Finite Group Databasebeta

← #13277000

Subgroups — #13277000

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic, complemented
2C2×#89761C211yesmaximal, characteristic
3C2×#89761C211yesmaximal, characteristic
4C2×#89761C211yesmaximal, characteristic
5C2×#89759C211yesmaximal, characteristic
6C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
7C2×D7×#95C211yesmaximal, characteristic
8#11729322C211yesmaximal, characteristic, complemented
9#11729321C211yesmaximal, characteristic, complemented
10#11729320C211yesmaximal, characteristic, complemented
11#11729319C211yesmaximal, characteristic, complemented
12#11729290C211yesmaximal, characteristic, complemented
13(C2×D7)⋊#95C211yesmaximal, characteristic
14#11727161C211yesmaximal, characteristic, complemented
15Dic7⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C7×#389—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
52#89761—24no—
53#89761—24no—
54#89761C418yescomplemented
55#89759—24no—
56C4×(C2×D7)⋊C4—24no—
57D7×#95—24no—
58#14004—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—41no—
88C22×C4×D7—41no—
89C22×C4×D7—41no—
90C22×C4×D7—41no—
91C22×C4×D7—41no—
92C22×C4×D7—41no—
93C22×C4×D7C2×C414yes—
94C22×C4×D7Q814yes—
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⋊C4—22no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—22no—
103C2×C7×C4⋊C4—41no—
104C2×C7×C4⋊C4—41no—
105C2×C7×C4⋊C4—41no—
106C2×C7×C4⋊C4C2×C414yescomplemented
107C2×C42×C7—22no—
108C2×C42×C7—22no—
109C2×C42×C7—41no—
110C2×(C2×D7)⋊C4—22no—
111C2×(C2×D7)⋊C4—22no—
112C2×(C2×D7)⋊C4—22no—
113C2×(C2×D7)⋊C4—22no—
114C2×(C2×D7)⋊C4—22no—
115C2×(C2×D7)⋊C4—22no—
116C2×(C2×D7)⋊C4—22no—
117C2×(C2×D7)⋊C4C2×C414yes—
118C2×(C2×D7)⋊C4C2×C414yes—
119C2×(C2×D7)⋊C4D414yes—
120C2×(C2×D7)⋊C4D414yes—
121C2×(C2×D7)⋊C4Q814yes—
122C2×C4⋊Dic7—22no—
123C2×C4⋊Dic7—22no—
124C2×C4⋊Dic7—41no—
125C2×Dic7⋊C4—22no—
126C2×Dic7⋊C4—22no—
127C2×Dic7⋊C4—22no—
128C2×Dic7⋊C4—22no—
129C2×Dic7⋊C4—41no—
130C2×Dic7⋊C4—41no—
131C2×Dic7⋊C4—41no—
132C2×Dic7⋊C4—41no—
133C2×Dic7⋊C4C2×C414yescomplemented
134C2×C4×Dic7—22no—
135C2×C4×Dic7—22no—
136C2×C4×Dic7—41no—
137C7×#95—22no—
138C7×#95D414yes—
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⋊#95—41no—
152C7⋊#95—41no—
153C7⋊#95C2×C414yescomplemented
154C7⋊#95C2×C414yescomplemented
155C2×#389D711yescharacteristic, complemented
156C2×#385—71no—
157C2×#385—71no—
158C2×#385—71no—
159C2×#380—71no—
160C2×C4×C22⋊C4—71no—
161C22×#95—71no—
162#1444—71no—
163#1442—71no—
164#1441—71no—
165#1441—71no—
166#1436—71no—
167#1436—71no—
168C4⋊#95—71no—
169C22⋊#95—71no—
170C24×C7C2411yescharacteristic
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7—21no—
175C23×D7—21no—
176C23×D7—21no—
177C23×D7—21no—
178C23×D7—21no—
179C23×D7C22×C412yes—
180C23×D7C2×D412yes—
181C23×D7C2×D412yes—
182C23×D7C2×Q812yes—
183C23×D7C2×Q812yes—
184C23×D7#4112yes—
185C23×D7#4112yes—
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×D412yes—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×Q812yes—
232C22×C4×C7C2×Q812yes—
233C22×C4×C7#4112yes—
