Finite Group Databasebeta

← C71×#23854 #31844726

Subgroups — C71×#23854 #31844726

Order 18176.

1794 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C71C211yesmaximal, characteristic, complemented
2C2×#548×C71C211yesmaximal, characteristic, complemented
3C2×#452×C71C211yesmaximal, characteristic, complemented
4C2×#451×C71C211yesmaximal, characteristic, complemented
5C2×#448×C71C211yesmaximal, characteristic, complemented
6C71×#2407C211yesmaximal, characteristic, complemented
7C71×#2015C211yesmaximal, characteristic, complemented
8C71×#2012C211yesmaximal, characteristic, complemented
9C71×#2000C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1892C211yesmaximal, characteristic, complemented
12C71×#1880C211yesmaximal, characteristic, complemented
13C71×#1878C211yesmaximal, characteristic, complemented
14C71×#1869C211yesmaximal, characteristic, complemented
15C71×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic
17C22×#41×C71C2211yescharacteristic
18C23×Q8×C71C2211yescharacteristic
19C2×#135×C71—24no—
20C2×#135×C71—24no—
21C2×#135×C71—24no—
22C22×Q16×C71C2211yescharacteristic
23C22×Q16×C71C2211yescharacteristic
24C22×SD16×C71C2211yescharacteristic
25C22×SD16×C71C2211yescharacteristic
26C22×SD16×C71C2211yescharacteristic
27C22×D8×C71C2211yescharacteristic
28C23×C8×C71C2211yescharacteristic
29#548×C71—24no—
30#548×C71—24no—
31C2×#124×C71—21no—
32C2×#124×C71C2211yescharacteristic
33C2×C22⋊Q8×C71—21no—
34C2×C22⋊Q8×C71C2211yescharacteristic
35C2×C22⋊Q8×C71C2211yescharacteristic
36C2×#121×C71—21no—
37C2×#121×C71C2211yescharacteristic
38C2×#121×C71C2211yescharacteristic
39C2×C4×Q8×C71C2211yescharacteristic
40C2×C4×D4×C71—21no—
41C2×C4×D4×C71C2211yescharacteristic
42#452×C71—24no—
43#451×C71—24no—
44#448×C71—24no—
45C2×#103×C71C2211yescharacteristic
46C2×#103×C71C2211yescharacteristic
47C2×#103×C71C2211yescharacteristic
48C2×#103×C71C2211yescharacteristic
49C2×#103×C71C2211yescharacteristic
50C2×#102×C71C2211yescharacteristic
51C2×#102×C71C2211yescharacteristic
52C2×#102×C71C2211yescharacteristic
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C22⋊C8×C71C2211yescharacteristic
55C2×C22⋊C8×C71C2211yescharacteristic
56#394×C71—21no—
57#392×C71—21no—
58#391×C71C2211yescharacteristic
59#390×C71C2211yescharacteristic
60#386×C71—21no—
61#385×C71—21no—
62#380×C71C2211yescharacteristic
63#340×C71C2211yescharacteristic
64#340×C71C2211yescharacteristic
65#336×C71C2211yescharacteristic
66#336×C71C2211yescharacteristic
67C2×#41×C71—22no—
68C2×#41×C71—22no—
69C2×#41×C71—22no—
70C2×#41×C71—22no—
71C2×#41×C71—22no—
72C2×#41×C71—22no—
73C2×#41×C71—22no—
74C2×#41×C71—41no—
75C2×#41×C71—41no—
76C2×#41×C71—41no—
77C2×#41×C71—41no—
78C2×#41×C71D414yescomplemented
79C22×Q8×C71—22no—
80C22×Q8×C71—22no—
81C22×Q8×C71—21no—
82C22×Q8×C71—22no—
83C22×Q8×C71—22no—
84C22×Q8×C71—41no—
85C22×Q8×C71—41no—
86C22×Q8×C71C2311yescharacteristic
87C22×Q8×C71C2311yescharacteristic
88C22×Q8×C71C2311yescharacteristic
89C22×D4×C71—21no—
90C22×D4×C71—21no—
91C22×D4×C71—21no—
92C22×D4×C71—21no—
93C22×D4×C71D411yescharacteristic
94C22×D4×C71C2311yescharacteristic
95C22×D4×C71C2311yescharacteristic
96C23×C4×C71—21no—
97C23×C4×C71—21no—
98C23×C4×C71—21no—
