Finite Group Databasebeta

← C2×#22600827 #32876033

Subgroups — C2×#22600827 #32876033

Order 18176.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986706C211yesmaximal, characteristic, complemented
2C2×#17986695C211yesmaximal, characteristic
3#22600827C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986335C211yesmaximal, characteristic, complemented
6C2×#17986318C211yesmaximal, characteristic, complemented
7C2×#17986341C211yesmaximal, characteristic, complemented
8C2×#17986313C211yesmaximal, characteristic, complemented
9C2×#17986307C211yesmaximal, characteristic, complemented
10C2×#17986280C211yesmaximal, characteristic, complemented
11C2×#17986245C211yesmaximal, characteristic, complemented
12C2×#17986228C211yesmaximal, characteristic, complemented
13C2×#17986101C211yesmaximal, characteristic, complemented
14C2×#17986041C211yesmaximal, characteristic, complemented
15C22×#14556062C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C22×#11765854C2211yescharacteristic
18#17986706—24no—
19#17986706C2218yescomplemented
20#17986695—24no—
21#17986695C2218yes—
22C2×#14556128C2211yescharacteristic
23C2×#14556123—21no—
24C2×#14556120C2211yescharacteristic
25C2×#14556119—21no—
26C2×#14556110—21no—
27C2×#14556107C2211yescharacteristic
28C2×#14556107C2211yescharacteristic
29C2×#14556105—21no—
30C2×#14556105—21no—
31C2×#14556102C2211yescharacteristic
32C2×#14556102C2211yescharacteristic
33C2×#14556100—21no—
34C2×C4×Dic142C2211yescharacteristic
35C2×C4×D284C2211yescharacteristic
36C2×D4×Dic71—21no—
37C2×(C22⋊D71)⋊C4—21no—
38C2×#14556087C2211yescharacteristic
39C22×C4⋊Dic71C2211yescharacteristic
40C22×C4⋊Dic71C2211yescharacteristic
41C22×C4⋊Dic71C2211yescharacteristic
42#17986408C2218yescomplemented
43#17986341C2218yescomplemented
44#17986335C2218yescomplemented
45#17986318C2218yescomplemented
46#17986313C2218yescomplemented
47#17986307C2218yescomplemented
48#17986280C2218yescomplemented
49#17986245C2218yescomplemented
50#17986228C2218yescomplemented
51#17986101C2218yescomplemented
52#17986041C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556062C2211yescharacteristic
56C2×#14556062C2211yescharacteristic
57C2×#14556062C2211yescharacteristic
58C2×#14556062C2211yescharacteristic
59C2×#14556062C2218yescomplemented
60C2×#14556060C2211yescharacteristic
61C2×#14556060C2211yescharacteristic
62C2×#14556060C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556053C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#435×C71C2218yescomplemented
73C2×C4⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C22⋊D71—21no—
82C23×Dic71—21no—
83C23×Dic71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C2×#11765854—24no—
87C2×#11765854C2314yes—
88#14556128—22no—
89#14556128C2314yes—
90#14556123—28no—
91#14556120—22no—
92#14556120C2314yes—
93#14556119—28no—
94#14556110—28no—
95#14556107—22no—
96#14556107—22no—
97#14556107C2314yes—
98#14556107C2314yes—
99#14556105—28no—
100#14556105—28no—
101#14556102—22no—
102#14556102—22no—
103#14556102C2314yes—
104#14556102C2314yes—
105#14556100—28no—
106C4×Dic142—22no—
107C4×Dic142C2314yes—
108C4×D284—22no—
109C4×D284C2314yes—
110D4×Dic71—28no—
111(C22⋊D71)⋊C4—28no—
112#14556087—22no—
113#14556087C2314yes—
114C2×C4⋊Dic71—22no—
115C2×C4⋊Dic71—22no—
