Finite Group Databasebeta

← #13277702

Subgroups — #13277702

Order 1792.

1426 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89745C211yesmaximal, characteristic
2C2×#89753C211yesmaximal, characteristic
3C2×#89419C211yesmaximal, characteristic
4C2×#89424C211yesmaximal, characteristic
5C2×#89421C211yesmaximal, characteristic
6C7×#1445C211yesmaximal, characteristic
7#11727165C211yesmaximal, characteristic
8#11727163C211yesmaximal, characteristic
9#11727163C211yesmaximal, characteristic
10#11727161C211yesmaximal, characteristic
11#11727161C211yesmaximal, characteristic
12#11727159C211yesmaximal, characteristic
13#11727157C211yesmaximal, characteristic
14#11727156C211yesmaximal, characteristic
15Dic7×#95C211yesmaximal, characteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C4⋊Dic7C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
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
51#89753—24no—
52#89745C418yescomplemented
53#89424—24no—
54#89421—24no—
55#89419—24no—
56#14060—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⋊Dic7—22no—
80C2×C4⋊Dic7C2×C414yes—
81C2×Dic7⋊C4—22no—
82C2×Dic7⋊C4—22no—
83C2×Dic7⋊C4—22no—
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⋊C4C2×C414yes—
94C2×Dic7⋊C4C2×C414yes—
95C2×Dic7⋊C4D414yes—
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—22no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—41no—
108C2×C4×Dic7—41no—
109C2×C4×Dic7—41no—
110C2×C4×Dic7C2×C414yes—
111C7×#95—22no—
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—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95C2×C414yes—
130C7⋊#95C2×C414yes—
131C7⋊#95D414yes—
132C7⋊#95Q814yes—
133C2×#389—71no—
134C2×#389—71no—
135C2×#387—71no—
136C2×#387—71no—
137C2×C4×C4⋊C4—71no—
138#1445D711yescharacteristic
139#1441—71no—
140#1441—71no—
141#1441—71no—
142#1436—71no—
143#1436—71no—
144#1436—71no—
145#1434—71no—
146#1434—71no—
147C4×#95—71no—
148C24×C7C2411yescharacteristic
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×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7C22×C412yes—
191C22×C4×C7C22×C412yes—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2×D412yes—
195C22×C4×C7C2×Q812yes—
196C22×C4×C7#4112yes—
197C22×C4×C7#4112yes—
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×Dic7C22×C412yes—
240C22×Dic7C22×C412yes—
241C22×Dic7C22×C412yes—
242C22×Dic7C22×C412yes—
243C22×Dic7C2×D412yes—
244C22×Dic7C2×D412yes—
245C22×Dic7C2×D412yes—
246C22×Dic7C2×D412yes—
247C22×Dic7C2×Q812yes—
248C22×Dic7C2×Q812yes—
249C22×Dic7#4112yes—
250C22×Dic7#4112yes—
251C22×Dic7#4112yes—
252C22×Dic7#4112yes—
253C22×Dic7#4112yes—
254C7×C4⋊C4—28no—
255C4⋊Dic7—28no—
256C4⋊Dic7—44no—
257Dic7⋊C4—28no—
258Dic7⋊C4—28no—
259Dic7⋊C4—28no—
260Dic7⋊C4—28no—
261Dic7⋊C4—44no—
262C4×Dic7—28no—
263C4×Dic7—44no—
264C4×Dic7—44no—
265C4×Dic7—44no—
266C4×Dic7—44no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4—71no—
273C22×C4⋊C4—71no—
274C22×C4⋊C4C2×D711yescharacteristic
275C22×C42—71no—
276C22×C42—71no—
277C22×C42—71no—
278C22×C42—71no—
279C22×C42—71no—
280#389—78no—
281#389—144no—
282#387—144no—
283#387—144no—
284C4×C4⋊C4—144no—
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×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95C2×D711yescharacteristic
302C2×#95C2×D711yescharacteristic
303C2×#95C2×D711yescharacteristic
304C2×#95C2×D711yescharacteristic
305C2×#95C2×D711yescharacteristic
306C2×#95C2×D711yescharacteristic
307C23×C7C23×C411yescharacteristic
308C23×C7C22×D411yescharacteristic
309C23×C7C22×D411yescharacteristic
310C23×C7C22×Q811yescharacteristic
311C23×C7C2×#4111yescharacteristic
312C23×C7C2×#4111yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7H(5,𝔽2)11yescharacteristic
319C23×C72−1+411yescharacteristic
320C23×C72−1+411yescharacteristic
321C23×C72−1+411yescharacteristic
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—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
