Finite Group Databasebeta

← C2×#22599972 #32872583

Subgroups — C2×#22599972 #32872583

Order 18176.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556159C211yesmaximal, characteristic, complemented
2C22×#14556153C211yesmaximal, characteristic, complemented
3C2×#17986645C211yesmaximal, characteristic, complemented
4#22599972C2116yesmaximal, direct product factor
5C2×#17986381C211yesmaximal, characteristic, complemented
6C2×#17986255C211yesmaximal, characteristic, complemented
7C2×#17986250C211yesmaximal, characteristic, complemented
8C2×#17986221C211yesmaximal, characteristic, complemented
9C2×#17986211C211yesmaximal, characteristic, complemented
10C2×#17986161C211yesmaximal, characteristic, complemented
11C2×#17986142C211yesmaximal, characteristic, complemented
12C2×#17986138C211yesmaximal, characteristic, complemented
13C2×#17986149C211yesmaximal, characteristic, complemented
14C2×C4×#11765852C211yesmaximal, characteristic, complemented
15C2×#17986077C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C2×#14556159—28no—
20C2×#14556159C2218yescomplemented
21C2×#14556153—28no—
22C2×#14556153C2218yescomplemented
23C22×#11765855C2211yescharacteristic, complemented
24C22×#11765855C2211yescharacteristic, complemented
25C22×#11765853C2211yescharacteristic, complemented
26C22×#11765852C2211yescharacteristic
27C22×#11765852C2211yescharacteristic
28C22×#11765852C2211yescharacteristic
29C22×#11765852C2211yescharacteristic
30C22×#11765850C2211yescharacteristic
31C22×#11765850C2211yescharacteristic
32C22×#11765849C2211yescharacteristic
33C22×#11765849C2211yescharacteristic, complemented
34#17986645—24no—
35#17986645C2218yescomplemented
36C2×#14556116C2211yescharacteristic
37C2×#14556113—21no—
38C2×#14556107C2211yescharacteristic
39C2×#14556102C2211yescharacteristic
40C2×#14556101—21no—
41C2×#14556096—21no—
42C2×C4×D284C2211yescharacteristic
43C2×C22⋊C4×D71—21no—
44#17986381C2218yescomplemented
45#17986255C2218yescomplemented
46#17986250C2218yescomplemented
47#17986221C2218yescomplemented
48#17986211C2218yescomplemented
49#17986161C2218yescomplemented
50#17986149C2218yescomplemented
51#17986142C2218yescomplemented
52#17986138C2218yescomplemented
53C4×#11765852C2218yescomplemented
54#17986077C2218yescomplemented
55C2×#14556059C2211yescharacteristic, complemented
56C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
57C2×#14556052C2211yescharacteristic, complemented
58C2×#14556052C2211yescharacteristic, complemented
59C2×#14556051C2211yescharacteristic, complemented
60C2×#14556049C2211yescharacteristic, complemented
61C2×#14556048C2211yescharacteristic
62C2×#14556048C2211yescharacteristic
63C2×C22⋊(C71⋊C8)C2211yescharacteristic
64C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