234C22×C4×C7#4112yes—
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×Dic7—21no—
273C22×Dic7—21no—
274C22×Dic7—21no—
275C22×Dic7—21no—
276C22×Dic7C22×C412yes—
277C22×Dic7C22×C412yes—
278C22×Dic7C22×C412yes—
279C22×Dic7C2×D412yes—
280C22×Dic7C2×D412yes—
281C22×Dic7C2×Q812yes—
282C22×Dic7C2×Q812yes—
283C22×Dic7#4112yes—
284C2×C4×D7—28no—
285C2×C4×D7—28no—
286C2×C4×D7—28no—
287C2×C4×D7—28no—
288C2×C4×D7—28no—
289C2×C4×D7—44no—
290C2×C4×D7—44no—
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—
302C2×C4×D7—44no—
303C2×C4×D7—44no—
304C2×C4×D7—44no—
305C7×C4⋊C4—28no—
306C7×C4⋊C4—44no—
307C7×C4⋊C4—44no—
308C7×C4⋊C4—44no—
309C42×C7—44no—
310(C2×D7)⋊C4—28no—
311(C2×D7)⋊C4—28no—
312(C2×D7)⋊C4—44no—
313(C2×D7)⋊C4C4⋊C4116yescomplemented
314C4⋊Dic7—44no—
315Dic7⋊C4—44no—
316Dic7⋊C4—44no—
317Dic7⋊C4—44no—
318C4×Dic7—44no—
319C24×C4—71no—
320C24×C4—71no—
321C24×C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326C22×C4⋊C4C2×D711yescharacteristic
327C22×C4⋊C4C2×D711yescharacteristic
328C22×C4⋊C4C2×D711yescharacteristic
329C22×C4⋊C4C2×D711yescharacteristic
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C42—71no—
335C22×C42C2×D711yescharacteristic
336#389—24no—
337#385—78no—
338#385—144no—
339#385—144no—
340#380—144no—
341C4×C22⋊C4—144no—
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×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—71no—
357C2×#95—71no—
358C2×#95—144no—
359C2×#95C2×D711yescharacteristic
360C2×#95C2×D711yescharacteristic
361C23×C7C23×C411yescharacteristic
362C23×C7C22×D411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C22×D411yescharacteristic
365C23×C7C22×Q811yescharacteristic
366C23×C7C22×Q811yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7H(5,𝔽2)11yescharacteristic
373C23×C7H(5,𝔽2)11yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C72−1+411yescharacteristic
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—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—22no—
404C22×D7C2×C4⋊C414yes—
405C22×D7C4×D414yes—
406C22×D7C4×Q814yes—
407C22×D7#12114yes—
408C22×D7C22⋊Q814yes—
409C22×D7#12514yes—
410C22×D7C4⋊Q814yes—
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—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
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×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7C2×C4⋊C414yes—
458C2×C4×C7C4×D414yes—
459C2×C4×C7C22⋊Q814yes—
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—22no—
480C2×Dic7—22no—
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×Dic7—41no—
503C2×Dic7—41no—
504C2×Dic7—41no—
505C2×Dic7—41no—
506C2×Dic7—41no—
507C2×Dic7—41no—
508C2×Dic7C2×C4⋊C414yes—
509C4×D7—416no—
510C4×D7—416no—
511C4×D7—416no—
512C25—71no—
513C23×C4—71no—
514C23×C4—71no—
515C23×C4—71no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4—71no—
519C23×C4—74no—
520C23×C4—74no—
521C23×C4—71no—
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—281no—
536C23×C4—281no—
537C23×C4—281no—
538C23×C4—281no—
539C23×C4—281no—
540C23×C4—281no—
