Finite Group Databasebeta

← C71×#24450 #31845322

Subgroups — C71×#24450 #31845322

Order 18176.

1620 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C71C211yesmaximal, characteristic, complemented
2C2×#468×C71C211yesmaximal, characteristic, complemented
3C2×#449×C71C211yesmaximal, characteristic, complemented
4C2×#447×C71C211yesmaximal, characteristic, complemented
5C2×#418×C71C211yesmaximal, characteristic, complemented
6C71×#2414C211yesmaximal, characteristic, complemented
7C71×#2042C211yesmaximal, characteristic, complemented
8C71×#2033C211yesmaximal, characteristic, complemented
9C71×#2012C211yesmaximal, characteristic, complemented
10C71×#1999C211yesmaximal, characteristic, complemented
11C71×#1879C211yesmaximal, characteristic, complemented
12C71×#1873C211yesmaximal, characteristic, complemented
13C71×#1870C211yesmaximal, characteristic, complemented
14C71×#1862C211yesmaximal, characteristic, complemented
15C71×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C71C2211yescharacteristic
17C23×D4×C71C2211yescharacteristic
18C22×SD16×C71C2211yescharacteristic, complemented
19C22×D8×C71C2211yescharacteristic
20C22×D8×C71C2211yescharacteristic
21C22×M16×C71C2211yescharacteristic
22#546×C71—24no—
23#546×C71—24no—
24C2×#124×C71C2211yescharacteristic
25C2×#123×C71—21no—
26C2×C22⋊Q8×C71C2211yescharacteristic
27C2×#121×C71—21no—
28C2×#121×C71C2211yescharacteristic
29C2×#121×C71C2211yescharacteristic
30C2×#121×C71C2211yescharacteristic, complemented
31C2×#120×C71—21no—
32C2×C4×D4×C71C2211yescharacteristic
33C2×C4×D4×C71C2211yescharacteristic
34C2×#117×C71C2211yescharacteristic
35C22×C22⋊C4×C71—21no—
36#468×C71—24no—
37#449×C71—24no—
38#447×C71—24no—
39C2×#107×C71C2211yescharacteristic, complemented
40#418×C71—24no—
41C2×#103×C71C2211yescharacteristic, complemented
42C2×#103×C71C2211yescharacteristic, complemented
43C2×#103×C71C2211yescharacteristic, complemented
44C2×#102×C71C2211yescharacteristic
45C2×#102×C71C2211yescharacteristic
46C2×#102×C71C2211yescharacteristic
47C2×#102×C71C2211yescharacteristic
48C2×#102×C71C2211yescharacteristic
49C2×#102×C71C2211yescharacteristic
50C2×#102×C71C2211yescharacteristic, complemented
51C2×C22⋊C8×C71C2211yescharacteristic
52C2×C22⋊C8×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic, complemented
54#394×C71—21no—
55#392×C71—21no—
56#390×C71—21no—
57#390×C71C2211yescharacteristic, complemented
58#389×C71C2211yescharacteristic, complemented
59#388×C71—21no—
60#380×C71C2211yescharacteristic, complemented
61#340×C71C2211yescharacteristic, complemented
62#340×C71C2211yescharacteristic, complemented
63#336×C71C2211yescharacteristic, complemented
64#336×C71C2211yescharacteristic, complemented
65C25×C71—21no—
66C2×#41×C71—22no—
67C2×#41×C71—22no—
68C2×#41×C71—22no—
69C2×#41×C71—22no—
70C2×#41×C71—41no—
71C2×#41×C71—41no—
72C22×Q8×C71C2311yescharacteristic
73C22×D4×C71—22no—
74C22×D4×C71—22no—
75C22×D4×C71—21no—
76C22×D4×C71—21no—
77C22×D4×C71—21no—
78C22×D4×C71—21no—
79C22×D4×C71—21no—
80C22×D4×C71—22no—
81C22×D4×C71—41no—
82C22×D4×C71—41no—
83C22×D4×C71D411yescharacteristic
84C22×D4×C71D414yescomplemented
85C22×D4×C71C2311yescharacteristic
86C22×D4×C71C2311yescharacteristic
