Finite Group Databasebeta

← C2×#22598579 #32865742

Subgroups — C2×#22598579 #32865742

Order 18176.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986602C211yesmaximal, characteristic, complemented
2C2×#17986473C211yesmaximal, characteristic, complemented
3#22598579C2116yesmaximal, direct product factor
4C2×#17986323C211yesmaximal, characteristic, complemented
5C2×#17986302C211yesmaximal, characteristic, complemented
6C2×#17986298C211yesmaximal, characteristic, complemented
7C2×#17986193C211yesmaximal, characteristic, complemented
8C2×#17986193C211yesmaximal, characteristic, complemented
9C2×#17986135C211yesmaximal, characteristic, complemented
10C2×#17986132C211yesmaximal, characteristic, complemented
11C2×#17986110C211yesmaximal, characteristic, complemented
12C2×#17986108C211yesmaximal, characteristic, complemented
13C2×#17986081C211yesmaximal, characteristic, complemented
14C2×#17986079C211yesmaximal, characteristic, complemented
15C2×#17986057C211yesmaximal, characteristic, complemented
16C2×#482×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C22×D568C2211yescharacteristic
19C22×D568C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765850C2211yescharacteristic
22#17986602—24no—
23#17986602C2218yescomplemented
24C2×#14556124C2211yescharacteristic, complemented
25C2×#14556119C2211yescharacteristic, complemented
26C2×#14556112—21no—
27C2×#14556110—21no—
28C2×#14556102C2211yescharacteristic
29C2×#14556100—21no—
30C2×#14556099—21no—
31#17986473—24no—
32#17986473C2218yescomplemented
33C2×C4×D284—21no—
34C2×C4×D284—21no—
35C2×D4×Dic71C2211yescharacteristic, complemented
36C2×#14556090C2211yescharacteristic
37C2×#14556090C2211yescharacteristic
38C2×#14556090C2211yescharacteristic
39C2×#14556090C2211yescharacteristic
40C2×#14556090C2211yescharacteristic, complemented
41C2×#14556087C2211yescharacteristic
42C2×C22⋊C4×D71—21no—
43C2×C22⋊C4×D71—21no—
44#17986323C2218yescomplemented
45#17986302C2218yescomplemented
46#17986298C2218yescomplemented
47#17986193C2218yescomplemented
48#17986193C2218yescomplemented
49#17986135C2218yescomplemented
50#17986132C2218yescomplemented
51#17986110C2218yescomplemented
52#17986108C2218yescomplemented
53#17986081C2218yescomplemented
54#17986079C2218yescomplemented
55#17986057C2218yescomplemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59C2×Dic71⋊C8C2211yescharacteristic, complemented
60C2×#14556050C2211yescharacteristic
61C2×#14556050C2211yescharacteristic
62C2×#14556048C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64C2×#14556048C2211yescharacteristic, complemented
65C2×#14556048C2211yescharacteristic, complemented
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×#14556038C2211yescharacteristic, complemented
68C2×C8×Dic71C2211yescharacteristic, complemented
