C71—24no—
313C22×C71—48no—
314C22×C71—42no—
315C22×C71—42no—
316C22×C71D4×Q812yes—
317C22×C71#57512yes—
318C22×C71#57712yes—
319C22×C71C23×D411yescharacteristic
320C4×C71—24no—
321C4×C71—22no—
322C4×C71—22no—
323C4×C71—42no—
324C4×C71—42no—
325C4×C71D4×Q812yes—
326C4×C71C23×Q811yescharacteristic
327C4×C71C2×2−1+411yescharacteristic
328Dic71—22no—
329Dic71—22no—
330Dic71—22no—
331Dic71—22no—
332Dic71—42no—
333Dic71—42no—
334Dic71—42no—
335Dic71—42no—
336C2×#3388—711nomaximal, Sylow
337C2×C71—44no—
338C2×C71#338814yescomplemented
339C2×C71C2×D4×Q811yescharacteristic
340C2×C71C2×#57511yescharacteristic
341C2×C71C2×#57711yescharacteristic
342C2×#557—711no—
343C2×#554—711no—
344#3388—7116no—
345C2×#501—711no—
346C2×#501—711no—
347C2×#499—711no—
348C2×#479—711no—
349C2×#479—711no—
350C2×#475—711no—
351C2×#478—711no—
352C2×#478—711no—
353C2×#476—711no—
354C2×#446—711no—
355C2×#440—711no—
356C2×#440—711no—
357C2×C4×SD16D7111yescharacteristic
358C71C2×#338811yescharacteristic, complemented, Sylow
359C22×SD16C2×D7111yescharacteristic
360#557—718no—
361#557—1424no—
362#554—718no—
363#554—1424no—
364C2×C4⋊Q8—711no—
365C2×C4⋊Q8—711no—
366C2×C4⋊Q8—1421no—
367C2×#125—711no—
368C2×#125—711no—
369C2×#125—711no—
370C2×#125—711no—
371C2×#125—1421no—
372C2×#125—1421no—
373C2×C22⋊Q8—1421no—
374C2×C22⋊Q8—1421no—
375C2×C22⋊Q8—1421no—
376C2×C4×Q8—711no—
377C2×C4×Q8—711no—
378C2×C4×Q8—711no—
379C2×C4×Q8—1421no—
380C2×C4×Q8C2×D7111yescharacteristic
381C2×C4×D4—711no—
382C2×C4×D4—711no—
383C2×C4×D4C2×D7111yescharacteristic
384C22×C4⋊C4—1421no—
385#501—718no—
386#501—718no—
387#499—718no—
388#479—718no—
389#479—718no—
390#478—718no—
391#478—718no—
392#476—718no—
393#475—718no—
394#446—718no—
395#440—718no—
396#440—718no—
397C4×SD16C2×D7118yes—
398C2×#107—711no—
399C2×#107—711no—
400C2×#107—711no—
401C2×#107—711no—
402C2×#106—711no—
403C2×#106—711no—
404C2×#106—711no—
405C2×#106—711no—
406C2×#106C2×D7111yescharacteristic
407C2×C4⋊C8—711no—
408C2×C4⋊C8—711no—
409C2×C4⋊C8—711no—
410C2×#103—711no—
411C2×#103—711no—
412C2×#103C2×D7111yescharacteristic
413C2×#102—711no—
414C2×#102—711no—
415C2×#102C2×D7111yescharacteristic
416C2×#97—711no—
417C2×#97—711no—
418C2×C4×C8C2×D7111yescharacteristic
419C22×Q8—711no—
420C22×Q8—1421no—
421C22×Q8—1421no—
422C22×Q8C22×D7111yescharacteristic
423C22×D4C22×D7111yescharacteristic
424C23×C4—21no—
425C23×C4—1421no—
426C23×C4—1421no—
427C2×SD16Dic14218yescomplemented
428C2×SD16C22×D7114yes—
429C22×C8—711no—
430C22×C8—711no—
431C22×C8C22×D7111yescharacteristic
432C22×C8C22×D7111yescharacteristic
433C4⋊Q8—714no—
434C4⋊Q8—714no—
435C4⋊Q8—1422no—
436C4⋊Q8—1422no—
437C4⋊Q8—1428no—
438#125—714no—
439#125—714no—
440#125—714no—
441#125—714no—