87C22×D4×C71C2311yescharacteristic
88C23×C4×C71—21no—
89C23×C4×C71—21no—
90C23×C4×C71C2311yescharacteristic
91C23×C4×C71C2311yescharacteristic
92C2×SD16×C71—22no—
93C2×SD16×C71—22no—
94C2×SD16×C71—41no—
95C2×D8×C71—22no—
96C2×D8×C71—22no—
97C2×D8×C71—22no—
98C2×D8×C71—22no—
99C2×D8×C71—41no—
100C2×D8×C71—41no—
101C2×M16×C71—22no—
102C2×M16×C71—22no—
103C2×M16×C71—41no—
104C22×C8×C71C2311yescharacteristic
105C22×C8×C71C2311yescharacteristic
106C22×C8×C71C2311yescharacteristic
107C22×C8×C71C2311yescharacteristic
108#124×C71—22no—
109#124×C71—22no—
110#123×C71—28no—
111C22⋊Q8×C71—22no—
112C22⋊Q8×C71D414yescomplemented
113#121×C71—28no—
114#121×C71—22no—
115#121×C71—22no—
116#121×C71—22no—
117#121×C71—22no—
118#121×C71—22no—
119#121×C71—41no—
120#120×C71—28no—
121C4×D4×C71—22no—
122C4×D4×C71—22no—
123C4×D4×C71—22no—
124C4×D4×C71—22no—
125#117×C71—22no—
126#117×C71—41no—
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71—21no—
129C2×C4⋊C4×C71D411yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C4⋊C4×C71C2311yescharacteristic
132C2×C4⋊C4×C71C2311yescharacteristic
133C2×C4⋊C4×C71C2311yescharacteristic
134C2×C22⋊C4×C71—28no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71—21no—
137C2×C22⋊C4×C71—21no—
138C2×C22⋊C4×C71—21no—
139C2×C22⋊C4×C71—21no—
140C2×C22⋊C4×C71—21no—
141C2×C22⋊C4×C71—21no—
142C2×C22⋊C4×C71—21no—
143C2×C22⋊C4×C71—21no—
144C2×C22⋊C4×C71—21no—
145C2×C22⋊C4×C71—21no—
146C2×C22⋊C4×C71D411yescharacteristic
147C2×C22⋊C4×C71D411yescharacteristic
148C2×C42×C71—21no—
149C2×C42×C71C2311yescharacteristic
150#107×C71—22no—
151#103×C71—22no—
152#103×C71—22no—
153#103×C71—41no—
154#102×C71—22no—
155#102×C71—22no—
156#102×C71—22no—
157#102×C71—22no—
158#102×C71—22no—
159#102×C71—22no—
160#102×C71D414yescomplemented
161C22⋊C8×C71—22no—
162C22⋊C8×C71—22no—
163C22⋊C8×C71—41no—
164#95×C71—21no—
165#95×C71—21no—
166C24×C71—21no—
167C24×C71—21no—
168C24×C71—24no—
169C24×C71—21no—
170C24×C71—42no—
171C24×C71—42no—
172C24×C71—42no—
173C24×C71—42no—
174C24×C71—81no—
175C24×C71—81no—
176C24×C71C2×D411yescharacteristic
177C24×C71C2×D411yescharacteristic
178#41×C71—44no—
179#41×C71—44no—
180#41×C71—44no—
181#41×C71—44no—
182C2×Q8×C71—21no—
183C2×Q8×C71—21no—
184C2×Q8×C71—21no—
185C2×Q8×C71—21no—
186C2×Q8×C71—21no—
187C2×Q8×C71C2×D412yes—
188C2×D4×C71—28no—
189C2×D4×C71—24no—
190C2×D4×C71—22no—
191C2×D4×C71—24no—
192C2×D4×C71—24no—
193C2×D4×C71—21no—
194C2×D4×C71—21no—
195C2×D4×C71—21no—
196C2×D4×C71—21no—
197C2×D4×C71—21no—
198C2×D4×C71—21no—
199C2×D4×C71—21no—
200C2×D4×C71—21no—
201C2×D4×C71—21no—
202C2×D4×C71—21no—
203C2×D4×C71—21no—
204C2×D4×C71—21no—
205C2×D4×C71—21no—
206C2×D4×C71—21no—
207C2×D4×C71—44no—
208C2×D4×C71—44no—
209C2×D4×C71—44no—
210C2×D4×C71—41no—
211C2×D4×C71—41no—
212C2×D4×C71—42no—
213C2×D4×C71—42no—
214C2×D4×C71—42no—
215C2×D4×C71—42no—
216C2×D4×C71—42no—
217C2×D4×C71—42no—
218C2×D4×C71—42no—
219C2×D4×C71—81no—
220C2×D4×C71—81no—
221C2×D4×C71—81no—
222C2×D4×C71—81no—
223C2×D4×C71—81no—
224C2×D4×C71C2×D412yes—
225C2×D4×C71C2×D412yes—
226C2×D4×C71C2×D412yes—
227C2×D4×C71#4112yes—
228C22×C4×C71—21no—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—24no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—24no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—42no—