541C23×C4C22×D711yescharacteristic
542C23×C4C22×D711yescharacteristic
543C23×C4C22×D711yescharacteristic
544C23×C4C22×D711yescharacteristic
545C23×C4C22×D711yescharacteristic
546C23×C4C22×D711yescharacteristic
547C23×C4C22×D711yescharacteristic
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—74no—
560C2×C4⋊C4—142no—
561C2×C4⋊C4—142no—
562C2×C4⋊C4—142no—
563C2×C4⋊C4—142no—
564C2×C4⋊C4—142no—
565C2×C4⋊C4—142no—
566C2×C4⋊C4—281no—
567C2×C4⋊C4—281no—
568C2×C4⋊C4—281no—
569C2×C4⋊C4—281no—
570C2×C4⋊C4—281no—
571C2×C4⋊C4C4×D714yescomplemented
572C2×C22⋊C4—74no—
573C2×C22⋊C4—74no—
574C2×C22⋊C4—74no—
575C2×C22⋊C4—74no—
576C2×C22⋊C4—74no—
577C2×C22⋊C4—142no—
578C2×C22⋊C4—142no—
579C2×C22⋊C4—142no—
580C2×C22⋊C4—142no—
581C2×C22⋊C4—142no—
582C2×C22⋊C4—142no—
583C2×C22⋊C4—142no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—41no—
587C2×C42—142no—
588C2×C42—142no—
589C2×C42—281no—
590#95—22no—
591#95—74no—
592#95—74no—
593#95—142no—
594#95—142no—
595#95—142no—
596#95—142no—
597#95—142no—
598#95—142no—
599#95—142no—
600#95—142no—
601#95—142no—
602#95—142no—
603#95—142no—
604#95—142no—
605#95—281no—
606#95—281no—
607#95C22⋊D714yes—
608C22×C7C22×C4⋊C411yescharacteristic
609C22×C7C2×C4×D411yescharacteristic
610C22×C7C2×C4×D411yescharacteristic
611C22×C7C2×C4×Q811yescharacteristic
612C22×C7C4×#4111yescharacteristic
613C22×C7#51811yescharacteristic
614C22×C7#52011yescharacteristic
615C22×C7C2×#12111yescharacteristic
616C22×C7C2×C22⋊Q811yescharacteristic
617C22×C7C2×C22⋊Q811yescharacteristic
618C22×C7#52511yescharacteristic
619C22×C7C2×#12511yescharacteristic
620C22×C7#52911yescharacteristic
621C22×C7C2×C4⋊Q811yescharacteristic
622C22×C7#53311yescharacteristic
623C22×C7#53811yescharacteristic
624C22×C7#53911yescharacteristic
625C22×C7#54311yescharacteristic
626C22×C7#54411yescharacteristic
627C22×C7D4211yescharacteristic
628C22×C7D4211yescharacteristic
629C22×C7#54611yescharacteristic
630C22×C7#54611yescharacteristic
631C22×C7#54611yescharacteristic
632C22×C7#54611yescharacteristic
633C22×C7#54611yescharacteristic
634C22×C7#54711yescharacteristic
635C22×C7#54711yescharacteristic
636C22×C7D4×Q811yescharacteristic
637C22×C7#55111yescharacteristic
638C22×C7#55111yescharacteristic
639C22×C7#55211yescharacteristic
640C22×C7#55411yescharacteristic
641C22×C7#55411yescharacteristic
642C22×C7#55411yescharacteristic
643C2×D7—24no—
644C2×D7—24no—
645C2×D7—24no—
646C2×D7—24no—
647C2×D7—24no—
648C2×D7—24no—
649C2×D7—24no—
650C2×D7—24no—
651C2×D7—24no—
652C2×D7—24no—
653C2×D7—24no—
654C2×D7—24no—
655C2×D7—24no—
656C2×D7—24no—
657C2×D7#38918yescomplemented
658C4×C7—24no—
659C4×C7—24no—
660C4×C7—24no—
661C4×C7—42no—
662C4×C7—42no—
663C4×C7—42no—
664C4×C7—81no—
665Dic7—24no—
666Dic7—42no—
667Dic7—42no—
668Dic7—42no—
669Dic7—42no—
670Dic7—42no—
671Dic7—81no—
672C24—72no—
673C24—72no—
674C24—72no—
675C24—72no—
676C24—72no—
677C24—72no—
678C24—72no—
679C24—141no—
680C24—141no—
681C24—141no—
682C24—141no—
683C24—141no—
684C24—141no—
685C24—141no—
686C24—141no—
687C24C23×D711yescharacteristic
