Finite Group Databasebeta

← #13275763

Subgroups — #13275763

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×#6435C211yesmaximal, characteristic
2C2×#89759C211yesmaximal, characteristic
3C2×#89436C211yesmaximal, characteristic
4C2×#89439C211yesmaximal, characteristic
5C2×D7×#95C211yesmaximal, characteristic
6C7×#1436C211yesmaximal, characteristic, complemented
7#11729322C211yesmaximal, characteristic, complemented
8#11729290C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727174C211yesmaximal, characteristic, complemented
12#11727168C211yesmaximal, characteristic, complemented
13#11727167C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, 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×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×#6435—24no—
32C2×#6435—24no—
33C2×#6435—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#89759—24no—
55#89439—24no—
56#89436—24no—
57D7×#95C418yescomplemented
58#13878—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—41no—
87C22×C4×D7—41no—
88C22×C4×D7—41no—
89C22×C4×D7—41no—
90C22×C4×D7C2×C414yes—
91C22×C4×D7C2×C414yes—
92C22×C4×D7C2×C414yes—
93C22×C4×D7D414yes—
94C22×C4×D7Q814yes—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—41no—
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)⋊C4D414yes—
112C2×(C2×D7)⋊C4D414yes—
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—41no—
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⋊C4—22no—
124C2×Dic7⋊C4—22no—
125C2×Dic7⋊C4—22no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4—41no—
128C2×C4×Dic7—22no—
129C2×C4×Dic7—22no—
130C2×C4×Dic7—22no—
131#6435—232no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C7×#95—41no—
136C7×#95C2×C414yes—
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⋊#95C2×C414yes—
150C7⋊#95C2×C414yes—
151C7⋊#95C2×C414yes—
152C22×#117—71no—
153C2×#381—71no—
154C2×#380—71no—
155C2×#380—71no—
156C22×#95—71no—
157#1444—71no—
158#1444—71no—
159#1442—71no—
160#1442—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×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7C22×C412yes—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×Q812yes—
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×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7C22×C412yes—
273C22×Dic7C22×C412yes—
274C22×Dic7C22×C412yes—
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—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×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—28no—
310Dic7⋊C4—28no—
311Dic7⋊C4—44no—
312Dic7⋊C4—44no—
313C4×Dic7—28no—
314C24×C4—71no—
315C24×C4—71no—
316C24×C4—71no—
317C2×#117—144no—
318C2×#117—144no—
319C2×#117—144no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4C2×D711yescharacteristic
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C42—71no—
331C22×C42C2×D711yescharacteristic
332#381—144no—
333#380—144no—
334#380—144no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—78no—
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×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—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×C7C2×C4⋊C414yes—
454C2×C4×C7#11714yescomplemented
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—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
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×Dic7C2×C4⋊C414yes—
503C2×Dic7#11714yescomplemented
504C4×D7—232no—
505C4×D7—416no—
506C4×D7—416no—
507C25—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—74no—
511C23×C4—74no—
512C23×C4—74no—
513C23×C4—71no—
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—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
543#117—1432no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
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×C4⋊C4—142no—
556C2×C4⋊C4—142no—
557C2×C4⋊C4—142no—
558C2×C4⋊C4—142no—
559C2×C4⋊C4—281no—
560C2×C4⋊C4—281no—
561C2×C4⋊C4—281no—
562C2×C22⋊C4—74no—
563C2×C22⋊C4—74no—
564C2×C22⋊C4—142no—
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—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—142no—
578C2×C42—142no—
579C2×C42—142no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—41no—
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—281no—
597#95—281no—
598#95—281no—
599#95C4×D714yes—
600C22×C7C22×C4⋊C411yescharacteristic
601C22×C7C2×#11711yescharacteristic
602C22×C7C2×#11711yescharacteristic
603C22×C7C2×C4×D411yescharacteristic
604C22×C7C2×C4×D411yescharacteristic
605C22×C7#51811yescharacteristic
606C22×C7#51911yescharacteristic
607C22×C7C2×#12011yescharacteristic
608C22×C7C2×C22⋊Q811yescharacteristic
609C22×C7C2×C22⋊Q811yescharacteristic
610C22×C7C2×#12311yescharacteristic
611C22×C7#53211yescharacteristic
612C22×C7#53211yescharacteristic
613C22×C7#53311yescharacteristic
614C22×C7#53311yescharacteristic
615C22×C7#53711yescharacteristic
616C22×C7#53711yescharacteristic
617C22×C7#54411yescharacteristic
618C22×C7#54411yescharacteristic
619C22×C7#54611yescharacteristic
620C22×C7#54611yescharacteristic
621C22×C7#54611yescharacteristic
622C22×C7#54611yescharacteristic
623C22×C7#54711yescharacteristic
624C22×C7#54711yescharacteristic
625C22×C7#54711yescharacteristic
626C22×C7#54711yescharacteristic
