Finite Group Databasebeta

← C2×#22600542 #32874250

Subgroups — C2×#22600542 #32874250

Order 18176.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986697C211yesmaximal, characteristic, complemented
2C2×#17986637C211yesmaximal, characteristic, complemented
3#22600542C2116yesmaximal, direct product factor
4C2×#17986355C211yesmaximal, characteristic, complemented
5C2×#17986338C211yesmaximal, characteristic, complemented
6C2×#17986312C211yesmaximal, characteristic, complemented
7C2×#17986301C211yesmaximal, characteristic, complemented
8C2×#17986252C211yesmaximal, characteristic, complemented
9C2×#17986248C211yesmaximal, characteristic, complemented
10C2×#17986217C211yesmaximal, characteristic, complemented
11C2×#17986144C211yesmaximal, characteristic, complemented
12C2×#17986134C211yesmaximal, characteristic, complemented
13C2×#17986079C211yesmaximal, characteristic, complemented
14C2×#17986075C211yesmaximal, characteristic, complemented
15C2×#17986002C211yesmaximal, characteristic, complemented
16C2×#417×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C22×#11765852C2211yescharacteristic, complemented
19C22×D568C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765848C2211yescharacteristic
22#17986697—24no—
23#17986697C2218yescomplemented
24#17986637—24no—
25#17986637C2218yescomplemented
26C2×#14556123—21no—
27C2×#14556119C2211yescharacteristic, complemented
28C2×#14556117C2211yescharacteristic
29C2×#14556113—21no—
30C2×#14556111—21no—
31C2×#14556104C2211yescharacteristic
32C2×#14556103C2211yescharacteristic
33C2×#14556102—21no—
34C2×#14556102C2211yescharacteristic
35C2×#14556102C2211yescharacteristic, complemented
36C2×#14556100—21no—
37C2×#14556096—21no—
38C2×D4×Dic71C2211yescharacteristic
39C2×#14556090C2211yescharacteristic, complemented
40C2×C4×C22⋊D71—21no—
41C2×C4×C22⋊D71C2211yescharacteristic
42C2×#14556086C2211yescharacteristic
43C22×(C2×D71)⋊C4—21no—
44#17986355C2218yescomplemented
45#17986338C2218yescomplemented
46#17986312C2218yescomplemented
47#17986301C2218yescomplemented
48#17986252C2218yescomplemented
49#17986248C2218yescomplemented
50#17986217C2218yescomplemented
51#17986144C2218yescomplemented
52#17986134C2218yescomplemented
53#17986079C2218yescomplemented
54#17986075C2218yescomplemented
55C2×#14556061C2211yescharacteristic, complemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556060C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59#17986002C2218yescomplemented
60C2×#14556052C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic
62C2×#14556050C2211yescharacteristic, complemented
63C2×#14556049C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic, complemented
69C22×#41×C71C2211yescharacteristic
70C22×M16×C71C2211yescharacteristic, complemented
71C22×C4⋊C4×C71C2211yescharacteristic, complemented
72#417×C71C2218yescomplemented