442#125—1428no—
443#125—1422no—
444#125—1422no—
445#125—1428no—
446#125—1422no—
447#125—1422no—
448C22⋊Q8—1428no—
449C22⋊Q8—1428no—
450C22⋊Q8—1428no—
451C4×Q8—22no—
452C4×Q8—714no—
453C4×Q8—714no—
454C4×Q8—714no—
455C4×Q8—714no—
456C4×Q8—1428no—
457C4×Q8—1422no—
458C4×Q8—1422no—
459C4×Q8C22×D7114yes—
460C4×D4—22no—
461C4×D4—714no—
462C4×D4—714no—
463C4×D4—1422no—
464C4×D4—1422no—
465C4×D4C22×D7114yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—711no—
468C2×C4⋊C4—711no—
469C2×C4⋊C4—711no—
470C2×C4⋊C4—711no—
471C2×C4⋊C4—711no—
472C2×C4⋊C4—711no—
473C2×C4⋊C4—711no—
474C2×C4⋊C4—1428no—
475C2×C4⋊C4—1421no—
476C2×C4⋊C4—1421no—
477C2×C4⋊C4—1421no—
478C2×C4⋊C4—1421no—
479C2×C4⋊C4—1421no—
480C2×C4⋊C4—1421no—
481C2×C4⋊C4—1421no—
482C2×C4⋊C4—1421no—
483C2×C4⋊C4—1421no—
484C2×C4⋊C4—1421no—
485C2×C4⋊C4—1421no—
486C2×C4⋊C4—1421no—
487C2×C4⋊C4C22×D7111yescharacteristic
488C2×C4⋊C4C22×D7111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—1421no—
491C2×C22⋊C4—1421no—
492C2×C42—21no—
493C2×C42—711no—
494C2×C42—711no—
495C2×C42—1421no—
496C2×C42—1421no—
497C2×C42C22×D7111yescharacteristic
498#107—714no—
499#107—714no—
500#107—714no—
501#107—714no—
502#106—714no—
503#106—714no—
504#106—714no—
505#106—714no—
506#106C22×D7114yes—
507C4⋊C8—714no—
508C4⋊C8—714no—
509C4⋊C8—714no—
510#103—714no—
511#103—714no—
512#103C22×D7114yes—
513#102—714no—
514#102—714no—
515#102C22×D7114yes—
516#97—714no—
517#97—714no—
518C4×C8C22×D7114yes—
519C24—21no—
520C2×Q8—21no—
521C2×Q8—22no—
522C2×Q8—2842no—
523C2×Q8—2844no—
524C2×Q8—5682no—
525C2×Q8—714no—
526C2×Q8—1424no—
527C2×Q8—1424no—
528C2×Q8C2×Dic14214yes—
529C2×Q8C23×D7112yes—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4C2×Dic14214yes—
533C2×D4C23×D7112yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—82no—
539C22×C4—2844no—
540C22×C4—5682no—
541C22×C4—711no—
542C22×C4—711no—
543C22×C4—711no—
544C22×C4—711no—
545C22×C4—1424no—
546C22×C4—1421no—
547C22×C4—1421no—
548C22×C4—1421no—
549C22×C4—1421no—
550C22×C4—1424no—
551C22×C4D4×D7111yescharacteristic
552C22×C4D4×D7111yescharacteristic
553C22×C4C23×D7111yescharacteristic
554SD16C2×Dic142116yescomplemented
555C2×C8—22no—
556C2×C8—712no—
557C2×C8—712no—
558C2×C8—1422no—
559C2×C8—1422no—
560C2×C8C2×Dic14214yes—
561C2×C8C23×D7112yes—
562C2×C8C23×D7112yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—714no—
567C4⋊C4—714no—
568C4⋊C4—714no—
569C4⋊C4—712no—
570C4⋊C4—712no—
571C4⋊C4—712no—
572C4⋊C4—712no—
573C4⋊C4—1424no—
574C4⋊C4—1424no—
575C4⋊C4—1424no—
576C4⋊C4—1424no—
577C4⋊C4—1424no—
578C4⋊C4—1424no—
579C4⋊C4—1424no—
580C4⋊C4—1424no—
581C4⋊C4—1424no—
582C4⋊C4—1424no—
583C4⋊C4—1424no—
584C4⋊C4—1424no—
585C4⋊C4—1421no—
586C4⋊C4—1421no—
587C4⋊C4—1421no—