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×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7C4×D414yes—
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—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
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×Dic7—41no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7#11714yes—
424C2×Dic7C4×D414yes—
425C2×Dic7C4×Q814yes—
426C2×Dic7#12114yes—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4C22×D711yescharacteristic
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439C23×C4C22×D711yescharacteristic
440C23×C4C22×D711yescharacteristic
441C23×C4C22×D711yescharacteristic
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—74no—
445C2×C4⋊C4—74no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—74no—
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—142no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—142no—
463C2×C4⋊C4—142no—
464C2×C4⋊C4—281no—
465C2×C4⋊C4C4×D714yes—
466C2×C42—74no—
467C2×C42—142no—
468C2×C42—142no—
469C2×C42—142no—
470C2×C42—142no—
471C2×C42—142no—
472C2×C42—142no—
473C2×C42—142no—
474C2×C42—142no—
475C2×C42—142no—
476C2×C42—142no—
477C2×C42—142no—
478C2×C42—281no—
479C2×C42—281no—
480C2×C42—281no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—74no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—142no—
492#95—142no—
493#95—142no—
494#95—142no—
495#95—142no—
496#95—142no—
497#95—142no—
498#95—142no—
499#95—142no—
500#95—142no—
501#95—281no—
502#95—281no—
503C22×C7C2×#11711yescharacteristic
504C22×C7C2×C4×D411yescharacteristic
505C22×C7C2×C4×D411yescharacteristic
506C22×C7C2×C4×Q811yescharacteristic
507C22×C7C4×#4111yescharacteristic
508C22×C7#51911yescharacteristic
509C22×C7#52011yescharacteristic
510C22×C7C2×#12111yescharacteristic
511C22×C7#52511yescharacteristic
512C22×C7#52911yescharacteristic
513C22×C7#52911yescharacteristic
514C22×C7#52911yescharacteristic
515C22×C7#53211yescharacteristic
516C22×C7#53311yescharacteristic
517C22×C7#53311yescharacteristic
518C22×C7#53911yescharacteristic
519C22×C7#53911yescharacteristic
520C22×C7#54111yescharacteristic
521C22×C7#54111yescharacteristic
522C22×C7#54611yescharacteristic
523C22×C7#54611yescharacteristic
524C22×C7#54711yescharacteristic
525C22×C7#54711yescharacteristic
526C22×C7#54711yescharacteristic
527C22×C7#54811yescharacteristic
528C22×C7D4×Q811yescharacteristic
529C22×C7D4×Q811yescharacteristic
530C22×C7#55211yescharacteristic
531C22×C7#55211yescharacteristic
532C22×C7#55211yescharacteristic
533C22×C7#55211yescharacteristic
534C22×C7#55311yescharacteristic
535C22×C7#55411yescharacteristic
536C22×C7#55611yescharacteristic
537C22×C7#55711yescharacteristic
538C4×C7—24no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7—42no—
544C4×C7—81no—
545Dic7—24no—
546Dic7—24no—
547Dic7—24no—
548Dic7—24no—
549Dic7—42no—
550Dic7—42no—
551Dic7—42no—
552Dic7—81no—
553C24C23×D711yescharacteristic
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—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—72no—
596C22×C4—72no—
597C22×C4—72no—
598C22×C4—72no—
599C22×C4—72no—
600C22×C4—72no—
601C22×C4—72no—
602C22×C4—72no—
603C22×C4—72no—
604C22×C4—72no—
605C22×C4—72no—
606C22×C4—72no—
607C22×C4—72no—
608C22×C4—72no—
609C22×C4—72no—
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×C4—141no—
645C22×C4—141no—
646C22×C4—141no—
647C22×C4—141no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4C2×C4×D712yes—
652C22×C4C2×C4×D712yes—
653C22×C4C2×C4×D712yes—
654C22×C4D4×D712yes—
655C22×C4D4×D712yes—
656C22×C4#115912yes—
657C22×C4#115912yes—
658C22×C4Q8×D712yes—
659C4⋊C4—28no—
660C4⋊C4—148no—
661C4⋊C4—148no—
662C4⋊C4—148no—
663C4⋊C4—148no—
664C4⋊C4—148no—
665C4⋊C4—284no—
666C4⋊C4—284no—
667C42—148no—
668C42—284no—
669C42—284no—
670C42—284no—
671C42—284no—
672C2×C7#229511yescharacteristic
673C2×C7C4×#12111yescharacteristic
674C2×C7#233611yescharacteristic