116C2×C4⋊Dic71—22no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2314yes—
122C2×C4⋊Dic71C2314yes—
123C2×C4⋊Dic71C2314yes—
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×C4⋊Dic71C2311yescharacteristic
128C2×C4⋊Dic71C2311yescharacteristic
129C2×C4⋊Dic71C2311yescharacteristic
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4—21no—
135C2×C22⋊Dic71—21no—
136C2×C22⋊Dic71—21no—
137C2×C22⋊Dic71—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143#14556062C2314yes—
144#14556062C2314yes—
145#14556062C2314yes—
146#14556062C2314yes—
147#14556062C2314yes—
148#14556062C2314yes—
149#14556060C2314yes—
150#14556060C2314yes—
151#14556060C2314yes—
152#14556053C2314yes—
153#14556053C2314yes—
154#14556053C2314yes—
155#14556050C2314yes—
156#14556050C2314yes—
157#14556050C2314yes—
158C22×D4×C71D411yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C2×M16×C71—24no—
162C2×M16×C71C2314yes—
163C22×C8×C71—24no—
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2314yes—
168C22×C8×C71C2311yescharacteristic
169C4×D4×C71D414yes—
170C4×D4×C71C2314yes—
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C42×C71C2311yescharacteristic
175C4⋊C8×C71C2314yes—
176C22⋊C8×C71C2314yes—
177C22⋊C8×C71C2314yes—
178#97×C71C2314yes—
179C23×D71—21no—
180C2×Dic142—22no—
181C2×Dic142—22no—
182C2×Dic142—21no—
183C2×Dic142—24no—
184C2×Dic142—82no—
185C2×Dic142C2412yes—
186C2×D284—22no—
187C2×D284—22no—
188C2×D284—21no—
189C2×D284C2412yes—
190C2×C22⋊D71—24no—
191C2×C22⋊D71—24no—
192C2×C22⋊D71—44no—
193C2×C22⋊D71—82no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—21no—
201C22×Dic71—24no—
202C22×Dic71—24no—
203C22×Dic71—24no—
204C22×Dic71—82no—
205C22×Dic71—82no—
206C22×Dic71—82no—
207C2×C4×D71—24no—
208C2×C4×D71—82no—
209#11765854—28no—
210C4⋊Dic71—21no—
211C4⋊Dic71—21no—
212C4⋊Dic71—21no—
213C4⋊Dic71—24no—
214C4⋊Dic71—24no—
215C4⋊Dic71—21no—
216C4⋊Dic71—21no—
217C4⋊Dic71—24no—
218C4⋊Dic71—24no—
219C4⋊Dic71—21no—
220C4⋊Dic71C2412yes—
221C4⋊Dic71C2412yes—
222C4⋊Dic71C2412yes—
223C4⋊Dic71C2412yes—
224C4⋊Dic71C2412yes—
225C4⋊Dic71C2412yes—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4—24no—
231C22⋊Dic71—24no—
232C22⋊Dic71—24no—
233C22⋊Dic71—24no—
234(C2×D71)⋊C4—24no—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237C4×Dic71—24no—
238C4×Dic71—24no—
239C24×C71C2×D411yescharacteristic
240C24×C71C2×D411yescharacteristic
241C2×D4×C71—24no—
242C2×D4×C71C2×D414yes—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D412yes—
252C22×C4×C71C2×D412yes—
253C22×C4×C71C2412yes—
254C22×C4×C71C2412yes—
255C22×C4×C71C2411yescharacteristic
256M16×C71—28no—
257C2×C8×C71—22no—
258C2×C8×C71—22no—
259C2×C8×C71—22no—
260C2×C8×C71—28no—
261C2×C8×C71#4114yes—
262C2×C8×C71C2412yes—
263C2×C8×C71C2412yes—
264C2×C8×C71C2412yes—
265C2×C8×C71C2412yes—
266C4⋊C4×C71C2×D414yes—
267C22⋊C4×C71C2×D414yes—
268C22⋊C4×C71C2×D414yes—
269C42×C71C2×D412yes—
270C42×C71C2412yes—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71#13714yes—
277C23×C71C22×D412yes—
278C23×C71C22×D412yes—
279C23×C71C22×D411yescharacteristic
280C22×D71—22no—
281C22×D71—42no—
282C22×D71—42no—
283C22×D71—42no—
284D4×C71—28no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—24no—
290C2×C4×C71—24no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71C22×D412yes—