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—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—72no—
726C22×C4—72no—
727C22×C4—72no—
728C22×C4—72no—
729C22×C4—72no—
730C22×C4—72no—
731C22×C4—72no—
732C22×C4—72no—
733C22×C4—148no—
734C22×C4—148no—
735C22×C4—148no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
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—141no—
766C22×C4—141no—
767C22×C4—141no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—148no—
771C22×C4—148no—
772C22×C4—141no—
773C22×C4—141no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—141no—
779C22×C4—284no—
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×C4—284no—
792C22×C4—284no—
793C22×C4—284no—
794C22×C4—284no—
795C22×C4C2×C4×D712yes—
796C22×C4C2×C4×D712yes—
797C22×C4C2×C4×D712yes—
798C22×C4#115712yes—
799C22×C4D4×D712yes—
800C22×C4D4×D712yes—
801C22×C4Q8×D712yes—
802C22×C4Q8×D712yes—
803C22×C4#116112yes—
804C22×C4C2×C22⋊D712yes—
805C22×C4C2×C22⋊D712yes—
806C22×C4C2×C22⋊D712yes—
807C4⋊C4—28no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—284no—
812C4⋊C4—284no—
813C4⋊C4—284no—
814C4⋊C4—284no—
815C22⋊C4—716no—
816C22⋊C4—148no—
817C22⋊C4—148no—
818C22⋊C4—284no—
819C42—44no—
820C42—284no—
821C2×C7C2×#38911yescharacteristic
822C2×C7C4×C22⋊Q811yescharacteristic
823C2×C7#232911yescharacteristic
824C2×C7D4×C4⋊C411yescharacteristic
825C2×C7#234911yescharacteristic
826C2×C7#235811yescharacteristic
827C2×C7#235911yescharacteristic
828C2×C7#242411yescharacteristic
829C2×C7#242511yescharacteristic
830C2×C7#243711yescharacteristic
831C2×C7#243811yescharacteristic
832C2×C7#244011yescharacteristic
833C2×C7#247311yescharacteristic
834C2×C7#250511yescharacteristic
835C2×C7#254911yescharacteristic
836D7—28no—
837C23—74no—
838C23—74no—
839C23—74no—
840C23—74no—
841C23—74no—
842C23—74no—
843C23—74no—
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—
862C23—142no—
863C23—142no—
864C23—142no—
865C23—142no—
866C23—142no—
867C23—142no—
868C23—142no—
869C23—142no—
870C23—142no—
871C23—142no—
872C23C22×C4×D711yescharacteristic
873C23C2×#115711yescharacteristic
874C23C2×D4×D711yescharacteristic
875C23C2×D4×D711yescharacteristic
876C23#654811yescharacteristic
877C23#654811yescharacteristic
878C23C2×Q8×D711yescharacteristic
879C23C2×Q8×D711yescharacteristic
880C23C2×#116111yescharacteristic
881C23#655111yescharacteristic
882C23D7×#4111yescharacteristic
883C23D7×#4111yescharacteristic
884C23D7×#4111yescharacteristic
885C23#655311yescharacteristic
886C23C22×C22⋊D711yescharacteristic
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—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
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—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—74no—
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—142no—
954C2×C4—142no—
955C2×C4—2816no—
956C2×C4—2816no—
957C2×C4—2816no—
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—281no—
978C2×C4—281no—
979C2×C4—281no—
980C2×C4—281no—
981C2×C4—281no—
982C2×C4—281no—