675C2×C7#234411yescharacteristic
676C2×C7#235211yescharacteristic
677C2×C7#236011yescharacteristic
678C2×C7#236511yescharacteristic
679C2×C7#242511yescharacteristic
680C2×C7#242911yescharacteristic
681C2×C7#246211yescharacteristic
682C2×C7#246611yescharacteristic
683C2×C7#251911yescharacteristic
684C2×C7#253311yescharacteristic
685C2×C7#255611yescharacteristic
686C2×C7#259011yescharacteristic
687C23C22×C4×D711yescharacteristic
688C23C2×D4×D711yescharacteristic
689C23C2×D4×D711yescharacteristic
690C23C2×#115911yescharacteristic
691C23C2×#115911yescharacteristic
692C23C2×Q8×D711yescharacteristic
693C23#655111yescharacteristic
694C23D7×#4111yescharacteristic
695C23D7×#4111yescharacteristic
696C23D7×#4111yescharacteristic
697C23D7×#4111yescharacteristic
698C23D7×#4111yescharacteristic
699C23#655311yescharacteristic
700C23#655411yescharacteristic
701C23#655411yescharacteristic
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—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
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—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—74no—
751C2×C4—74no—
752C2×C4—74no—
753C2×C4—74no—
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—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—142no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
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×C4—281no—
797C2×C4—281no—
798C2×C4—281no—
799C2×C4—281no—
800C2×C4—281no—
801C2×C4—281no—
802C2×C4—281no—
803C2×C4—281no—
804C2×C4—281no—
805C2×C4—281no—
806C2×C4(C22⋊D7)⋊C414yes—
807C7#1406011yescharacteristic, complemented, Sylow
808C22C2×(C22⋊D7)⋊C411yescharacteristic
809C22#9020711yescharacteristic
810C22D7×#11711yescharacteristic
811C22C4×#115911yescharacteristic
812C22C4×D4×D711yescharacteristic
813C22C4×Q8×D711yescharacteristic
814C22#9026511yescharacteristic
815C22D7×#12111yescharacteristic
816C22#9029711yescharacteristic
817C22#9031311yescharacteristic
818C22#9031611yescharacteristic
819C22#9032311yescharacteristic
820C22#9032411yescharacteristic
821C22#9032611yescharacteristic
822C22#9033011yescharacteristic
823C22#9034011yescharacteristic
824C22#9034111yescharacteristic
825C22#9034111yescharacteristic
826C22#9034511yescharacteristic
827C22#9034611yescharacteristic
828C22#9034611yescharacteristic
829C22#9034611yescharacteristic
830C22#9035611yescharacteristic
831C22#9036711yescharacteristic
832C22#9037111yescharacteristic
833C22#9037611yescharacteristic
834C22#9037911yescharacteristic
835C22#9038411yescharacteristic
836C22#9038711yescharacteristic
837C22#9039311yescharacteristic
838C22#9039711yescharacteristic
839C22#9039811yescharacteristic
840C22#9040011yescharacteristic
841C22#9040711yescharacteristic
842C22#9041811yescharacteristic
843C4—24no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—81no—
850C4—144no—
851C4—144no—
852C4—144no—
853C4—144no—
854C4—282no—
855C4—282no—
856C4—282no—
857C4—561no—
858C2#1173150511yescharacteristic
859C2#1173238311yescharacteristic
860C2#1173240411yescharacteristic
861C2#1173241211yescharacteristic
862C2#1173275011yescharacteristic
863C2#1173373611yescharacteristic
864C2#1173406011yescharacteristic
865C2#1173491611yescharacteristic
866C2#1173511711yescharacteristic
867C2#1173518911yescharacteristic
868C2#1173519611yescharacteristic
869C2#1173547811yescharacteristic
870C2#1173548411yescharacteristic
871C2#1173562011yescharacteristic
872C2#1173564211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1445C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1445D7
hypocenterC7#14060
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
52. #89745C4semidirect
807. C7#14060semidirect

Maximal subgroups

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

subgroupindex
C2×#897452
C2×#897532
C2×#894192
C2×#894242
C2×#894212
C7×#14452
#117271652
#117271632
#117271612
#117271592
#117271572
#117271562
Dic7×#952
#140607