Finite Group Databasebeta

← #13282588

Subgroups — #13282588

Order 1792.

1398 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6453C211yesmaximal, characteristic
2C2×#89426C211yesmaximal, characteristic
3C2×#89425C211yesmaximal, characteristic
4C7×#1445C211yesmaximal, characteristic
5#11729323C211yesmaximal, characteristic
6#11727175C211yesmaximal, characteristic
7#11727175C211yesmaximal, characteristic
8#11727165C211yesmaximal, characteristic
9#11727165C211yesmaximal, characteristic
10#11727161C211yesmaximal, characteristic
11#11727161C211yesmaximal, characteristic
12Dic7⋊#95C211yesmaximal, characteristic
13Dic7⋊#95C211yesmaximal, characteristic
14#11727156C211yesmaximal, characteristic
15#11727156C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C4⋊Dic7C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C2×#6453—24no—
28C2×#6453—24no—
29C2×#6453C418yescomplemented
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89426—24no—
55#89425—24no—
56#14474—71nomaximal, Sylow
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4C2×C414yes—
75C2×C4⋊Dic7—22no—
76C2×C4⋊Dic7—22no—
77C2×C4⋊Dic7—22no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7C2×C414yes—
80C2×C4⋊Dic7C2×C414yes—
81C2×C4⋊Dic7C2×C414yes—
82C2×C4⋊Dic7D414yes—
83C2×C4⋊Dic7D414yes—
84C2×Dic7⋊C4—22no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4—22no—
88C2×Dic7⋊C4—22no—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—41no—
93C2×Dic7⋊C4—41no—
94C2×Dic7⋊C4C2×C414yes—
95C2×Dic7⋊C4C2×C414yes—
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—22no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—41no—
103C2×C4×Dic7—41no—
104C2×C4×Dic7C2×C414yes—
105#6453—232no—
106C7×#95—22no—
107C7×#95—22no—
108C7×#95—22no—
109C7×#95—22no—
110C7×#95—41no—
111C7×#95—41no—
112C7⋊#95—22no—
113C7⋊#95—22no—
114C7⋊#95—22no—
115C7⋊#95—22no—
116C7⋊#95—22no—
117C7⋊#95—22no—
118C7⋊#95—22no—
119C7⋊#95—22no—
120C7⋊#95—22no—
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—41no—
125C7⋊#95—41no—
126C7⋊#95—41no—
127C7⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C22×#125—71no—
131C2×#387—71no—
132C2×#387—71no—
133#1445—71no—
134#1445—71no—
135#1445—71no—
136#1445D711yescharacteristic
137#1441—71no—
138#1441—71no—
139#1436—71no—
140#1436—71no—
141C4⋊#95—71no—
142C4⋊#95—71no—
143#1434—71no—
144#1434—71no—
145C24×C7C2411yescharacteristic
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7C22×C412yes—
189C22×C4×C7C22×C412yes—
190C22×C4×C7C22×C412yes—
191C22×C4×C7C2×D412yes—
192C22×C4×C7C2×D412yes—
193C22×C4×C7#4112yes—
194C22×C4×C7#4112yes—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7C22×C412yes—
242C22×Dic7C22×C412yes—
243C22×Dic7C22×C412yes—
244C22×Dic7C22×C412yes—
245C22×Dic7C2×D412yes—
246C22×Dic7C2×D412yes—
247C22×Dic7C2×D412yes—
248C22×Dic7C2×D412yes—
249C22×Dic7#4112yes—
250C22×Dic7#4112yes—
251C7×C4⋊C4—28no—
252C4⋊Dic7—28no—
253C4⋊Dic7—28no—
254C4⋊Dic7C22⋊C4116yes—
255Dic7⋊C4—28no—
256Dic7⋊C4—28no—
257Dic7⋊C4—44no—
258Dic7⋊C4—44no—
259C4×Dic7—28no—
260C4×Dic7—44no—
261C4×Dic7—44no—
262C2×#125—78no—
263C2×#125—144no—
