Finite Group Databasebeta

← #13285117

Subgroups — #13285117

Order 1792.

2430 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D7C211yesmaximal, characteristic
2C2×#89761C211yesmaximal, characteristic
3C2×#89440C211yesmaximal, characteristic
4C2×#89436C211yesmaximal, characteristic
5C2×#89436C211yesmaximal, characteristic
6C7×#1436C211yesmaximal, characteristic, complemented
7#11729318C211yesmaximal, characteristic, complemented
8#11729290C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727161C211yesmaximal, characteristic, complemented
12#11727161C211yesmaximal, characteristic, complemented
13#11727160C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727159C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×C42×D7—24no—
32C2×C42×D7—24no—
33C2×C42×D7—24no—
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#89761—24no—
55#89440—24no—
56#89436—24no—
57#89436C418yescomplemented
58#14705—71nomaximal, Sylow
59C24×D7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7—22no—
78C22×C4×D7—22no—
79C22×C4×D7—22no—
80C22×C4×D7—22no—
81C22×C4×D7—22no—
82C22×C4×D7—22no—
83C22×C4×D7—22no—
84C22×C4×D7—22no—
85C22×C4×D7—22no—
86C22×C4×D7—22no—
87C22×C4×D7—22no—
88C22×C4×D7—22no—
89C22×C4×D7—22no—
90C22×C4×D7C2×C414yes—
91C22×C4×D7D414yes—
92C22×C4×D7D414yes—
93C22×C4×D7D414yes—
94C22×C4×D7Q814yes—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C42×C7—22no—
99C2×C42×C7—22no—
100C2×C42×C7—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—22no—
105C2×(C2×D7)⋊C4—22no—
106C2×(C2×D7)⋊C4—22no—
107C2×(C2×D7)⋊C4—22no—
108C2×(C2×D7)⋊C4—22no—
109C2×(C2×D7)⋊C4—22no—
110C2×(C2×D7)⋊C4—22no—
111C2×(C2×D7)⋊C4C2×C414yes—
112C2×(C2×D7)⋊C4C2×C414yes—
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—22no—
128C2×C4×Dic7—22no—
129C2×C4×Dic7—22no—
130C2×C4×Dic7—22no—
131C42×D7—232no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95C2×C414yescomplemented
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—22no—
146C7⋊#95—22no—
147C7⋊#95—22no—
148C7⋊#95—22no—
149C7⋊#95C2×C414yescomplemented
150C7⋊#95C2×C414yescomplemented
151C7⋊#95C2×C414yescomplemented
152C23×C42—71no—
153C2×#385—71no—
154C2×#385—71no—
155C2×#381—71no—
156C2×#381—71no—
157#1436—71no—
158#1436—71no—
159#1436—71no—
160#1436—71no—
161#1436—71no—
162#1436—71no—
163#1436—71no—
164#1436D711yescharacteristic, complemented
165C22⋊#95—71no—
166C22⋊#95—71no—
167C24×C7C2411yescharacteristic
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7—21no—
175C23×D7—21no—
176C23×D7C22×C412yes—
177C23×D7C2×D412yes—
178C23×D7C2×D412yes—
179C23×D7C2×D412yes—
180C23×D7C2×Q812yes—
181C23×D7#4112yes—
182C23×D7#4112yes—
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×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7C22×C412yes—
222C22×C4×C7C22×C412yes—
223C22×C4×C7C22×C412yes—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×Q812yes—
228C22×C4×C7#4112yes—
229C22×C4×C7#4112yes—
230C22×C4×C7#4112yes—
231C22×C4×C7#4112yes—
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×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C2×D412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7C2×D412yes—