69C2×#121×C71C2211yescharacteristic
70C2×#117×C71C2211yescharacteristic
71#482×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic, complemented
73C2×#106×C71C2211yescharacteristic, complemented
74C2×#102×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic, complemented
76C2×C22⋊C8×C71C2211yescharacteristic
77C24×D71—21no—
78C22×D284—24no—
79C22×D284—24no—
80C22×D284—21no—
81C22×D284—22no—
82C22×D284C2314yes—
83C22×D284C2311yescharacteristic
84C22×D284C2311yescharacteristic
85C22×D284C2311yescharacteristic
86C22×C22⋊D71—21no—
87C22×C22⋊D71—21no—
88C22×C22⋊D71—21no—
89C23×Dic71—21no—
90C22×C4×D71—21no—
91C22×C4×D71—21no—
92C22×C4×D71—21no—
93C22×C4×D71—21no—
94C22×C4×D71—21no—
95C2×D568—24no—
96C2×D568—24no—
97C2×D568C2314yes—
98C2×D568C2314yes—
99C2×#11765850—24no—
100C2×#11765850—24no—
101C2×#11765850C2314yes—
102C2×#11765850C2314yes—
103C22×C71⋊C8C2311yescharacteristic
104C22×C71⋊C8C2311yescharacteristic
105#14556124—22no—
106#14556124C2314yescomplemented
107#14556119—22no—
108#14556119C2314yescomplemented
109#14556112—28no—
110#14556110—28no—
111#14556102—22no—
112#14556102C2314yes—
113#14556100—28no—
114#14556099—28no—
115C4×D284—28no—
116C4×D284—28no—
117D4×Dic71—22no—
118D4×Dic71C2314yescomplemented
119#14556090—22no—
120#14556090—22no—
121#14556090—22no—
122#14556090—22no—
123#14556090—22no—
124#14556090C2314yes—
125#14556090C2314yes—
126#14556090C2314yes—
127#14556090C2314yes—
128#14556090C2314yescomplemented
129#14556087D414yes—
130#14556087C2314yes—
131C2×C4⋊Dic71—21no—
132C2×C4⋊Dic71D411yescharacteristic
133C2×C4⋊Dic71D411yescharacteristic
134C2×C4⋊Dic71C2311yescharacteristic
135C2×Dic71⋊C4—21no—
136C2×C22⋊Dic71—21no—
137C2×C22⋊Dic71D411yescharacteristic
138C2×C22⋊Dic71D411yescharacteristic
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—21no—
145C22⋊C4×D71—28no—
146C22⋊C4×D71—28no—
147C2×C4×Dic71C2311yescharacteristic
148C2×C4×Dic71C2311yescharacteristic
149#14556061C2314yescomplemented
150#14556059C2314yescomplemented
151Dic71⋊C8C2314yescomplemented
152Dic71⋊C8C2314yescomplemented
153#14556050C2314yes—
154#14556050C2314yes—
155#14556048C2314yes—
156#14556048C2314yes—
157#14556048C2314yescomplemented
158#14556048C2314yescomplemented
159C22⋊(C71⋊C8)C2314yes—
160#14556038C2314yescomplemented
161C8×Dic71C2314yescomplemented
162C22×D4×C71—21no—
163C22×D4×C71C2311yescharacteristic
164C23×C4×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167#121×C71—22no—
168#121×C71C2314yes—
169#117×C71—22no—
170#117×C71C2314yes—
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C42×C71—21no—
177#107×C71C2314yescomplemented
178#106×C71C2314yescomplemented
179#102×C71C2314yescomplemented
180#102×C71C2314yescomplemented
181C22⋊C8×C71C2314yes—
182C23×D71—21no—
183C23×D71—21no—
184C23×D71—28no—
185C23×D71—24no—
186C23×D71—21no—
187C23×D71—82no—