99C23×C4×C71C2311yescharacteristic
100C23×C4×C71C2311yescharacteristic
101#135×C71—232no—
102C2×Q16×C71—22no—
103C2×Q16×C71—22no—
104C2×Q16×C71—22no—
105C2×Q16×C71—22no—
106C2×Q16×C71—41no—
107C2×Q16×C71D414yescomplemented
108C2×SD16×C71—22no—
109C2×SD16×C71—22no—
110C2×SD16×C71—22no—
111C2×SD16×C71—22no—
112C2×SD16×C71—22no—
113C2×SD16×C71—22no—
114C2×SD16×C71—22no—
115C2×SD16×C71—41no—
116C2×SD16×C71D414yescomplemented
117C2×D8×C71—22no—
118C2×D8×C71—22no—
119C2×D8×C71—22no—
120C22×C8×C71—22no—
121C22×C8×C71—22no—
122C22×C8×C71—22no—
123C22×C8×C71C2311yescharacteristic
124C22×C8×C71C2311yescharacteristic
125C22×C8×C71C2311yescharacteristic
126C22×C8×C71C2311yescharacteristic
127#124×C71—28no—
128#124×C71—22no—
129#124×C71—22no—
130C22⋊Q8×C71—28no—
131C22⋊Q8×C71—22no—
132C22⋊Q8×C71—22no—
133C22⋊Q8×C71—41no—
134C22⋊Q8×C71D414yescomplemented
135#121×C71—28no—
136#121×C71—22no—
137#121×C71—22no—
138#121×C71—22no—
139#121×C71—41no—
140C4×Q8×C71—22no—
141C4×Q8×C71—22no—
142C4×D4×C71—28no—
143C4×D4×C71—22no—
144C4×D4×C71—22no—
145C2×C4⋊C4×C71—21no—
146C2×C4⋊C4×C71—21no—
147C2×C4⋊C4×C71—21no—
148C2×C4⋊C4×C71D411yescharacteristic
149C2×C4⋊C4×C71C2311yescharacteristic
150C2×C4⋊C4×C71C2311yescharacteristic
151C2×C4⋊C4×C71C2311yescharacteristic
152C2×C22⋊C4×C71—21no—
153C2×C22⋊C4×C71—21no—
154C2×C22⋊C4×C71—21no—
155C2×C22⋊C4×C71—21no—
156C2×C22⋊C4×C71—21no—
157C2×C22⋊C4×C71—21no—
158C2×C22⋊C4×C71—21no—
159C2×C22⋊C4×C71—21no—
160C2×C22⋊C4×C71—21no—
161C2×C22⋊C4×C71D411yescharacteristic
162C2×C22⋊C4×C71D411yescharacteristic
163C2×C42×C71—21no—
164C2×C42×C71C2311yescharacteristic
165#103×C71—22no—
166#103×C71—22no—
167#103×C71—22no—
168#103×C71—22no—
169#103×C71—22no—
170#102×C71—22no—
171#102×C71—41no—
172#102×C71—41no—
173C22⋊C8×C71—22no—
174C22⋊C8×C71—22no—
175C22⋊C8×C71—22no—
176#95×C71—21no—
177#95×C71—21no—
178#95×C71—21no—
179C24×C71—21no—
180C24×C71—21no—
181C24×C71C2×D411yescharacteristic
182C24×C71C2×D411yescharacteristic
183#41×C71—28no—
184#41×C71—28no—
185#41×C71—44no—
186#41×C71—44no—
187#41×C71—44no—
188#41×C71—44no—
189#41×C71—44no—
190#41×C71—44no—
191C2×Q8×C71—24no—
192C2×Q8×C71—21no—
193C2×Q8×C71—21no—
194C2×Q8×C71—21no—
195C2×Q8×C71—21no—
196C2×Q8×C71—21no—
197C2×Q8×C71—21no—
198C2×Q8×C71—21no—
199C2×Q8×C71—21no—
200C2×Q8×C71—21no—
201C2×Q8×C71—21no—
202C2×Q8×C71—21no—
203C2×Q8×C71—21no—
204C2×Q8×C71—21no—
205C2×Q8×C71—42no—
206C2×Q8×C71—42no—
207C2×Q8×C71—44no—
208C2×Q8×C71—44no—
209C2×Q8×C71—44no—
210C2×Q8×C71—44no—
211C2×Q8×C71C2×D412yes—
212C2×Q8×C71C2×D412yes—
213C2×Q8×C71C2×D412yes—
214C2×Q8×C71C2×D412yes—
215C2×Q8×C71C2×D412yes—
216C2×D4×C71—24no—
217C2×D4×C71—22no—
218C2×D4×C71—24no—
219C2×D4×C71—22no—
220C2×D4×C71—21no—
221C2×D4×C71—21no—
222C2×D4×C71—21no—
223C2×D4×C71—21no—
224C2×D4×C71—21no—
225C2×D4×C71—21no—
226C2×D4×C71—21no—
227C2×D4×C71—21no—
228C2×D4×C71—21no—
229C2×D4×C71—21no—
230C2×D4×C71—41no—
231C2×D4×C71—42no—
232C2×D4×C71—42no—
233C2×D4×C71—42no—
234C2×D4×C71—42no—
235C2×D4×C71—42no—
236C2×D4×C71—42no—
237C2×D4×C71—42no—
238C2×D4×C71—42no—
239C2×D4×C71—42no—
240C2×D4×C71—81no—
241C2×D4×C71C2×D412yes—