246C22×C4×C71—42no—
247C22×C4×C71—81no—
248C22×C4×C71—81no—
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D412yes—
254C22×C4×C71C2×D412yes—
255C22×C4×C71C2411yescharacteristic
256SD16×C71—44no—
257D8×C71—44no—
258D8×C71—44no—
259M16×C71—44no—
260C2×C8×C71—21no—
261C2×C8×C71—21no—
262C2×C8×C71—21no—
263C2×C8×C71—21no—
264C2×C8×C71—21no—
265C2×C8×C71—21no—
266C2×C8×C71—21no—
267C2×C8×C71—21no—
268C2×C8×C71—21no—
269C2×C8×C71—21no—
270C2×C8×C71—21no—
271C2×C8×C71C2×D412yes—
272C4⋊C4×C71—24no—
273C4⋊C4×C71—22no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71—21no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—81no—
281C4⋊C4×C71C2×D412yes—
282C4⋊C4×C71C2×D412yes—
283C22⋊C4×C71—24no—
284C22⋊C4×C71—24no—
285C22⋊C4×C71—24no—
286C22⋊C4×C71—24no—
287C22⋊C4×C71—22no—
288C22⋊C4×C71—24no—
289C22⋊C4×C71—22no—
290C22⋊C4×C71—42no—
291C22⋊C4×C71—42no—
292C22⋊C4×C71—42no—
293C22⋊C4×C71—42no—
294C22⋊C4×C71—81no—
295C22⋊C4×C71—81no—
296C42×C71—21no—
297C42×C71—21no—
298C42×C71—42no—
299C23×C71—22no—
300C23×C71—21no—
301C23×C71—22no—
302C23×C71—21no—
303C23×C71—22no—
304C23×C71—21no—
305C23×C71—21no—
306C23×C71—21no—
307C23×C71—21no—
308C23×C71—22no—
309C23×C71—21no—
310C23×C71—21no—
311C23×C71—21no—
312C23×C71—21no—
313C23×C71—21no—
314C23×C71—21no—
315C23×C71—21no—
316C23×C71—48no—
317C23×C71—48no—
318C23×C71—41no—
319C23×C71—41no—
320C23×C71—41no—
321C23×C71—41no—
322C23×C71—41no—
323C23×C71—41no—
324C23×C71—41no—
325C23×C71—41no—
326C23×C71—41no—
327C23×C71—41no—
328C23×C71—41no—
329C23×C71—41no—
330C23×C71—41no—
331C23×C71—41no—
332C23×C71—41no—
333C23×C71—41no—
334C23×C71—41no—
335C23×C71—84no—
336C23×C71—84no—
337C23×C71—84no—
338C23×C71—84no—
339C23×C71—84no—
340C23×C71#12012yes—
341C23×C71C22×D411yescharacteristic
342Q8×C71—22no—
343Q8×C71—22no—
344Q8×C71—41no—
345Q8×C71—41no—
346D4×C71—22no—
347D4×C71—22no—
348D4×C71—22no—
349D4×C71—22no—
350D4×C71—22no—
351D4×C71—48no—
352D4×C71—44no—
353D4×C71—48no—
354D4×C71—41no—
355D4×C71—41no—
356D4×C71—41no—
357D4×C71—41no—
358D4×C71—41no—
359D4×C71—41no—
360D4×C71—84no—
361D4×C71—84no—
362D4×C71—84no—
363D4×C71#12114yes—
364C2×C4×C71—21no—
365C2×C4×C71—21no—
366C2×C4×C71—22no—
367C2×C4×C71—22no—
368C2×C4×C71—22no—
369C2×C4×C71—22no—
370C2×C4×C71—21no—
371C2×C4×C71—21no—
372C2×C4×C71—22no—
373C2×C4×C71—21no—
374C2×C4×C71—22no—
375C2×C4×C71—22no—
376C2×C4×C71—21no—
377C2×C4×C71—21no—
378C2×C4×C71—21no—
379C2×C4×C71—21no—
380C2×C4×C71—21no—
381C2×C4×C71—21no—
382C2×C4×C71—48no—
383C2×C4×C71—41no—
384C2×C4×C71—41no—
385C2×C4×C71—41no—
386C2×C4×C71—41no—
387C2×C4×C71—41no—
388C2×C4×C71—41no—
389C2×C4×C71—41no—
390C2×C4×C71—41no—
391C2×C4×C71—41no—
392C2×C4×C71—41no—
393C2×C4×C71—41no—
394C2×C4×C71—41no—
395C2×C4×C71—41no—
396C2×C4×C71—41no—
397C2×C4×C71—41no—
398C2×C4×C71—41no—
399C2×C4×C71—84no—
400C2×C4×C71#12012yes—
401C2×C4×C71C22×D411yescharacteristic
402C2×C4×C71C22×D411yescharacteristic
403C2×C4×C71C22×D411yescharacteristic
404C2×C4×C71C2×#4111yescharacteristic
405C2×C4×C71H(5,𝔽2)11yescharacteristic
406C2×C4×C71H(5,𝔽2)11yescharacteristic
407C8×C71—22no—
408C8×C71—41no—
409C8×C71—41no—
410C8×C71—41no—
411C22×C71—22no—
