Finite Group Databasebeta

← C2×#22598571 #32865733

Subgroups — C2×#22598571 #32865733

Order 18176.

2058 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×#17986620C211yesmaximal, characteristic
2C2×#17986476C211yesmaximal, characteristic, complemented
3#22598571C2116yesmaximal, direct product factor
4C2×#17986341C211yesmaximal, characteristic, complemented
5C2×#17986324C211yesmaximal, characteristic
6C2×#17986295C211yesmaximal, characteristic, complemented
7C2×#17986285C211yesmaximal, characteristic, complemented
8C2×#17986222C211yesmaximal, characteristic, complemented
9C2×#17986222C211yesmaximal, characteristic, complemented
10C2×#17986157C211yesmaximal, characteristic, complemented
11C2×#17986140C211yesmaximal, characteristic
12C2×#17986107C211yesmaximal, characteristic, complemented
13C2×#17986101C211yesmaximal, characteristic, complemented
14C2×C4×Dic284C211yesmaximal, characteristic, complemented
15C2×C4×#11765854C211yesmaximal, characteristic, complemented
16C2×#433×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C22×Dic284C2211yescharacteristic
19C22×Dic284C2211yescharacteristic
20C22×#11765854C2211yescharacteristic
21C22×#11765854C2211yescharacteristic
22#17986620—24no—
23#17986620C2218yes—
24C2×#14556128C2211yescharacteristic
25C2×#14556123—21no—
26C2×#14556116C2211yescharacteristic
27C2×#14556114—21no—
28C2×#14556110—21no—
29C2×#14556107C2211yescharacteristic
30C2×#14556106—21no—
31C2×#14556102C2211yescharacteristic
32#17986476—24no—
33#17986476C2218yescomplemented
34C2×C4×Dic142C2211yescharacteristic
35C2×C4×Dic142C2211yescharacteristic
36C2×C4×Dic142C2211yescharacteristic
37C2×C4×Dic142C2211yescharacteristic
38C2×C4×Dic142C2211yescharacteristic
39C2×#14556093—21no—
40C2×#14556093—21no—
41C2×C4×D284C2211yescharacteristic
42C2×#14556087C2211yescharacteristic
43C2×#14556084—21no—
44C2×#14556084—21no—
45#17986341C2218yescomplemented
46#17986324C2218yes—
47#17986295C2218yescomplemented
48#17986285C2218yescomplemented
49#17986222C2218yescomplemented
50#17986222C2218yescomplemented
51#17986157C2218yescomplemented
52#17986140C2218yes—
53#17986107C2218yescomplemented
54#17986101C2218yescomplemented
55C4×Dic284C2218yescomplemented
56C4×#11765854C2218yescomplemented
57C2×#14556062C2211yescharacteristic
58C2×#14556062C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556060C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556053C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556053C2211yescharacteristic
66C2×#14556053C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C2×#117×C71C2211yescharacteristic
70#433×C71C2218yescomplemented
71C2×C4⋊C8×C71C2211yescharacteristic
72C2×C4⋊C8×C71C2211yescharacteristic
73C2×C22⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×#97×C71C2211yescharacteristic
76C2×C4×C8×C71C2211yescharacteristic
77C22×Dic142—24no—
78C22×Dic142—24no—
79C22×Dic142—21no—
80C22×Dic142—22no—
81C22×Dic142—21no—
82C22×Dic142C2314yes—
83C22×Dic142C2311yescharacteristic
84C22×Dic142C2311yescharacteristic
85C22×Dic142C2311yescharacteristic
86C22×D284C2311yescharacteristic
87C22×C22⋊D71—21no—
88C23×Dic71—21no—
89C22×C4×D71—21no—
90C2×Dic284—24no—
91C2×Dic284—24no—
92C2×Dic284C2314yes—
93C2×Dic284C2314yes—
94C2×#11765854—24no—
95C2×#11765854—24no—