65C2×C4×C71⋊C8C2211yescharacteristic, complemented
66C22×#41×C71C2211yescharacteristic
67C23×Q8×C71C2211yescharacteristic, complemented
68#548×C71—24no—
69#548×C71C2218yescomplemented
70C2×#124×C71—21no—
71C2×#124×C71C2211yescharacteristic, complemented
72C2×C22⋊Q8×C71—21no—
73C2×C22⋊Q8×C71C2211yescharacteristic
74C2×#121×C71—21no—
75C2×#121×C71C2211yescharacteristic, complemented
76C2×C4×Q8×C71C2211yescharacteristic, complemented
77C2×C4×D4×C71—21no—
78C2×C4×D4×C71C2211yescharacteristic
79C24×D71—21no—
80C2×#11765865—24no—
81C2×#11765865—22no—
82C2×#11765865—42no—
83C2×#11765865C2314yes—
84C22×Dic142C2311yescharacteristic
85C22×D284—24no—
86C22×D284—22no—
87C22×D284—21no—
88C22×D284—42no—
89C22×D284C2311yescharacteristic
90C22×D284C2314yes—
91C22×D284C2311yescharacteristic
92C22×C22⋊D71—21no—
93C22×C22⋊D71—21no—
94C22×C4×D71—21no—
95C22×C4×D71—21no—
96#14556159—232no—
97#14556153—232no—
98C2×#11765855—24no—
99C2×#11765855—24no—
100C2×#11765855C2314yescomplemented
101C2×#11765855C2314yescomplemented
102C2×#11765853—42no—
103C2×#11765853C2314yescomplemented
104C2×#11765852—24no—
105C2×#11765852—24no—
106C2×#11765852—42no—
107C2×#11765852D418yescomplemented
108C2×#11765852C2314yes—
109C2×#11765852C2314yes—
110C2×#11765852C2314yes—
111C2×#11765852C2314yes—
112C2×#11765850—24no—
113C2×#11765850—24no—
114C2×#11765850C2314yes—
115C2×#11765850C2314yes—
116C2×#11765849—24no—
117C2×#11765849—24no—
118C2×#11765849C2314yes—
119C2×#11765849C2314yescomplemented
120C22×C71⋊C8C2311yescharacteristic
121C22×C71⋊C8C2311yescharacteristic
122C22×C71⋊C8C2311yescharacteristic
123C22×C71⋊C8C2311yescharacteristic
124#14556116—22no—
125#14556116C2314yes—
126#14556113—28no—
127#14556107—22no—
128#14556107C2314yes—
129#14556102—22no—
130#14556102C2314yes—
131#14556101—28no—
132#14556096—28no—
133C4×D284—22no—
134C4×D284C2314yes—
135C2×C4⋊Dic71C2311yescharacteristic
136C2×Dic71⋊C4—21no—
137C2×C22⋊Dic71—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C22⋊C4×D71—28no—
143#14556059C2314yescomplemented
144C4⋊(C71⋊C8)C2314yescomplemented
145#14556052C2314yescomplemented
146#14556052C2314yescomplemented
147#14556051C2314yescomplemented
148#14556049C2314yescomplemented
149#14556048C2314yes—
150#14556048C2314yes—
151C22⋊(C71⋊C8)C2314yes—
152C22⋊(C71⋊C8)C2314yescomplemented
153C4×C71⋊C8C2314yescomplemented
154C2×#41×C71—22no—
155C2×#41×C71—24no—
156C2×#41×C71—42no—
157C2×#41×C71C2314yes—
158C22×Q8×C71—21no—
159C22×Q8×C71—22no—
160C22×Q8×C71—24no—
161C22×Q8×C71—42no—
162C22×Q8×C71C2311yescharacteristic
163C22×Q8×C71C2311yescharacteristic
164C22×Q8×C71C2314yescomplemented
165C22×D4×C71—21no—
166C22×D4×C71—21no—
167C22×D4×C71D411yescharacteristic
168C22×D4×C71C2311yescharacteristic
169C23×C4×C71—21no—
170C23×C4×C71—21no—
171C23×C4×C71C2311yescharacteristic
