Finite Group Databasebeta

← C2×#22597916 #32864553

Subgroups — C2×#22597916 #32864553

Order 18176.

3046 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556149C211yesmaximal, characteristic, complemented
2C23×C8×D71C211yesmaximal, characteristic, complemented
3C2×#17986512C211yesmaximal, characteristic, complemented
4C2×#17986509C211yesmaximal, characteristic, complemented
5#22597916C2116yesmaximal, direct product factor
6C2×#17986239C211yesmaximal, characteristic, complemented
7C2×#17986238C211yesmaximal, characteristic, complemented
8C2×#17986234C211yesmaximal, characteristic, complemented
9C2×#17986233C211yesmaximal, characteristic, complemented
10C2×#17986229C211yesmaximal, characteristic, complemented
11C2×#17986228C211yesmaximal, characteristic, complemented
12C2×#17986225C211yesmaximal, characteristic, complemented
13C2×#17986034C211yesmaximal, characteristic, complemented
14C2×#17985994C211yesmaximal, characteristic, complemented
15C2×#17985992C211yesmaximal, characteristic, complemented
16C2×#465×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×#11765864C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556149—28no—
21C2×#14556149C2218yescomplemented
22C22×#11765855C2211yescharacteristic, complemented
23C22×#11765854C2211yescharacteristic, complemented
24C22×#11765850C2211yescharacteristic, complemented
25C23×C71⋊C8C2211yescharacteristic
26C22×C8×D71—28no—
27C22×C8×D71C2211yescharacteristic
28C22×C8×D71C2211yescharacteristic
29C22×C8×D71C2211yescharacteristic
30C22×C8×D71C2211yescharacteristic
31C22×C8×D71C2218yescomplemented
32#17986512—24no—
33#17986512C2218yescomplemented
34#17986509—24no—
35#17986509C2218yescomplemented
36C2×#14556113—21no—
37C2×#14556110—21no—
38C2×#14556108C2211yescharacteristic
39C2×#14556107C2211yescharacteristic
40C2×#14556104C2211yescharacteristic
41C2×#14556103C2211yescharacteristic
42C2×#14556102C2211yescharacteristic
43C2×#14556099C2211yescharacteristic
44C2×#14556098—21no—
45C2×#14556096—21no—
46C2×D4×Dic71—21no—
47C2×#14556090—21no—
48C2×(C22⋊D71)⋊C4—21no—
49C2×(C22⋊D71)⋊C4—21no—
50C2×#14556086C2211yescharacteristic
51C2×#14556086C2211yescharacteristic
52#17986239C2218yescomplemented
53#17986238C2218yescomplemented
54#17986234C2218yescomplemented
55#17986233C2218yescomplemented
56#17986229C2218yescomplemented
57#17986228C2218yescomplemented
58#17986225C2218yescomplemented
59#17986034C2218yescomplemented
60C2×#14556061C2211yescharacteristic, complemented
61C2×#14556061C2211yescharacteristic, complemented
62C2×#14556060C2211yescharacteristic, complemented
63#17985994C2218yescomplemented
64#17985992C2218yescomplemented
65C2×#14556053C2211yescharacteristic, complemented
66C2×#14556052C2211yescharacteristic, complemented
67C2×#14556051C2211yescharacteristic, complemented