983C2×C4—281no—
984C2×C4—281no—
985C2×C4D7×C4⋊C414yes—
986C2×C4C4×C22⋊D714yes—
987C2×C4#650914yes—
988C7#1400411yescharacteristic, complemented, Sylow
989C22—78no—
990C22—144no—
991C22—144no—
992C22—144no—
993C22—144no—
994C22—144no—
995C22—144no—
996C22—144no—
997C22—144no—
998C22—144no—
999C22—144no—
1000C22—144no—
1001C22—144no—
1002C22—144no—
1003C22—144no—
1004C22C2×D7×C4⋊C411yescharacteristic
1005C22#9019511yescharacteristic
1006C22#9019811yescharacteristic
1007C22#9020211yescharacteristic
1008C22C4×D4×D711yescharacteristic
1009C22#9023611yescharacteristic
1010C22#9024111yescharacteristic
1011C22#9024711yescharacteristic
1012C22C4×Q8×D711yescharacteristic
1013C22C4×#116111yescharacteristic
1014C22#9026911yescharacteristic
1015C22#9027111yescharacteristic
1016C22D7×#12111yescharacteristic
1017C22#9030111yescharacteristic
1018C22#9030311yescharacteristic
1019C22#9030411yescharacteristic
1020C22D7×C22⋊Q811yescharacteristic
1021C22#9032111yescharacteristic
1022C22#9032511yescharacteristic
1023C22#9032811yescharacteristic
1024C22D7×#12511yescharacteristic
1025C22#9038111yescharacteristic
1026C22#9038311yescharacteristic
1027C22#9038411yescharacteristic
1028C22D7×C4⋊Q811yescharacteristic
1029C22#9041711yescharacteristic
1030C22#9042011yescharacteristic
1031C22#9042111yescharacteristic
1032C22C2×C4×C22⋊D711yescharacteristic
1033C22D4×C22⋊D711yescharacteristic
1034C22D4×C22⋊D711yescharacteristic
1035C22C2×#650911yescharacteristic
1036C22Q8×C22⋊D711yescharacteristic
1037C22#9051911yescharacteristic
1038C22#9052011yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—81no—
1046C4—144no—
1047C4—282no—
1048C4—282no—
1049C4—282no—
1050C4—282no—
1051C4—282no—
1052C4—561no—
1053C2—148no—
1054C2D7×#38911yescharacteristic
1055C2#1173364411yescharacteristic
1056C2#1173364811yescharacteristic
1057C2#1173364911yescharacteristic
1058C2#1173366211yescharacteristic
1059C2#1173366711yescharacteristic
1060C2#1173368611yescharacteristic
1061C2#1173368911yescharacteristic
1062C2C4⋊C4×C22⋊D711yescharacteristic
1063C2#1173984311yescharacteristic
1064C2C4×#650911yescharacteristic
1065C2#1174015211yescharacteristic
1066C2#1174026111yescharacteristic
1067C2#1174047711yescharacteristic
1068C2#1174067811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#389D7
hypocenterC7#14004
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C7×#389C2semidirect
8. #11729322C2semidirect
9. #11729321C2semidirect
10. #11729320C2semidirect
11. #11729319C2semidirect
12. #11729290C2semidirect
14. #11727161C2semidirect
15. Dic7⋊#95C2semidirect
54. #89761C4semidirect
106. C2×C7×C4⋊C4C2×C4semidirect
133. C2×Dic7⋊C4C2×C4semidirect
153. C7⋊#95C2×C4semidirect
154. C7⋊#95C2×C4semidirect
155. C2×#389D7semidirect
313. (C2×D7)⋊C4C4⋊C4semidirect
571. C2×C4⋊C4C4×D7semidirect
657. C2×D7#389semidirect
988. C7#14004semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#897612
C2×#897592
C2×C4×(C2×D7)⋊C42
C2×D7×#952
#117293222
#117293212
#117293202
#117293192
#117292902
(C2×D7)⋊#952
#117271612
Dic7⋊#952
#140047