276C22×Dic7C2×Q812yes—
277C22×Dic7#4112yes—
278C22×Dic7#4112yes—
279C22×Dic7#4112yes—
280C22×Dic7#4112yes—
281C2×C4×D7—28no—
282C2×C4×D7—28no—
283C2×C4×D7—28no—
284C2×C4×D7—28no—
285C2×C4×D7—28no—
286C2×C4×D7—28no—
287C2×C4×D7—28no—
288C2×C4×D7—28no—
289C2×C4×D7—28no—
290C2×C4×D7—28no—
291C2×C4×D7—28no—
292C2×C4×D7—28no—
293C2×C4×D7—28no—
294C2×C4×D7—28no—
295C2×C4×D7—28no—
296C2×C4×D7—28no—
297C2×C4×D7—28no—
298C2×C4×D7—28no—
299C2×C4×D7—28no—
300C2×C4×D7—28no—
301C2×C4×D7C4⋊C4116yescomplemented
302C7×C4⋊C4—44no—
303C42×C7—28no—
304(C2×D7)⋊C4—28no—
305(C2×D7)⋊C4—28no—
306(C2×D7)⋊C4—44no—
307(C2×D7)⋊C4—44no—
308C4⋊Dic7—44no—
309Dic7⋊C4—44no—
310Dic7⋊C4—44no—
311C4×Dic7—28no—
312C4×Dic7—28no—
313C4×Dic7—28no—
314C24×C4—71no—
315C24×C4—71no—
316C24×C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4C2×D711yescharacteristic
321C22×C22⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C42—71no—
326C22×C42—71no—
327C22×C42—71no—
328C22×C42—144no—
329C22×C42—144no—
330C22×C42—144no—
331C22×C42C2×D711yescharacteristic
332#385—144no—
333#385—144no—
334#381—78no—
335#381—144no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95C2×D711yescharacteristic
352C2×#95C2×D711yescharacteristic
353C2×#95C2×D711yescharacteristic
354C2×#95C2×D711yescharacteristic
355C2×#95C2×D711yescharacteristic
356C23×C7C23×C411yescharacteristic
357C23×C7C22×D411yescharacteristic
358C23×C7C22×D411yescharacteristic
359C23×C7C22×D411yescharacteristic
360C23×C7C22×Q811yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7C2×#4111yescharacteristic
363C23×C7C2×#4111yescharacteristic
364C23×C7C2×#4111yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—22no—
389C22×D7—22no—
390C22×D7—22no—
391C22×D7—22no—
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7C2×C4⋊C414yes—
400C22×D7C4×D414yes—
401C22×D7C4×D414yes—
402C22×D7#12014yes—
403C22×D7C22⋊Q814yes—
404C22×D7C22⋊Q814yes—
405C22×D7#12314yes—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7C2×C4⋊C414yes—
453C2×C4×C7#12314yes—
454C2×C4×C7#12314yes—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7—41no—
494C2×Dic7—41no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C2×Dic7C2×C4⋊C414yes—
502C2×Dic7#12314yes—
503C2×Dic7#12314yes—
504C4×D7—232no—
505C4×D7—232no—
506C4×D7—232no—
507C25—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—71no—
511C23×C4—74no—
512C23×C4—74no—
513C23×C4—74no—
514C23×C4—71no—
515C23×C4—71no—
516C23×C4—74no—
517C23×C4—74no—
518C23×C4—71no—
519C23×C4—71no—
520C23×C4—142no—
521C23×C4—142no—
522C23×C4—142no—
523C23×C4—142no—
524C23×C4—142no—
525C23×C4—142no—
526C23×C4—142no—
527C23×C4—142no—
528C23×C4—142no—
529C23×C4—142no—
530C23×C4—142no—
531C23×C4—142no—
532C23×C4—142no—
533C23×C4—142no—
534C23×C4—142no—
535C23×C4—142no—
536C23×C4C22×D711yescharacteristic
537C23×C4C22×D711yescharacteristic
538C23×C4C22×D711yescharacteristic
539C23×C4C22×D711yescharacteristic
540C23×C4C22×D711yescharacteristic
541C23×C4C22×D711yescharacteristic
542C23×C4C22×D711yescharacteristic
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—142no—
547C2×C4⋊C4—142no—
548C2×C4⋊C4—142no—
549C2×C4⋊C4—142no—
550C2×C4⋊C4—142no—