188C23×D71—82no—
189C2×D284—28no—
190C2×D284—216no—
191C2×D284—21no—
192C2×D284—21no—
193C2×D284—24no—
194C2×D284—22no—
195C2×D284—22no—
196C2×D284—28no—
197C2×D284—28no—
198C2×D284—22no—
199C2×D284—22no—
200C2×D284—21no—
201C2×D284#4114yes—
202C2×D284#4114yes—
203C2×D284C2412yes—
204C2×D284C2412yes—
205C2×D284C2412yes—
206C2×C22⋊D71—24no—
207C2×C22⋊D71—24no—
208C2×C22⋊D71—24no—
209C2×C22⋊D71—82no—
210C2×C22⋊D71—82no—
211C2×C22⋊D71—82no—
212C22×Dic71—21no—
213C22×Dic71—24no—
214C22×Dic71—82no—
215C22×Dic71C2×D411yescharacteristic
216C22×Dic71C2×D411yescharacteristic
217C22×Dic71C2×D411yescharacteristic
218C22×Dic71C2×D411yescharacteristic
219C2×C4×D71—24no—
220C2×C4×D71—24no—
221C2×C4×D71—24no—
222C2×C4×D71—24no—
223C2×C4×D71—24no—
224C2×C4×D71—82no—
225C2×C4×D71—82no—
226C2×C4×D71—82no—
227C2×C4×D71—82no—
228C2×C4×D71—82no—
229D568—28no—
230D568—28no—
231#11765850—28no—
232#11765850—28no—
233C2×C71⋊C8—22no—
234C2×C71⋊C8—22no—
235C2×C71⋊C8C2412yes—
236C2×C71⋊C8C2412yes—
237C4⋊Dic71—21no—
238C4⋊Dic71—24no—
239C4⋊Dic71C2×D414yes—
240C4⋊Dic71C2×D414yes—
241C4⋊Dic71C2412yes—
242Dic71⋊C4—24no—
243C22⋊Dic71—24no—
244C22⋊Dic71C2×D414yes—
245C22⋊Dic71C2×D414yes—
246(C2×D71)⋊C4—24no—
247(C2×D71)⋊C4—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252C4×Dic71C2×D412yes—
253C4×Dic71C2×D412yes—
254C4×Dic71C2412yes—
255C4×Dic71C2412yes—
256C24×C71—21no—
257C24×C71C2×D411yescharacteristic
258C2×D4×C71—24no—
259C2×D4×C71—21no—
260C2×D4×C71—22no—
261C2×D4×C71—22no—
262C2×D4×C71—82no—
263C2×D4×C71C2412yes—
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—21no—
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D412yes—
271C22×C4×C71C2412yes—
272C22×C4×C71C2411yescharacteristic
273C2×C8×C71—22no—
274C2×C8×C71—22no—
275C2×C8×C71C2412yes—
276C2×C8×C71C2412yes—
277C4⋊C4×C71—21no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71C2412yes—
281C4⋊C4×C71C2412yes—
282C4⋊C4×C71C2412yes—
283C22⋊C4×C71—24no—
284C22⋊C4×C71—24no—
285C42×C71—24no—
286C23×C71—22no—
287C23×C71—22no—
288C23×C71—22no—
289C23×C71—22no—
290C23×C71—42no—
291C23×C71—42no—
292C23×C71—42no—
293C23×C71C22×D412yes—
294C23×C71C22×D411yescharacteristic
295C22×D71—24no—
296C22×D71—24no—
297C22×D71—22no—
298C22×D71—22no—
299C22×D71—216no—
300C22×D71—22no—
301C22×D71—42no—
302C22×D71—42no—
303C22×D71—42no—
304C22×D71—42no—
305C22×D71—42no—
306C22×D71—42no—
307C22×D71—42no—
308C22×D71—84no—
309C22×D71—84no—
310C22×D71—816no—
311D4×C71—22no—
312D4×C71—22no—
313D4×C71—42no—
314D4×C71—84no—
315C2×C4×C71—22no—
316C2×C4×C71—24no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—42no—
323C2×C4×C71—42no—
324C2×C4×C71—42no—
325C2×C4×C71C22×D412yes—
326C2×C4×C71C22×D411yescharacteristic
327C2×C4×C71C2×#4112yes—
328C2×C4×C71C2×#4112yes—
329C2×C4×C71C2511yescharacteristic
330C22⋊D71—84no—