73C2×#103×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C24×D71—21no—
78C22×D284—21no—
79C22×D284C2311yescharacteristic
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71—21no—
83C22×C22⋊D71—21no—
84C22×C22⋊D71D411yescharacteristic
85C2×D4×D71—22no—
86C2×D4×D71—24no—
87C2×D4×D71—42no—
88C2×D4×D71C2314yes—
89C23×Dic71—21no—
90C22×C4×D71—21no—
91C22×C4×D71C2311yescharacteristic
92C2×#11765852—42no—
93C2×#11765852C2314yescomplemented
94C2×D568—42no—
95C2×D568C2314yes—
96C2×#11765850—24no—
97C2×#11765850C2314yes—
98C2×#11765848—42no—
99C2×#11765848C2314yes—
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102#14556123—28no—
103#14556119—22no—
104#14556119C2314yescomplemented
105#14556117—22no—
106#14556117C2314yes—
107#14556113—28no—
108#14556111—28no—
109#14556104—22no—
110#14556104C2314yes—
111#14556103—22no—
112#14556103C2314yes—
113#14556102—28no—
114#14556102—22no—
115#14556102—22no—
116#14556102C2314yes—
117#14556102C2314yescomplemented
118#14556100—28no—
119#14556096—28no—
120D4×Dic71—22no—
121D4×Dic71C2314yes—
122#14556090—22no—
123#14556090C2314yescomplemented
124C4×C22⋊D71—28no—
125C4×C22⋊D71D414yes—
126C4×C22⋊D71C2314yes—
127#14556086—22no—
128#14556086C2314yes—
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4D411yescharacteristic
135C2×C22⋊Dic71—21no—
136C2×C22⋊Dic71D411yescharacteristic
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—28no—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4D411yescharacteristic
147C2×C4×Dic71—21no—
148C2×C4×Dic71C2311yescharacteristic
149#14556061C2314yescomplemented
150#14556061C2314yescomplemented
151#14556060C2314yescomplemented
152Dic71⋊C8C2314yescomplemented
153#14556052C2314yescomplemented
154#14556050C2314yes—
155#14556050C2314yescomplemented
156#14556049C2314yes—
157#14556048C2314yes—
158#14556048C2314yes—
159C22⋊(C71⋊C8)C2314yescomplemented
160(C2×D71)⋊C8C2314yes—
161C8×Dic71C2314yescomplemented
162C2×#41×C71—22no—
163C2×#41×C71—24no—
164C2×#41×C71—42no—
165C2×#41×C71C2314yes—
166C22×Q8×C71C2311yescharacteristic
167C22×D4×C71—21no—
168C22×D4×C71C2311yescharacteristic
169C23×C4×C71—21no—
170C23×C4×C71—21no—
171C23×C4×C71C2311yescharacteristic
172C2×M16×C71—42no—
173C2×M16×C71C2314yescomplemented
174C22×C8×C71C2311yescharacteristic
175C22×C8×C71C2311yescharacteristic
176C2×C4⋊C4×C71—22no—
177C2×C4⋊C4×C71—21no—
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C4⋊C4×C71C2311yescharacteristic
180C2×C4⋊C4×C71C2314yescomplemented
181#103×C71C2314yescomplemented
182#103×C71C2314yescomplemented
183#102×C71C2314yes—
184#102×C71C2314yes—
185C23×D71—21no—
186C23×D71—21no—
187C23×D71—24no—
188C23×D71—44no—
189C23×D71—44no—
190C23×D71—82no—
191C23×D71C2×D411yescharacteristic
192C2×D284—22no—
193C2×D284—22no—
194C2×D284—22no—
195C2×D284—22no—
196C2×D284—21no—
197C2×D284—21no—
198C2×D284—24no—