172C23×C4×C71C2311yescharacteristic
173#124×C71—28no—
174#124×C71—22no—
175#124×C71C2314yescomplemented
176C22⋊Q8×C71—22no—
177C22⋊Q8×C71—28no—
178C22⋊Q8×C71C2314yes—
179#121×C71—28no—
180#121×C71—22no—
181#121×C71C2314yescomplemented
182C4×Q8×C71—22no—
183C4×Q8×C71C2314yescomplemented
184C4×D4×C71—28no—
185C4×D4×C71D414yes—
186C4×D4×C71C2314yes—
187C2×C4⋊C4×C71—21no—
188C2×C4⋊C4×C71—21no—
189C2×C4⋊C4×C71D411yescharacteristic
190C2×C4⋊C4×C71C2311yescharacteristic
191C2×C22⋊C4×C71—21no—
192C2×C22⋊C4×C71—21no—
193C2×C22⋊C4×C71—21no—
194C2×C22⋊C4×C71—21no—
195C2×C22⋊C4×C71D411yescharacteristic
196C2×C22⋊C4×C71D411yescharacteristic
197C2×C42×C71—21no—
198C2×C42×C71C2311yescharacteristic
199C23×D71—21no—
200C23×D71—21no—
201C23×D71—24no—
202C23×D71—44no—
203C23×D71—44no—
204C23×D71—82no—
205#11765865—28no—
206#11765865—44no—
207#11765865—48no—
208C2×Dic142—22no—
209C2×Dic142—22no—
210C2×Dic142—21no—
211C2×Dic142C2412yes—
212C2×D284—21no—
213C2×D284—22no—
214C2×D284—22no—
215C2×D284—22no—
216C2×D284—28no—
217C2×D284—24no—
218C2×D284—21no—
219C2×D284—44no—
220C2×D284—48no—
221C2×D284—44no—
222C2×D284C2×D414yes—
223C2×D284C2412yes—
224C2×D284C2412yes—
225C2×C22⋊D71—24no—
226C2×C22⋊D71—24no—
227C2×C22⋊D71—44no—
228C2×C22⋊D71—82no—
229C22×Dic71—21no—
230C22×Dic71—21no—
231C2×C4×D71—24no—
232C2×C4×D71—24no—
233C2×C4×D71—44no—
234C2×C4×D71—82no—
235#11765855—28no—
236#11765855—28no—
237#11765853—44no—
238#11765852—28no—
239#11765852—28no—
240#11765852—44no—
241#11765852C2×D4116yescomplemented
242#11765850—28no—
243#11765850—28no—
244#11765849—28no—
245#11765849—28no—
246C2×C71⋊C8—22no—
247C2×C71⋊C8—22no—
248C2×C71⋊C8—22no—
249C2×C71⋊C8C2×D414yes—
250C2×C71⋊C8C2412yes—
251C2×C71⋊C8C2412yes—
252C2×C71⋊C8C2412yes—
253C2×C71⋊C8C2412yes—
254C4⋊Dic71—21no—
255C4⋊Dic71C2412yes—
256Dic71⋊C4—24no—
257C22⋊Dic71—24no—
258(C2×D71)⋊C4—24no—
259(C2×D71)⋊C4—24no—
260(C2×D71)⋊C4—24no—
261(C2×D71)⋊C4—24no—
262C24×C71—21no—
263C24×C71C2×D411yescharacteristic
264C24×C71C2×D411yescharacteristic
265#41×C71—28no—
266#41×C71—44no—
267#41×C71—48no—
268C2×Q8×C71—21no—
269C2×Q8×C71—21no—
270C2×Q8×C71—24no—
271C2×Q8×C71—22no—
272C2×Q8×C71—28no—
273C2×Q8×C71—22no—
274C2×Q8×C71—22no—
275C2×Q8×C71—44no—
276C2×Q8×C71—44no—
277C2×Q8×C71—48no—
278C2×Q8×C71C2×D414yes—
279C2×Q8×C71C2412yes—
280C2×Q8×C71C2412yes—
281C2×D4×C71—24no—
282C2×D4×C71—24no—
283C2×D4×C71—22no—
284C2×D4×C71—21no—
285C2×D4×C71—22no—
286C2×D4×C71—42no—
287C2×D4×C71—44no—
288C2×D4×C71—44no—
289C2×D4×C71C2×D414yes—
290C2×D4×C71C2412yes—
291C22×C4×C71—21no—
292C22×C4×C71—22no—
293C22×C4×C71—22no—
294C22×C4×C71—22no—
295C22×C4×C71—22no—
296C22×C4×C71—21no—
297C22×C4×C71—21no—
298C22×C4×C71—24no—
299C22×C4×C71—24no—
300C22×C4×C71—44no—
301C22×C4×C71—44no—