331C22⋊D71—84no—
332C22⋊D71—84no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—42no—
339C2×Dic71—84no—
340C2×Dic71C22×D412yes—
341C2×Dic71C22×D412yes—
342C2×Dic71C22×D412yes—
343C2×Dic71C22×D412yes—
344D284—216no—
345D284—24no—
346D284—24no—
347D284—22no—
348D284—22no—
349D284—22no—
350D284—22no—
351D284—42no—
352D284C2×#4114yes—
353D284C2×#4114yes—
354C4×D71—84no—
355C4×D71—84no—
356C4×D71—84no—
357C4×D71—84no—
358C4×D71—84no—
359C8×C71—22no—
360C8×C71—22no—
361C71⋊C8—22no—
362C71⋊C8—22no—
363C22×C71—22no—
364C22×C71—22no—
365C22×C71—22no—
366C22×C71—44no—
367C22×C71—42no—
368C22×C71—42no—
369C22×C71—42no—
370C22×C71—84no—
371C22×C71#52512yes—
372C22×C71#57612yes—
373C22×C71#57612yes—
374C22×C71C23×D411yescharacteristic
375C2×D71—24no—
376C2×D71—24no—
377C2×D71—48no—
378C2×D71—48no—
379C2×D71—42no—
380C2×D71—42no—
381C2×D71—42no—
382C2×D71—42no—
383C2×D71—42no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—816no—
387C2×D71—84no—
388C4×C71—22no—
389C4×C71—42no—
390C4×C71—42no—
391C4×C71—42no—
392C4×C71#52512yes—
393C4×C71C22×#4111yescharacteristic
394C4×C71C22×#4111yescharacteristic
395Dic71—22no—
396Dic71—22no—
397Dic71—22no—
398Dic71—22no—
399Dic71—42no—
400C2×#3122—711nomaximal, Sylow
401C2×C71—42no—
402C2×C71—82no—
403C2×C71#312214yescomplemented
404C2×C71C2×#52511yescharacteristic
405C2×C71C2×#57611yescharacteristic
406C2×C71C2×#57611yescharacteristic
407D71—44no—
408D71—44no—
409D71—82no—
410C2×#540—711no—
411C2×#518—711no—
412#3122—7116no—
413C2×#482—711no—
414C2×#482D7111yescharacteristic, complemented
415C2×#478—711no—
416C2×#478—711no—
417C2×#459—711no—
418C2×#459—711no—
419C2×#447—711no—
420C2×#447—711no—
421C2×#442—711no—
422C2×#442—711no—
423C2×C4×D8—711no—
424C2×C4×D8—711no—
425C2×#433—711no—
426C71C2×#312211yescharacteristic, complemented, Sylow
427C23×D4—711no—
428C22×D8—711no—
429C22×D8—711no—
430C22×D8—711no—
431C22×D8—711no—
432#540—718no—
433#540—1424no—
434C2×#127—711no—
435C2×#125—711no—
436C2×#123—1421no—
437C2×#123—1421no—
438C2×#121—711no—
439C2×#121—1421no—
440C2×#121—1421no—
441C2×#121C2×D7111yescharacteristic
442#518—718no—
443#518—1424no—
444C2×C4×D4—711no—
445C2×C4×D4—711no—
446C2×C4×D4—711no—
447C2×C4×D4—711no—
448C2×C4×D4—711no—
449C2×C4×D4—711no—
450C2×C4×D4—1421no—
451C2×C4×D4—1421no—
452C2×#117—711no—
453C2×#117C2×D7111yescharacteristic
454C22×C22⋊C4—1421no—
455C22×C22⋊C4—1421no—
456#482—718no—
457#482C2×D7118yescomplemented
458#478—718no—
459#478—718no—
460#459—718no—
461#459—718no—
462#447—718no—
463#447—718no—
464#442—718no—
465#442—718no—
466C4×D8—718no—
467C4×D8—718no—
468#433—718no—
469C2×#107—711no—
470C2×#107C2×D7111yescharacteristic, complemented
471C2×#106—711no—
472C2×#106C2×D7111yescharacteristic, complemented
473C2×C4⋊C8—711no—
474C2×C4⋊C8—711no—
475C2×#102—711no—