242C2×D4×C71C2×D412yes—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—24no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—24no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—42no—
262C22×C4×C71—42no—
263C22×C4×C71—42no—
264C22×C4×C71—42no—
265C22×C4×C71—42no—
266C22×C4×C71—42no—
267C22×C4×C71—42no—
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D412yes—
273C22×C4×C71C2×D412yes—
274C22×C4×C71C2411yescharacteristic
275Q16×C71—28no—
276Q16×C71—44no—
277SD16×C71—28no—
278SD16×C71—28no—
279SD16×C71—44no—
280D8×C71—28no—
281C2×C8×C71—28no—
282C2×C8×C71—21no—
283C2×C8×C71—21no—
284C2×C8×C71—21no—
285C2×C8×C71—21no—
286C2×C8×C71—21no—
287C2×C8×C71—21no—
288C2×C8×C71—21no—
289C2×C8×C71—21no—
290C2×C8×C71—21no—
291C2×C8×C71—21no—
292C2×C8×C71C2×D412yes—
293C2×C8×C71C2×D412yes—
294C4⋊C4×C71—24no—
295C4⋊C4×C71—24no—
296C4⋊C4×C71—22no—
297C4⋊C4×C71—21no—
298C4⋊C4×C71—21no—
299C4⋊C4×C71—21no—
300C4⋊C4×C71—21no—
301C4⋊C4×C71—21no—
302C4⋊C4×C71—42no—
303C4⋊C4×C71C2×D412yes—
304C22⋊C4×C71—24no—
305C22⋊C4×C71—24no—
306C22⋊C4×C71—24no—
307C22⋊C4×C71—24no—
308C22⋊C4×C71—22no—
309C22⋊C4×C71—22no—
310C22⋊C4×C71—42no—
311C22⋊C4×C71—42no—
312C22⋊C4×C71—42no—
313C22⋊C4×C71—81no—
314C22⋊C4×C71—81no—
315C42×C71—24no—
316C42×C71—21no—
317C42×C71—21no—
318C23×C71—21no—
319C23×C71—21no—
320C23×C71—21no—
321C23×C71—21no—
322C23×C71—21no—
323C23×C71—21no—
324C23×C71—21no—
325C23×C71—21no—
326C23×C71—21no—
327C23×C71—21no—
328C23×C71—21no—
329C23×C71—21no—
330C23×C71—22no—
331C23×C71—22no—
332C23×C71—41no—
333C23×C71—41no—
334C23×C71—41no—
335C23×C71—41no—
336C23×C71—41no—
337C23×C71—41no—
338C23×C71—41no—
339C23×C71—41no—
340C23×C71—41no—
341C23×C71—41no—
342C23×C71—41no—
343C23×C71—41no—
344C23×C71#12012yes—
345C23×C71#13512yescomplemented
346C23×C71C22×D411yescharacteristic
347Q8×C71—22no—
348Q8×C71—22no—
349Q8×C71—22no—
350Q8×C71—22no—
351Q8×C71—22no—
352Q8×C71—22no—
353Q8×C71—22no—
354Q8×C71—48no—
355Q8×C71—41no—
356Q8×C71—41no—
357Q8×C71—41no—
358Q8×C71—41no—
359Q8×C71#12014yes—
360D4×C71—22no—
361D4×C71—22no—
362D4×C71—22no—
363D4×C71—22no—
364D4×C71—48no—
365D4×C71—44no—
366D4×C71—48no—
367D4×C71—48no—
368D4×C71—41no—
369D4×C71—41no—
370D4×C71—41no—
371D4×C71—41no—
372D4×C71—84no—
373C2×C4×C71—22no—
374C2×C4×C71—21no—
375C2×C4×C71—21no—
376C2×C4×C71—22no—
377C2×C4×C71—22no—
378C2×C4×C71—22no—
379C2×C4×C71—22no—
380C2×C4×C71—22no—
381C2×C4×C71—22no—
382C2×C4×C71—21no—
383C2×C4×C71—21no—
384C2×C4×C71—22no—
385C2×C4×C71—22no—
386C2×C4×C71—21no—
387C2×C4×C71—21no—
388C2×C4×C71—22no—
389C2×C4×C71—21no—
390C2×C4×C71—21no—
391C2×C4×C71—21no—
392C2×C4×C71—21no—
393C2×C4×C71—21no—
394C2×C4×C71—48no—
395C2×C4×C71—48no—
396C2×C4×C71—48no—
397C2×C4×C71—41no—
398C2×C4×C71—41no—
399C2×C4×C71—41no—
400C2×C4×C71—41no—
401C2×C4×C71—41no—
402C2×C4×C71—41no—
403C2×C4×C71—41no—
404C2×C4×C71—41no—
405C2×C4×C71—41no—
406C2×C4×C71—41no—
407C2×C4×C71—41no—
408C2×C4×C71—41no—
409C2×C4×C71—41no—
410C2×C4×C71—41no—
411C2×C4×C71—41no—
412C2×C4×C71—41no—
413C2×C4×C71#12012yes—
414C2×C4×C71C22×D411yescharacteristic
415C2×C4×C71C22×D411yescharacteristic
416C2×C4×C71C22×D411yescharacteristic
417C2×C4×C71C22×D411yescharacteristic
418C2×C4×C71H(5,𝔽2)11yescharacteristic
419C2×C4×C71H(5,𝔽2)11yescharacteristic
420C8×C71—22no—