302C22×C4×C71C2×D411yescharacteristic
303C22×C4×C71C2×D411yescharacteristic
304C22×C4×C71C2×D411yescharacteristic
305C22×C4×C71C2×D412yes—
306C22×C4×C71C2×D412yes—
307C22×C4×C71C2×D411yescharacteristic
308C22×C4×C71C2412yes—
309C22×C4×C71C2412yes—
310C22×C4×C71C2411yescharacteristic
311C4⋊C4×C71—24no—
312C4⋊C4×C71—24no—
313C4⋊C4×C71—21no—
314C4⋊C4×C71C2×D414yes—
315C4⋊C4×C71C2412yes—
316C22⋊C4×C71—24no—
317C22⋊C4×C71—24no—
318C22⋊C4×C71—24no—
319C22⋊C4×C71—24no—
320C22⋊C4×C71C2×D414yes—
321C22⋊C4×C71C2×D414yes—
322C42×C71—24no—
323C42×C71C2×D412yes—
324C42×C71C2412yes—
325C23×C71—22no—
326C23×C71—22no—
327C23×C71—22no—
328C23×C71—22no—
329C23×C71—22no—
330C23×C71—22no—
331C23×C71—22no—
332C23×C71—42no—
333C23×C71—42no—
334C23×C71—42no—
335C23×C71C22×D412yes—
336C23×C71C22×D412yes—
337C23×C71C22×D411yescharacteristic
338C22×D71—24no—
339C22×D71—22no—
340C22×D71—22no—
341C22×D71—48no—
342C22×D71—42no—
343C22×D71—42no—
344C22×D71—48no—
345C22×D71—42no—
346C22×D71—42no—
347C22×D71—42no—
348C22×D71—84no—
349C22×D71—816no—
350Q8×C71—24no—
351Q8×C71—22no—
352Q8×C71—22no—
353Q8×C71—22no—
354Q8×C71—48no—
355Q8×C71—42no—
356Q8×C71C22×D414yes—
357D4×C71—22no—
358D4×C71—22no—
359D4×C71—44no—
360D4×C71—48no—
361D4×C71—48no—
362D4×C71—42no—
363C2×C4×C71—22no—
364C2×C4×C71—22no—
365C2×C4×C71—24no—
366C2×C4×C71—22no—
367C2×C4×C71—22no—
368C2×C4×C71—22no—
369C2×C4×C71—24no—
370C2×C4×C71—24no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—22no—
374C2×C4×C71—22no—
375C2×C4×C71—22no—
376C2×C4×C71—22no—
377C2×C4×C71—48no—
378C2×C4×C71—48no—
379C2×C4×C71—42no—
380C2×C4×C71—42no—
381C2×C4×C71C22×D412yes—
382C2×C4×C71C22×D412yes—
383C2×C4×C71C22×D412yes—
384C2×C4×C71C22×D412yes—
385C2×C4×C71C22×D412yes—
386C2×C4×C71C22×D411yescharacteristic
387C2×C4×C71H(5,𝔽2)12yes—
388C2×C4×C71C2511yescharacteristic
389C22⋊D71—48no—
390C22⋊D71—84no—
391C2×Dic71—22no—
392C2×Dic71—22no—
393C2×Dic71—42no—
394C2×Dic71—42no—
395D284—24no—
396D284—22no—
397D284—22no—
398D284—22no—
399D284—48no—
400D284—42no—
401D284C22×D414yes—
402C4×D71—48no—
403C4×D71—84no—
404Dic142—22no—
405Dic142—22no—
406Dic142—42no—
407C71⋊C8—22no—
408C71⋊C8—22no—
409C71⋊C8—22no—
410C71⋊C8C22×D414yes—
411C22×C71—22no—
412C22×C71—22no—
413C22×C71—22no—
414C22×C71—22no—
415C22×C71—22no—
416C22×C71—22no—
417C22×C71—44no—
418C22×C71—44no—
419C22×C71—42no—
420C22×C71—42no—
421C22×C71—42no—
422C22×C71—84no—
423C22×C71D4212yes—
424C22×C71#57512yes—
425C22×C71#57712yes—
426C22×C71C23×D411yescharacteristic
427C2×D71—24no—
428C2×D71—48no—
429C2×D71—42no—
430C2×D71—42no—
431C2×D71—42no—
432C2×D71—42no—
433C2×D71—42no—
434C2×D71—816no—
435C2×D71—84no—
436C4×C71—22no—
437C4×C71—22no—
438C4×C71—24no—
439C4×C71—22no—
440C4×C71—22no—
441C4×C71—42no—
442C4×C71—42no—
443C4×C71D4212yes—