199C2×D284—82no—
200C2×D284C2412yes—
201C2×D284C2412yes—
202C2×C22⋊D71—24no—
203C2×C22⋊D71—24no—
204C2×C22⋊D71—24no—
205C2×C22⋊D71—42no—
206C2×C22⋊D71—44no—
207C2×C22⋊D71—44no—
208C2×C22⋊D71—82no—
209C2×C22⋊D71C2×D414yes—
210D4×D71—28no—
211D4×D71—44no—
212D4×D71—48no—
213C22×Dic71—21no—
214C22×Dic71—21no—
215C22×Dic71—24no—
216C22×Dic71—82no—
217C22×Dic71C2×D411yescharacteristic
218C22×Dic71C2×D411yescharacteristic
219C22×Dic71C2×D411yescharacteristic
220C2×C4×D71—22no—
221C2×C4×D71—22no—
222C2×C4×D71—24no—
223C2×C4×D71—82no—
224C2×C4×D71C2×D412yes—
225C2×C4×D71C2412yes—
226#11765852—44no—
227D568—44no—
228#11765850—28no—
229#11765848—44no—
230C2×C71⋊C8—22no—
231C2×C71⋊C8—22no—
232C2×C71⋊C8C2412yes—
233C2×C71⋊C8C2412yes—
234C4⋊Dic71—21no—
235C4⋊Dic71—21no—
236C4⋊Dic71—24no—
237C4⋊Dic71C2412yes—
238C4⋊Dic71C2412yes—
239Dic71⋊C4—24no—
240Dic71⋊C4—24no—
241Dic71⋊C4C2×D414yes—
242C22⋊Dic71—24no—
243C22⋊Dic71C2×D414yes—
244(C2×D71)⋊C4—24no—
245(C2×D71)⋊C4—24no—
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—
252(C2×D71)⋊C4C2×D414yes—
253C4×Dic71—24no—
254C4×Dic71C2×D412yes—
255C4×Dic71C2412yes—
256C24×C71—21no—
257C24×C71C2×D411yescharacteristic
258#41×C71—28no—
259#41×C71—44no—
260#41×C71—48no—
261C2×Q8×C71—21no—
262C2×Q8×C71—22no—
263C2×Q8×C71—22no—
264C2×Q8×C71C2412yes—
265C2×D4×C71—24no—
266C2×D4×C71—21no—
267C2×D4×C71—22no—
268C2×D4×C71—44no—
269C2×D4×C71#4114yes—
270C2×D4×C71C2412yes—
271C22×C4×C71—22no—
272C22×C4×C71—22no—
273C22×C4×C71—21no—
274C22×C4×C71—21no—
275C22×C4×C71—21no—
276C22×C4×C71—24no—
277C22×C4×C71—24no—
278C22×C4×C71—44no—
279C22×C4×C71—82no—
280C22×C4×C71C2×D411yescharacteristic
281C22×C4×C71C2×D412yes—
282C22×C4×C71C2412yes—
283C22×C4×C71C2411yescharacteristic
284M16×C71—44no—
285C2×C8×C71—22no—
286C2×C8×C71—22no—
287C2×C8×C71C2412yes—
288C2×C8×C71C2412yes—
289C4⋊C4×C71—21no—
290C4⋊C4×C71—21no—
291C4⋊C4×C71—24no—
292C4⋊C4×C71C2412yes—
293C4⋊C4×C71C2412yes—
294C23×C71—22no—
295C23×C71—24no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—42no—
300C23×C71—42no—
301C23×C71C22×D412yes—
302C23×C71C22×D411yescharacteristic
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—48no—
309C22×D71—48no—
310C22×D71—42no—
311C22×D71—42no—
312C22×D71—42no—
313C22×D71—42no—
314C22×D71—42no—
315C22×D71—42no—
316C22×D71—84no—
317C22×D71—816no—
318C22×D71C22×D412yes—
319Q8×C71—22no—
320Q8×C71—22no—
321Q8×C71—42no—
322D4×C71—24no—
323D4×C71—22no—
324D4×C71—48no—
325D4×C71C2×#4114yes—
326C2×C4×C71—22no—
327C2×C4×C71—24no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—48no—
334C2×C4×C71—42no—
335C2×C4×C71—42no—
336C2×C4×C71—42no—
337C2×C4×C71—84no—
338C2×C4×C71C22×D412yes—
339C2×C4×C71C22×D411yescharacteristic
340C2×C4×C71C2×#4112yes—
341C2×C4×C71H(5,𝔽2)12yes—
342C2×C4×C71C2511yescharacteristic
343C22⋊D71—44no—
344C22⋊D71—48no—
345C22⋊D71—48no—