96C2×#11765854C2314yes—
97C2×#11765854C2314yes—
98#14556128—22no—
99#14556128C2314yes—
100#14556123—28no—
101#14556116—22no—
102#14556116C2314yes—
103#14556114—28no—
104#14556110—28no—
105#14556107—22no—
106#14556107C2314yes—
107#14556106—28no—
108#14556102—22no—
109#14556102C2314yes—
110C4×Dic142—22no—
111C4×Dic142—22no—
112C4×Dic142—22no—
113C4×Dic142—22no—
114C4×Dic142—22no—
115C4×Dic142C2314yes—
116C4×Dic142C2314yes—
117C4×Dic142C2314yes—
118C4×Dic142C2314yes—
119C4×Dic142C2314yes—
120#14556093—28no—
121#14556093—28no—
122C4×D284—22no—
123C4×D284C2314yes—
124#14556087—22no—
125#14556087C2314yes—
126#14556084—28no—
127#14556084—28no—
128C2×C4⋊Dic71—21no—
129C2×C4⋊Dic71C2311yescharacteristic
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×Dic71⋊C4—21no—
138C2×Dic71⋊C4—21no—
139C2×C22⋊Dic71—21no—
140C2×C22⋊Dic71—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—21no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71—21no—
147C2×C4×Dic71—21no—
148C2×C4×Dic71—21no—
149C2×C4×Dic71—21no—
150C2×C4×Dic71—21no—
151#14556062C2314yes—
152#14556062C2314yes—
153#14556060C2314yes—
154#14556060C2314yes—
155#14556053C2314yes—
156#14556053C2314yes—
157#14556053C2314yes—
158#14556053C2314yes—
159#14556053C2314yes—
160#14556053C2314yes—
161#14556050C2314yes—
162#14556050C2314yes—
163C23×C4×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2311yescharacteristic
168#117×C71D414yes—
169#117×C71C2314yes—
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C4⋊C8×C71C2314yes—
177C4⋊C8×C71C2314yes—
178C22⋊C8×C71C2314yes—
179C22⋊C8×C71C2314yes—
180#97×C71C2314yes—
181C4×C8×C71C2314yes—
182C23×D71—21no—
183C2×Dic142—28no—
184C2×Dic142—216no—
185C2×Dic142—24no—
186C2×Dic142—21no—
187C2×Dic142—21no—
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—28no—
191C2×Dic142—28no—
192C2×Dic142—22no—
193C2×Dic142—22no—
194C2×Dic142—21no—
195C2×Dic142—24no—
196C2×Dic142—82no—
197C2×Dic142#4114yes—
198C2×Dic142#4114yes—
199C2×Dic142C2412yes—
200C2×Dic142C2412yes—
201C2×Dic142C2412yes—
202C2×D284—22no—
203C2×D284—22no—
204C2×D284—21no—
205C2×D284C2412yes—
206C2×C22⋊D71—24no—
207C2×C22⋊D71—82no—
208C22×Dic71—28no—
209C22×Dic71—21no—
210C22×Dic71—21no—
211C22×Dic71—24no—
212C22×Dic71—21no—
213C22×Dic71—21no—
214C22×Dic71—21no—
215C22×Dic71—21no—
216C22×Dic71—21no—
217C2×C4×D71—24no—
218C2×C4×D71—82no—
219Dic284—28no—
220Dic284—28no—
221#11765854—28no—
222#11765854—28no—
223C4⋊Dic71—24no—
224C4⋊Dic71—21no—
225C4⋊Dic71—21no—
226C4⋊Dic71—21no—
227C4⋊Dic71—21no—
228C4⋊Dic71C2412yes—
229C4⋊Dic71C2412yes—
230C4⋊Dic71C2412yes—
231C4⋊Dic71C2412yes—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234Dic71⋊C4—24no—
235Dic71⋊C4—24no—
236Dic71⋊C4—24no—
237Dic71⋊C4—24no—
238C22⋊Dic71—24no—
239C22⋊Dic71—24no—
240(C2×D71)⋊C4—24no—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—24no—
243(C2×D71)⋊C4—24no—
244C4×Dic71—24no—
245C4×Dic71—24no—
246C4×Dic71—24no—
247C4×Dic71—24no—
248C4×Dic71—24no—
249C4×Dic71—24no—
250C24×C71C2×D411yescharacteristic
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D412yes—
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2412yes—
260C22×C4×C71C2411yescharacteristic
261C2×C8×C71—22no—
262C2×C8×C71—22no—
263C2×C8×C71—22no—
264C2×C8×C71—22no—
265C2×C8×C71C2412yes—