444C4×C71C23×D411yescharacteristic
445C4×C71C2×H(5,𝔽2)11yescharacteristic
446Dic71—42no—
447Dic71—42no—
448C2×#3275—711nomaximal, Sylow
449C2×C71—42no—
450C2×C71—42no—
451C2×C71—82no—
452C2×C71#327514yescomplemented
453C2×C71C2×D4211yescharacteristic
454C2×C71C2×#57511yescharacteristic
455C2×C71C2×#57711yescharacteristic
456D71—44no—
457D71—82no—
458C22×#137—711no—
459C22×AGL(1,ℤ/8)—711no—
460C2×#548D7111yescharacteristic, complemented
461C2×#546—711no—
462#3275—7116no—
463C2×#495—711no—
464C2×#470—711no—
465C2×#469—711no—
466C2×#464—711no—
467C2×#463—711no—
468C2×#452—711no—
469C2×#449—711no—
470C2×#448—711no—
471C2×#450—711no—
472C2×C4×SD16—711no—
473C2×#436—711no—
474C71C2×#327511yescharacteristic, complemented, Sylow
475C22×#41—711no—
476C22×#41C2×D7111yescharacteristic
477C23×Q8C2×D7111yescharacteristic, complemented
478C23×D4—711no—
479C2×#137—718no—
480C2×#137—1428no—
481C2×AGL(1,ℤ/8)—718no—
482C2×AGL(1,ℤ/8)—1428no—
483C22×Q16—711no—
484C22×Q16—711no—
485C22×SD16—711no—
486C22×SD16—711no—
487C22×SD16—711no—
488C22×SD16—711no—
489C22×SD16—711no—
490C22×D8—711no—
491C22×D8—711no—
492C22×M16—711no—
493C22×M16—711no—
494#548—24no—
495#548C2×D7118yescomplemented
496#546—718no—
497#546—1424no—
498C2×#124—21no—
499C2×#124—711no—
500C2×#124C2×D7111yescharacteristic, complemented
501C2×#123—1421no—
502C2×C22⋊Q8—21no—
503C2×C22⋊Q8—711no—
504C2×C22⋊Q8C2×D7111yescharacteristic
505C2×#121—21no—
506C2×#121—711no—
507C2×#121—1421no—
508C2×#121C2×D7111yescharacteristic, complemented
509C2×#120—1421no—
510C2×C4×Q8C2×D7111yescharacteristic, complemented
511C2×C4×D4—21no—
512C2×C4×D4—711no—
513C2×C4×D4C2×D7111yescharacteristic
514C22×C22⋊C4—1421no—
515#495—718no—
516#470—718no—
517#469—718no—
518#464—718no—
519#463—718no—
520#452—718no—
521#450—718no—
522#449—718no—
523#448—718no—
524C4×SD16—718no—
525#436—718no—
526C2×#106—711no—
527C2×C4⋊C8—711no—
528C2×#103—711no—
529C2×#103—711no—
530C2×#103—711no—
531C2×#102—711no—
532C2×#102—711no—
533C2×#102—711no—
534C2×C22⋊C8—711no—
535C2×C22⋊C8—711no—
536C2×C4×C8—711no—
537C25—1421no—
538C2×#41—22no—
539C2×#41—24no—
540C2×#41—42no—
541C2×#41—2842no—
542C2×#41—714no—
543C2×#41—1424no—
544C2×#41—1422no—
545C2×#41C22×D7114yes—
546C22×Q8—21no—
547C22×Q8—22no—
548C22×Q8—24no—
549C22×Q8—42no—
550C22×Q8—711no—
551C22×Q8C22×D7111yescharacteristic
552C22×Q8C22×D7111yescharacteristic
553C22×Q8C22×D7114yescomplemented
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—2842no—
557C22×D4—714no—
558C22×D4—711no—
559C22×D4—711no—
560C22×D4—1424no—
561C22×D4—1421no—
562C22×D4—1421no—
563C22×D4—1421no—
564C22×D4—1422no—
565C22×D4C22⋊D7111yescharacteristic
566C22×D4C22×D7111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—1421no—
570C23×C4—1421no—
571C23×C4C22×D7111yescharacteristic