627C22×C7#55111yescharacteristic
628C22×C7#55111yescharacteristic
629C22×C7#55111yescharacteristic
630C22×C7#55111yescharacteristic
631C22×C7#55211yescharacteristic
632C22×C7#55211yescharacteristic
633C22×C7#55211yescharacteristic
634C22×C7#55211yescharacteristic
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—42no—
653C4×C7—42no—
654C4×C7—42no—
655C4×C7—81no—
656C4×C7—81no—
657Dic7—24no—
658Dic7—24no—
659Dic7—42no—
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—21no—
719C22×C4—21no—
720C22×C4—72no—
721C22×C4—72no—
722C22×C4—72no—
723C22×C4—72no—
724C22×C4—72no—
725C22×C4—72no—
726C22×C4—716no—
727C22×C4—72no—
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—141no—
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—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—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—148no—
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×C4C2×C4×D712yes—
791C22×C4C2×C4×D712yes—
792C22×C4C2×C4×D712yes—
793C22×C4#115712yes—
794C22×C4#115712yes—
795C22×C4D4×D712yes—
796C22×C4D4×D712yes—
797C22×C4D4×D712yes—
798C22×C4Q8×D712yes—
799C4⋊C4—44no—
800C4⋊C4—148no—
801C4⋊C4—148no—
802C4⋊C4—284no—
803C4⋊C4—284no—
804C4⋊C4—284no—
805C22⋊C4—148no—
806C22⋊C4—148no—
807C22⋊C4—284no—
808C22⋊C4—284no—
809C42—28no—
810C42—148no—
811C2×C7#228511yescharacteristic
812C2×C7C2×#38511yescharacteristic
813C2×C7#231611yescharacteristic
814C2×C7#234211yescharacteristic
815C2×C7#234211yescharacteristic
816C2×C7#234411yescharacteristic
817C2×C7#234411yescharacteristic
818C2×C7#243011yescharacteristic
819C2×C7#243011yescharacteristic
820C2×C7#243811yescharacteristic
821C2×C7#243811yescharacteristic
822C2×C7#243811yescharacteristic
823C2×C7#243811yescharacteristic
824C2×C7#249811yescharacteristic
825C2×C7#249811yescharacteristic
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
868C23#654811yescharacteristic
869C23C2×Q8×D711yescharacteristic
870C23#655111yescharacteristic
871C23D7×#4111yescharacteristic
872C23D7×#4111yescharacteristic
873C23D7×#4111yescharacteristic
874C23D7×#4111yescharacteristic
875C23#655311yescharacteristic
876C23#655411yescharacteristic
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—74no—
925C2×C4—74no—
926C2×C4—1432no—
927C2×C4—142no—
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—2816no—
949C2×C4—2816no—
950C2×C4—281no—
951C2×C4—281no—
952C2×C4—281no—
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—281no—
976C2×C4#643514yescomplemented
977C2×C4D7×C4⋊C414yes—
978C7#1387811yescharacteristic, 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×#643511yescharacteristic
995C22#9018111yescharacteristic
996C22C2×D7×C4⋊C411yescharacteristic
997C22#9019811yescharacteristic
998C22D7×#11711yescharacteristic
999C22#9021811yescharacteristic
1000C22#9022011yescharacteristic
1001C22C4×D4×D711yescharacteristic
1002C22C4×D4×D711yescharacteristic
1003C22#9023611yescharacteristic
1004C22#9023911yescharacteristic
1005C22#9023911yescharacteristic
1006C22#9024111yescharacteristic
1007C22#9024211yescharacteristic
1008C22#9024711yescharacteristic
1009C22#9026311yescharacteristic
1010C22#9026911yescharacteristic
1011C22#9026911yescharacteristic
1012C22#9027211yescharacteristic
1013C22D7×#12011yescharacteristic
1014C22#9029911yescharacteristic
1015C22#9030311yescharacteristic
1016C22D7×C22⋊Q811yescharacteristic
1017C22D7×C22⋊Q811yescharacteristic
1018C22#9032011yescharacteristic
1019C22#9032211yescharacteristic
1020C22D7×#12311yescharacteristic
1021C22#9034511yescharacteristic
1022C22#9034611yescharacteristic
1023C22#9037011yescharacteristic
1024C22#9038011yescharacteristic
1025C22#9038411yescharacteristic
1026C22#9039611yescharacteristic
1027C22#9039911yescharacteristic
1028C22#9042011yescharacteristic
1029C4—24no—
1030C4—24no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—81no—
1035C4—81no—
1036C4—144no—
1037C4—144no—
1038C4—282no—
1039C4—282no—
1040C4—282no—
1041C4—561no—
1042C4—561no—
1043C2—148no—
1044C2#1173101911yescharacteristic
1045C2#1173119811yescharacteristic
1046C2#1173121211yescharacteristic
1047C2D7×#38511yescharacteristic
1048C2#1173205111yescharacteristic
1049C2#1173234111yescharacteristic
1050C2#1173240611yescharacteristic
1051C2#1173276211yescharacteristic
1052C2#1173276311yescharacteristic
1053C2#1173278411yescharacteristic
1054C2#1173327711yescharacteristic
1055C2#1173331411yescharacteristic
1056C2#1173364011yescharacteristic
1057C2#1173366711yescharacteristic
1058C2#1173407211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#13878
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. #11729322C2semidirect
8. #11729290C2semidirect
11. #11727174C2semidirect
12. #11727168C2semidirect
13. #11727167C2semidirect
14. #11727161C2semidirect
15. #11727160C2semidirect
57. D7×#95C4semidirect
164. #1436D7semidirect
301. C2×C4×D7C4⋊C4semidirect
454. C2×C4×C7#117semidirect
503. C2×Dic7#117semidirect
976. C2×C4#6435semidirect
978. C7#13878semidirect

Maximal subgroups

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

subgroupindex
C22×#64352
C2×#897592
C2×#894362
C2×#894392
C2×D7×#952
C7×#14362
#117293222
#117292902
(C2×D7)⋊#952
#117271742
#117271682
#117271672
#117271612
#117271602
#138787