264C2×#125—144no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4C2×D711yescharacteristic
273C22×C42—71no—
274C22×C42—71no—
275C22×C42—71no—
276#387—144no—
277#387—144no—
278C2×#95—71no—
279C2×#95—71no—
280C2×#95—71no—
281C2×#95—71no—
282C2×#95—71no—
283C2×#95—71no—
284C2×#95—71no—
285C2×#95—71no—
286C2×#95—71no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95C2×D711yescharacteristic
297C2×#95C2×D711yescharacteristic
298C2×#95C2×D711yescharacteristic
299C2×#95C2×D711yescharacteristic
300C2×#95C2×D711yescharacteristic
301C2×#95C2×D711yescharacteristic
302C23×C7C23×C411yescharacteristic
303C23×C7C22×D411yescharacteristic
304C23×C7C22×D411yescharacteristic
305C23×C7C2×#4111yescharacteristic
306C23×C7C2×#4111yescharacteristic
307C23×C7C2×#4111yescharacteristic
308C23×C7C2×#4111yescharacteristic
309C23×C7H(5,𝔽2)11yescharacteristic
310C23×C7H(5,𝔽2)11yescharacteristic
311C23×C72−1+411yescharacteristic
312C23×C72−1+411yescharacteristic
313C23×C72−1+411yescharacteristic
314C23×C72−1+411yescharacteristic
315C23×C72−1+411yescharacteristic
316C23×C72−1+411yescharacteristic
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7C2×C22⋊C414yes—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—41no—
391C2×Dic7—41no—
392C2×Dic7—41no—
393C2×Dic7—41no—
394C2×Dic7—41no—
395C2×Dic7—41no—
396C2×Dic7—41no—
397C2×Dic7—41no—
398C2×Dic7—41no—
399C2×Dic7—41no—
400C2×Dic7—41no—
401C2×Dic7—41no—
402C2×Dic7—41no—
403C2×Dic7—41no—
404C2×Dic7—41no—
405C2×Dic7—41no—
406C2×Dic7—41no—
407C2×Dic7—41no—
408C2×Dic7—41no—
409C2×Dic7—41no—
410C2×Dic7—41no—
411C2×Dic7—41no—
412C2×Dic7—41no—
413C2×Dic7—41no—
414C2×Dic7—41no—
415C2×Dic7—41no—
416C2×Dic7—41no—
417C2×Dic7—41no—
418C2×Dic7—41no—
419C2×Dic7—41no—
420C2×Dic7C2×C22⋊C414yes—
421C2×Dic7C2×C22⋊C414yes—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4C22×D711yescharacteristic
431C23×C4C22×D711yescharacteristic
432C23×C4C22×D711yescharacteristic
433C23×C4C22×D711yescharacteristic
434C23×C4C22×D711yescharacteristic
435C23×C4C22×D711yescharacteristic
436C23×C4C22×D711yescharacteristic
437#125—1432no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—74no—
441C2×C4⋊C4—74no—
442C2×C4⋊C4—74no—
443C2×C4⋊C4—74no—
444C2×C4⋊C4—74no—
445C2×C4⋊C4—74no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—142no—
448C2×C4⋊C4—142no—
449C2×C4⋊C4—142no—
450C2×C4⋊C4—142no—
451C2×C4⋊C4—142no—
452C2×C4⋊C4—142no—
453C2×C4⋊C4—142no—
454C2×C4⋊C4—142no—
455C2×C4⋊C4—142no—
456C2×C4⋊C4—142no—
457C2×C4⋊C4—142no—
458C2×C4⋊C4—142no—
459C2×C4⋊C4—281no—
460C2×C4⋊C4—281no—
461C2×C4⋊C4C4×D714yes—
462C2×C42—74no—
463C2×C42—142no—
464C2×C42—142no—
465C2×C42—142no—
466C2×C42—142no—
467C2×C42—142no—
468C2×C42—142no—
469C2×C42—281no—
470C2×C42—281no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—41no—
476#95—41no—
477#95—142no—
478#95—142no—
479#95—142no—
480#95—142no—
481#95—142no—
482#95—142no—
483#95—142no—
484#95—142no—
485#95—142no—
486#95—142no—
487#95—142no—
488#95—142no—
489#95—281no—
490#95—281no—
491#95—281no—
492#95—281no—
493#95—281no—
494#95—281no—
495C22×C7C22×C22⋊C411yescharacteristic
496C22×C7C4×#4111yescharacteristic
497C22×C7C4×#4111yescharacteristic