572C23×C4C22×D7111yescharacteristic
573#137—14232no—
574AGL(1,ℤ/8)—14232no—
575C2×Q16—714no—
576C2×Q16—714no—
577C2×Q16—1424no—
578C2×Q16—1424no—
579C2×SD16—2842no—
580C2×SD16—2842no—
581C2×SD16—714no—
582C2×SD16—714no—
583C2×SD16—718no—
584C2×SD16—714no—
585C2×SD16—714no—
586C2×SD16—714no—
587C2×SD16—1424no—
588C2×SD16—1424no—
589C2×D8—714no—
590C2×D8—714no—
591C2×D8—1424no—
592C2×D8—1424no—
593C2×M16—714no—
594C2×M16—714no—
595C2×M16—1424no—
596C2×M16—1424no—
597C22×C8—711no—
598C22×C8—711no—
599C22×C8—711no—
600C22×C8—711no—
601#124—28no—
602#124—22no—
603#124—714no—
604#124—1422no—
605#124C22×D7114yescomplemented
606#123—1428no—
607C22⋊Q8—22no—
608C22⋊Q8—28no—
609C22⋊Q8—714no—
610C22⋊Q8—1422no—
611C22⋊Q8C22×D7114yes—
612#121—28no—
613#121—22no—
614#121—714no—
615#121—1422no—
616#121—1428no—
617#121C22×D7114yescomplemented
618#120—1428no—
619C4×Q8—22no—
620C4×Q8C22×D7114yescomplemented
621C4×D4—28no—
622C4×D4—714no—
623C4×D4—1422no—
624C4×D4C22⋊D7114yes—
625C4×D4C22×D7114yes—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—711no—
629C2×C4⋊C4—1421no—
630C2×C4⋊C4C22⋊D7111yescharacteristic
631C2×C4⋊C4C22×D7111yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—1421no—
637C2×C22⋊C4—1421no—
638C2×C22⋊C4—1421no—
639C2×C22⋊C4—1421no—
640C2×C22⋊C4—1421no—
641C2×C22⋊C4—1428no—
642C2×C22⋊C4C22⋊D7111yescharacteristic
643C2×C22⋊C4C22⋊D7111yescharacteristic
644C2×C42—21no—
645C2×C42C22×D7111yescharacteristic
646#106—714no—
647C4⋊C8—714no—
648#103—714no—
649#103—714no—
650#103—714no—
651#102—714no—
652#102—714no—
653#102—714no—
654C22⋊C8—714no—
655C22⋊C8—714no—
656C4×C8—714no—
657C24—21no—
658C24—2844no—
659C24—2844no—
660C24—5682no—
661C24—1421no—
662C24—1424no—
663C24—1421no—
664C24C2×C22⋊D7111yescharacteristic
665C24C2×C22⋊D7111yescharacteristic
666#41—28no—
667#41—44no—
668#41—48no—
669#41—2848no—
670#41—2844no—
671#41—1428no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—22no—
676C2×Q8—28no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—48no—
682C2×Q8—712no—
683C2×Q8—1422no—
684C2×Q8—1422no—
685C2×Q8—1421no—
686C2×Q8D4×D7114yes—
687C2×Q8C23×D7112yes—
688C2×Q8C23×D7112yes—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—22no—
692C2×D4—21no—
693C2×D4—22no—
694C2×D4—42no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—2844no—
698C2×D4—2848no—
699C2×D4—2844no—
700C2×D4—2844no—
701C2×D4—5682no—
702C2×D4—714no—
703C2×D4—712no—
704C2×D4—712no—
705C2×D4—1428no—
706C2×D4—1424no—
707C2×D4—1424no—
708C2×D4—1422no—
709C2×D4—1424no—
710C2×D4—1421no—
711C2×D4—1421no—
712C2×D4—1422no—
713C2×D4—1422no—
714C2×D4C2×C22⋊D7114yes—
715C2×D4C23×D7112yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—2844no—
728C22×C4—5682no—
729C22×C4—1421no—
730C22×C4—1421no—
731C22×C4—1424no—
732C22×C4—1424no—