551C2×C4⋊C4—142no—
552C2×C4⋊C4—142no—
553C2×C4⋊C4—142no—
554C2×C4⋊C4—142no—
555C2×C22⋊C4—74no—
556C2×C22⋊C4—74no—
557C2×C22⋊C4—142no—
558C2×C22⋊C4—142no—
559C2×C22⋊C4—142no—
560C2×C22⋊C4—142no—
561C2×C22⋊C4—142no—
562C2×C22⋊C4—142no—
563C2×C22⋊C4—142no—
564C2×C22⋊C4—142no—
565C2×C22⋊C4—142no—
566C2×C22⋊C4—142no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—1432no—
571C2×C42—142no—
572C2×C42—142no—
573C2×C42—142no—
574C2×C42—142no—
575C2×C42—142no—
576C2×C42—142no—
577C2×C42—142no—
578C2×C42—142no—
579C2×C42—142no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—74no—
585#95—74no—
586#95—74no—
587#95—142no—
588#95—142no—
589#95—142no—
590#95—142no—
591#95—142no—
592#95—142no—
593#95—142no—
594#95—142no—
595#95—142no—
596#95—142no—
597#95—142no—
598#95—142no—
599#95C4×D714yescomplemented
600C22×C7C22×C4⋊C411yescharacteristic
601C22×C7C2×C4×D411yescharacteristic
602C22×C7C2×C4×D411yescharacteristic
603C22×C7C4×#4111yescharacteristic
604C22×C7C4×#4111yescharacteristic
605C22×C7C4×#4111yescharacteristic
606C22×C7C4×#4111yescharacteristic
607C22×C7C2×#12011yescharacteristic
608C22×C7C2×C22⋊Q811yescharacteristic
609C22×C7C2×C22⋊Q811yescharacteristic
610C22×C7C2×#12311yescharacteristic
611C22×C7C2×#12311yescharacteristic
612C22×C7C2×#12311yescharacteristic
613C22×C7C2×#12311yescharacteristic
614C22×C7C2×#12311yescharacteristic
615C22×C7#52511yescharacteristic
616C22×C7#52511yescharacteristic
617C22×C7#52511yescharacteristic
618C22×C7#52511yescharacteristic
619C22×C7#52511yescharacteristic
620C22×C7#52511yescharacteristic
621C22×C7#52511yescharacteristic
622C22×C7#52511yescharacteristic
623C22×C7#52911yescharacteristic
624C22×C7#52911yescharacteristic
625C22×C7#52911yescharacteristic
626C22×C7#52911yescharacteristic
627C22×C7#52911yescharacteristic
628C22×C7#52911yescharacteristic
629C22×C7#52911yescharacteristic
630C22×C7#52911yescharacteristic
631C22×C7#53311yescharacteristic
632C22×C7#53311yescharacteristic
633C22×C7#53311yescharacteristic
634C22×C7#53311yescharacteristic
635C2×D7—24no—
636C2×D7—24no—
637C2×D7—24no—
638C2×D7—24no—
639C2×D7—24no—
640C2×D7—24no—
641C2×D7—24no—
642C2×D7—24no—
643C2×D7—24no—
644C2×D7—24no—
645C2×D7—24no—
646C2×D7—24no—
647C2×D7—24no—
648C2×D7—24no—
649C2×D7#38518yes—
650C4×C7—24no—
651C4×C7—24no—
652C4×C7—24no—
653C4×C7—42no—
654C4×C7—42no—
655C4×C7—81no—
656C4×C7—81no—
657Dic7—24no—
658Dic7—24no—
659Dic7—24no—
660Dic7—42no—
661Dic7—42no—
662Dic7—81no—
663Dic7—81no—
664C24—72no—
665C24—72no—
666C24—72no—
667C24—72no—
668C24—72no—
669C24—72no—
670C24—72no—
671C24—141no—
672C24—141no—
673C24—141no—
674C24—141no—
675C24—141no—
676C24—141no—
677C24—141no—
678C24—141no—
679C24C23×D711yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—72no—
719C22×C4—72no—
720C22×C4—72no—
721C22×C4—72no—
722C22×C4—72no—
723C22×C4—72no—
724C22×C4—72no—
725C22×C4—72no—
726C22×C4—72no—
727C22×C4—716no—
728C22×C4—72no—
729C22×C4—72no—
730C22×C4—148no—
731C22×C4—148no—
732C22×C4—148no—
733C22×C4—148no—
734C22×C4—148no—
735C22×C4—148no—
736C22×C4—148no—
737C22×C4—148no—
738C22×C4—148no—
739C22×C4—148no—
740C22×C4—148no—
741C22×C4—148no—
742C22×C4—148no—