346C22⋊D71—84no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—42no—
353C2×Dic71—42no—
354C2×Dic71—84no—
355C2×Dic71C22×D412yes—
356C2×Dic71C22×D412yes—
357C2×Dic71C22×D412yes—
358D284—22no—
359D284—22no—
360D284—22no—
361D284—22no—
362D284—42no—
363D284—42no—
364D284—84no—
365C4×D71—24no—
366C4×D71—22no—
367C4×D71—22no—
368C4×D71—84no—
369C8×C71—22no—
370C8×C71—22no—
371C71⋊C8—22no—
372C71⋊C8—22no—
373C22×C71—24no—
374C22×C71—22no—
375C22×C71—22no—
376C22×C71—22no—
377C22×C71—48no—
378C22×C71—44no—
379C22×C71—42no—
380C22×C71—42no—
381C22×C71#54612yes—
382C22×C71#57512yes—
383C22×C71#57612yes—
384C22×C71C23×D411yescharacteristic
385C2×D71—22no—
386C2×D71—22no—
387C2×D71—22no—
388C2×D71—44no—
389C2×D71—42no—
390C2×D71—42no—
391C2×D71—42no—
392C2×D71—42no—
393C2×D71—42no—
394C2×D71—42no—
395C2×D71—816no—
396C2×D71—84no—
397C2×D71—84no—
398C4×C71—22no—
399C4×C71—42no—
400C4×C71—42no—
401C4×C71—42no—
402C4×C71#54612yes—
403C4×C71C22×#4111yescharacteristic
404C4×C71C2×H(5,𝔽2)11yescharacteristic
405Dic71—22no—
406Dic71—22no—
407Dic71—22no—
408Dic71—42no—
409Dic71—42no—
410C2×#3322—711nomaximal, Sylow
411C2×C71—44no—
412C2×C71—42no—
413C2×C71#332214yescomplemented
414C2×C71C2×#54611yescharacteristic
415C2×C71C2×#57511yescharacteristic
416C2×C71C2×#57611yescharacteristic
417D71—42no—
418D71—82no—
419D71—82no—
420C2×#553—711no—
421C2×#546—711no—
422#3322—7116no—
423C2×#488—711no—
424C2×#485—711no—
425C2×#480—711no—
426C2×#478—711no—
427C2×#469—711no—
428C2×#468—711no—
429C2×#463—711no—
430C2×#449—711no—
431C2×#447—711no—
432C2×C4×D8—711no—
433C2×#436—711no—
434C2×#417D7111yescharacteristic, complemented
435C2×#418—711no—
436C71C2×#332211yescharacteristic, complemented, Sylow
437C22×#41C2×D7111yescharacteristic
438C23×D4—711no—
439C22×SD16—711no—
440C22×D8—711no—
441C22×D8—711no—
442C22×M16—711no—
443C22×M16C2×D7111yescharacteristic, complemented
444#553—718no—
445#553—1424no—
446#546—718no—
447#546—1424no—
448C2×#126—1421no—
449C2×#125—711no—
450C2×#124—711no—
451C2×#123—1421no—
452C2×#123—1421no—
453C2×C22⋊Q8—711no—
454C2×#121—711no—
455C2×#121—711no—
456C2×#121—711no—
457C2×#121—1421no—
458C2×#121—1421no—
459C2×#120—1421no—
460C2×C4×D4—711no—
461C2×C4×D4—711no—
462C2×C4×D4—711no—
463C2×C4×D4—1421no—
464C2×#117—711no—
465C22×C4⋊C4C2×D7111yescharacteristic, complemented
466C22×C22⋊C4—1421no—
467#488—718no—
468#485—718no—
469#480—718no—
470#478—718no—
471#469—718no—
472#468—718no—
473#463—718no—
474#449—718no—
475#447—718no—
476C4×D8—718no—
477#436—718no—
478C2×#107—711no—
479C2×#107—711no—
480C2×#106—711no—
481C2×C4⋊C8—711no—
482#418—718no—
483#417C2×D7118yescomplemented
484C2×#103—711no—
485C2×#103C2×D7111yescharacteristic, complemented
486C2×#103C2×D7111yescharacteristic, complemented
487C2×#102—711no—
488C2×#102—711no—
489C2×#102—711no—
490C2×#102—711no—
491C2×#102—711no—