68C2×#14556050C2211yescharacteristic, complemented
69C2×#14556049C2211yescharacteristic, complemented
70C2×#14556048C2211yescharacteristic, complemented
71C22×SD16×C71C2211yescharacteristic, complemented
72C23×C8×C71C2211yescharacteristic
73C2×C22⋊Q8×C71C2211yescharacteristic
74C2×#121×C71C2211yescharacteristic
75#465×C71C2218yescomplemented
76C2×#106×C71C2211yescharacteristic, complemented
77C2×#103×C71C2211yescharacteristic, complemented
78C2×#102×C71C2211yescharacteristic, complemented
79C24×D71D411yescharacteristic
80C2×#11765866—22no—
81C2×#11765866—24no—
82C2×#11765866—24no—
83C2×#11765866C2314yes—
84C2×#11765864—22no—
85C2×#11765864—24no—
86C2×#11765864—24no—
87C2×#11765864C2314yes—
88C22×Dic142C2311yescharacteristic
89C22×D284—21no—
90C22×D284—21no—
91C22×D284C2311yescharacteristic
92C22×C22⋊D71—21no—
93C22×C22⋊D71—21no—
94C22×C22⋊D71—21no—
95C23×Dic71—21no—
96C23×Dic71D411yescharacteristic
97C22×C4×D71—24no—
98C22×C4×D71—24no—
99C22×C4×D71—21no—
100C22×C4×D71D411yescharacteristic
101C22×C4×D71D411yescharacteristic
102C22×C4×D71D414yes—
103C22×C4×D71C2311yescharacteristic
104C22×C4×D71C2314yes—
105C22×C4×D71C2311yescharacteristic
106#14556149—232no—
107C2×#11765855—24no—
108C2×#11765855C2314yescomplemented
109C2×#11765854—24no—
110C2×#11765854C2314yescomplemented
111C2×#11765850—24no—
112C2×#11765850C2314yescomplemented
113C22×C71⋊C8—24no—
114C22×C71⋊C8C2314yes—
115C22×C71⋊C8C2311yescharacteristic
116C22×C71⋊C8C2311yescharacteristic
117C2×C8×D71—24no—
118C2×C8×D71—24no—
119C2×C8×D71—232no—
120C2×C8×D71—24no—
121C2×C8×D71D418yescomplemented
122C2×C8×D71C2314yes—
123C2×C8×D71C2314yes—
124C2×C8×D71C2314yes—
125C2×C8×D71C2314yes—
126#14556113—28no—
127#14556110—28no—
128#14556108—22no—
129#14556108C2314yes—
130#14556107—22no—
131#14556107C2314yes—
132#14556104—22no—
133#14556104C2314yes—
134#14556103—22no—
135#14556103C2314yes—
136#14556102—22no—
137#14556102C2314yes—
138#14556099—22no—
139#14556099C2314yes—
140#14556098—28no—
141#14556096—28no—
142D4×Dic71—28no—
143#14556090—28no—
144(C22⋊D71)⋊C4—28no—
145(C22⋊D71)⋊C4—28no—
146#14556086—22no—
147#14556086—22no—
148#14556086C2314yes—
149#14556086C2314yes—
150C2×C4⋊Dic71—21no—
151C2×C4⋊Dic71C2311yescharacteristic
152C2×C4⋊Dic71C2311yescharacteristic
153C2×Dic71⋊C4—21no—
154C2×Dic71⋊C4—21no—
155C2×C22⋊Dic71—21no—
156C2×C22⋊Dic71—21no—
157C2×(C2×D71)⋊C4—21no—
158C2×(C2×D71)⋊C4—21no—
159C2×(C2×D71)⋊C4—21no—
160C2×(C2×D71)⋊C4—21no—
161C2×(C2×D71)⋊C4—21no—
162C2×(C2×D71)⋊C4—21no—
163C2×C4×Dic71—21no—
164C2×C4×Dic71—21no—
165#14556061C2314yescomplemented
166#14556061C2314yescomplemented
167#14556060C2314yescomplemented
168#14556053C2314yescomplemented
169#14556052C2314yescomplemented
170#14556051C2314yescomplemented
171#14556050C2314yescomplemented