733C22×C4C2×C22⋊D7112yes—
734C22×C4C2×C22⋊D7112yes—
735C22×C4C2×C22⋊D7111yescharacteristic
736C22×C4C2×C22⋊D7111yescharacteristic
737C22×C4C2×C22⋊D7111yescharacteristic
738C22×C4C2×C22⋊D7111yescharacteristic
739C22×C4C23×D7112yes—
740C22×C4C23×D7112yes—
741C22×C4C23×D7111yescharacteristic
742Q16—1428no—
743Q16—1428no—
744SD16—2844no—
745SD16—2844no—
746SD16—7116no—
747SD16—1428no—
748SD16—1428no—
749D8—1428no—
750D8—1428no—
751M16—1428no—
752M16—1428no—
753C2×C8—714no—
754C2×C8—712no—
755C2×C8—712no—
756C2×C8—712no—
757C2×C8—712no—
758C2×C8—1422no—
759C2×C8—1422no—
760C2×C8—1422no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—712no—
765C4⋊C4—1424no—
766C4⋊C4—1421no—
767C4⋊C4C2×C22⋊D7114yes—
768C4⋊C4C23×D7112yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—1424no—
774C22⋊C4—1424no—
775C22⋊C4—1424no—
776C22⋊C4—1424no—
777C22⋊C4—1424no—
778C22⋊C4C2×C22⋊D7114yes—
779C22⋊C4C2×C22⋊D7114yes—
780C42—24no—
781C42C2×C22⋊D7112yes—
782C42C23×D7112yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—2848no—
794C23—2848no—
795C23—2842no—
796C23—2842no—
797C23—2842no—
798C23—2842no—
799C23—2842no—
800C23—5684no—
801C23—56816no—
802C23—1422no—
803C23—1422no—
804C23—1424no—
805C23C22×C22⋊D7112yes—
806C23C22×C22⋊D7112yes—
807C23C22×C22⋊D7111yescharacteristic
808Q8—22no—
809Q8—24no—
810Q8—22no—
811Q8—22no—
812Q8—48no—
813Q8—42no—
814Q8—2842no—
815Q8—1422no—
816Q8—1422no—
817Q8C2×D4×D7114yes—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—48no—
822D4—48no—
823D4—42no—
824D4—2848no—
825D4—2848no—
826D4—2842no—
827D4—5684no—
828D4—714no—
829D4—1422no—
830D4—1422no—
831D4—1422no—
832D4—1424no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—48no—
848C2×C4—48no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—2848no—
852C2×C4—2842no—
853C2×C4—2842no—
854C2×C4—5684no—
855C2×C4—1422no—
856C2×C4—1422no—
857C2×C4C2×D4×D7112yes—
858C2×C4C22×C22⋊D7112yes—
859C2×C4C22×C22⋊D7112yes—
860C2×C4C22×C22⋊D7112yes—
861C2×C4C22×C22⋊D7112yes—
862C2×C4C22×C22⋊D7111yescharacteristic
863C2×C4#1455617312yes—
864C2×C4C24×D7111yescharacteristic
865C8—714no—
866C8—1422no—
867C8—1422no—
868C8—1422no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—84no—
881C22—2848no—
882C22—2842no—
883C22—2842no—
884C22—2842no—
885C22—2842no—
886C22—2842no—
887C22—56816no—
888C22—5684no—
889C22—1424no—
890C22D4×C22⋊D7112yes—
891C22#1798679712yes—
892C22#1798680712yes—
893C22C23×C22⋊D7111yescharacteristic
894C4—22no—
895C4—22no—
896C4—24no—
897C4—22no—
898C4—22no—
899C4—42no—
900C4—42no—
901C4—2842no—
902C4—2842no—
903C4D4×C22⋊D7112yes—
904C4C22×D4×D7111yescharacteristic
905C4C2×#1455617311yescharacteristic
906C2—42no—
907C2—42no—
908C2—82no—
909C2—2844no—
910C2—5682no—
911C2#2259997214yesdirect product factor