412C22×C71—24no—
413C22×C71—22no—
414C22×C71—22no—
415C22×C71—42no—
416C22×C71—42no—
417C22×C71—41no—
418C22×C71—42no—
419C22×C71—41no—
420C22×C71—42no—
421C22×C71—41no—
422C22×C71—42no—
423C22×C71—41no—
424C22×C71—42no—
425C22×C71—41no—
426C22×C71—42no—
427C22×C71—41no—
428C22×C71—42no—
429C22×C71—41no—
430C22×C71—42no—
431C22×C71—41no—
432C22×C71—41no—
433C22×C71—41no—
434C22×C71—41no—
435C22×C71—816no—
436C22×C71—81no—
437C22×C71—81no—
438C22×C71—81no—
439C22×C71—81no—
440C22×C71—81no—
441C22×C71—81no—
442C22×C71—81no—
443C22×C71—81no—
444C22×C71—81no—
445C22×C71—81no—
446C22×C71—81no—
447C22×C71C2×#12011yescharacteristic
448C22×C71D4211yescharacteristic
449C22×C71#54611yescharacteristic
450C22×C71#57511yescharacteristic
451C22×C71#57511yescharacteristic
452C22×C71#57611yescharacteristic
453C22×C71#57611yescharacteristic
454C4×C71—22no—
455C4×C71—41no—
456C4×C71—42no—
457C4×C71—41no—
458C4×C71—41no—
459C4×C71—42no—
460C4×C71—42no—
461C4×C71—81no—
462C4×C71—81no—
463C4×C71C2×#12111yescharacteristic
464C4×C71#53411yescharacteristic
465C4×C71D4211yescharacteristic
466C4×C71#54611yescharacteristic
467#24450C7111yesmaximal, characteristic, direct product factor, Sylow
468C2×C71—42no—
469C2×C71—44no—
470C2×C71—81no—
471C2×C71—82no—
472C2×C71—161no—
473C2×C71#241011yescharacteristic
474C2×C71#300511yescharacteristic
475C2×C71#300811yescharacteristic
476C2×C71#326811yescharacteristic
477C2×C71#327311yescharacteristic
478C2×C71#331911yescharacteristic
479C2×C71#332211yescharacteristic
480C2×#546C2×C7111yescharacteristic, complemented
481C2×#468C2×C7111yescharacteristic, complemented
482C2×#449C2×C7111yescharacteristic, complemented
483C2×#447C2×C7111yescharacteristic, complemented
484C2×#418C2×C7111yescharacteristic, complemented
485#2414C2×C7111yescharacteristic, complemented
486#2042C2×C7111yescharacteristic, complemented
487#2033C2×C7111yescharacteristic, complemented
488#2012C2×C7111yescharacteristic, complemented
489#1999C2×C7111yescharacteristic, complemented
490#1879C2×C7111yescharacteristic, complemented
491#1873C2×C7111yescharacteristic, complemented
492#1870C2×C7111yescharacteristic, complemented
493#1862C2×C7111yescharacteristic, complemented
494#1788C2×C7111yescharacteristic, complemented
495C71#2445011yescharacteristic, direct product factor, Sylow
496C22×#41C22×C7111yescharacteristic
497C23×D4C22×C7111yescharacteristic
498C22×SD16C22×C7111yescharacteristic, complemented
499C22×D8C22×C7111yescharacteristic
500C22×D8C22×C7111yescharacteristic
501C22×M16C22×C7111yescharacteristic
502#546—24no—
503#546—24no—
504C2×#124C22×C7111yescharacteristic
505C2×#123—21no—
506C2×C22⋊Q8C22×C7111yescharacteristic
507C2×#121—21no—
508C2×#121C22×C7111yescharacteristic
509C2×#121C22×C7111yescharacteristic
510C2×#121C22×C7111yescharacteristic, complemented
511C2×#120—21no—
512C2×C4×D4C22×C7111yescharacteristic
513C2×C4×D4C22×C7111yescharacteristic
514C2×#117C22×C7111yescharacteristic
515C22×C22⋊C4—21no—
516#468—24no—
517#449—24no—
518#447—24no—
519C2×#107C22×C7111yescharacteristic, complemented
520#418—24no—
521C2×#103C22×C7111yescharacteristic, complemented
522C2×#103C22×C7111yescharacteristic, complemented
523C2×#103C22×C7111yescharacteristic, complemented