743C22×C4—148no—
744C22×C4—148no—
745C22×C4—148no—
746C22×C4—148no—
747C22×C4—148no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—141no—
760C22×C4—148no—
761C22×C4—148no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—141no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—141no—
773C22×C4—141no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—141no—
779C22×C4—141no—
780C22×C4—141no—
781C22×C4—141no—
782C22×C4—141no—
783C22×C4—141no—
784C22×C4—141no—
785C22×C4—141no—
786C22×C4—141no—
787C22×C4—141no—
788C22×C4C2×C4×D712yes—
789C22×C4C2×C4×D712yes—
790C22×C4C2×C4×D712yes—
791C22×C4#115712yes—
792C22×C4#115712yes—
793C22×C4D4×D712yes—
794C22×C4D4×D712yes—
795C22×C4D4×D712yes—
796C22×C4#115912yes—
797C22×C4Q8×D712yes—
798C22×C4#116112yes—
799C4⋊C4—44no—
800C4⋊C4—284no—
801C4⋊C4—284no—
802C4⋊C4—284no—
803C22⋊C4—148no—
804C22⋊C4—148no—
805C22⋊C4—284no—
806C22⋊C4—284no—
807C42—28no—
808C42—148no—
809C42—148no—
810C42—148no—
811C2×C7C2×#38511yescharacteristic
812C2×C7#229611yescharacteristic
813C2×C7#229611yescharacteristic
814C2×C7C4×#12311yescharacteristic
815C2×C7C4×#12311yescharacteristic
816C2×C7C4×#12311yescharacteristic
817C2×C7C4×#12311yescharacteristic
818C2×C7#284911yescharacteristic
819C2×C7#284911yescharacteristic
820C2×C7#285311yescharacteristic
821C2×C7#285311yescharacteristic
822C2×C7#285511yescharacteristic
823C2×C7#285511yescharacteristic
824C2×C7#285511yescharacteristic
825C2×C7#285511yescharacteristic
826D7—28no—
827C23—74no—
828C23—74no—
829C23—74no—
830C23—74no—
831C23—74no—
832C23—74no—
833C23—74no—
834C23—142no—
835C23—142no—
836C23—142no—
837C23—142no—
838C23—142no—
839C23—142no—
840C23—142no—
841C23—142no—
842C23—142no—
843C23—142no—
844C23—142no—
845C23—142no—
846C23—142no—
847C23—142no—
848C23—142no—
849C23—142no—
850C23—142no—
851C23—142no—
852C23—142no—
853C23—142no—
854C23—142no—
855C23—142no—
856C23—142no—
857C23—142no—
858C23—142no—
859C23—142no—
860C23—142no—
861C23—142no—
862C23C22×C4×D711yescharacteristic
863C23C2×#115711yescharacteristic
864C23C2×#115711yescharacteristic
865C23C2×D4×D711yescharacteristic
866C23C2×D4×D711yescharacteristic
867C23C2×D4×D711yescharacteristic
868C23C2×#115911yescharacteristic
869C23C2×Q8×D711yescharacteristic
870C23C2×#116111yescharacteristic
871C23D7×#4111yescharacteristic
872C23D7×#4111yescharacteristic
873C23D7×#4111yescharacteristic
874C23D7×#4111yescharacteristic
875C23D7×#4111yescharacteristic
876C23D7×#4111yescharacteristic
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—74no—
924C2×C4—74no—
925C2×C4—74no—
926C2×C4—1432no—
927C2×C4—1432no—
928C2×C4—1432no—
929C2×C4—142no—
930C2×C4—142no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—142no—
935C2×C4—142no—
936C2×C4—142no—
937C2×C4—142no—
938C2×C4—142no—
939C2×C4—142no—
940C2×C4—142no—
941C2×C4—142no—
942C2×C4—142no—
943C2×C4—142no—
944C2×C4—142no—
945C2×C4—142no—
946C2×C4—142no—
947C2×C4—142no—
948C2×C4—142no—
949C2×C4—142no—
950C2×C4—142no—
951C2×C4—142no—
952C2×C4—142no—
953C2×C4—281no—
954C2×C4—281no—
955C2×C4—281no—
956C2×C4—281no—
957C2×C4—281no—
958C2×C4—281no—
959C2×C4—281no—
960C2×C4—281no—
961C2×C4—281no—
962C2×C4—281no—
