Finite Group Databasebeta

← #13285016

Subgroups — #13285016

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×#89426C211yesmaximal, characteristic, complemented
5C2×#89424C211yesmaximal, characteristic, complemented
6C7×#1436C211yesmaximal, characteristic, complemented
7#11729318C211yesmaximal, characteristic, complemented
8#11729290C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11(C2×D7)⋊#95C211yesmaximal, characteristic
12(C2×D7)⋊#95C211yesmaximal, characteristic
13#11727161C211yesmaximal, characteristic, complemented
14#11727157C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, 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#89440C418yescomplemented
56#89426—24no—
57#89424—24no—
58#14695—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×D7—22no—
91C22×C4×D7—22no—
92C22×C4×D7C2×C414yes—
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⋊Dic7C2×C414yescomplemented
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4C2×C414yescomplemented
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×Dic7D414yes—
130C2×C4×Dic7D414yes—
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⋊#95—22no—
150C7⋊#95—22no—
151C7⋊#95C2×C414yescomplemented
152C23×C42—71no—
153C2×#387—71no—
154C2×#387—71no—
155C2×#385—71no—
156C2×#385—71no—
157#1436—71no—
158#1436—71no—
159#1436—71no—
160#1436D711yescharacteristic, complemented
161#1434—71no—
162#1434—71no—
163C22⋊#95—71no—
164C22⋊#95—71no—
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×Q812yes—
179C23×D7#4112yes—
180C23×D7#4112yes—
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×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×Q812yes—
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×D7—28no—
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—28no—
309Dic7⋊C4—28no—
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#387—144no—
333#387—144no—
334#385—78no—
335#385—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×D7#11714yes—
400C22×D7C4×D414yes—
401C22×D7C4×Q814yes—
402C22×D7C22⋊Q814yes—
403C22×D7#12314yes—
404C22×D7#12514yes—
405C22×D7#12614yes—
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×C7C4×D414yes—
453C2×C4×C7C22⋊Q814yes—
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×Dic7C4×D414yes—
502C2×Dic7#12014yes—
503C2×Dic7C22⋊Q814yes—
504C4×D7—232no—
505C4×D7—232no—
506C4×D7—232no—
507C25—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—71no—
511C23×C4—71no—
512C23×C4—71no—
513C23×C4—74no—
514C23×C4—74no—
515C23×C4—74no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4—142no—
519C23×C4—142no—
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—74no—
547C2×C4⋊C4—74no—
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—74no—
571C2×C42—74no—
572C2×C42—1432no—
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—142no—
586#95—142no—
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×C7C2×#11711yescharacteristic
601C22×C7C2×C4×D411yescharacteristic
602C22×C7C2×C4×D411yescharacteristic
603C22×C7C2×C4×D411yescharacteristic
604C22×C7C2×C4×Q811yescharacteristic
605C22×C7C4×#4111yescharacteristic
606C22×C7C4×#4111yescharacteristic
607C22×C7C2×#12011yescharacteristic
608C22×C7C2×C22⋊Q811yescharacteristic
609C22×C7C2×C22⋊Q811yescharacteristic
610C22×C7C2×C22⋊Q811yescharacteristic
611C22×C7C2×#12311yescharacteristic
612C22×C7C2×#12311yescharacteristic
613C22×C7#52511yescharacteristic
614C22×C7#52511yescharacteristic
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×C7C2×#12511yescharacteristic
624C22×C7C2×#12611yescharacteristic
625C22×C7#52911yescharacteristic
626C22×C7#52911yescharacteristic
627C22×C7#52911yescharacteristic
628C22×C7#52911yescharacteristic
629C22×C7#52911yescharacteristic
630C22×C7#52911yescharacteristic
631C22×C7#52911yescharacteristic
632C22×C7#52911yescharacteristic
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#38718yescomplemented
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—72no—
728C22×C4—72no—
729C22×C4—148no—
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—141no—
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—148no—
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—148no—
801C4⋊C4—148no—
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×#38711yescharacteristic
812C2×C7#229011yescharacteristic
813C2×C7#229011yescharacteristic
814C2×C7C4×#12011yescharacteristic
815C2×C7C4×#12311yescharacteristic
816C2×C7C4×C22⋊Q811yescharacteristic
817C2×C7C4×C22⋊Q811yescharacteristic
818C2×C7#284811yescharacteristic
819C2×C7#284911yescharacteristic
820C2×C7#285111yescharacteristic
821C2×C7#285111yescharacteristic
822C2×C7#285211yescharacteristic
823C2×C7#285211yescharacteristic
824C2×C7#285311yescharacteristic
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×C4#645614yes—
977C2×C4#645914yes—
978C7#1469511yescharacteristic, 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×#645611yescharacteristic
997C22C2×#645911yescharacteristic
998C22D7×#11711yescharacteristic
999C22#9021911yescharacteristic
1000C22#9021911yescharacteristic
1001C22C4×#115911yescharacteristic
1002C22C4×D4×D711yescharacteristic
1003C22C4×D4×D711yescharacteristic
1004C22#9023811yescharacteristic
1005C22#9023811yescharacteristic
1006C22#9023811yescharacteristic
1007C22#9023811yescharacteristic
1008C22#9024811yescharacteristic
1009C22C4×Q8×D711yescharacteristic
1010C22#9026911yescharacteristic
1011C22#9027111yescharacteristic
1012C22#9027111yescharacteristic
1013C22D7×#12011yescharacteristic
1014C22#9029711yescharacteristic
1015C22#9029711yescharacteristic
1016C22D7×C22⋊Q811yescharacteristic
1017C22D7×C22⋊Q811yescharacteristic
1018C22#9031811yescharacteristic
1019C22#9031811yescharacteristic
1020C22D7×#12311yescharacteristic
1021C22#9034711yescharacteristic
1022C22#9034711yescharacteristic
1023C22#9037111yescharacteristic
1024C22D7×#12511yescharacteristic
1025C22#9038211yescharacteristic
1026C22D7×#12611yescharacteristic
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#1173119911yescharacteristic
1046C2C4×#645911yescharacteristic
1047C2#1173182411yescharacteristic
1048C2#1173210011yescharacteristic
1049C2#1173238111yescharacteristic
1050C2D7×#38711yescharacteristic
1051C2#1173289011yescharacteristic
1052C2#1173289111yescharacteristic
1053C2#1173289211yescharacteristic
1054C2#1173289411yescharacteristic
1055C2#1173340311yescharacteristic
1056C2#1173341011yescharacteristic
1057C2#1173373011yescharacteristic
1058C2#1173410811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#14695
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#89426C2semidirect
5. C2×#89424C2semidirect
6. C7×#1436C2semidirect
7. #11729318C2semidirect
8. #11729290C2semidirect
13. #11727161C2semidirect
14. #11727157C2semidirect
15. #11727155C2semidirect
55. #89440C4semidirect
115. C2×C4⋊Dic7C2×C4semidirect
121. C2×Dic7⋊C4C2×C4semidirect
136. C7×#95C2×C4semidirect
151. C7⋊#95C2×C4semidirect
160. #1436D7semidirect
599. #95C4×D7semidirect
649. C2×D7#387semidirect
978. C7#14695semidirect

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×#894262
C2×#894242
C7×#14362
#117293182
#117292902
(C2×D7)⋊#952
#117271612
#117271572
#117271552
#146957