524C2×#102C22×C7111yescharacteristic
525C2×#102C22×C7111yescharacteristic
526C2×#102C22×C7111yescharacteristic
527C2×#102C22×C7111yescharacteristic
528C2×#102C22×C7111yescharacteristic
529C2×#102C22×C7111yescharacteristic
530C2×#102C22×C7111yescharacteristic, complemented
531C2×C22⋊C8C22×C7111yescharacteristic
532C2×C22⋊C8C22×C7111yescharacteristic, complemented
533C2×C22⋊C8C22×C7111yescharacteristic, complemented
534#394—21no—
535#392—21no—
536#390—21no—
537#390C22×C7111yescharacteristic, complemented
538#389C22×C7111yescharacteristic, complemented
539#388—21no—
540#380C22×C7111yescharacteristic, complemented
541#340C22×C7111yescharacteristic, complemented
542#340C22×C7111yescharacteristic, complemented
543#336C22×C7111yescharacteristic, complemented
544#336C22×C7111yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C7111yescharacteristic
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4D4×C7111yescharacteristic
564C22×D4D4×C7114yescomplemented
565C22×D4C23×C7111yescharacteristic
566C22×D4C23×C7111yescharacteristic
567C22×D4C23×C7111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C7111yescharacteristic
571C23×C4C23×C7111yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—41no—
580C2×D8—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8C23×C7111yescharacteristic
585C22×C8C23×C7111yescharacteristic
586C22×C8C23×C7111yescharacteristic
587C22×C8C23×C7111yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C7114yescomplemented
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C7111yescharacteristic
610C2×C4⋊C4C23×C7111yescharacteristic
611C2×C4⋊C4C23×C7111yescharacteristic
612C2×C4⋊C4C23×C7111yescharacteristic
613C2×C4⋊C4C23×C7111yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C7111yescharacteristic
627C2×C22⋊C4D4×C7111yescharacteristic
628C2×C42—21no—
629C2×C42C23×C7111yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102D4×C7114yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—24no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C7111yescharacteristic
657C24C2×D4×C7111yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C7112yes—
668C2×D4—28no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—41no—
691C2×D4—41no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C7112yes—
705C2×D4C2×D4×C7112yes—
706C2×D4C2×D4×C7112yes—
707C2×D4#41×C7112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C7111yescharacteristic
730C22×C4C2×D4×C7111yescharacteristic
731C22×C4C2×D4×C7111yescharacteristic
732C22×C4C2×D4×C7111yescharacteristic
733C22×C4C2×D4×C7112yes—
734C22×C4C2×D4×C7112yes—
735C22×C4C24×C7111yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739M16—44no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8C2×D4×C7112yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C7112yes—
762C4⋊C4C2×D4×C7112yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—24no—
769C22⋊C4—22no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23#120×C7112yes—
821C23C22×D4×C7111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—48no—
832D4—48no—
833D4—44no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C7114yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C7112yes—