421C8×C71—22no—
422C8×C71—41no—
423C8×C71—41no—
424C22×C71—22no—
425C22×C71—22no—
426C22×C71—22no—
427C22×C71—22no—
428C22×C71—22no—
429C22×C71—22no—
430C22×C71—41no—
431C22×C71—41no—
432C22×C71—41no—
433C22×C71—41no—
434C22×C71—41no—
435C22×C71—41no—
436C22×C71—41no—
437C22×C71—41no—
438C22×C71—42no—
439C22×C71—42no—
440C22×C71—42no—
441C22×C71—42no—
442C22×C71—42no—
443C22×C71—42no—
444C22×C71—81no—
445C22×C71—81no—
446C22×C71—81no—
447C22×C71—81no—
448C22×C71—81no—
449C22×C71—81no—
450C22×C71—81no—
451C22×C71—81no—
452C22×C71C2×#12011yescharacteristic
453C22×C71D4211yescharacteristic
454C22×C71D4211yescharacteristic
455C22×C71C2×#13511yescharacteristic
456C22×C71#57511yescharacteristic
457C22×C71#57711yescharacteristic
458C22×C71#57811yescharacteristic
459C4×C71—22no—
460C4×C71—24no—
461C4×C71—41no—
462C4×C71—42no—
463C4×C71—42no—
464C4×C71—41no—
465C4×C71—42no—
466C4×C71—41no—
467C4×C71—81no—
468C4×C71—81no—
469C4×C71C2×#12011yescharacteristic
470C4×C71#53411yescharacteristic
471C4×C71D4211yescharacteristic
472C4×C71D4211yescharacteristic
473#23854C7111yesmaximal, characteristic, direct product factor, Sylow
474C2×C71—42no—
475C2×C71—42no—
476C2×C71—82no—
477C2×C71—82no—
478C2×C71#240311yescharacteristic
479C2×C71#300211yescharacteristic
480C2×C71#301311yescharacteristic
481C2×C71#326911yescharacteristic
482C2×C71#327111yescharacteristic
483C2×C71#328211yescharacteristic
484C2×C71#328511yescharacteristic
485C22×#135C2×C7111yescharacteristic, complemented
486C2×#548C2×C7111yescharacteristic, complemented
487C2×#452C2×C7111yescharacteristic, complemented
488C2×#451C2×C7111yescharacteristic, complemented
489C2×#448C2×C7111yescharacteristic, complemented
490#2407C2×C7111yescharacteristic, complemented
491#2015C2×C7111yescharacteristic, complemented
492#2012C2×C7111yescharacteristic, complemented
493#2000C2×C7111yescharacteristic, complemented
494#1999C2×C7111yescharacteristic, complemented
495#1892C2×C7111yescharacteristic, complemented
496#1880C2×C7111yescharacteristic, complemented
497#1878C2×C7111yescharacteristic, complemented
498#1869C2×C7111yescharacteristic, complemented
499#1788C2×C7111yescharacteristic, complemented
500C71#2385411yescharacteristic, direct product factor, Sylow
501C22×#41C22×C7111yescharacteristic
502C22×#41C22×C7111yescharacteristic
503C23×Q8C22×C7111yescharacteristic
504C2×#135—24no—
505C2×#135—24no—
506C2×#135—24no—
507C22×Q16C22×C7111yescharacteristic
508C22×Q16C22×C7111yescharacteristic
509C22×SD16C22×C7111yescharacteristic
510C22×SD16C22×C7111yescharacteristic
511C22×SD16C22×C7111yescharacteristic
512C22×D8C22×C7111yescharacteristic
513C23×C8C22×C7111yescharacteristic
514#548—24no—
515#548—24no—
516C2×#124—21no—
517C2×#124C22×C7111yescharacteristic
518C2×C22⋊Q8—21no—
519C2×C22⋊Q8C22×C7111yescharacteristic
520C2×C22⋊Q8C22×C7111yescharacteristic
521C2×#121—21no—
522C2×#121C22×C7111yescharacteristic
523C2×#121C22×C7111yescharacteristic
524C2×C4×Q8C22×C7111yescharacteristic
525C2×C4×D4—21no—
526C2×C4×D4C22×C7111yescharacteristic
527#452—24no—
528#451—24no—
529#448—24no—
530C2×#103C22×C7111yescharacteristic
531C2×#103C22×C7111yescharacteristic
532C2×#103C22×C7111yescharacteristic