296C2×C4×C71C22×D412yes—
297C2×C4×C71C22×D412yes—
298C2×C4×C71C22×D412yes—
299C2×C4×C71C22×D411yescharacteristic
300C2×C4×C71C2×#4112yes—
301C2×C4×C712−1+412yes—
302C2×C4×C71C2511yescharacteristic
303C22⋊D71—48no—
304C22⋊D71—84no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—42no—
313C2×Dic71—42no—
314C2×Dic71—42no—
315C2×Dic71—42no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319C2×Dic71—84no—
320C2×Dic71—84no—
321C2×Dic71—84no—
322D284—22no—
323D284—22no—
324D284—42no—
325C4×D71—84no—
326Dic142—22no—
327Dic142—22no—
328Dic142—42no—
329Dic142—84no—
330C8×C71—22no—
331C8×C71—22no—
332C8×C71—22no—
333C8×C71C2×#4114yes—
334C22×C71—28no—
335C22×C71—22no—
336C22×C71—22no—
337C22×C71—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—44no—
341C22×C71#54712yes—
342C22×C71C2×#13714yes—
343C22×C71C2×#13712yes—
344C22×C71#57612yes—
345C22×C71C23×D411yescharacteristic
346C2×D71—42no—
347C2×D71—42no—
348C2×D71—42no—
349C2×D71—84no—
350C4×C71—22no—
351C4×C71—22no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71#54712yes—
355C4×C71C22×#4111yescharacteristic
356C4×C71C2×2−1+411yescharacteristic
357Dic71—42no—
358Dic71—42no—
359Dic71—42no—
360Dic71—42no—
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364C2×#3346—711nomaximal, Sylow
365C2×C71—24no—
366C2×C71—42no—
367C2×C71#334614yescomplemented
368C2×C71C2×#54711yescharacteristic
369C2×C71C22×#13711yescharacteristic
370C2×C71C2×#57611yescharacteristic
371D71—82no—
372C2×#554—711no—
373C2×#553—711no—
374#3346—7116no—
375C2×#501—711no—
376C2×#484—711no—
377C2×#481—711no—
378C2×#485—711no—
379C2×#480—711no—
380C2×#479—711no—
381C2×#474—711no—
382C2×#468—711no—
383C2×#465—711no—
384C2×#440—711no—
385C2×#435D7111yescharacteristic, complemented
386C2×#428—711no—
387C22×#107—711no—
388C71C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—711no—
390C22×M16C2×D7111yescharacteristic
391C23×C8C2×D7111yescharacteristic
392#554—718no—
393#554—1424no—
394#553—718no—
395#553—1424no—
396C2×C4⋊Q8—711no—
397C2×#126—1421no—
398C2×#125—711no—
399C2×#125—1421no—
400C2×#123—1421no—
401C2×C22⋊Q8—711no—
402C2×C22⋊Q8—711no—
403C2×C22⋊Q8—1421no—
404C2×C22⋊Q8—1421no—
405C2×#121—711no—
406C2×#121—711no—
407C2×#121—1421no—
408C2×C4×Q8—711no—
409C2×C4×D4—711no—
410C2×C4×D4—1421no—
411C2×C4×D4—1421no—
412C2×C4×D4C2×D7111yescharacteristic
413C2×#117—711no—
414C22×C4⋊C4—711no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4—711no—
417#501—718no—
418#485—718no—
419#484—718no—
420#481—718no—
421#480—718no—
422#479—718no—
423#474—718no—
424#468—718no—
425#465—718no—
426#440—718no—
427#435C2×D7118yescomplemented
428#428—718no—
429C2×#107—711no—
430C2×#107—711no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#107—718no—
434C2×#107—711no—
435C2×#107—711no—
436C2×#106—711no—
437C2×#106—711no—
438C2×#106—711no—
439C2×C4⋊C8C2×D7111yescharacteristic
440C2×#103—711no—
441C2×#103—711no—
442C2×#103—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×#102—711no—
446C2×C22⋊C8C2×D7111yescharacteristic
447C2×C22⋊C8C2×D7111yescharacteristic
448C2×#97C2×D7111yescharacteristic
449C22×Q8—711no—
450C22×Q8—1421no—
451C22×D4—711no—
452C22×D4—1421no—
453C22×D4—1421no—
454C22×D4D28411yescharacteristic
455C23×C4—1421no—