172#14556049C2314yescomplemented
173#14556048C2314yescomplemented
174C22×Q8×C71C2311yescharacteristic
175C22×D4×C71—21no—
176C22×D4×C71C2311yescharacteristic
177C23×C4×C71C2311yescharacteristic
178C2×SD16×C71—24no—
179C2×SD16×C71C2314yescomplemented
180C22×C8×C71—24no—
181C22×C8×C71C2311yescharacteristic
182C22×C8×C71C2314yes—
183C22×C8×C71C2311yescharacteristic
184C22⋊Q8×C71—22no—
185C22⋊Q8×C71C2314yes—
186#121×C71—22no—
187#121×C71C2314yes—
188C2×C4⋊C4×C71—21no—
189C2×C4⋊C4×C71C2311yescharacteristic
190C2×C4⋊C4×C71C2311yescharacteristic
191C2×C22⋊C4×C71—21no—
192C2×C22⋊C4×C71—21no—
193#106×C71C2314yescomplemented
194#103×C71C2314yescomplemented
195#102×C71C2314yescomplemented
196C23×D71—24no—
197C23×D71—24no—
198C23×D71—24no—
199C23×D71—21no—
200C23×D71C2×D414yes—
201C23×D71C2×D411yescharacteristic
202C23×D71C2×D411yescharacteristic
203#11765866—28no—
204#11765866—28no—
205#11765866—48no—
206#11765864—28no—
207#11765864—28no—
208#11765864—48no—
209C2×Dic142—22no—
210C2×Dic142—22no—
211C2×Dic142—21no—
212C2×Dic142C2412yes—
213C2×D284—22no—
214C2×D284—22no—
215C2×D284—24no—
216C2×D284—24no—
217C2×D284—21no—
218C2×D284—44no—
219C2×D284—44no—
220C2×D284C2412yes—
221C2×C22⋊D71—24no—
222C2×C22⋊D71—24no—
223C2×C22⋊D71—24no—
224C2×C22⋊D71—44no—
225C2×C22⋊D71—44no—
226C2×C22⋊D71—44no—
227C22×Dic71—24no—
228C22×Dic71—21no—
229C22×Dic71—21no—
230C22×Dic71—21no—
231C22×Dic71—24no—
232C22×Dic71—44no—
233C22×Dic71C2×D411yescharacteristic
234C22×Dic71C2×D414yes—
235C22×Dic71C2×D411yescharacteristic
236C2×C4×D71—24no—
237C2×C4×D71—22no—
238C2×C4×D71—22no—
239C2×C4×D71—24no—
240C2×C4×D71—216no—
241C2×C4×D71—28no—
242C2×C4×D71—28no—
243C2×C4×D71—24no—
244C2×C4×D71—44no—
245C2×C4×D71C2×D414yes—
246C2×C4×D71C2×D412yes—
247C2×C4×D71C2×D414yes—
248C2×C4×D71C2×D412yes—
249C2×C4×D71C2×D414yes—
250C2×C4×D71#4114yes—
251C2×C4×D71C2412yes—
252C2×C4×D71C2412yes—
253#11765855—28no—
254#11765854—28no—
255#11765850—28no—
256C2×C71⋊C8—22no—
257C2×C71⋊C8—28no—
258C2×C71⋊C8C2×D414yes—
259C2×C71⋊C8C2412yes—
260C2×C71⋊C8C2412yes—
261C8×D71—28no—
262C8×D71—28no—
263C8×D71—28no—
264C8×D71C2×D4116yescomplemented
265C4⋊Dic71—21no—
266C4⋊Dic71—21no—
267C4⋊Dic71—24no—
268C4⋊Dic71C2412yes—
269C4⋊Dic71C2412yes—
270Dic71⋊C4—24no—
271Dic71⋊C4—24no—
272C22⋊Dic71—24no—
273C22⋊Dic71—24no—
274(C2×D71)⋊C4—24no—
275(C2×D71)⋊C4—24no—
276(C2×D71)⋊C4—24no—
277(C2×D71)⋊C4—24no—
278(C2×D71)⋊C4—24no—
279(C2×D71)⋊C4—24no—
280C4×Dic71—24no—
281C4×Dic71—24no—
282C24×C71—21no—
283C24×C71C2×D411yescharacteristic
284C2×Q8×C71—21no—
285C2×Q8×C71—22no—
286C2×Q8×C71—22no—
287C2×Q8×C71C2412yes—
288C2×D4×C71—24no—
289C2×D4×C71—22no—
290C2×D4×C71—21no—
291C2×D4×C71—22no—
292C2×D4×C71—44no—
293C2×D4×C71C2412yes—
294C22×C4×C71—22no—
295C22×C4×C71—22no—
296C22×C4×C71—21no—