588C4⋊C4—1421no—
589C4⋊C4C23×D7112yes—
590C4⋊C4C23×D7112yes—
591C22⋊C4—24no—
592C22⋊C4—1424no—
593C22⋊C4—1424no—
594C42—24no—
595C42—712no—
596C42—712no—
597C42—712no—
598C42—712no—
599C42—1424no—
600C42—1424no—
601C42D4×D7112yes—
602C42C23×D7112yes—
603C23—22no—
604C23—24no—
605C23—42no—
606C23—42no—
607C23C2×D4×D7111yescharacteristic
608Q8—22no—
609Q8—24no—
610Q8—2844no—
611Q8—2848no—
612Q8—5684no—
613Q8C22×Dic14214yes—
614D4—22no—
615D4—24no—
616D4C22×Dic14214yes—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—84no—
626C2×C4—2842no—
627C2×C4—2842no—
628C2×C4—2842no—
629C2×C4—2842no—
630C2×C4—2848no—
631C2×C4—5684no—
632C2×C4—712no—
633C2×C4—712no—
634C2×C4—712no—
635C2×C4—712no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1422no—
643C2×C4—1422no—
644C2×C4C2×D4×D7112yes—
645C2×C4C2×D4×D7112yes—
646C2×C4C2×D4×D7111yescharacteristic
647C2×C4C22×Dic14212yes—
648C2×C4#1455617512yes—
649C2×C4C24×D7111yescharacteristic
650C8—22no—
651C8—1422no—
652C8—1422no—
653C8C22×Dic14214yes—
654C22—24no—
655C22—48no—
656C22—42no—
657C22—42no—
658C22D4×Dic14212yes—
659C22#1798679612yes—
660C22#1798680512yes—
661C22C22×D4×D7111yescharacteristic
662C4—22no—
663C4—24no—
664C4—22no—
665C4—42no—
666C4—42no—
667C4—2842no—
668C4—2842no—
669C4—2842no—
670C4—2842no—
671C4—1422no—
672C4—1422no—
673C4—1422no—
674C4—1422no—
675C4D4×Dic14212yes—
676C4C23×Dic14211yescharacteristic
677C4C2×#1455617511yescharacteristic
678C2—44no—
679C2#2260128114yesdirect product factor
680C2C2×D4×Dic14211yescharacteristic
681C2C2×#1798679611yescharacteristic
682C2C2×#1798680511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×C4×SD16×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71C23
hypercenterC2×C4×SD16D71
hypocenterC71C2×#3388
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#17986725C2semidirect
3. #22601281C2direct (N × H)
4. C2×#17986406C2semidirect
5. C2×#17986406C2semidirect
6. C2×#17986401C2semidirect
7. C2×#17986306C2semidirect
8. C2×#17986304C2semidirect
9. C2×#17986282C2semidirect
13. C2×#17986129C2semidirect
18. #17986725C22semidirect
40. #17986406C22semidirect
41. #17986406C22semidirect
42. #17986401C22semidirect
43. #17986306C22semidirect
44. #17986304C22semidirect
48. #17986282C22semidirect
49. #17986129C22semidirect
159. C2×SD16×C71Q8semidirect
247. SD16×C71C2×Q8semidirect
338. C2×C71#3388semidirect
358. C71C2×#3388semidirect
427. C2×SD16Dic142semidirect
554. SD16C2×Dic142semidirect
679. C2#22601281direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867252
C2×#179867082
#226012812
C2×#179864062
C2×#179864012
C2×#179863062
C2×#179863042
C2×#179862822
C2×#179863012
C2×#179862992
C2×#179862872
C2×#179861292
C2×#179861002
C2×C4×SD16×C712
C2×#338871