Finite Group Databasebeta

← #13277455

Subgroups — #13277455

Order 1792.

2222 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×D7×C4⋊C4C211yesmaximal, characteristic
2C2×#89761C211yesmaximal, characteristic
3C2×#89753C211yesmaximal, characteristic, complemented
4C2×#89424C211yesmaximal, characteristic, complemented
5C2×#89438C211yesmaximal, characteristic
6C7×#1441C211yesmaximal, characteristic, complemented
7#11729321C211yesmaximal, characteristic, complemented
8(C2×D7)⋊#95C211yesmaximal, characteristic
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11(C2×D7)⋊#95C211yesmaximal, characteristic
12#11727167C211yesmaximal, characteristic, complemented
13#11727163C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×D7×C4⋊C4—24no—
32C2×D7×C4⋊C4—24no—
33C2×D7×C4⋊C4—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#89761C418yescomplemented
55#89753—24no—
56#89438—24no—
57#89424—24no—
58#14039—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—41no—
90C22×C4×D7—41no—
91C22×C4×D7—41no—
92C22×C4×D7—41no—
93C22×C4×D7C2×C414yes—
94C22×C4×D7D414yes—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—22no—
100C2×C7×C4⋊C4C2×C414yescomplemented
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)⋊C4C2×C414yes—
111C2×(C2×D7)⋊C4C2×C414yes—
112C2×(C2×D7)⋊C4Q814yes—
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7D414yes—
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×Dic7⋊C4—22no—
123C2×Dic7⋊C4C2×C414yescomplemented
124C2×Dic7⋊C4D414yes—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—22no—
128C2×C4×Dic7—22no—
129C2×C4×Dic7—41no—
130C2×C4×Dic7—41no—
131D7×C4⋊C4—232no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C7×#95—41no—
136C7×#95—41no—
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—41no—
147C7⋊#95—41no—
148C7⋊#95—41no—
149C7⋊#95—41no—
150C7⋊#95C2×C414yescomplemented
151C7⋊#95C2×C414yescomplemented
152C23×C4⋊C4—71no—
153C2×#387—71no—
154C2×#387—71no—
155C2×#385—71no—
156C2×C4×C22⋊C4—71no—
157#1442—71no—
158#1442—71no—
159#1441—71no—
160#1441D711yescharacteristic, complemented
161#1436—71no—
162#1436—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×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C22×C412yes—
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×D412yes—
230C22×C4×C7C2×Q812yes—
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×Dic7—21no—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C22×C412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7C2×D412yes—
276C22×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7C2×Q812yes—
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—44no—
292C2×C4×D7—44no—
293C2×C4×D7—44no—
294C2×C4×D7—44no—
295C2×C4×D7—44no—
296C2×C4×D7—44no—
297C2×C4×D7—44no—
298C2×C4×D7—44no—
299C2×C4×D7—44no—
300C2×C4×D7—44no—
301C2×C4×D7—44no—
302C7×C4⋊C4—28no—
303C7×C4⋊C4—28no—
304(C2×D7)⋊C4—28no—
305(C2×D7)⋊C4—28no—
306(C2×D7)⋊C4—28no—
307(C2×D7)⋊C4—44no—
308C4⋊Dic7—28no—
309Dic7⋊C4—28no—
310Dic7⋊C4—28no—
311Dic7⋊C4—28no—
312C4×Dic7—44no—
313C4×Dic7—44no—
314C24×C4—71no—
315C24×C4—71no—
316C24×C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—144no—
322C22×C4⋊C4—144no—
323C22×C4⋊C4—144no—
324C22×C4⋊C4C2×D711yescharacteristic
325C22×C4⋊C4C2×D711yescharacteristic
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C42—71no—
331C22×C42—71no—
332#387—144no—
333#387—144no—
334#385—78no—
335C4×C22⋊C4—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×C7H(5,𝔽2)11yescharacteristic
368C23×C7H(5,𝔽2)11yescharacteristic
369C23×C72−1+411yescharacteristic
370C23×C72−1+411yescharacteristic
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—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
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×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7C4×D414yes—
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×Dic7—41no—
502C2×Dic7C4×D414yes—
503C2×Dic7#12014yes—