456C23×C4—1421no—
457C23×C4—1421no—
458C23×C4—1421no—
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7111yescharacteristic
461C2×SD16—714no—
462C2×SD16—1424no—
463C2×M16—24no—
464C2×M16C22×D7114yes—
465C22×C8—24no—
466C22×C8C22×D7111yescharacteristic
467C22×C8C22×D7114yes—
468C22×C8C22×D7111yescharacteristic
469C22×C8C22×D7111yescharacteristic
470C22×C8C22×D7111yescharacteristic
471C4⋊Q8—714no—
472C4⋊Q8—1422no—
473#126—1428no—
474#125—714no—
475#125—1428no—
476#125—1422no—
477#123—1428no—
478C22⋊Q8—714no—
479C22⋊Q8—714no—
480C22⋊Q8—1422no—
481C22⋊Q8—1422no—
482C22⋊Q8—1428no—
483C22⋊Q8—1428no—
484#121—714no—
485#121—714no—
486#121—1428no—
487#121—1422no—
488#121—1422no—
489C4×Q8—714no—
490C4×Q8—1422no—
491C4×D4—714no—
492C4×D4—1428no—
493C4×D4—1428no—
494C4×D4—1422no—
495C4×D4D28414yes—
496C4×D4C22×D7114yes—
497#117—714no—
498#117—1422no—
499C2×C4⋊C4—711no—
500C2×C4⋊C4—711no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4—711no—
503C2×C4⋊C4—711no—
504C2×C4⋊C4—714no—
505C2×C4⋊C4—714no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—711no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4—1422no—
512C2×C4⋊C4—1422no—
513C2×C4⋊C4—1422no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1421no—
517C2×C4⋊C4—1421no—
518C2×C4⋊C4—1421no—
519C2×C4⋊C4—1421no—
520C2×C4⋊C4D28411yescharacteristic
521C2×C22⋊C4—1421no—
522C2×C22⋊C4—1421no—
523C2×C22⋊C4—1421no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4D28411yescharacteristic
528C2×C22⋊C4D28411yescharacteristic
529C2×C42—1421no—
530C2×C42—1421no—
531C2×C42C22×D7111yescharacteristic
532#107—714no—
533#107—714no—
534#107—714no—
535#107—714no—
536#107—714no—
537#107—714no—
538#106—714no—
539#106—714no—
540#106—714no—
541C4⋊C8C22×D7114yes—
542#103—714no—
543#103—714no—
544#103—714no—
545#102—714no—
546#102—714no—
547#102—714no—
548C22⋊C8C22×D7114yes—
549C22⋊C8C22×D7114yes—
550#97C22×D7114yes—
551C24—1421no—
552C24C2×D28411yescharacteristic
553C24C2×D28411yescharacteristic
554C2×Q8—5682no—
555C2×Q8—712no—
556C2×Q8—1422no—
557C2×Q8—1422no—
558C2×Q8—1421no—
559C2×Q8—1424no—
560C2×D4—24no—
561C2×D4—2844no—
562C2×D4—5682no—
563C2×D4—712no—
564C2×D4—1424no—
565C2×D4—1424no—
566C2×D4—1421no—
567C2×D4—1422no—
568C2×D4—1422no—
569C2×D4C2×D28414yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—5682no—
575C22×C4—5682no—
576C22×C4—5682no—
577C22×C4—5682no—
578C22×C4—1421no—
579C22×C4—1421no—
580C22×C4—1421no—
581C22×C4—1421no—
582C22×C4—1421no—
583C22×C4—1421no—
584C22×C4—1421no—
585C22×C4—1424no—
586C22×C4—1424no—
587C22×C4—1424no—
588C22×C4—1424no—
589C22×C4C2×D28412yes—
590C22×C4C2×D28412yes—
591C22×C4C2×D28411yescharacteristic
592C22×C4C2×D28411yescharacteristic
593C22×C4C2×D28411yescharacteristic
594C22×C4C2×D28411yescharacteristic
595C22×C4C23×D7112yes—
596C22×C4C23×D7112yes—
597C22×C4C23×D7111yescharacteristic
598SD16—1428no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#1176586414yes—
605C2×C8C23×D7112yes—
606C2×C8C23×D7112yes—
607C2×C8C23×D7112yes—
608C2×C8C23×D7112yes—
609C4⋊C4—712no—
610C4⋊C4—712no—
611C4⋊C4—712no—
612C4⋊C4—712no—
613C4⋊C4—712no—
614C4⋊C4—712no—
615C4⋊C4—1424no—
616C4⋊C4—1424no—
617C4⋊C4—1424no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1421no—
621C4⋊C4—1421no—
622C4⋊C4—1421no—
623C4⋊C4—1424no—