533C2×#103C22×C7111yescharacteristic
534C2×#103C22×C7111yescharacteristic
535C2×#102C22×C7111yescharacteristic
536C2×#102C22×C7111yescharacteristic
537C2×#102C22×C7111yescharacteristic
538C2×C22⋊C8C22×C7111yescharacteristic
539C2×C22⋊C8C22×C7111yescharacteristic
540C2×C22⋊C8C22×C7111yescharacteristic
541#394—21no—
542#392—21no—
543#391C22×C7111yescharacteristic
544#390C22×C7111yescharacteristic
545#386—21no—
546#385—21no—
547#380C22×C7111yescharacteristic
548#340C22×C7111yescharacteristic
549#340C22×C7111yescharacteristic
550#336C22×C7111yescharacteristic
551#336C22×C7111yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—41no—
560C2×#41—41no—
561C2×#41—41no—
562C2×#41—41no—
563C2×#41D4×C7114yescomplemented
564C22×Q8—22no—
565C22×Q8—22no—
566C22×Q8—21no—
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—41no—
570C22×Q8—41no—
571C22×Q8C23×C7111yescharacteristic
572C22×Q8C23×C7111yescharacteristic
573C22×Q8C23×C7111yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C7111yescharacteristic
579C22×D4C23×C7111yescharacteristic
580C22×D4C23×C7111yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C7111yescharacteristic
585C23×C4C23×C7111yescharacteristic
586#135—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—41no—
592C2×Q16D4×C7114yescomplemented
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C7114yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—22no—
605C22×C8—22no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8C23×C7111yescharacteristic
609C22×C8C23×C7111yescharacteristic
610C22×C8C23×C7111yescharacteristic
611C22×C8C23×C7111yescharacteristic
612#124—28no—
613#124—22no—
614#124—22no—
615C22⋊Q8—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—41no—
619C22⋊Q8D4×C7114yescomplemented
620#121—28no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—41no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×D4—28no—
628C4×D4—22no—
629C4×D4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4D4×C7111yescharacteristic
634C2×C4⋊C4C23×C7111yescharacteristic
635C2×C4⋊C4C23×C7111yescharacteristic
636C2×C4⋊C4C23×C7111yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4D4×C7111yescharacteristic
647C2×C22⋊C4D4×C7111yescharacteristic
648C2×C42—21no—
649C2×C42C23×C7111yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—22no—
654#103—22no—
655#102—22no—
656#102—41no—
657#102—41no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C7111yescharacteristic
667C24C2×D4×C7111yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676C2×Q8—24no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8C2×D4×C7112yes—
697C2×Q8C2×D4×C7112yes—
698C2×Q8C2×D4×C7112yes—
699C2×Q8C2×D4×C7112yes—
700C2×Q8C2×D4×C7112yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—81no—
726C2×D4C2×D4×C7112yes—
727C2×D4C2×D4×C7112yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—24no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—24no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C7111yescharacteristic
754C22×C4C2×D4×C7111yescharacteristic
755C22×C4C2×D4×C7111yescharacteristic
756C22×C4C2×D4×C7111yescharacteristic
757C22×C4C2×D4×C7112yes—
758C22×C4C2×D4×C7112yes—
759C22×C4C24×C7111yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C7112yes—
