Finite Group Databasebeta

← #31905325

Subgroups — #31905325

Order 18176.

1186 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D71)⋊C8C211yesmaximal, characteristic
2C2×#17985856C211yesmaximal, characteristic
3C2×#17985856C211yesmaximal, characteristic
4C2×#17985762C211yesmaximal, characteristic, complemented
5C2×#17985761C211yesmaximal, characteristic, complemented
6C2×#17985761C211yesmaximal, characteristic, complemented
7C2×#340×C71C211yesmaximal, characteristic, complemented
8C23×C4×D71C2211yescharacteristic
9C23×C71⋊C8C2211yescharacteristic
10C22×C4⋊Dic71C2211yescharacteristic
11C22×C4⋊Dic71C2211yescharacteristic
12C22×(C2×D71)⋊C4—21no—
13C22×(C2×D71)⋊C4—21no—
14C2×(C2×D71)⋊C8—22no—
15C2×(C2×D71)⋊C8—22no—
16C2×(C2×D71)⋊C8—22no—
17#17985856—22no—
18#17985856—22no—
19#17985856—22no—
20#17985856C414yescomplemented
21C2×C71⋊#95—21no—
22C2×C71⋊#95—21no—
23#17985762—22no—
24#17985761—22no—
25#17985761—22no—
26C23×C8×C71C2211yescharacteristic
27C22×C4⋊C4×C71C2211yescharacteristic
28C22×C4⋊C4×C71C2211yescharacteristic
29#340×C71—22no—
30C24×D71D411yescharacteristic
31C23×Dic71—21no—
32C23×Dic71—21no—
33C23×Dic71D411yescharacteristic
34C22×C4×D71—21no—
35C22×C4×D71—21no—
36C22×C4×D71—21no—
37C22×C4×D71—21no—
38C22×C4×D71—21no—
39C22×C4×D71—21no—
40C22×C4×D71—21no—
41C22×C4×D71—21no—
42C22×C4×D71—21no—
43C22×C4×D71—21no—
44C22×C4×D71—21no—
45C22×C4×D71—21no—
46C22×C4×D71C2×C412yes—
47C22×C4×D71D412yes—
48C22×C71⋊C8—21no—
49C22×C71⋊C8—21no—
50C22×C71⋊C8—21no—
51C22×C71⋊C8—21no—
52C22×C71⋊C8—21no—
53C22×C71⋊C8—21no—
54C22×C71⋊C8D412yes—
55C2×C4⋊Dic71—21no—
56C2×C4⋊Dic71—21no—
57C2×C4⋊Dic71—21no—
58C2×C4⋊Dic71—21no—
59C2×C4⋊Dic71—21no—
60C2×C4⋊Dic71—21no—
61C2×C4⋊Dic71—21no—
62C2×C4⋊Dic71—21no—
63C2×C4⋊Dic71—21no—
64C2×C4⋊Dic71—21no—
65C2×C4⋊Dic71C2×C412yes—
66C2×C4⋊Dic71D412yes—
67C2×(C2×D71)⋊C4—24no—
68C2×(C2×D71)⋊C4—24no—
69C2×(C2×D71)⋊C4—42no—
70C2×(C2×D71)⋊C4—42no—
71C2×(C2×D71)⋊C4—42no—
72C2×(C2×D71)⋊C4—42no—
73(C2×D71)⋊C8—28no—
74C71⋊#95—24no—
75C71⋊#95—24no—
76C23×C4×C71—21no—
77C23×C4×C71—21no—
78C23×C4×C71C2311yescharacteristic
79C22×C8×C71—21no—
80C22×C8×C71—21no—
81C22×C8×C71—21no—
82C22×C8×C71—21no—
83C22×C8×C71—21no—
84C22×C8×C71—21no—
85C22×C8×C71D412yes—
86C2×C4⋊C4×C71—21no—
87C2×C4⋊C4×C71—21no—
88C2×C4⋊C4×C71—21no—
89C2×C4⋊C4×C71—21no—
90C2×C4⋊C4×C71—21no—
91C2×C4⋊C4×C71—21no—
92C2×C4⋊C4×C71—21no—
93C2×C4⋊C4×C71—21no—
94C2×C4⋊C4×C71—21no—
95C2×C4⋊C4×C71—21no—
96C2×C4⋊C4×C71C2×C412yes—
97C2×C4⋊C4×C71D412yes—
98C23×D71—21no—
99C23×D71—21no—
100C23×D71—21no—
101C23×D71—21no—
102C23×D71—21no—
103C23×D71—21no—
104C23×D71—21no—
105C23×D71—21no—
106C23×D71—21no—
107C23×D71—21no—
108C23×D71—21no—
109C23×D71—21no—
110C23×D71C22⋊C412yes—
111C23×D71SD1612yes—
112C23×D71Q1612yes—
113C22×Dic71—21no—
114C22×Dic71—21no—
115C22×Dic71—21no—