963C2×C4—281no—
964C2×C4—281no—
965C2×C4—281no—
966C2×C4—281no—
967C2×C4—281no—
968C2×C4—281no—
969C2×C4—281no—
970C2×C4—281no—
971C2×C4—281no—
972C2×C4—281no—
973C2×C4—281no—
974C2×C4—281no—
975C2×C4#644614yes—
976C2×C4D7×C4⋊C414yes—
977C2×C4#645714yes—
978C7#1470511yescharacteristic, complemented, Sylow
979C22—78no—
980C22—144no—
981C22—144no—
982C22—144no—
983C22—144no—
984C22—144no—
985C22—144no—
986C22—144no—
987C22—144no—
988C22—144no—
989C22—144no—
990C22—144no—
991C22—144no—
992C22—144no—
993C22—144no—
994C22C4×#115711yescharacteristic
995C22C2×#644611yescharacteristic
996C22C2×D7×C4⋊C411yescharacteristic
997C22C2×#645711yescharacteristic
998C22#9021311yescharacteristic
999C22#9021911yescharacteristic
1000C22#9021911yescharacteristic
1001C22C4×#115911yescharacteristic
1002C22C4×D4×D711yescharacteristic
1003C22C4×D4×D711yescharacteristic
1004C22#9023811yescharacteristic
1005C22#9023811yescharacteristic
1006C22#9023811yescharacteristic
1007C22#9023811yescharacteristic
1008C22#9024811yescharacteristic
1009C22C4×#116111yescharacteristic
1010C22#9026911yescharacteristic
1011C22#9026911yescharacteristic
1012C22#9027111yescharacteristic
1013C22D7×#12011yescharacteristic
1014C22#9029711yescharacteristic
1015C22#9029711yescharacteristic
1016C22D7×C22⋊Q811yescharacteristic
1017C22D7×C22⋊Q811yescharacteristic
1018C22#9031811yescharacteristic
1019C22#9031811yescharacteristic
1020C22D7×#12311yescharacteristic
1021C22D7×#12311yescharacteristic
1022C22D7×#12311yescharacteristic
1023C22#9037111yescharacteristic
1024C22#9037911yescharacteristic
1025C22#9038211yescharacteristic
1026C22#9039711yescharacteristic
1027C22#9039711yescharacteristic
1028C22#9041911yescharacteristic
1029C4—24no—
1030C4—24no—
1031C4—24no—
1032C4—42no—
1033C4—42no—
1034C4—81no—
1035C4—81no—
1036C4—144no—
1037C4—144no—
1038C4—144no—
1039C4—282no—
1040C4—282no—
1041C4—561no—
1042C4—561no—
1043C2—148no—
1044C2C4×#644611yescharacteristic
1045C2#1173120011yescharacteristic
1046C2C4×#645711yescharacteristic
1047C2D7×#38511yescharacteristic
1048C2#1173210111yescharacteristic
1049C2#1173238111yescharacteristic
1050C2#1173238511yescharacteristic
1051C2#1173289211yescharacteristic
1052C2#1173289311yescharacteristic
1053C2#1173289311yescharacteristic
1054C2#1173289811yescharacteristic
1055C2#1173340411yescharacteristic
1056C2#1173340811yescharacteristic
1057C2#1173373211yescharacteristic
1058C2#1173410811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#14705
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. C7×#1436C2semidirect
7. #11729318C2semidirect
8. #11729290C2semidirect
11. #11727161C2semidirect
12. #11727161C2semidirect
13. #11727160C2semidirect
14. #11727160C2semidirect
15. #11727159C2semidirect
57. #89436C4semidirect
136. C7×#95C2×C4semidirect
149. C7⋊#95C2×C4semidirect
150. C7⋊#95C2×C4semidirect
151. C7⋊#95C2×C4semidirect
164. #1436D7semidirect
301. C2×C4×D7C4⋊C4semidirect
599. #95C4×D7semidirect
978. C7#14705semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D72
C2×#897612
C2×#894402
C2×#894362
C7×#14362
#117293182
#117292902
(C2×D7)⋊#952
#117271612
#117271602
#117271592
#147057