297C22×C4×C71—21no—
298C22×C4×C71—21no—
299C22×C4×C71C2×D411yescharacteristic
300C22×C4×C71C2×D412yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2411yescharacteristic
303SD16×C71—28no—
304C2×C8×C71—22no—
305C2×C8×C71—28no—
306C2×C8×C71C2×D414yes—
307C2×C8×C71C2412yes—
308C2×C8×C71C2412yes—
309C4⋊C4×C71—24no—
310C4⋊C4×C71—21no—
311C4⋊C4×C71—21no—
312C4⋊C4×C71C2412yes—
313C4⋊C4×C71C2412yes—
314C22⋊C4×C71—24no—
315C22⋊C4×C71—24no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71—42no—
320C23×C71—42no—
321C23×C71—42no—
322C23×C71#13514yescomplemented
323C23×C71C22×D412yes—
324C23×C71C22×D411yescharacteristic
325C22×D71—232no—
326C22×D71—22no—
327C22×D71—22no—
328C22×D71—22no—
329C22×D71—22no—
330C22×D71—28no—
331C22×D71—28no—
332C22×D71—28no—
333C22×D71—22no—
334C22×D71—42no—
335C22×D71—42no—
336C22×D71—42no—
337C22×D71#12114yes—
338C22×D71#13514yescomplemented
339C22×D71C22×D412yes—
340C22×D71C22×D412yes—
341Q8×C71—22no—
342Q8×C71—22no—
343Q8×C71—42no—
344D4×C71—22no—
345D4×C71—22no—
346D4×C71—48no—
347D4×C71—42no—
348C2×C4×C71—22no—
349C2×C4×C71—24no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—22no—
354C2×C4×C71—22no—
355C2×C4×C71—42no—
356C2×C4×C71—42no—
357C2×C4×C71—42no—
358C2×C4×C71C22×D412yes—
359C2×C4×C71C22×D411yescharacteristic
360C2×C4×C71C22×D412yes—
361C2×C4×C71C2×#4112yes—
362C2×C4×C71C2511yescharacteristic
363C22⋊D71—48no—
364C22⋊D71—48no—
365C22⋊D71—48no—
366C2×Dic71—22no—
367C2×Dic71—28no—
368C2×Dic71—22no—
369C2×Dic71—22no—
370C2×Dic71—22no—
371C2×Dic71—42no—
372C2×Dic71—42no—
373C2×Dic71—42no—
374C2×Dic71—48no—
375C2×Dic71#12114yes—
376C2×Dic71C22×D412yes—
377C2×Dic71C22×D412yes—
378D284—22no—
379D284—22no—
380D284—48no—
381D284—48no—
382D284—42no—
383C4×D71—28no—
384C4×D71—24no—
385C4×D71—22no—
386C4×D71—22no—
387C4×D71—28no—
388C4×D71—48no—
389C4×D71#12118yes—
390C4×D71C22×D414yes—
391C4×D71C2×#4114yes—
392Dic142—22no—
393Dic142—22no—
394Dic142—42no—
395C8×C71—22no—
396C8×C71C22×D414yes—
397C71⋊C8—22no—
398C71⋊C8C22×D414yes—
399C22×C71—22no—
400C22×C71—28no—
401C22×C71—22no—
402C22×C71—42no—
403C22×C71—42no—
404C22×C71—42no—
405C22×C71—84no—
406C22×C71C2×#12112yes—
407C22×C71C2×#13512yes—
408C22×C71C2×#13512yes—
409C22×C71C2×#13514yescomplemented
410C22×C71C23×D411yescharacteristic
411C2×D71—232no—
412C2×D71—22no—
413C2×D71—28no—
414C2×D71—28no—
415C2×D71—22no—
416C2×D71—22no—
417C2×D71—22no—
418C2×D71—42no—
419C2×D71—42no—
420C2×D71—42no—
421C2×D71—84no—
422C2×D71C2×#12114yes—
423C2×D71C2×#13514yescomplemented
424C4×C71—22no—
425C4×C71—42no—
426C4×C71—42no—
427C4×C71—42no—
428C4×C71C2×#12112yes—
429C4×C71C23×D411yescharacteristic
430C4×C71C22×#4111yescharacteristic
431Dic71—22no—
432Dic71—42no—
433Dic71—42no—
434Dic71—42no—
435Dic71C2×#12114yes—