476C2×#102—711no—
477C2×#102—711no—
478C2×#102—711no—
479C2×#102—711no—
480C2×#102—711no—
481C2×#102C2×D7111yescharacteristic, complemented
482C2×#102C2×D7111yescharacteristic, complemented
483C2×C22⋊C8—711no—
484C2×C22⋊C8C2×D7111yescharacteristic
485C2×#97—711no—
486C2×C4×C8—711no—
487C25—1421no—
488C22×D4—21no—
489C22×D4—711no—
490C22×D4—711no—
491C22×D4—711no—
492C22×D4—714no—
493C22×D4—1424no—
494C22×D4—1424no—
495C22×D4—1421no—
496C22×D4—1421no—
497C22×D4—1421no—
498C22×D4—1421no—
499C22×D4—1422no—
500C22×D4C22×D7111yescharacteristic
501C23×C4—1421no—
502C23×C4—1421no—
503C23×C4—1421no—
504C23×C4—1421no—
505C23×C4—1421no—
506C23×C4—1421no—
507C23×C4C22×D7111yescharacteristic
508C2×D8—714no—
509C2×D8—714no—
510C2×D8—714no—
511C2×D8—714no—
512C2×D8—1424no—
513C2×D8—1424no—
514C2×D8—1424no—
515C2×D8—1424no—
516C22×C8—711no—
517C22×C8—711no—
518C22×C8C22×D7111yescharacteristic
519C22×C8C22×D7111yescharacteristic
520#127—714no—
521#127—1422no—
522#125—714no—
523#125—1422no—
524#123—1428no—
525#123—1428no—
526#121—22no—
527#121—714no—
528#121—1428no—
529#121—1428no—
530#121—1422no—
531#121C22×D7114yes—
532C4×D4—714no—
533C4×D4—714no—
534C4×D4—714no—
535C4×D4—714no—
536C4×D4—714no—
537C4×D4—714no—
538C4×D4—1428no—
539C4×D4—1428no—
540C4×D4—1422no—
541C4×D4—1422no—
542C4×D4—1422no—
543C4×D4—1422no—
544C4×D4—1422no—
545C4×D4—1422no—
546#117—22no—
547#117—714no—
548#117—714no—
549#117C22×D7114yes—
550C2×C4⋊C4—711no—
551C2×C4⋊C4—711no—
552C2×C4⋊C4—711no—
553C2×C4⋊C4—1421no—
554C2×C4⋊C4—1421no—
555C2×C4⋊C4C22×D7111yescharacteristic
556C2×C4⋊C4C22×D7111yescharacteristic
557C2×C4⋊C4C22×D7111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—711no—
561C2×C22⋊C4—711no—
562C2×C22⋊C4—1428no—
563C2×C22⋊C4—1428no—
564C2×C22⋊C4—1421no—
565C2×C22⋊C4—1421no—
566C2×C22⋊C4—1421no—
567C2×C22⋊C4—1421no—
568C2×C22⋊C4—1421no—
569C2×C22⋊C4—1421no—
570C2×C22⋊C4—1421no—
571C2×C42—21no—
572C2×C42—711no—
573C2×C42—711no—
574#107—714no—
575#107C22×D7114yescomplemented
576#106—714no—
577#106C22×D7114yescomplemented
578C4⋊C8—714no—
579C4⋊C8—714no—
580#102—714no—
581#102—714no—
582#102—714no—
583#102—714no—
584#102—714no—
585#102—714no—
586#102C22×D7114yescomplemented
587#102C22×D7114yescomplemented
588C22⋊C8—714no—
589C22⋊C8C22×D7114yes—
590#97—714no—
591C4×C8—714no—
592C24—21no—
593C24—5682no—
594C24—5682no—
595C24—1428no—
596C24—1421no—
597C24—1421no—
598C24—1421no—
599C24—1424no—
600C24D4×D7111yescharacteristic
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—82no—
606C2×D4—5682no—
607C2×D4—5682no—
608C2×D4—5682no—
609C2×D4—714no—
610C2×D4—714no—
611C2×D4—712no—
612C2×D4—712no—
613C2×D4—712no—
614C2×D4—1428no—
615C2×D4—1428no—
616C2×D4—1428no—
617C2×D4—14216no—
618C2×D4—1424no—
619C2×D4—1424no—
620C2×D4—1424no—
621C2×D4—1421no—
622C2×D4—1424no—
623C2×D4—1421no—