116C22×Dic71—21no—
117C22×Dic71—21no—
118C22×Dic71—21no—
119C22×Dic71—22no—
120C22×Dic71—22no—
121C22×Dic71—41no—
122C22×Dic71—41no—
123C22×Dic71—41no—
124C22×Dic71—41no—
125C22×Dic71—41no—
126C22×Dic71—41no—
127C22×Dic71—41no—
128C22×Dic71—41no—
129C22×Dic71—41no—
130C22×Dic71—41no—
131C22×Dic71—41no—
132C22×Dic71—41no—
133C22×Dic71C22⋊C412yes—
134C2×C4×D71—22no—
135C2×C4×D71—22no—
136C2×C4×D71—22no—
137C2×C4×D71—22no—
138C2×C4×D71—22no—
139C2×C4×D71—22no—
140C2×C4×D71—22no—
141C2×C4×D71—22no—
142C2×C4×D71—22no—
143C2×C4×D71—22no—
144C2×C4×D71—22no—
145C2×C4×D71—22no—
146C2×C4×D71—41no—
147C2×C4×D71—41no—
148C2×C4×D71—41no—
149C2×C4×D71—41no—
150C2×C4×D71—41no—
151C2×C4×D71—41no—
152C2×C4×D71—41no—
153C2×C4×D71—41no—
154C2×C4×D71—41no—
155C2×C4×D71—41no—
156C2×C4×D71—41no—
157C2×C4×D71—41no—
158C2×C4×D71—41no—
159C2×C4×D71—41no—
160C2×C4×D71—41no—
161C2×C4×D71—41no—
162C2×C71⋊C8—22no—
163C2×C71⋊C8—22no—
164C2×C71⋊C8—22no—
165C2×C71⋊C8—41no—
166C2×C71⋊C8—41no—
167C2×C71⋊C8—41no—
168C2×C71⋊C8—41no—
169C4⋊Dic71—22no—
170C4⋊Dic71—22no—
171C4⋊Dic71—22no—
172C4⋊Dic71—22no—
173C4⋊Dic71—41no—
174C4⋊Dic71—41no—
175C4⋊Dic71—41no—
176C4⋊Dic71—41no—
177(C2×D71)⋊C4—48no—
178(C2×D71)⋊C4—48no—
179C24×C71C2×D411yescharacteristic
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—41no—
183C22×C4×C71—41no—
184C22×C4×C71—41no—
185C22×C4×C71—41no—
186C22×C4×C71—41no—
187C22×C4×C71—41no—
188C22×C4×C71—41no—
189C22×C4×C71—41no—
190C22×C4×C71—41no—
191C22×C4×C71—41no—
192C22×C4×C71—41no—
193C22×C4×C71—41no—
194C22×C4×C71C22×C411yescharacteristic
195C22×C4×C71C2×D411yescharacteristic
196C22×C4×C71C2×D411yescharacteristic
197C22×C4×C71C2×D411yescharacteristic
198C22×C4×C71C2×D411yescharacteristic
199C22×C4×C71C2×D411yescharacteristic
200C22×C4×C71#4111yescharacteristic
201C22×C4×C71#4111yescharacteristic
202C22×C4×C71#4111yescharacteristic
203C22×C4×C71#4111yescharacteristic
204C22×C4×C71#4111yescharacteristic
205C22×C4×C71#4111yescharacteristic
206C22×C4×C71#4111yescharacteristic
207C22×C4×C71#4111yescharacteristic
208C2×C8×C71—22no—
209C2×C8×C71—22no—
210C2×C8×C71—22no—
211C2×C8×C71—41no—
212C2×C8×C71—41no—
213C2×C8×C71—41no—
214C2×C8×C71—41no—
215C4⋊C4×C71—22no—
216C4⋊C4×C71—22no—
217C4⋊C4×C71—22no—
218C4⋊C4×C71—22no—
219C4⋊C4×C71—41no—
220C4⋊C4×C71—41no—
221C4⋊C4×C71—41no—
222C4⋊C4×C71—41no—
223C23×C71C2×C22⋊C411yescharacteristic
224C23×C71#12011yescharacteristic
225C23×C71#12111yescharacteristic
226C23×C71#12111yescharacteristic
227C23×C71#12311yescharacteristic
228C23×C71#12311yescharacteristic
229C23×C71#12311yescharacteristic
230C23×C71C2×SD1611yescharacteristic
231C23×C71C2×Q1611yescharacteristic
232C23×C71#13511yescharacteristic
233C23×C71#13511yescharacteristic
234C23×C71AGL(1,ℤ/8)11yescharacteristic
235C23×C71AGL(1,ℤ/8)11yescharacteristic