492C2×#102C2×D7111yescharacteristic
493C2×#102C2×D7111yescharacteristic
494C2×C22⋊C8—711no—
495C2×C22⋊C8—711no—
496C2×C4×C8—711no—
497C25—1421no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D7114yes—
502C22×Q8C22×D7111yescharacteristic
503C22×D4—21no—
504C22×D4—2842no—
505C22×D4—711no—
506C22×D4—714no—
507C22×D4—711no—
508C22×D4—711no—
509C22×D4—1421no—
510C22×D4—1422no—
511C22×D4—1421no—
512C22×D4—1421no—
513C22×D4—1424no—
514C22×D4—1421no—
515C22×D4C22×D7111yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—711no—
519C23×C4—1421no—
520C23×C4—1421no—
521C23×C4C22×D7111yescharacteristic
522C2×SD16—2842no—
523C2×SD16—714no—
524C2×D8—2842no—
525C2×D8—714no—
526C2×D8—714no—
527C2×D8—1424no—
528C2×M16—42no—
529C2×M16—2842no—
530C2×M16—714no—
531C2×M16C22×D7114yescomplemented
532C22×C8—711no—
533C22×C8—711no—
534C22×C8C22×D7111yescharacteristic
535C22×C8C22×D7111yescharacteristic
536#126—1428no—
537#125—714no—
538#125—1422no—
539#124—714no—
540#124—1422no—
541#123—1428no—
542#123—1428no—
543C22⋊Q8—714no—
544C22⋊Q8—1422no—
545#121—714no—
546#121—714no—
547#121—714no—
548#121—1428no—
549#121—1422no—
550#121—1428no—
551#121—1422no—
552#121—1422no—
553#120—1428no—
554C4×D4—714no—
555C4×D4—714no—
556C4×D4—714no—
557C4×D4—714no—
558C4×D4—1422no—
559C4×D4—1422no—
560C4×D4—1428no—
561#117—714no—
562#117—1422no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—711no—
566C2×C4⋊C4—711no—
567C2×C4⋊C4—711no—
568C2×C4⋊C4—1421no—
569C2×C4⋊C4—1421no—
570C2×C4⋊C4—1421no—
571C2×C4⋊C4C22×D7111yescharacteristic
572C2×C4⋊C4C22×D7111yescharacteristic
573C2×C4⋊C4C22×D7114yescomplemented
574C2×C22⋊C4—711no—
575C2×C22⋊C4—711no—
576C2×C22⋊C4—1428no—
577C2×C22⋊C4—1421no—
578C2×C22⋊C4—1421no—
579C2×C22⋊C4—1421no—
580C2×C22⋊C4—1421no—
581C2×C22⋊C4—1421no—
582C2×C22⋊C4—1421no—
583C2×C22⋊C4—1421no—
584C2×C22⋊C4—1421no—
585C2×C22⋊C4—1421no—
586C2×C42—711no—
587C2×C42—1421no—
588#107—714no—
589#107—714no—
590#106—714no—
591C4⋊C8—714no—
592#103—714no—
593#103C22×D7114yescomplemented
594#103C22×D7114yescomplemented
595#102—714no—
596#102—714no—
597#102—714no—
598#102—714no—
599#102—714no—
600#102C22×D7114yes—
601#102C22×D7114yes—
602C22⋊C8—714no—
603C22⋊C8—714no—
604C4×C8—714no—
605C24—21no—
606C24—2844no—
607C24—2844no—
608C24—5682no—
609C24—711no—
610C24—1424no—
611C24—1421no—
612C24—1421no—
613C24D4×D7111yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D7112yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—44no—
625C2×D4—2844no—
626C2×D4—2848no—
627C2×D4—2844no—
628C2×D4—2844no—
629C2×D4—2842no—
630C2×D4—5682no—
631C2×D4—5682no—
632C2×D4—714no—
633C2×D4—712no—
634C2×D4—712no—
635C2×D4—1424no—
636C2×D4—1424no—
637C2×D4—1424no—
638C2×D4—1428no—
639C2×D4—1424no—
640C2×D4—1421no—
641C2×D4—1421no—
642C2×D4—1422no—
643C2×D4—1422no—
644C2×D4—1422no—
645C2×D4—1422no—
646C2×D4#1176586514yes—