266C2×C8×C71C2412yes—
267C2×C8×C71C2412yes—
268C2×C8×C71C2412yes—
269C4⋊C4×C71C2×D414yes—
270C4⋊C4×C71C2×D414yes—
271C22⋊C4×C71C2×D414yes—
272C22⋊C4×C71C2×D414yes—
273C42×C71C2×D412yes—
274C42×C71C2×D412yes—
275C42×C71C2412yes—
276C42×C71C2412yes—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71C22×D412yes—
281C23×C71C22×D411yescharacteristic
282C22×D71—22no—
283C22×D71—42no—
284C22×D71—42no—
285C22×D71—42no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—24no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71C22×D412yes—
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×C71C2×#4112yes—
302C2×C4×C71C2511yescharacteristic
303C22⋊D71—84no—
304C2×Dic71—216no—
305C2×Dic71—24no—
306C2×Dic71—24no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—42no—
315C2×Dic71—42no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319D284—22no—
320D284—22no—
321D284—42no—
322C4×D71—84no—
323Dic142—216no—
324Dic142—24no—
325Dic142—24no—
326Dic142—22no—
327Dic142—22no—
328Dic142—22no—
329Dic142—22no—
330Dic142—42no—
331Dic142—84no—
332Dic142C2×#4114yes—
333Dic142C2×#4114yes—
334C8×C71—22no—
335C8×C71—22no—
336C8×C71—22no—
337C8×C71—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—22no—
341C22×C71—44no—
342C22×C71#52512yes—
343C22×C71#57712yes—
344C22×C71#57812yes—
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—22no—
355C4×C71#52512yes—
356C4×C71C22×#4111yescharacteristic
357C4×C71C22×#4111yescharacteristic
358Dic71—24no—
359Dic71—24no—
360Dic71—42no—
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364Dic71—42no—
365C2×#3121—711nomaximal, Sylow
366C2×C71—42no—
367C2×C71#312114yescomplemented
368C2×C71C2×#52511yescharacteristic
369C2×C71C2×#57711yescharacteristic
370C2×C71C2×#57811yescharacteristic
371D71—82no—
372C2×#542—711no—
373C2×#519—711no—
374#3121—7116no—
375C2×#485—711no—
376C2×#482—711no—
377C2×#477—711no—
378C2×#475—711no—
379C2×#464—711no—
380C2×#464—711no—
381C2×#451—711no—
382C2×#448—711no—
383C2×#441—711no—
384C2×#440—711no—
385C2×C4×Q16—711no—
386C2×C4×SD16—711no—
387C2×#433D7111yescharacteristic, complemented
388C71C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8—711no—
390C22×Q16—711no—
391C22×Q16—711no—
392C22×SD16—711no—
393C22×SD16—711no—
394#542—718no—
395#542—1424no—
396C2×C4⋊Q8—711no—
397C2×#126—1421no—
398C2×#124—711no—
399C2×#124—1421no—
400C2×#123—1421no—
401C2×C22⋊Q8—711no—
402C2×C22⋊Q8—1421no—
403C2×#121—711no—
404#519—718no—
405#519—1424no—
406C2×C4×Q8—711no—
407C2×C4×Q8—711no—
408C2×C4×Q8—711no—
409C2×C4×Q8—711no—
410C2×C4×Q8—711no—
411C2×C4×Q8—1421no—
412C2×C4×Q8—1421no—
413C2×C4×D4—711no—
414C2×#117—711no—
415C2×#117—1421no—
416C2×#117—1421no—
417C2×#117C2×D7111yescharacteristic
418#485—718no—
419#482—718no—
420#477—718no—
421#475—718no—
422#464—718no—
423#464—718no—
424#451—718no—
425#448—718no—
426#441—718no—
427#440—718no—
428C4×Q16—718no—
429C4×SD16—718no—
430#433C2×D7118yescomplemented
431C2×#107—711no—
432C2×#107—711no—
433C2×#106—711no—
434C2×#106—711no—
435C2×C4⋊C8C2×D7111yescharacteristic
436C2×C4⋊C8C2×D7111yescharacteristic
437C2×#103—711no—
438C2×#103—711no—
439C2×#103—711no—
440C2×#103—711no—
441C2×#103—711no—
442C2×#103—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×C22⋊C8C2×D7111yescharacteristic