236C23×C71AGL(1,ℤ/8)11yescharacteristic
237C23×C71#13711yescharacteristic
238C22×D71—22no—
239C22×D71—22no—
240C22×D71—22no—
241C22×D71—22no—
242C22×D71—22no—
243C22×D71—22no—
244C22×D71—22no—
245C22×D71—22no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—22no—
249C22×D71—22no—
250C22×D71—22no—
251C22×D71—22no—
252C22×D71—22no—
253C22×D71—22no—
254C22×D71—22no—
255C22×D71—22no—
256C22×D71—41no—
257C22×D71—41no—
258C22×D71—41no—
259C22×D71—41no—
260C22×D71—41no—
261C22×D71—41no—
262C22×D71—41no—
263C22×D71—41no—
264C22×D71—41no—
265C22×D71—41no—
266C22×D71—41no—
267C22×D71—41no—
268C22×D71—41no—
269C22×D71—41no—
270C22×D71—41no—
271C22×D71—41no—
272C22×D71#10314yes—
273C2×C4×C71—42no—
274C2×C4×C71—42no—
275C2×C4×C71—42no—
276C2×C4×C71—42no—
277C2×C4×C71—42no—
278C2×C4×C71—42no—
279C2×C4×C71—81no—
280C2×C4×C71—81no—
281C2×C4×C71—81no—
282C2×C4×C71—81no—
283C2×C4×C71—81no—
284C2×C4×C71—81no—
285C2×C4×C71—81no—
286C2×C4×C71—81no—
287C2×C4×C71#11711yescharacteristic
288C2×C4×C71#11711yescharacteristic
289C2×C4×C71C4×D411yescharacteristic
290C2×C4×C71C4×D411yescharacteristic
291C2×C4×C71C4×D411yescharacteristic
292C2×C4×C71C4×D411yescharacteristic
293C2×C4×C71#12011yescharacteristic
294C2×C4×C71#12111yescharacteristic
295C2×C4×C71#12111yescharacteristic
296C2×C4×C71#12111yescharacteristic
297C2×C4×C71#12111yescharacteristic
298C2×C4×C71#12111yescharacteristic
299C2×C4×C71#12111yescharacteristic
300C2×C4×C71#12311yescharacteristic
301C2×C4×C71#12311yescharacteristic
302C2×C4×C71#12311yescharacteristic
303C2×C4×C71#12311yescharacteristic
304C2×C4×C71#12311yescharacteristic
305C2×C4×C71#12311yescharacteristic
306C2×C4×C71#12311yescharacteristic
307C2×C4×C71#12411yescharacteristic
308C2×C4×C71#12411yescharacteristic
309C2×C4×C71#12411yescharacteristic
310C2×C4×C71#12411yescharacteristic
311C2×C4×C71#12611yescharacteristic
312C2×C4×C71#12611yescharacteristic
313C2×C4×C71#12611yescharacteristic
314C2×C4×C71#12611yescharacteristic
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—41no—
319C2×Dic71—41no—
320C2×Dic71—41no—
321C2×Dic71—41no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71—42no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—81no—
329C2×Dic71—81no—
330C2×Dic71—81no—
331C2×Dic71—81no—
332C2×Dic71—81no—
333C2×Dic71—81no—
334C2×Dic71—81no—
335C2×Dic71—81no—
336C4×D71—42no—
337C4×D71—42no—
338C4×D71—42no—
339C4×D71—42no—
340C4×D71—42no—
341C4×D71—42no—
342C4×D71—42no—
343C4×D71—42no—
344C8×C71—42no—
345C71⋊C8—42no—
346C22×C71#38111yescharacteristic
347C22×C71#38611yescharacteristic
348C22×C71#38611yescharacteristic
349C22×C71#39411yescharacteristic
350C22×C71#39411yescharacteristic
351C22×C71#39711yescharacteristic
352C22×C71#39711yescharacteristic
353C22×C71C2×#10311yescharacteristic
354C22×C71#41611yescharacteristic