436C2×#3050—711nomaximal, Sylow
437C2×C71—24no—
438C2×C71—82no—
439C2×C71#305014yescomplemented
440C2×C71C22×#12111yescharacteristic
441C2×C71C22×#13511yescharacteristic
442C2×C71C22×#13511yescharacteristic
443D71—24no—
444D71—24no—
445D71—82no—
446C22×#135—711no—
447C24×C8—711no—
448C2×#525—711no—
449C2×#525—711no—
450#3050—7116no—
451C2×#467—711no—
452C2×#467—711no—
453C2×#466—711no—
454C2×#466—711no—
455C2×#465—711no—
456C2×#465—711no—
457C2×#465—711no—
458C2×#465D7111yescharacteristic, complemented
459C2×#427—711no—
460C2×#416—711no—
461C2×#416—711no—
462C71C2×#305011yescharacteristic, complemented, Sylow
463C22×#41—711no—
464C22×#41—711no—
465C24×C4—711no—
466C2×#135—718no—
467C2×#135—1428no—
468C22×Q16—711no—
469C22×SD16—711no—
470C22×SD16C2×D7111yescharacteristic, complemented
471C22×D8—711no—
472C23×C8—711no—
473C23×C8—711no—
474C23×C8—711no—
475C23×C8—711no—
476C23×C8—711no—
477C23×C8—718no—
478C23×C8—1428no—
479C23×C8C2×D7111yescharacteristic
480#525—718no—
481#525—718no—
482#525—1424no—
483#525—1424no—
484C2×#123—1421no—
485C2×#123—1421no—
486C2×C22⋊Q8—711no—
487C2×C22⋊Q8—711no—
488C2×C22⋊Q8—711no—
489C2×C22⋊Q8C2×D7111yescharacteristic
490C2×#121—711no—
491C2×#121—711no—
492C2×#121—711no—
493C2×#121C2×D7111yescharacteristic
494C2×#120—1421no—
495C2×#120—1421no—
496C2×C4×D4—1421no—
497C2×C4×D4—1421no—
498C2×C4×D4—1421no—
499C2×C4×D4—1421no—
500C2×#117—711no—
501C2×#117—711no—
502#467—718no—
503#467—718no—
504#466—718no—
505#466—718no—
506#465—718no—
507#465—718no—
508#465—718no—
509#465C2×D7118yescomplemented
510#427—718no—
511C2×#107—711no—
512C2×#107—711no—
513C2×#106—711no—
514C2×#106C2×D7111yescharacteristic, complemented
515#416—718no—
516#416—718no—
517C2×#103—711no—
518C2×#103—711no—
519C2×#103—711no—
520C2×#103C2×D7111yescharacteristic, complemented
521C2×#102—711no—
522C2×#102—711no—
523C2×#102—711no—
524C2×#102C2×D7111yescharacteristic, complemented
525C25—711no—
526C2×#41—714no—
527C2×#41—714no—
528C2×#41—1424no—
529C2×#41—1424no—
530C2×#41—1424no—
531C2×#41—1424no—
532C2×#41—1422no—
533C2×#41—1422no—
534C22×Q8—711no—
535C22×Q8C22×D7111yescharacteristic
536C22×D4—21no—
537C22×D4—711no—
538C22×D4—1421no—
539C22×D4—1421no—
540C22×D4—1421no—
541C22×D4—1421no—
542C22×D4—1421no—
543C22×D4C22×D7111yescharacteristic
544C23×C4—711no—
545C23×C4—711no—
546C23×C4—711no—
547C23×C4—711no—
548C23×C4—714no—
549C23×C4—711no—
550C23×C4—714no—
551C23×C4—1421no—
552C23×C4—1424no—
553C23×C4—1424no—
554C23×C4—1421no—
555C23×C4C22×D7111yescharacteristic
556#135—14232no—
557C2×Q16—714no—
558C2×Q16—1424no—
559C2×SD16—24no—
560C2×SD16—714no—
561C2×SD16—1424no—
562C2×SD16C22×D7114yescomplemented
563C2×D8—714no—
564C2×D8—1424no—
565C22×C8—24no—
566C22×C8—711no—
567C22×C8—718no—
568C22×C8—714no—
569C22×C8—711no—
570C22×C8—714no—