446C2×C22⋊C8C2×D7111yescharacteristic
447C2×#97C2×D7111yescharacteristic
448C2×C4×C8C2×D7111yescharacteristic
449C22×Q8—711no—
450C22×Q8—711no—
451C22×Q8—711no—
452C22×Q8—714no—
453C22×Q8—1424no—
454C22×Q8—1424no—
455C22×Q8—1421no—
456C22×Q8—1421no—
457C22×Q8—1422no—
458C22×D4—711no—
459C22×D4—1421no—
460C23×C4—1421no—
461C23×C4—1421no—
462C23×C4C22×D7111yescharacteristic
463C2×Q16—714no—
464C2×Q16—714no—
465C2×Q16—1424no—
466C2×Q16—1424no—
467C2×SD16—714no—
468C2×SD16—714no—
469C2×SD16—1424no—
470C2×SD16—1424no—
471C22×C8C22×D7111yescharacteristic
472C22×C8C22×D7111yescharacteristic
473C22×C8C22×D7111yescharacteristic
474C22×C8C22×D7111yescharacteristic
475C4⋊Q8—714no—
476C4⋊Q8—1422no—
477#126—1428no—
478#124—714no—
479#124—1428no—
480#124—1422no—
481#123—1428no—
482C22⋊Q8—714no—
483C22⋊Q8—1422no—
484C22⋊Q8—1428no—
485#121—714no—
486#121—1422no—
487C4×Q8—714no—
488C4×Q8—714no—
489C4×Q8—714no—
490C4×Q8—714no—
491C4×Q8—714no—
492C4×Q8—1428no—
493C4×Q8—1428no—
494C4×Q8—1422no—
495C4×Q8—1422no—
496C4×Q8—1422no—
497C4×Q8—1422no—
498C4×Q8—1422no—
499C4×D4—714no—
500C4×D4—1422no—
501#117—714no—
502#117—1422no—
503#117—1428no—
504#117—1428no—
505#117D28414yes—
506#117C22×D7114yes—
507C2×C4⋊C4—711no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—711no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1421no—
517C2×C4⋊C4—1421no—
518C2×C4⋊C4D28411yescharacteristic
519C2×C4⋊C4D28411yescharacteristic
520C2×C22⋊C4—1421no—
521C2×C22⋊C4—1421no—
522C2×C22⋊C4—1421no—
523C2×C22⋊C4—1421no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4D28411yescharacteristic
527C2×C22⋊C4D28411yescharacteristic
528C2×C42—1421no—
529C2×C42—1421no—
530C2×C42—1421no—
531C2×C42—1421no—
532C2×C42—1421no—
533C2×C42—1421no—
534C2×C42C22×D7111yescharacteristic
535C2×C42C22×D7111yescharacteristic
536#107—714no—
537#107—714no—
538#106—714no—
539#106—714no—
540C4⋊C8C22×D7114yes—
541C4⋊C8C22×D7114yes—
542#103—714no—
543#103—714no—
544#103—714no—
545#103—714no—
546#103—714no—
547#103—714no—
548#102—714no—
549#102—714no—
550C22⋊C8C22×D7114yes—
551C22⋊C8C22×D7114yes—
552#97C22×D7114yes—
553C4×C8C22×D7114yes—
554C24—1421no—
555C24C2×D28411yescharacteristic
556C2×Q8—5682no—
557C2×Q8—714no—
558C2×Q8—714no—
559C2×Q8—712no—
560C2×Q8—712no—
561C2×Q8—712no—
562C2×Q8—1428no—
563C2×Q8—1428no—
564C2×Q8—1428no—
565C2×Q8—14216no—
566C2×Q8—1422no—
567C2×Q8—1422no—
568C2×Q8—1421no—
569C2×Q8—1424no—
570C2×Q8—1424no—
571C2×Q8—1421no—
572C2×Q8—1421no—
573C2×Q8—1422no—
574C2×Q8—1422no—
575C2×D4—5682no—
576C2×D4—712no—
577C2×D4—1424no—
578C2×D4—1421no—
579C2×D4—1422no—
580C2×D4—1422no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—5682no—
584C22×C4—1421no—
585C22×C4—1421no—
586C22×C4—1421no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1424no—
590C22×C4—1428no—
591C22×C4—1424no—
592C22×C4—1421no—
593C22×C4—1421no—
594C22×C4C2×D28412yes—
595C22×C4C2×D28411yescharacteristic
596C22×C4C2×D28411yescharacteristic
597C22×C4C2×D28411yescharacteristic
598C22×C4C2×D28411yescharacteristic
599C22×C4C2×D28411yescharacteristic
600C22×C4C23×D7112yes—
601C22×C4C23×D7111yescharacteristic
602Q16—1428no—
603Q16—1428no—
604SD16—1428no—
605SD16—1428no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D7112yes—
611C2×C8C23×D7112yes—
612C2×C8C23×D7112yes—