498C22×C7#51911yescharacteristic
499C22×C7#51911yescharacteristic
500C22×C7#52011yescharacteristic
501C22×C7#52011yescharacteristic
502C22×C7#53611yescharacteristic
503C22×C7#53611yescharacteristic
504C22×C7#53611yescharacteristic
505C22×C7#53611yescharacteristic
506C22×C7#53911yescharacteristic
507C22×C7#53911yescharacteristic
508C22×C7#53911yescharacteristic
509C22×C7#53911yescharacteristic
510C22×C7#54111yescharacteristic
511C22×C7#54111yescharacteristic
512C22×C7#54111yescharacteristic
513C22×C7#54111yescharacteristic
514C22×C7#54611yescharacteristic
515C22×C7#54611yescharacteristic
516C22×C7#54711yescharacteristic
517C22×C7#54711yescharacteristic
518C22×C7#54811yescharacteristic
519C22×C7#54811yescharacteristic
520C22×C7#55011yescharacteristic
521C22×C7#55011yescharacteristic
522C22×C7#55211yescharacteristic
523C22×C7#55211yescharacteristic
524C22×C7#55211yescharacteristic
525C22×C7#55211yescharacteristic
526C22×C7#56211yescharacteristic
527C22×C7#56311yescharacteristic
528C22×C7#56311yescharacteristic
529C22×C7#56411yescharacteristic
530C4×C7—24no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—81no—
536C4×C7—81no—
537Dic7—24no—
538Dic7—24no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543Dic7—81no—
544Dic7—81no—
545C24C23×D711yescharacteristic
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—72no—
594C22×C4—72no—
595C22×C4—72no—
596C22×C4—72no—
597C22×C4—72no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—141no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—141no—
615C22×C4—141no—
616C22×C4—141no—
617C22×C4—141no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—141no—
625C22×C4—141no—
626C22×C4—141no—
627C22×C4—141no—
628C22×C4—141no—
629C22×C4—141no—
630C22×C4—141no—
631C22×C4—141no—
632C22×C4—141no—
633C22×C4—141no—
634C22×C4—141no—
635C22×C4—141no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—141no—
642C22×C4—141no—
643C22×C4—141no—
644C22×C4C2×C4×D712yes—
645C22×C4C2×C4×D712yes—
646C22×C4C2×C4×D712yes—
647C22×C4D4×D712yes—
648C22×C4D4×D712yes—
649C22×C4#115912yes—
650C22×C4#116112yes—
651C4⋊C4—28no—
652C4⋊C4—716no—
653C4⋊C4—148no—
654C4⋊C4—148no—
655C4⋊C4—148no—
656C4⋊C4—148no—
657C4⋊C4—284no—
658C4⋊C4—284no—
659C42—148no—
660C42—284no—
661C42—284no—
662C2×C7#231011yescharacteristic
663C2×C7#233611yescharacteristic
664C2×C7#233611yescharacteristic
665C2×C7#233911yescharacteristic
666C2×C7#234111yescharacteristic
667C2×C7#237111yescharacteristic
668C2×C7#238211yescharacteristic
669C2×C7#269011yescharacteristic
670C2×C7#269011yescharacteristic
671C2×C7#269411yescharacteristic
672C2×C7#269411yescharacteristic
673C2×C7#271911yescharacteristic
674C2×C7#271911yescharacteristic
675C2×C7#272111yescharacteristic
676C2×C7#272111yescharacteristic
677C23C22×C4×D711yescharacteristic
678C23C2×D4×D711yescharacteristic
679C23C2×D4×D711yescharacteristic
680C23C2×#115911yescharacteristic
681C23#654811yescharacteristic
682C23C2×#116111yescharacteristic
683C23#655111yescharacteristic
684C23D7×#4111yescharacteristic
685C23D7×#4111yescharacteristic
686C23#655311yescharacteristic
687C23#655411yescharacteristic