571C22×C8—714no—
572C22×C8—714no—
573C22×C8—714no—
574C22×C8—1424no—
575C22×C8—14232no—
576C22×C8—1424no—
577C22×C8—1424no—
578C22×C8—1424no—
579C22×C8C22×D7111yescharacteristic
580C22×C8C22×D7114yes—
581C22×C8C22×D7111yescharacteristic
582#123—1428no—
583#123—1428no—
584C22⋊Q8—22no—
585C22⋊Q8—714no—
586C22⋊Q8—714no—
587C22⋊Q8—714no—
588C22⋊Q8—1422no—
589C22⋊Q8—1422no—
590C22⋊Q8—1422no—
591C22⋊Q8C22×D7114yes—
592#121—22no—
593#121—714no—
594#121—714no—
595#121—714no—
596#121—1422no—
597#121—1422no—
598#121—1422no—
599#121C22×D7114yes—
600#120—1428no—
601#120—1428no—
602C4×D4—1428no—
603C4×D4—1428no—
604C4×D4—1428no—
605C4×D4—1428no—
606#117—714no—
607#117—714no—
608#117—1422no—
609#117—1422no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—711no—
612C2×C4⋊C4—711no—
613C2×C4⋊C4—1421no—
614C2×C4⋊C4—1421no—
615C2×C4⋊C4—1421no—
616C2×C4⋊C4C22×D7111yescharacteristic
617C2×C4⋊C4C22×D7111yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—1421no—
621C2×C22⋊C4—1421no—
622C2×C22⋊C4—1421no—
623C2×C22⋊C4—1421no—
624C2×C22⋊C4—1421no—
625C2×C22⋊C4—1421no—
626C2×C22⋊C4—1421no—
627C2×C22⋊C4—1421no—
628C2×C42—1421no—
629C2×C42—1421no—
630#107—714no—
631#107—714no—
632#106—714no—
633#106C22×D7114yescomplemented
634#103—714no—
635#103—714no—
636#103—714no—
637#103C22×D7114yescomplemented
638#102—714no—
639#102—714no—
640#102—714no—
641#102C22×D7114yescomplemented
642C24—21no—
643C24—711no—
644C24—711no—
645C24—714no—
646C24—1424no—
647C24—1424no—
648C24—1421no—
649C24—1424no—
650C24D4×D7111yescharacteristic
651#41—2848no—
652#41—2848no—
653#41—1428no—
654#41—1428no—
655#41—1428no—
656#41—1428no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—712no—
661C2×Q8—1422no—
662C2×Q8—1422no—
663C2×Q8—1421no—
664C2×Q8C23×D7112yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—44no—
670C2×D4—2844no—
671C2×D4—2844no—
672C2×D4—2844no—
673C2×D4—2844no—
674C2×D4—2844no—
675C2×D4—712no—
676C2×D4—1424no—
677C2×D4—1424no—
678C2×D4—1424no—
679C2×D4—1424no—
680C2×D4—1424no—
681C2×D4—1421no—
682C2×D4—1422no—
683C2×D4—1422no—
684C2×D4C23×D7112yes—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—2844no—
691C22×C4—2844no—
692C22×C4—711no—
693C22×C4—712no—
694C22×C4—714no—
695C22×C4—714no—
696C22×C4—712no—
697C22×C4—714no—
698C22×C4—711no—
699C22×C4—714no—
700C22×C4—712no—
701C22×C4—714no—
702C22×C4—712no—
703C22×C4—1424no—
704C22×C4—1428no—
705C22×C4—1424no—
706C22×C4—1428no—
707C22×C4—14216no—
708C22×C4—1424no—
709C22×C4—1424no—
710C22×C4—1421no—
711C22×C4—1421no—
712C22×C4—1421no—
713C22×C4—1424no—
714C22×C4—1422no—
715C22×C4—1422no—
716C22×C4D4×D7112yes—
717C22×C4D4×D7111yescharacteristic
718C22×C4C23×D7112yes—
719C22×C4C23×D7111yescharacteristic
720Q16—1428no—
721SD16—28no—
722SD16—1428no—
723D8—1428no—
724C2×C8—22no—