881C2×C4C22×D4×C7111yescharacteristic
882C2×C4C22×D4×C7111yescharacteristic
883C2×C4C22×D4×C7111yescharacteristic
884C2×C4C2×#41×C7111yescharacteristic
885C2×C4H(5,𝔽2)×C7111yescharacteristic
886C2×C4H(5,𝔽2)×C7111yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—41no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C7111yescharacteristic
928C22D42×C7111yescharacteristic
929C22#546×C7111yescharacteristic
930C22#575×C7111yescharacteristic
931C22#575×C7111yescharacteristic
932C22#576×C7111yescharacteristic
933C22#576×C7111yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C7111yescharacteristic
944C4#534×C7111yescharacteristic
945C4D42×C7111yescharacteristic
946C4#546×C7111yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—161no—
952C2C71×#241011yescharacteristic
953C2C71×#300511yescharacteristic
954C2C71×#300811yescharacteristic
955C2C71×#326811yescharacteristic
956C2C71×#327311yescharacteristic
957C2C71×#331911yescharacteristic
958C2C71×#332211yescharacteristic
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. C2×#546×C71C2semidirect
2. C2×#468×C71C2semidirect
3. C2×#449×C71C2semidirect
4. C2×#447×C71C2semidirect
5. C2×#418×C71C2semidirect
6. C71×#2414C2semidirect
7. C71×#2042C2semidirect
8. C71×#2033C2semidirect
9. C71×#2012C2semidirect
10. C71×#1999C2semidirect
11. C71×#1879C2semidirect
12. C71×#1873C2semidirect
13. C71×#1870C2semidirect
14. C71×#1862C2semidirect
15. C71×#1788C2semidirect
18. C22×SD16×C71C22semidirect
30. C2×#121×C71C22semidirect
39. C2×#107×C71C22semidirect
41. C2×#103×C71C22semidirect
42. C2×#103×C71C22semidirect
43. C2×#103×C71C22semidirect
50. C2×#102×C71C22semidirect
52. C2×C22⋊C8×C71C22semidirect
53. C2×C22⋊C8×C71C22semidirect
57. #390×C71C22semidirect
58. #389×C71C22semidirect
60. #380×C71C22semidirect
61. #340×C71C22semidirect
62. #340×C71C22semidirect
63. #336×C71C22semidirect
64. #336×C71C22semidirect
84. C22×D4×C71D4semidirect
112. C22⋊Q8×C71D4semidirect
160. #102×C71D4semidirect
467. #24450C71direct (N × H)
480. C2×#546C2×C71semidirect
481. C2×#468C2×C71semidirect
482. C2×#449C2×C71semidirect
483. C2×#447C2×C71semidirect
484. C2×#418C2×C71semidirect
485. #2414C2×C71semidirect
486. #2042C2×C71semidirect
487. #2033C2×C71semidirect
488. #2012C2×C71semidirect
489. #1999C2×C71semidirect
490. #1879C2×C71semidirect
491. #1873C2×C71semidirect
492. #1870C2×C71semidirect
493. #1862C2×C71semidirect
494. #1788C2×C71semidirect
495. C71#24450direct (N × H)
498. C22×SD16C22×C71semidirect
510. C2×#121C22×C71semidirect
519. C2×#107C22×C71semidirect
521. C2×#103C22×C71semidirect
522. C2×#103C22×C71semidirect
523. C2×#103C22×C71semidirect
530. C2×#102C22×C71semidirect
532. C2×C22⋊C8C22×C71semidirect
533. C2×C22⋊C8C22×C71semidirect
537. #390C22×C71semidirect
538. #389C22×C71semidirect
540. #380C22×C71semidirect
541. #340C22×C71semidirect
542. #340C22×C71semidirect
543. #336C22×C71semidirect
544. #336C22×C71semidirect
564. C22×D4D4×C71semidirect
592. C22⋊Q8D4×C71semidirect
640. #102D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C712
C2×#468×C712
C2×#449×C712
C2×#447×C712
C2×#418×C712
C71×#24142
C71×#20422
C71×#20332
C71×#20122
C71×#19992
C71×#18792
C71×#18732
C71×#18702
C71×#18622
C71×#17882
#2445071