647C2×D4C23×D7112yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—44no—
656C22×C4—82no—
657C22×C4—5682no—
658C22×C4—5682no—
659C22×C4—711no—
660C22×C4—711no—
661C22×C4—711no—
662C22×C4—712no—
663C22×C4—712no—
664C22×C4—1424no—
665C22×C4—1421no—
666C22×C4—1421no—
667C22×C4—1424no—
668C22×C4—1422no—
669C22×C4—1422no—
670C22×C4D4×D7112yes—
671C22×C4D4×D7111yescharacteristic
672C22×C4C23×D7112yes—
673C22×C4C23×D7111yescharacteristic
674SD16—2844no—
675D8—2844no—
676D8—1428no—
677M16—44no—
678M16—2844no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—712no—
682C2×C8—712no—
683C2×C8—1422no—
684C2×C8—1422no—
685C2×C8C23×D7112yes—
686C2×C8C23×D7112yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—714no—
691C4⋊C4—712no—
692C4⋊C4—712no—
693C4⋊C4—1424no—
694C4⋊C4—1424no—
695C4⋊C4—1424no—
696C4⋊C4—1421no—
697C4⋊C4—1421no—
698C4⋊C4C23×D7112yes—
699C4⋊C4C23×D7112yes—
700C22⋊C4—714no—
701C22⋊C4—714no—
702C22⋊C4—1424no—
703C22⋊C4—1424no—
704C22⋊C4—1424no—
705C22⋊C4—1424no—
706C22⋊C4—1424no—
707C22⋊C4—1424no—
708C22⋊C4—1424no—
709C22⋊C4—1424no—
710C22⋊C4—1424no—
711C42—712no—
712C42—712no—
713C42—1424no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—2848no—
722C23—2848no—
723C23—2842no—
724C23—2842no—
725C23—2842no—
726C23—2842no—
727C23—2842no—
728C23—2842no—
729C23—56816no—
730C23—5684no—
731C23—712no—
732C23—1422no—
733C23—1422no—
734C23—1422no—
735C23—1422no—
736C23—1422no—
737C23C2×D4×D7112yes—
738C23C2×D4×D7111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—22no—
743D4—24no—
744D4—48no—
745D4—2848no—
746D4—2848no—
747D4—2844no—
748D4—2842no—
749D4—2842no—
750D4—5684no—
751D4—5684no—
752D4—1422no—
753D4—1422no—
754D4—1422no—
755D4—1422no—
756D4C2×#1176586514yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—48no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—84no—
769C2×C4—2842no—
770C2×C4—2842no—
771C2×C4—5684no—
772C2×C4—5684no—
773C2×C4—712no—
774C2×C4—712no—
775C2×C4—712no—
776C2×C4—1422no—
777C2×C4—1422no—
778C2×C4—1422no—
779C2×C4—1422no—
780C2×C4—1422no—
781C2×C4—1422no—
782C2×C4—1422no—
783C2×C4—1424no—
784C2×C4C2×D4×D7112yes—
785C2×C4C2×D4×D7111yescharacteristic
786C2×C4C2×#1176586512yes—
787C2×C4#1455617312yes—
788C2×C4C24×D7111yescharacteristic
789C8—22no—
790C8—22no—
791C8—1422no—
792C8—1422no—
793C22—22no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—48no—
801C22—2844no—
802C22—2842no—
803C22—2842no—
804C22—2842no—
805C22—2842no—
806C22—2842no—
807C22—2842no—
808C22—56816no—
809C22—5684no—
810C22—5684no—
811C22—1422no—
812C22—1422no—
813C22—1422no—
814C22#1798663912yes—
815C22#1798679812yes—
816C22#1798680312yes—
817C22C22×D4×D7111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—2842no—
823C4—2842no—
824C4—1422no—
825C4—1422no—
826C4—1422no—
827C4#1798663912yes—
828C4C22×#1176586511yescharacteristic