912C2C2×D4×C22⋊D7111yescharacteristic
913C2C2×#1798679711yescharacteristic
914C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#548×C71C2
socleC23×C71C22×D4
hypercenterC2×#548D71
hypocenterC71C2×#3275
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14556159C2semidirect
2. C22×#14556153C2semidirect
3. C2×#17986645C2semidirect
4. #22599972C2direct (N × H)
5. C2×#17986381C2semidirect
6. C2×#17986255C2semidirect
7. C2×#17986250C2semidirect
8. C2×#17986221C2semidirect
9. C2×#17986211C2semidirect
10. C2×#17986161C2semidirect
11. C2×#17986142C2semidirect
12. C2×#17986138C2semidirect
13. C2×#17986149C2semidirect
14. C2×C4×#11765852C2semidirect
15. C2×#17986077C2semidirect
16. C2×#548×C71C2semidirect
20. C2×#14556159C22semidirect
22. C2×#14556153C22semidirect
23. C22×#11765855C22semidirect
24. C22×#11765855C22semidirect
25. C22×#11765853C22semidirect
33. C22×#11765849C22semidirect
35. #17986645C22semidirect
44. #17986381C22semidirect
45. #17986255C22semidirect
46. #17986250C22semidirect
47. #17986221C22semidirect
48. #17986211C22semidirect
49. #17986161C22semidirect
50. #17986149C22semidirect
51. #17986142C22semidirect
52. #17986138C22semidirect
53. C4×#11765852C22semidirect
54. #17986077C22semidirect
55. C2×#14556059C22semidirect
56. C2×C4⋊(C71⋊C8)C22semidirect
57. C2×#14556052C22semidirect
58. C2×#14556052C22semidirect
59. C2×#14556051C22semidirect
60. C2×#14556049C22semidirect
64. C2×C22⋊(C71⋊C8)C22semidirect
65. C2×C4×C71⋊C8C22semidirect
67. C23×Q8×C71C22semidirect
69. #548×C71C22semidirect
71. C2×#124×C71C22semidirect
75. C2×#121×C71C22semidirect
76. C2×C4×Q8×C71C22semidirect
100. C2×#11765855C23semidirect
101. C2×#11765855C23semidirect
103. C2×#11765853C23semidirect
107. C2×#11765852D4semidirect
119. C2×#11765849C23semidirect
143. #14556059C23semidirect
144. C4⋊(C71⋊C8)C23semidirect
145. #14556052C23semidirect
146. #14556052C23semidirect
147. #14556051C23semidirect
148. #14556049C23semidirect
152. C22⋊(C71⋊C8)C23semidirect
153. C4×C71⋊C8C23semidirect
164. C22×Q8×C71C23semidirect
175. #124×C71C23semidirect
181. #121×C71C23semidirect
183. C4×Q8×C71C23semidirect
241. #11765852C2×D4semidirect
452. C2×C71#3275semidirect
460. C2×#548D71semidirect
474. C71C2×#3275semidirect
477. C23×Q8C2×D71semidirect
495. #548C2×D71semidirect
500. C2×#124C2×D71semidirect
508. C2×#121C2×D71semidirect
510. C2×C4×Q8C2×D71semidirect
553. C22×Q8C22×D71semidirect
605. #124C22×D71semidirect
617. #121C22×D71semidirect
620. C4×Q8C22×D71semidirect
911. C2#22599972direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561592
C22×#145561532
C2×#179866452
#225999722
C2×#179863812
C2×#179862552
C2×#179862502
C2×#179862212
C2×#179862112
C2×#179861612
C2×#179861422
C2×#179861382
C2×#179861492
C2×C4×#117658522
C2×#179860772
C2×#548×C712
C2×#327571