725C2×C8—28no—
726C2×C8—714no—
727C2×C8—712no—
728C2×C8—7116no—
729C2×C8—712no—
730C2×C8—1428no—
731C2×C8—1428no—
732C2×C8—1428no—
733C2×C8—1422no—
734C2×C8—1428no—
735C2×C8D4×D7114yes—
736C2×C8C23×D7112yes—
737C2×C8C23×D7112yes—
738C4⋊C4—24no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—712no—
742C4⋊C4—712no—
743C4⋊C4—1424no—
744C4⋊C4—1424no—
745C4⋊C4—1424no—
746C4⋊C4—1421no—
747C4⋊C4—1421no—
748C4⋊C4C23×D7112yes—
749C4⋊C4C23×D7112yes—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—1424no—
753C22⋊C4—1424no—
754C22⋊C4—1424no—
755C22⋊C4—1424no—
756C22⋊C4—1424no—
757C22⋊C4—1424no—
758C22⋊C4—1424no—
759C22⋊C4—1424no—
760C42—1424no—
761C42—1424no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—2842no—
769C23—2842no—
770C23—2842no—
771C23—712no—
772C23—712no—
773C23—714no—
774C23—714no—
775C23—1428no—
776C23—1428no—
777C23—14232no—
778C23—1422no—
779C23—1422no—
780C23—1422no—
781C23—1422no—
782C23—1422no—
783C23—1428no—
784C23#1455614914yescomplemented
785C23C2×D4×D7112yes—
786C23C2×D4×D7111yescharacteristic
787Q8—22no—
788Q8—22no—
789Q8—42no—
790Q8—2842no—
791Q8—1422no—
792Q8—1422no—
793D4—22no—
794D4—22no—
795D4—48no—
796D4—42no—
797D4—2848no—
798D4—2848no—
799D4—2848no—
800D4—2848no—
801D4—2848no—
802D4—2842no—
803D4—1422no—
804D4—1422no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—2848no—
816C2×C4—2842no—
817C2×C4—2842no—
818C2×C4—2842no—
819C2×C4—2848no—
820C2×C4—712no—
821C2×C4—714no—
822C2×C4—714no—
823C2×C4—714no—
824C2×C4—718no—
825C2×C4—712no—
826C2×C4—1428no—
827C2×C4—1428no—
828C2×C4—1422no—
829C2×C4—1422no—
830C2×C4—1422no—
831C2×C4—1428no—
832C2×C4—1422no—
833C2×C4—1422no—
834C2×C4—1422no—
835C2×C4—1424no—
836C2×C4C2×D4×D7112yes—
837C2×C4C2×D4×D7112yes—
838C2×C4C2×D4×D7111yescharacteristic
839C2×C4#41×D7112yes—
840C2×C4C24×D7111yescharacteristic
841C8—22no—
842C8—714no—
843C8—1422no—
844C8C2×D4×D7114yes—
845C22—28no—
846C22—22no—
847C22—22no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—2842no—
853C22—2842no—
854C22—2842no—
855C22—5684no—
856C22—714no—
857C22—714no—
858C22—14232no—
859C22—1428no—
860C22—1428no—
861C22—1422no—
862C22—1422no—
863C22—1422no—
864C22—1422no—
865C22#121×D7112yes—
866C22#135×D7112yes—
867C22C2×#1455614912yes—
868C22C2×#1455614914yescomplemented
869C22C22×D4×D7111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—2842no—
875C4—2842no—
876C4—2842no—
877C4—714no—
878C4—1422no—
879C4#121×D7112yes—
880C4C22×D4×D7111yescharacteristic
881C4C2×#41×D7111yescharacteristic
882C2—24no—
883C2—82no—
884C2—5682no—
885C2—1424no—
886C2—1424no—
887C2#2259791614yesdirect product factor
888C2C2×#121×D7111yescharacteristic
889C2C2×#135×D7111yescharacteristic
890C2C22×#1455614911yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#465×C71C2