624C4⋊C4—1424no—
625C4⋊C4—1421no—
626C4⋊C4—1421no—
627C4⋊C4—1424no—
628C4⋊C4—1421no—
629C4⋊C4—1424no—
630C4⋊C4C2×D28414yes—
631C22⋊C4—1424no—
632C22⋊C4—1424no—
633C22⋊C4—1424no—
634C22⋊C4—1424no—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4C2×D28414yes—
638C22⋊C4C2×D28414yes—
639C42—1424no—
640C42—1424no—
641C42C2×D28412yes—
642C42C23×D7112yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—2842no—
649C23—2842no—
650C23—2842no—
651C23—1422no—
652C23#1455616114yes—
653C23C22×D28412yes—
654C23C22×D28412yes—
655C23C22×D28411yescharacteristic
656Q8—2842no—
657Q8—5684no—
658Q8—1422no—
659Q8—1422no—
660D4—28no—
661D4—2848no—
662D4—2842no—
663D4—5684no—
664D4—1422no—
665D4—1422no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—2842no—
677C2×C4—2842no—
678C2×C4—2842no—
679C2×C4—2842no—
680C2×C4—2842no—
681C2×C4—2842no—
682C2×C4—2842no—
683C2×C4—5684no—
684C2×C4—5684no—
685C2×C4—5684no—
686C2×C4—5684no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4C22×D28412yes—
695C2×C4C22×D28412yes—
696C2×C4C22×D28412yes—
697C2×C4C22×D28412yes—
698C2×C4C22×D28411yescharacteristic
699C2×C4C2×#1176586412yes—
700C2×C4#1455617512yes—
701C2×C4C24×D7111yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#1176586414yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—2842no—
714C22—2842no—
715C22—2842no—
716C22—5684no—
717C22#1798665312yes—
718C22C2×#1455616114yes—
719C22C2×#1455616112yes—
720C22#1798680412yes—
721C22C23×D28411yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—2842no—
727C4—2842no—
728C4—2842no—
729C4—2842no—
730C4—2842no—
731C4—2842no—
732C4—2842no—
733C4#1798665312yes—
734C4C22×#1176586411yescharacteristic
735C4C2×#1455617511yescharacteristic
736C2—24no—
737C2—42no—
738C2—5682no—
739C2#2260082714yesdirect product factor
740C2C2×#1798665311yescharacteristic
741C2C22×#1455616111yescharacteristic
742C2C2×#1798680411yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986695C2
hypercenterC2×#435D71
hypocenterC71C2×#3346
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#17986706C2semidirect
3. #22600827C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986335C2semidirect
6. C2×#17986318C2semidirect
7. C2×#17986341C2semidirect
8. C2×#17986313C2semidirect
9. C2×#17986307C2semidirect
10. C2×#17986280C2semidirect
11. C2×#17986245C2semidirect
12. C2×#17986228C2semidirect
13. C2×#17986101C2semidirect
14. C2×#17986041C2semidirect
15. C22×#14556062C2semidirect
16. C2×#435×C71C2semidirect
19. #17986706C22semidirect
42. #17986408C22semidirect
43. #17986341C22semidirect
44. #17986335C22semidirect
45. #17986318C22semidirect
46. #17986313C22semidirect
47. #17986307C22semidirect
48. #17986280C22semidirect
49. #17986245C22semidirect
50. #17986228C22semidirect
51. #17986101C22semidirect
52. #17986041C22semidirect
59. C2×#14556062C22semidirect
72. #435×C71C22semidirect
367. C2×C71#3346semidirect
385. C2×#435D71semidirect
388. C71C2×#3346semidirect
427. #435C2×D71semidirect
739. C2#22600827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867062
C2×#179866952
#226008272
C2×#179864082
C2×#179863352
C2×#179863182
C2×#179863412
C2×#179863132
C2×#179863072
C2×#179862802
C2×#179862452
C2×#179862282
C2×#179861012
C2×#179860412
C22×#145560622
C2×#435×C712
C2×#334671