613C2×C8C23×D7112yes—
614C4⋊C4—712no—
615C4⋊C4—712no—
616C4⋊C4—712no—
617C4⋊C4—712no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
621C4⋊C4—1424no—
622C4⋊C4—1424no—
623C4⋊C4—1424no—
624C4⋊C4—1421no—
625C4⋊C4—1421no—
626C4⋊C4—1421no—
627C4⋊C4—1421no—
628C4⋊C4—1424no—
629C4⋊C4C2×D28414yes—
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—
641C42—1424no—
642C42—1424no—
643C42—1424no—
644C42—1424no—
645C42C2×D28412yes—
646C42C2×D28412yes—
647C42C23×D7112yes—
648C42C23×D7112yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2842no—
653C23—2842no—
654C23—2842no—
655C23—1422no—
656C23C22×D28412yes—
657C23C22×D28411yescharacteristic
658Q8—2842no—
659Q8—5684no—
660Q8—714no—
661Q8—714no—
662Q8—14216no—
663Q8—1422no—
664Q8—1422no—
665Q8—1422no—
666Q8—1422no—
667Q8—1424no—
668Q8—1424no—
669D4—2842no—
670D4—5684no—
671D4—1422no—
672D4—1422no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—2842no—
682C2×C4—2842no—
683C2×C4—2842no—
684C2×C4—2842no—
685C2×C4—2842no—
686C2×C4—5684no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—14216no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1424no—
696C2×C4—1424no—
697C2×C4C22×D28412yes—
698C2×C4C22×D28412yes—
699C2×C4C22×D28412yes—
700C2×C4C22×D28412yes—
701C2×C4C22×D28412yes—
702C2×C4C22×D28411yescharacteristic
703C2×C4#41×D7112yes—
704C2×C4#41×D7112yes—
705C2×C4C24×D7111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—2842no—
715C22—2842no—
716C22—2842no—
717C22—5684no—
718C22#1798651112yes—
719C22#1798681112yes—
720C22#1798681612yes—
721C22C23×D28411yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—2842no—
728C4—2842no—
729C4—2842no—
730C4—2842no—
731C4—2842no—
732C4—1424no—
733C4—1424no—
734C4#1798651112yes—
735C4C2×#41×D7111yescharacteristic
736C4C2×#41×D7111yescharacteristic
737C2—42no—
738C2—5682no—
739C2#2259857114yesdirect product factor
740C2C2×#1798651111yescharacteristic
741C2C2×#1798681111yescharacteristic
742C2C2×#1798681611yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#433×C71C2
socleC23×C71C22×D4
prime radicalC2×#14556102C22
hypercenterC2×#433D71
hypocenterC71C2×#3121
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. C2×#17986476C2semidirect
3. #22598571C2direct (N × H)
4. C2×#17986341C2semidirect
6. C2×#17986295C2semidirect
7. C2×#17986285C2semidirect
8. C2×#17986222C2semidirect
9. C2×#17986222C2semidirect
10. C2×#17986157C2semidirect
12. C2×#17986107C2semidirect
13. C2×#17986101C2semidirect
14. C2×C4×Dic284C2semidirect
15. C2×C4×#11765854C2semidirect
16. C2×#433×C71C2semidirect
33. #17986476C22semidirect
45. #17986341C22semidirect
47. #17986295C22semidirect
48. #17986285C22semidirect
49. #17986222C22semidirect
50. #17986222C22semidirect
51. #17986157C22semidirect
53. #17986107C22semidirect
54. #17986101C22semidirect
55. C4×Dic284C22semidirect
56. C4×#11765854C22semidirect
70. #433×C71C22semidirect
367. C2×C71#3121semidirect
387. C2×#433D71semidirect
388. C71C2×#3121semidirect
430. #433C2×D71semidirect
739. C2#22598571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
C2×#179864762
#225985712
C2×#179863412
C2×#179863242
C2×#179862952
C2×#179862852
C2×#179862222
C2×#179861572
C2×#179861402
C2×#179861072
C2×#179861012
C2×C4×Dic2842
C2×C4×#117658542
C2×#433×C712
C2×#312171