355C22×C71#41711yescharacteristic
356C22×C71#41811yescharacteristic
357C22×C71#44911yescharacteristic
358C22×C71#44911yescharacteristic
359C22×C71#45011yescharacteristic
360C22×C71#45111yescharacteristic
361C22×C71#46511yescharacteristic
362C22×C71#46511yescharacteristic
363C22×C71#46711yescharacteristic
364C22×C71#46711yescharacteristic
365C22×C71#46811yescharacteristic
366C22×C71#46811yescharacteristic
367C22×C71#46911yescharacteristic
368C22×C71#46911yescharacteristic
369C22×C71#48111yescharacteristic
370C22×C71#48111yescharacteristic
371C22×C71#48211yescharacteristic
372C22×C71#48211yescharacteristic
373C22×C71#48211yescharacteristic
374C22×C71#48211yescharacteristic
375C22×C71#48311yescharacteristic
376C22×C71#48411yescharacteristic
377C22×C71#48411yescharacteristic
378C22×C71#48411yescharacteristic
379C22×C71#48511yescharacteristic
380C22×C71#48511yescharacteristic
381C2×D71—24no—
382C2×D71—24no—
383C2×D71—24no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—42no—
388C2×D71—42no—
389C2×D71—42no—
390C2×D71—42no—
391C2×D71—42no—
392C2×D71—42no—
393C2×D71—42no—
394C2×D71—42no—
395C2×D71—42no—
396C4×C71—82no—
397C4×C71—82no—
398C4×C71#38811yescharacteristic
399C4×C71#38811yescharacteristic
400C4×C71#38811yescharacteristic
401C4×C71#38811yescharacteristic
402C4×C71#39411yescharacteristic
403C4×C71#39411yescharacteristic
404C4×C71#39711yescharacteristic
405C4×C71#39711yescharacteristic
406Dic71—42no—
407Dic71—82no—
408Dic71—82no—
409#11200—711nomaximal, Sylow
410C2×C71#144011yescharacteristic
411C2×C71#182411yescharacteristic
412C2×C71#182511yescharacteristic
413C2×C71#187211yescharacteristic
414C2×C71#187511yescharacteristic
415C2×C71#189211yescharacteristic
416C2×C71#189511yescharacteristic
417C2×C71#203411yescharacteristic
418C2×C71#203411yescharacteristic
419C2×C71#203611yescharacteristic
420C2×C71#203611yescharacteristic
421C2×C71#207611yescharacteristic
422C2×C71#207611yescharacteristic
423C2×C71#207711yescharacteristic
424C2×C71#207711yescharacteristic
425D71—44no—
426C22×C22⋊C8—711no—
427C2×#380—711no—
428C2×#380—711no—
429C2×#340—711no—
430C2×#340—711no—
431C2×#340—711no—
432C2×#340D7111yescharacteristic, complemented
433C71#1120011yescharacteristic, complemented, Sylow
434C24×C4—711no—
435C23×C8—711no—
436C23×C8C2×D7111yescharacteristic
437C22×C4⋊C4—711no—
438C22×C4⋊C4—711no—
439C22×C4⋊C4C2×D7111yescharacteristic
440C22×C4⋊C4C2×D7111yescharacteristic
441C22×C22⋊C4—1421no—
442C22×C22⋊C4—1421no—
443C2×C22⋊C8—1422no—
444C2×C22⋊C8—1422no—
445C2×C22⋊C8—1422no—
446#380—714no—
447#380—1422no—
448#380—1422no—
449#380—1422no—
450C2×#95—1421no—
451C2×#95—1421no—
452#340—22no—
453#340—1422no—
454#340—1422no—
455#340—1422no—
456C25—711no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4—711no—
460C23×C4—712no—
461C23×C4—712no—