829C4C2×#1455617311yescharacteristic
830C2—42no—
831C2—44no—
832C2—2842no—
833C2—5682no—
834C2—5682no—
835C2#2260054214yesdirect product factor
836C2C2×#1798663911yescharacteristic
837C2C2×#1798679811yescharacteristic
838C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#417×C71C2
socleC23×C71C22×D4
hypercenterC2×#417D71
hypocenterC71C2×#3322
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#17986697C2semidirect
2. C2×#17986637C2semidirect
3. #22600542C2direct (N × H)
4. C2×#17986355C2semidirect
5. C2×#17986338C2semidirect
6. C2×#17986312C2semidirect
7. C2×#17986301C2semidirect
8. C2×#17986252C2semidirect
9. C2×#17986248C2semidirect
10. C2×#17986217C2semidirect
11. C2×#17986144C2semidirect
12. C2×#17986134C2semidirect
13. C2×#17986079C2semidirect
14. C2×#17986075C2semidirect
15. C2×#17986002C2semidirect
16. C2×#417×C71C2semidirect
18. C22×#11765852C22semidirect
23. #17986697C22semidirect
25. #17986637C22semidirect
27. C2×#14556119C22semidirect
35. C2×#14556102C22semidirect
39. C2×#14556090C22semidirect
44. #17986355C22semidirect
45. #17986338C22semidirect
46. #17986312C22semidirect
47. #17986301C22semidirect
48. #17986252C22semidirect
49. #17986248C22semidirect
50. #17986217C22semidirect
51. #17986144C22semidirect
52. #17986134C22semidirect
53. #17986079C22semidirect
54. #17986075C22semidirect
55. C2×#14556061C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556060C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. #17986002C22semidirect
60. C2×#14556052C22semidirect
62. C2×#14556050C22semidirect
66. C2×C22⋊(C71⋊C8)C22semidirect
68. C2×C8×Dic71C22semidirect
70. C22×M16×C71C22semidirect
71. C22×C4⋊C4×C71C22semidirect
72. #417×C71C22semidirect
73. C2×#103×C71C22semidirect
74. C2×#103×C71C22semidirect
93. C2×#11765852C23semidirect
104. #14556119C23semidirect
117. #14556102C23semidirect
123. #14556090C23semidirect
149. #14556061C23semidirect
150. #14556061C23semidirect
151. #14556060C23semidirect
152. Dic71⋊C8C23semidirect
153. #14556052C23semidirect
155. #14556050C23semidirect
159. C22⋊(C71⋊C8)C23semidirect
161. C8×Dic71C23semidirect
173. C2×M16×C71C23semidirect
180. C2×C4⋊C4×C71C23semidirect
181. #103×C71C23semidirect
182. #103×C71C23semidirect
413. C2×C71#3322semidirect
434. C2×#417D71semidirect
436. C71C2×#3322semidirect
443. C22×M16C2×D71semidirect
465. C22×C4⋊C4C2×D71semidirect
483. #417C2×D71semidirect
485. C2×#103C2×D71semidirect
486. C2×#103C2×D71semidirect
531. C2×M16C22×D71semidirect
573. C2×C4⋊C4C22×D71semidirect
593. #103C22×D71semidirect
594. #103C22×D71semidirect
835. C2#22600542direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866972
C2×#179866372
#226005422
C2×#179863552
C2×#179863382
C2×#179863122
C2×#179863012
C2×#179862522
C2×#179862482
C2×#179862172
C2×#179861442
C2×#179861342
C2×#179860792
C2×#179860752
C2×#179860022
C2×#417×C712
C2×#332271