504C4×D7—232no—
505C4×D7—416no—
506C4×D7—416no—
507C25—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—71no—
511C23×C4—71no—
512C23×C4—71no—
513C23×C4—71no—
514C23×C4—74no—
515C23×C4—74no—
516C23×C4—71no—
517C23×C4—142no—
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—281no—
533C23×C4—281no—
534C23×C4—281no—
535C23×C4—281no—
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—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—74no—
549C2×C4⋊C4—74no—
550C2×C4⋊C4—74no—
551C2×C4⋊C4—1432no—
552C2×C4⋊C4—142no—
553C2×C4⋊C4—142no—
554C2×C4⋊C4—142no—
555C2×C4⋊C4—142no—
556C2×C4⋊C4—142no—
557C2×C4⋊C4—142no—
558C2×C4⋊C4—142no—
559C2×C4⋊C4—142no—
560C2×C4⋊C4—142no—
561C2×C4⋊C4C4×D714yescomplemented
562C2×C22⋊C4—74no—
563C2×C22⋊C4—74no—
564C2×C22⋊C4—74no—
565C2×C22⋊C4—142no—
566C2×C22⋊C4—142no—
567C2×C22⋊C4—142no—
568C2×C22⋊C4—142no—
569C2×C22⋊C4—142no—
570C2×C22⋊C4—142no—
571C2×C22⋊C4—142no—
572C2×C22⋊C4—142no—
573C2×C22⋊C4—142no—
574C2×C42—142no—
575C2×C42—142no—
576C2×C42—142no—
577C2×C42—142no—
578C2×C42—281no—
579C2×C42—281no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—41no—
584#95—41no—
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—281no—
597#95—281no—
598#95—281no—
599#95—281no—
600C22×C7C2×#11711yescharacteristic
601C22×C7C2×C4×D411yescharacteristic
602C22×C7C2×C4×D411yescharacteristic
603C22×C7C2×C4×D411yescharacteristic
604C22×C7C2×C4×Q811yescharacteristic
605C22×C7#52011yescharacteristic
606C22×C7#52011yescharacteristic
607C22×C7C2×#12011yescharacteristic
608C22×C7C2×C22⋊Q811yescharacteristic
609C22×C7C2×#12311yescharacteristic
610C22×C7#52511yescharacteristic
611C22×C7#52511yescharacteristic
612C22×C7#52511yescharacteristic
613C22×C7C2×#12511yescharacteristic
614C22×C7C2×#12611yescharacteristic
615C22×C7#53411yescharacteristic
616C22×C7#53611yescharacteristic
617C22×C7#53911yescharacteristic
618C22×C7#53911yescharacteristic
619C22×C7#54611yescharacteristic
620C22×C7#54611yescharacteristic
621C22×C7#54611yescharacteristic
622C22×C7#54611yescharacteristic
623C22×C7#54811yescharacteristic
624C22×C7#54811yescharacteristic
625C22×C7D4×Q811yescharacteristic
626C22×C7D4×Q811yescharacteristic
627C22×C7#55211yescharacteristic
628C22×C7#55211yescharacteristic
629C22×C7#55211yescharacteristic
630C22×C7#55211yescharacteristic
631C22×C7#55311yescharacteristic
632C22×C7#55311yescharacteristic
633C22×C7#55411yescharacteristic
634C22×C7#55411yescharacteristic
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—42no—
652C4×C7—42no—
653C4×C7—42no—
654C4×C7—42no—
655C4×C7—42no—
656C4×C7—81no—
657Dic7—24no—
658Dic7—24no—
659Dic7—42no—
660Dic7—42no—
661Dic7—42no—
662Dic7—42no—
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—21no—
719C22×C4—21no—
720C22×C4—21no—
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—72no—
730C22×C4—72no—
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—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—148no—
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—141no—
761C22×C4—141no—
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—284no—
781C22×C4—284no—
782C22×C4—284no—
783C22×C4—284no—
784C22×C4—284no—
785C22×C4—284no—
786C22×C4—284no—
787C22×C4—284no—
788C22×C4—284no—
789C22×C4—284no—
790C22×C4—284no—
791C22×C4C2×C4×D712yes—
792C22×C4C2×C4×D712yes—
793C22×C4C2×C4×D712yes—
794C22×C4D4×D712yes—
795C22×C4D4×D712yes—
796C22×C4D4×D712yes—
797C22×C4#115912yes—
798C22×C4Q8×D712yes—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—148no—
802C4⋊C4—148no—
803C4⋊C4—148no—
804C4⋊C4—148no—
805C22⋊C4—148no—
806C22⋊C4—148no—
807C22⋊C4—148no—
808C22⋊C4—284no—
809C42—284no—
810C42—284no—
811C2×C7C2×#38711yescharacteristic
812C2×C7C4×#12011yescharacteristic
813C2×C7#232211yescharacteristic
814C2×C7#235211yescharacteristic
815C2×C7#235211yescharacteristic
816C2×C7#236011yescharacteristic
817C2×C7#236011yescharacteristic
818C2×C7#240511yescharacteristic