624C2×D4—1421no—
625C2×D4—1422no—
626C2×D4—1422no—
627C2×D4—1422no—
628C2×D4—1422no—
629C2×D4C23×D7112yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—5682no—
636C22×C4—5682no—
637C22×C4—5682no—
638C22×C4—5682no—
639C22×C4—5682no—
640C22×C4—5682no—
641C22×C4—711no—
642C22×C4—711no—
643C22×C4—711no—
644C22×C4—711no—
645C22×C4—1424no—
646C22×C4—1424no—
647C22×C4—1424no—
648C22×C4—1424no—
649C22×C4—1424no—
650C22×C4—1421no—
651C22×C4—1424no—
652C22×C4D4×D7112yes—
653C22×C4D4×D7111yescharacteristic
654C22×C4C23×D7112yes—
655C22×C4C23×D7111yescharacteristic
656D8—1428no—
657D8—1428no—
658D8—1428no—
659D8—1428no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—712no—
663C2×C8—712no—
664C2×C8—1422no—
665C2×C8—1422no—
666C2×C8C23×D7112yes—
667C2×C8C23×D7112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—714no—
672C4⋊C4—714no—
673C4⋊C4—712no—
674C4⋊C4—1424no—
675C4⋊C4—1424no—
676C4⋊C4—1421no—
677C4⋊C4C23×D7112yes—
678C4⋊C4C23×D7112yes—
679C4⋊C4C23×D7112yes—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—714no—
683C22⋊C4—714no—
684C22⋊C4—1424no—
685C22⋊C4—1424no—
686C22⋊C4—1424no—
687C22⋊C4—1424no—
688C22⋊C4—1424no—
689C22⋊C4—1424no—
690C22⋊C4—1424no—
691C42—24no—
692C42—712no—
693C42—712no—
694C42—712no—
695C42—712no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—2842no—
704C23—2842no—
705C23—2842no—
706C23—2842no—
707C23—2842no—
708C23—2842no—
709C23—2842no—
710C23—5684no—
711C23—5684no—
712C23—56816no—
713C23—14216no—
714C23—1422no—
715C23—1422no—
716C23—1422no—
717C23—1424no—
718C23—1424no—
719C23C2×D4×D7112yes—
720C23C2×D4×D7111yescharacteristic
721D4—22no—
722D4—22no—
723D4—42no—
724D4—84no—
725D4—2842no—
726D4—5684no—
727D4—5684no—
728D4—5684no—
729D4—714no—
730D4—714no—
731D4—14216no—
732D4—1422no—
733D4—1422no—
734D4—1422no—
735D4—1422no—
736D4—1424no—
737D4—1424no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—2842no—
749C2×C4—5684no—
750C2×C4—5684no—
751C2×C4—5684no—
752C2×C4—5684no—
753C2×C4—5684no—
754C2×C4—5684no—
755C2×C4—712no—
756C2×C4—712no—
757C2×C4—712no—
758C2×C4—712no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4C2×D4×D7112yes—
765C2×C4C2×D4×D7111yescharacteristic
766C2×C4#41×D7112yes—
767C2×C4#41×D7112yes—
768C2×C4C24×D7111yescharacteristic
769C8—22no—
770C8—22no—
771C8—1422no—
772C8—1422no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—2842no—
782C22—2842no—
783C22—2842no—
784C22—2842no—
785C22—2848no—
786C22—2848no—
787C22—2842no—
788C22—2842no—
789C22—2842no—
790C22—56816no—
791C22—5684no—
792C22—1424no—
793C22—1424no—
794C22#1798650712yes—
795C22#1798680112yes—
796C22#1798680312yes—
797C22C22×D4×D7111yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—2842no—
803C4—1422no—
804C4—1422no—
805C4—1422no—
806C4—1422no—
807C4#1798650712yes—
808C4C2×#41×D7111yescharacteristic