462C23×C4—1421no—
463C23×C4—1421no—
464C23×C4—1421no—
465C23×C4—1421no—
466C23×C4—1421no—
467C23×C4—1421no—
468C23×C4—1421no—
469C23×C4—1421no—
470C23×C4—1421no—
471C23×C4—1421no—
472C23×C4—1421no—
473C23×C4—1421no—
474C23×C4—1421no—
475C23×C4—1421no—
476C23×C4C22×D7111yescharacteristic
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—712no—
484C22×C8—1421no—
485C22×C8—1421no—
486C22×C8—1421no—
487C22×C8—1421no—
488C22×C8—1421no—
489C22×C8—1421no—
490C22×C8D28412yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—712no—
502C2×C4⋊C4—712no—
503C2×C4⋊C4—1421no—
504C2×C4⋊C4—1421no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1421no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4C4×D7112yes—
514C2×C4⋊C4C22⋊D7112yes—
515C2×C22⋊C4—2842no—
516C2×C22⋊C4—2842no—
517C2×C22⋊C4—2842no—
518C2×C22⋊C4—2842no—
519C2×C22⋊C4—1424no—
520C2×C22⋊C4—1424no—
521C22⋊C8—1428no—
522#95—1424no—
523#95—1424no—
524C24—712no—
525C24—712no—
526C24—712no—
527C24—1421no—
528C24—1421no—
529C24—1421no—
530C24—1421no—
531C24—1421no—
532C24—1421no—
533C24—1421no—
534C24—1421no—
535C24—1421no—
536C24—1421no—
537C24—1421no—
538C24—1421no—
539C24D4×D7111yescharacteristic
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—2841no—
555C22×C4—2841no—
556C22×C4—2841no—
557C22×C4—2841no—
558C22×C4—2841no—
559C22×C4—2841no—
560C22×C4—2841no—
561C22×C4—2841no—
562C22×C4—2841no—
563C22×C4—2841no—
564C22×C4—2841no—
565C22×C4—2841no—
566C22×C4—2841no—
567C22×C4—2841no—
568C22×C4—2841no—
569C22×C4—2841no—
570C22×C4—2841no—
571C22×C4—2841no—
572C22×C4—2841no—
573C22×C4—2841no—
574C22×C4—2841no—
575C22×C4—2841no—
576C22×C4—2841no—
577C22×C4—2841no—
578C22×C4—2841no—
579C22×C4—2841no—
580C22×C4—2841no—
581C22×C4—2841no—
582C22×C4—712no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1421no—
586C22×C4—1421no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4—1422no—
599C22×C4—1422no—
600C22×C4—1422no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4C2×C4×D7111yescharacteristic
604C22×C4D4×D7111yescharacteristic
605C22×C4D4×D7111yescharacteristic
606C22×C4D4×D7111yescharacteristic
607C22×C4C2×C22⋊D7111yescharacteristic
608C22×C4C2×D28411yescharacteristic
609C22×C4#1176586411yescharacteristic
610C22×C4#1176586411yescharacteristic
611C22×C4#1176586511yescharacteristic
612C22×C4#1176586511yescharacteristic
613C22×C4#1176586511yescharacteristic
614C22×C4#1176586511yescharacteristic
615C22×C4#1176586611yescharacteristic
616C22×C4#1176586611yescharacteristic
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—2841no—
625C2×C8—2841no—
626C2×C8—2841no—
627C2×C8—2841no—
628C2×C8—1422no—
629C2×C8—1422no—
630C2×C8—1422no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—2841no—
640C4⋊C4—2841no—
641C4⋊C4—2841no—
642C4⋊C4—2841no—
643C4⋊C4—1422no—
644C4⋊C4—1422no—