socleC23×C71C22×D4
hypercenterC2×#465D71
hypocenterC71C2×#3050
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#14556149C2semidirect
2. C23×C8×D71C2semidirect
3. C2×#17986512C2semidirect
4. C2×#17986509C2semidirect
5. #22597916C2direct (N × H)
6. C2×#17986239C2semidirect
7. C2×#17986238C2semidirect
8. C2×#17986234C2semidirect
9. C2×#17986233C2semidirect
10. C2×#17986229C2semidirect
11. C2×#17986228C2semidirect
12. C2×#17986225C2semidirect
13. C2×#17986034C2semidirect
14. C2×#17985994C2semidirect
15. C2×#17985992C2semidirect
16. C2×#465×C71C2semidirect
21. C2×#14556149C22semidirect
22. C22×#11765855C22semidirect
23. C22×#11765854C22semidirect
24. C22×#11765850C22semidirect
31. C22×C8×D71C22semidirect
33. #17986512C22semidirect
35. #17986509C22semidirect
52. #17986239C22semidirect
53. #17986238C22semidirect
54. #17986234C22semidirect
55. #17986233C22semidirect
56. #17986229C22semidirect
57. #17986228C22semidirect
58. #17986225C22semidirect
59. #17986034C22semidirect
60. C2×#14556061C22semidirect
61. C2×#14556061C22semidirect
62. C2×#14556060C22semidirect
63. #17985994C22semidirect
64. #17985992C22semidirect
65. C2×#14556053C22semidirect
66. C2×#14556052C22semidirect
67. C2×#14556051C22semidirect
68. C2×#14556050C22semidirect
69. C2×#14556049C22semidirect
70. C2×#14556048C22semidirect
71. C22×SD16×C71C22semidirect
75. #465×C71C22semidirect
76. C2×#106×C71C22semidirect
77. C2×#103×C71C22semidirect
78. C2×#102×C71C22semidirect
108. C2×#11765855C23semidirect
110. C2×#11765854C23semidirect
112. C2×#11765850C23semidirect
121. C2×C8×D71D4semidirect
165. #14556061C23semidirect
166. #14556061C23semidirect
167. #14556060C23semidirect
168. #14556053C23semidirect
169. #14556052C23semidirect
170. #14556051C23semidirect
171. #14556050C23semidirect
172. #14556049C23semidirect
173. #14556048C23semidirect
179. C2×SD16×C71C23semidirect
193. #106×C71C23semidirect
194. #103×C71C23semidirect
195. #102×C71C23semidirect
264. C8×D71C2×D4semidirect
322. C23×C71#135semidirect
338. C22×D71#135semidirect
409. C22×C71C2×#135semidirect
423. C2×D71C2×#135semidirect
439. C2×C71#3050semidirect
458. C2×#465D71semidirect
462. C71C2×#3050semidirect
470. C22×SD16C2×D71semidirect
509. #465C2×D71semidirect
514. C2×#106C2×D71semidirect
520. C2×#103C2×D71semidirect
524. C2×#102C2×D71semidirect
562. C2×SD16C22×D71semidirect
633. #106C22×D71semidirect
637. #103C22×D71semidirect
641. #102C22×D71semidirect
784. C23#14556149semidirect
868. C22C2×#14556149semidirect
887. C2#22597916direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561492
C23×C8×D712
C2×#179865122
C2×#179865092
#225979162
C2×#179862392
C2×#179862382
C2×#179862342
C2×#179862332
C2×#179862292
C2×#179862282
C2×#179862252
C2×#179860342
C2×#179859942
C2×#179859922
C2×#465×C712
C2×#305071