809C4C2×#41×D7111yescharacteristic
810C2—42no—
811C2—82no—
812C2—2844no—
813C2—2844no—
814C2—5682no—
815C2#2259857914yesdirect product factor
816C2C2×#1798650711yescharacteristic
817C2C2×#1798680111yescharacteristic
818C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#482×C71C2
socleC23×C71C22×D4
hypercenterC2×#482D71
hypocenterC71C2×#3122
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#17986602C2semidirect
2. C2×#17986473C2semidirect
3. #22598579C2direct (N × H)
4. C2×#17986323C2semidirect
5. C2×#17986302C2semidirect
6. C2×#17986298C2semidirect
7. C2×#17986193C2semidirect
8. C2×#17986193C2semidirect
9. C2×#17986135C2semidirect
10. C2×#17986132C2semidirect
11. C2×#17986110C2semidirect
12. C2×#17986108C2semidirect
13. C2×#17986081C2semidirect
14. C2×#17986079C2semidirect
15. C2×#17986057C2semidirect
16. C2×#482×C71C2semidirect
23. #17986602C22semidirect
24. C2×#14556124C22semidirect
25. C2×#14556119C22semidirect
32. #17986473C22semidirect
35. C2×D4×Dic71C22semidirect
40. C2×#14556090C22semidirect
44. #17986323C22semidirect
45. #17986302C22semidirect
46. #17986298C22semidirect
47. #17986193C22semidirect
48. #17986193C22semidirect
49. #17986135C22semidirect
50. #17986132C22semidirect
51. #17986110C22semidirect
52. #17986108C22semidirect
53. #17986081C22semidirect
54. #17986079C22semidirect
55. #17986057C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556059C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. C2×Dic71⋊C8C22semidirect
64. C2×#14556048C22semidirect
65. C2×#14556048C22semidirect
67. C2×#14556038C22semidirect
68. C2×C8×Dic71C22semidirect
71. #482×C71C22semidirect
72. C2×#107×C71C22semidirect
73. C2×#106×C71C22semidirect
74. C2×#102×C71C22semidirect
75. C2×#102×C71C22semidirect
106. #14556124C23semidirect
108. #14556119C23semidirect
118. D4×Dic71C23semidirect
128. #14556090C23semidirect
149. #14556061C23semidirect
150. #14556059C23semidirect
151. Dic71⋊C8C23semidirect
152. Dic71⋊C8C23semidirect
157. #14556048C23semidirect
158. #14556048C23semidirect
160. #14556038C23semidirect
161. C8×Dic71C23semidirect
177. #107×C71C23semidirect
178. #106×C71C23semidirect
179. #102×C71C23semidirect
180. #102×C71C23semidirect
403. C2×C71#3122semidirect
414. C2×#482D71semidirect
426. C71C2×#3122semidirect
457. #482C2×D71semidirect
470. C2×#107C2×D71semidirect
472. C2×#106C2×D71semidirect
481. C2×#102C2×D71semidirect
482. C2×#102C2×D71semidirect
575. #107C22×D71semidirect
577. #106C22×D71semidirect
586. #102C22×D71semidirect
587. #102C22×D71semidirect
815. C2#22598579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866022
C2×#179864732
#225985792
C2×#179863232
C2×#179863022
C2×#179862982
C2×#179861932
C2×#179861352
C2×#179861322
C2×#179861102
C2×#179861082
C2×#179860812
C2×#179860792
C2×#179860572
C2×#482×C712
C2×#312271