645C4⋊C4—1422no—
646C4⋊C4—1422no—
647C22⋊C4—2848no—
648C22⋊C4—2848no—
649C23—2841no—
650C23—2841no—
651C23—2841no—
652C23—2841no—
653C23—2841no—
654C23—2841no—
655C23—2841no—
656C23—2841no—
657C23—2841no—
658C23—2841no—
659C23—2841no—
660C23—2841no—
661C23—2841no—
662C23—2841no—
663C23—2841no—
664C23—2841no—
665C23—714no—
666C23—1422no—
667C23—1422no—
668C23—1422no—
669C23—1422no—
670C23—1422no—
671C23—1422no—
672C23—1422no—
673C23—1422no—
674C23—1422no—
675C23—1422no—
676C23—1422no—
677C23—1422no—
678C23—1422no—
679C23—1422no—
680C23—1422no—
681C23—1422no—
682C23—1422no—
683C23—1422no—
684C23C22⋊C4×D7111yescharacteristic
685C23#1455609611yescharacteristic
686C23#1455610111yescharacteristic
687C23#1455610311yescharacteristic
688C23#1455611011yescharacteristic
689C23#1455611011yescharacteristic
690C23#1455611311yescharacteristic
691C23SD16×D7111yescharacteristic
692C23Q16×D7111yescharacteristic
693C23#1455614711yescharacteristic
694C23#1455614911yescharacteristic
695C23#1455615211yescharacteristic
696C23#1455615511yescharacteristic
697C23#1455615511yescharacteristic
698C23#1455616011yescharacteristic
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—2841no—
714C2×C4—2841no—
715C2×C4—2841no—
716C2×C4—2841no—
717C2×C4—2842no—
718C2×C4—2842no—
719C2×C4—2842no—
720C2×C4—2842no—
721C2×C4—2842no—
722C2×C4—2842no—
723C2×C4—2842no—
724C2×C4—2842no—
725C2×C4—2842no—
726C2×C4—2842no—
727C2×C4—2842no—
728C2×C4—2842no—
729C2×C4—2842no—
730C2×C4—2842no—
731C2×C4—5681no—
732C2×C4—5681no—
733C2×C4—5681no—
734C2×C4—5681no—
735C2×C4—5681no—
736C2×C4—5681no—
737C2×C4—5681no—
738C2×C4—5681no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4#1455608511yescharacteristic
743C2×C4#1455608611yescharacteristic
744C2×C4(C22⋊D71)⋊C411yescharacteristic
745C2×C4C4×C22⋊D7111yescharacteristic
746C2×C4#1455609011yescharacteristic
747C2×C4C4×D28411yescharacteristic
748C2×C4#1455609811yescharacteristic
749C2×C4#1455609911yescharacteristic
750C2×C4#1455610011yescharacteristic
751C2×C4#1455610111yescharacteristic
752C2×C4#1455610111yescharacteristic
753C2×C4#1455610211yescharacteristic
754C2×C4#1455610311yescharacteristic
755C2×C4#1455611011yescharacteristic
756C2×C4#1455611111yescharacteristic
757C2×C4#1455611211yescharacteristic
758C2×C4#1455611311yescharacteristic
759C2×C4#1455611311yescharacteristic
760C2×C4#1455611311yescharacteristic
761C2×C4#1455611311yescharacteristic
762C2×C4#1455611411yescharacteristic
763C2×C4#1455611411yescharacteristic
764C2×C4#1455611611yescharacteristic
765C2×C4#1455611711yescharacteristic
766C2×C4#1455612211yescharacteristic
767C2×C4#1455612311yescharacteristic
768C2×C4#1455612311yescharacteristic
769C2×C4#1455612311yescharacteristic
770C8—42no—
771C8—2842no—
772C22—2842no—
773C22—2842no—
774C22—2842no—
775C22—2842no—
776C22—2842no—