819C2×C7#240911yescharacteristic
820C2×C7#247311yescharacteristic
821C2×C7#247311yescharacteristic
822C2×C7#248111yescharacteristic
823C2×C7#248111yescharacteristic
824C2×C7#248411yescharacteristic
825C2×C7#257911yescharacteristic
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×D4×D711yescharacteristic
864C23C2×D4×D711yescharacteristic
865C23C2×D4×D711yescharacteristic
866C23C2×#115911yescharacteristic
867C23#654811yescharacteristic
868C23C2×Q8×D711yescharacteristic
869C23#655111yescharacteristic
870C23#655111yescharacteristic
871C23D7×#4111yescharacteristic
872C23D7×#4111yescharacteristic
873C23D7×#4111yescharacteristic
874C23D7×#4111yescharacteristic
875C23D7×#4111yescharacteristic
876C23#655311yescharacteristic
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—41no—
899C2×C4—41no—
900C2×C4—41no—
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—41no—
924C2×C4—41no—
925C2×C4—74no—
926C2×C4—74no—
927C2×C4—1432no—
928C2×C4—142no—
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—2816no—
953C2×C4—2816no—
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—281no—
976C2×C4—281no—
977C2×C4(C22⋊D7)⋊C414yes—
978C7#1403911yescharacteristic, 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—
994C22C2×(C22⋊D7)⋊C411yescharacteristic
995C22#9019511yescharacteristic
996C22D7×#11711yescharacteristic
997C22C4×D4×D711yescharacteristic
998C22C4×D4×D711yescharacteristic
999C22C4×Q8×D711yescharacteristic
1000C22#9026511yescharacteristic
1001C22D7×#12011yescharacteristic
1002C22#9029611yescharacteristic
1003C22#9029711yescharacteristic
1004C22#9029711yescharacteristic
1005C22#9030111yescharacteristic
1006C22#9030311yescharacteristic
1007C22#9030511yescharacteristic
1008C22D7×C22⋊Q811yescharacteristic
1009C22#9032411yescharacteristic
1010C22#9032411yescharacteristic
1011C22#9032611yescharacteristic
1012C22#9032711yescharacteristic
1013C22#9032911yescharacteristic
1014C22#9033011yescharacteristic
1015C22#9033011yescharacteristic
1016C22D7×#12311yescharacteristic
1017C22#9034511yescharacteristic
1018C22#9034711yescharacteristic
1019C22#9036711yescharacteristic
1020C22D7×#12511yescharacteristic
1021C22#9038311yescharacteristic
1022C22#9038411yescharacteristic
1023C22#9038411yescharacteristic
1024C22D7×#12611yescharacteristic
1025C22#9040011yescharacteristic
1026C22#9041511yescharacteristic
1027C22#9041811yescharacteristic
1028C22#9041811yescharacteristic
1029C4—24no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—81no—
1036C4—144no—
1037C4—144no—
1038C4—282no—
1039C4—282no—
1040C4—282no—
1041C4—282no—
1042C4—561no—
1043C2—148no—
1044C2#1173145711yescharacteristic
1045C2#1173210411yescharacteristic
1046C2D7×#38711yescharacteristic
1047C2#1173275011yescharacteristic
1048C2#1173342811yescharacteristic
1049C2#1173364111yescharacteristic
1050C2#1173406011yescharacteristic
1051C2#1173455111yescharacteristic
1052C2#1173461711yescharacteristic
1053C2#1173474911yescharacteristic
1054C2#1173486711yescharacteristic
1055C2#1173520111yescharacteristic
1056C2#1173520211yescharacteristic
1057C2#1173539911yescharacteristic
1058C2#1173558911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1441D7
hypocenterC7#14039
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#89753C2semidirect
4. C2×#89424C2semidirect
6. C7×#1441C2semidirect
7. #11729321C2semidirect
12. #11727167C2semidirect
13. #11727163C2semidirect
14. #11727161C2semidirect
15. #11727160C2semidirect
54. #89761C4semidirect
100. C2×C7×C4⋊C4C2×C4semidirect
123. C2×Dic7⋊C4C2×C4semidirect
150. C7⋊#95C2×C4semidirect
151. C7⋊#95C2×C4semidirect
160. #1441D7semidirect
561. C2×C4⋊C4C4×D7semidirect
649. C2×D7#387semidirect
978. C7#14039semidirect

Maximal subgroups

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

subgroupindex
C22×D7×C4⋊C42
C2×#897612
C2×#897532
C2×#894242
C2×#894382
C7×#14412
#117293212
(C2×D7)⋊#952
#117271672
#117271632
#117271612
#117271602
#140397