778C2×C8C2×D4×C7112yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—42no—
788C4⋊C4C2×D4×C7112yes—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C42—24no—
801C42—21no—
802C42—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—22no—
816C23—22no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23#120×C7112yes—
830C23#135×C7112yescomplemented
831C23C22×D4×C7111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—22no—
839Q8—48no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8#120×C7114yes—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—48no—
850D4—44no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—84no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4#120×C7112yes—
899C2×C4C22×D4×C7111yescharacteristic
900C2×C4C22×D4×C7111yescharacteristic
901C2×C4C22×D4×C7111yescharacteristic
902C2×C4C22×D4×C7111yescharacteristic
903C2×C4H(5,𝔽2)×C7111yescharacteristic
904C2×C4H(5,𝔽2)×C7111yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C7111yescharacteristic
938C22D42×C7111yescharacteristic
939C22D42×C7111yescharacteristic
940C22C2×#135×C7111yescharacteristic
941C22#575×C7111yescharacteristic
942C22#577×C7111yescharacteristic
943C22#578×C7111yescharacteristic
944C4—22no—
945C4—24no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×#120×C7111yescharacteristic
955C4#534×C7111yescharacteristic
956C4D42×C7111yescharacteristic
957C4D42×C7111yescharacteristic
958C2—42no—
959C2—42no—
960C2—82no—
961C2—82no—
962C2C71×#240311yescharacteristic
963C2C71×#300211yescharacteristic
964C2C71×#301311yescharacteristic
965C2C71×#326911yescharacteristic
966C2C71×#327111yescharacteristic
967C2C71×#328211yescharacteristic
968C2C71×#328511yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C2×C4×D4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C71C2semidirect
2. C2×#548×C71C2semidirect
3. C2×#452×C71C2semidirect
4. C2×#451×C71C2semidirect
5. C2×#448×C71C2semidirect
6. C71×#2407C2semidirect
7. C71×#2015C2semidirect
8. C71×#2012C2semidirect
9. C71×#2000C2semidirect
10. C71×#1999C2semidirect
11. C71×#1892C2semidirect
12. C71×#1880C2semidirect
13. C71×#1878C2semidirect
14. C71×#1869C2semidirect
15. C71×#1788C2semidirect
78. C2×#41×C71D4semidirect
107. C2×Q16×C71D4semidirect
116. C2×SD16×C71D4semidirect
134. C22⋊Q8×C71D4semidirect
345. C23×C71#135semidirect
473. #23854C71direct (N × H)
485. C22×#135C2×C71semidirect
486. C2×#548C2×C71semidirect
487. C2×#452C2×C71semidirect
488. C2×#451C2×C71semidirect
489. C2×#448C2×C71semidirect
490. #2407C2×C71semidirect
491. #2015C2×C71semidirect
492. #2012C2×C71semidirect
493. #2000C2×C71semidirect
494. #1999C2×C71semidirect
495. #1892C2×C71semidirect
496. #1880C2×C71semidirect
497. #1878C2×C71semidirect
498. #1869C2×C71semidirect
499. #1788C2×C71semidirect
500. C71#23854direct (N × H)
563. C2×#41D4×C71semidirect
592. C2×Q16D4×C71semidirect
601. C2×SD16D4×C71semidirect
619. C22⋊Q8D4×C71semidirect
830. C23#135×C71semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C712
C2×#548×C712
C2×#452×C712
C2×#451×C712
C2×#448×C712
C71×#24072
C71×#20152
C71×#20122
C71×#20002
C71×#19992
C71×#18922
C71×#18802
C71×#18782
C71×#18692
C71×#17882
#2385471