777C22—2842no—
778C22—2842no—
779C22—2842no—
780C22—2842no—
781C22—2842no—
782C22—2842no—
783C22—2842no—
784C22—1424no—
785C22—1424no—
786C22—1424no—
787C22#1798586111yescharacteristic
788C22#1798587511yescharacteristic
789C22#1798587711yescharacteristic
790C22#1798591411yescharacteristic
791C22#1798591611yescharacteristic
792C22#1798592611yescharacteristic
793C22#1798592811yescharacteristic
794C22#103×D7111yescharacteristic
795C22#1798599211yescharacteristic
796C22#1798599911yescharacteristic
797C22#1798600211yescharacteristic
798C22#1798614111yescharacteristic
799C22#1798614311yescharacteristic
800C22#1798614811yescharacteristic
801C22#1798615311yescharacteristic
802C22#1798622711yescharacteristic
803C22#1798622911yescharacteristic
804C22#1798623911yescharacteristic
805C22#1798624111yescharacteristic
806C22#1798624611yescharacteristic
807C22#1798624811yescharacteristic
808C22#1798625111yescharacteristic
809C22#1798625311yescharacteristic
810C22#1798631611yescharacteristic
811C22#1798631911yescharacteristic
812C22#1798632111yescharacteristic
813C22#1798632111yescharacteristic
814C22#1798632211yescharacteristic
815C22#1798632511yescharacteristic
816C22#1798632811yescharacteristic
817C22#1798633311yescharacteristic
818C22#1798633311yescharacteristic
819C22#1798633611yescharacteristic
820C22#1798633811yescharacteristic
821C22#1798634211yescharacteristic
822C4—82no—
823C4—82no—
824C4—2842no—
825C4—5682no—
826C4—5682no—
827C4#1798588811yescharacteristic
828C4#1798588911yescharacteristic
829C4#1798589011yescharacteristic
830C4#1798589111yescharacteristic
831C4#1798591511yescharacteristic
832C4#1798591711yescharacteristic
833C4#1798592511yescharacteristic
834C4#1798592811yescharacteristic
835C2—2844no—
836C2#2258658811yescharacteristic
837C2#2258842911yescharacteristic
838C2#2258843311yescharacteristic
839C2#2258864411yescharacteristic
840C2#2258865911yescharacteristic
841C2#2258876211yescharacteristic
842C2#2258877711yescharacteristic
843C2#2258952711yescharacteristic
844C2#2258953111yescharacteristic
845C2#2258954111yescharacteristic
846C2#2258954511yescharacteristic
847C2#2258977011yescharacteristic
848C2#2258977211yescharacteristic
849C2#2258977511yescharacteristic
850C2#2258977811yescharacteristic
subgroupG/H
centerC24D4×D71
commutatorC22×C4×C71C22×C4
FrattiniC23×C4C22×D71
FittingC2×#340×C71C2
socleC24×C71C2×D4
prime radicalC24×D71D4
cosocleC23×C4×C71C23
hypercenterC2×#340D71
hypocenterC71#11200
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#17985762C2semidirect
5. C2×#17985761C2semidirect
6. C2×#17985761C2semidirect
7. C2×#340×C71C2semidirect
20. #17985856C4semidirect
432. C2×#340D71semidirect
433. C71#11200semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D71)⋊C82
C2×#179858562
C2×#179857622
C2×#179857612
C2×#340×C712
#1120071