688C23#655411yescharacteristic
689C23#655411yescharacteristic
690C23#655411yescharacteristic
691C23#655411yescharacteristic
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—74no—
741C2×C4—74no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—142no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—281no—
767C2×C4—281no—
768C2×C4—281no—
769C2×C4—281no—
770C2×C4—281no—
771C2×C4—281no—
772C2×C4—281no—
773C2×C4—281no—
774C2×C4—281no—
775C2×C4—281no—
776C2×C4—281no—
777C2×C4—281no—
778C2×C4—281no—
779C2×C4—281no—
780C2×C4—281no—
781C2×C4—281no—
782C2×C4—281no—
783C2×C4—281no—
784C2×C4—281no—
785C2×C4—281no—
786C2×C4—281no—
787C2×C4—281no—
788C2×C4—281no—
789C2×C4—281no—
790C2×C4—281no—
791C2×C4—281no—
792C2×C4—281no—
793C2×C4—281no—
794C2×C4—281no—
795C2×C4—281no—
796C2×C4D7×C22⋊C414yes—
797C7#1447411yescharacteristic, complemented, Sylow
798C22C2×D7×C22⋊C411yescharacteristic
799C22#9020711yescharacteristic
800C22#9020711yescharacteristic
801C22C4×#115911yescharacteristic
802C22#9023711yescharacteristic
803C22C4×#116111yescharacteristic
804C22#9026511yescharacteristic
805C22#9028911yescharacteristic
806C22#9029011yescharacteristic
807C22#9031611yescharacteristic
808C22#9032111yescharacteristic
809C22#9032211yescharacteristic
810C22#9033311yescharacteristic
811C22#9033611yescharacteristic
812C22#9033711yescharacteristic
813C22#9033911yescharacteristic
814C22#9033911yescharacteristic
815C22#9033911yescharacteristic
816C22#9033911yescharacteristic
817C22#9034111yescharacteristic
818C22#9035111yescharacteristic
819C22#9035611yescharacteristic
820C22#9035811yescharacteristic
821C22#9036711yescharacteristic
822C22#9036811yescharacteristic
823C22C7⋊#56411yescharacteristic
824C22#9038511yescharacteristic
825C22#9038711yescharacteristic
826C22#9038811yescharacteristic
827C22#9039211yescharacteristic
828C22#9039811yescharacteristic
829C22#9039911yescharacteristic
830C22#9040311yescharacteristic
831C22#9040911yescharacteristic
832C22#9041711yescharacteristic
833C4—24no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—81no—
839C4—81no—
840C4—144no—
841C4—144no—
842C4—282no—
843C4—282no—
844C4—282no—
845C4—282no—
846C4—561no—
847C4—561no—
848C2#1173149811yescharacteristic
849C2#1173240411yescharacteristic
850C2#1173240511yescharacteristic
851C2#1173241611yescharacteristic
852C2#1173242311yescharacteristic
853C2#1173374611yescharacteristic
854C2#1173405811yescharacteristic
855C2#1173501811yescharacteristic
856C2#1173502011yescharacteristic
857C2#1173530511yescharacteristic
858C2#1173530711yescharacteristic
859C2#1173550911yescharacteristic
860C2#1173551511yescharacteristic
861C2#1173568211yescharacteristic
862C2#1173569211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1445C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1445D7
hypocenterC7#14474
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
29. C2×#6453C4semidirect
797. C7#14474semidirect

Maximal subgroups

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

subgroupindex
C22×#64532
C2×#894262
C2×#894252
C7×#14452
#117293232
#117271752
#117271652
#117271612
Dic7⋊#952
#117271562
#144747