Finite Group Databasebeta

← #13277751

Subgroups — #13277751

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6455C211yesmaximal, characteristic
2C2×C7×#387C211yesmaximal, characteristic, complemented
3C2×#89761C211yesmaximal, characteristic
4C2×#89712C211yesmaximal, characteristic
5C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
6#11729319C211yesmaximal, characteristic, complemented
7#11729318C211yesmaximal, characteristic, complemented
8#11727183C211yesmaximal, characteristic
9#11727182C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727174C211yesmaximal, characteristic, complemented
12#11727162C211yesmaximal, characteristic
13#11727160C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727156C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×#6455—24no—
34C2×#6455—24no—
35C2×#6455—24no—
36C7×#387—24no—
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
54C2×C7⋊#95C2211yescharacteristic
55#89761C418yescomplemented
56#89712—24no—
57C4×Dic7⋊C4—24no—
58#14063—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×D7C2×C414yes—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4C2×C414yes—
86C2×C7×C4⋊C4D414yes—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—22no—
92C2×(C2×D7)⋊C4—22no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—22no—
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4—41no—
104C2×(C2×D7)⋊C4—41no—
105C2×(C2×D7)⋊C4C2×C414yes—
106C2×(C2×D7)⋊C4C2×C414yes—
107C2×(C2×D7)⋊C4D414yes—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—41no—
119C2×Dic7⋊C4C2×C414yes—
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—22no—
128C2×C4×Dic7D414yes—
129#6455—232no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—41no—
144C7⋊#95—41no—
145C7⋊#95—41no—
146C7⋊#95C2×C414yes—
147C7⋊#95C2×C414yes—
148C22×#117—71no—
149C2×#388—71no—
150C2×#387D711yescharacteristic, complemented
151C2×#385—71no—
152C2×C4×C4⋊C4—71no—
153#1444—71no—
154#1441—71no—
155#1440—71no—
156#1439—71no—
157#1437—71no—
158#1436—71no—
159#1436—71no—
160#1436—71no—
161#1434—71no—
162C22⋊#95—71no—
163C24×C7C2411yescharacteristic
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
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×D7#4112yes—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
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×C7C22×C412yes—
219C22×C4×C7C22×C412yes—
220C22×C4×C7C22×C412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×D412yes—
223C22×C4×C7C2×D412yes—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7#4112yes—
227C22×C4×C7#4112yes—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
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×Dic7C22×C412yes—
268C22×Dic7C22×C412yes—
269C22×Dic7C22×C412yes—
270C22×Dic7C2×D412yes—
271C22×Dic7C2×D412yes—
272C22×Dic7C2×D412yes—
273C22×Dic7#4112yes—
274C22×Dic7#4112yes—
275C22×Dic7#4112yes—
276C22×Dic7#4112yes—
277C2×C4×D7—28no—
278C2×C4×D7—28no—
279C2×C4×D7—28no—
280C2×C4×D7—28no—
281C2×C4×D7—28no—
282C2×C4×D7—28no—
283C2×C4×D7—28no—
284C7×C4⋊C4—28no—
285C7×C4⋊C4—28no—
286C42×C7—44no—
287(C2×D7)⋊C4—28no—
288(C2×D7)⋊C4—28no—
289(C2×D7)⋊C4—28no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—44no—
292(C2×D7)⋊C4—44no—
293C4⋊Dic7—28no—
294Dic7⋊C4—28no—
295Dic7⋊C4—28no—
296Dic7⋊C4—44no—
297C4×Dic7—28no—
298C4×Dic7—28no—
299C4×Dic7—28no—
300C24×C4—71no—
301C2×#117—144no—
302C2×#117—144no—
303C2×#117—144no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4C2×D711yescharacteristic
309C22×C4⋊C4C2×D711yescharacteristic
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C42—71no—
317C22×C42—71no—
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320#388—144no—
321#387—24no—
322#385—78no—
323C4×C4⋊C4—144no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C23×C7C23×C411yescharacteristic
343C23×C7C22×D411yescharacteristic
344C23×C7C22×D411yescharacteristic
345C23×C7C22×D411yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7C2×#4111yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7C2×#4111yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7H(5,𝔽2)11yescharacteristic
354C23×C72−1+411yescharacteristic
355C23×C72−1+411yescharacteristic
356C23×C72−1+411yescharacteristic
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7—41no—
388C22×D7—41no—
389C22×D7—41no—
390C22×D7—41no—
391C22×D7C4×D414yes—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
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—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
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×C7C4×D414yes—
440C2×C4×C7#12014yes—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
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—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
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#11714yescomplemented
489C2×Dic7C4×D414yes—
490C4×D7—232no—
491C25—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—71no—
496C23×C4—71no—
497C23×C4—71no—
498C23×C4—74no—
499C23×C4—71no—
500C23×C4—142no—
501C23×C4—142no—
502C23×C4—142no—
503C23×C4—142no—
504C23×C4—142no—
505C23×C4—142no—
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C23×C4C22×D711yescharacteristic
509C23×C4C22×D711yescharacteristic
510C23×C4C22×D711yescharacteristic
511C23×C4C22×D711yescharacteristic
512C23×C4C22×D711yescharacteristic
513#117—1432no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—74no—
519C2×C4⋊C4—142no—
520C2×C4⋊C4—142no—
521C2×C4⋊C4—142no—
522C2×C4⋊C4—142no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—281no—
530C2×C4⋊C4C4×D714yes—
531C2×C4⋊C4C22⋊D714yes—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—142no—
536C2×C22⋊C4—142no—
537C2×C22⋊C4—142no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—142no—
547C2×C22⋊C4—142no—
548C2×C22⋊C4—281no—
549C2×C22⋊C4—281no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—74no—
554C2×C42—142no—
555C2×C42—142no—
556C2×C42—142no—
557C2×C42—142no—
558C2×C42—142no—
559C2×C42—142no—
560C2×C42—142no—
561C2×C42—142no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—74no—
567#95—74no—
568#95—142no—
569#95—142no—
570#95—142no—
571#95—142no—
572#95—142no—
573#95—142no—
574#95—142no—
575#95—142no—
576#95—142no—
577#95—281no—
578#95—281no—
579#95—281no—
580C22×C7C2×#11711yescharacteristic
581C22×C7C2×C4×D411yescharacteristic
582C22×C7C2×C4×D411yescharacteristic
583C22×C7C2×C4×D411yescharacteristic
584C22×C7C4×#4111yescharacteristic
585C22×C7#51911yescharacteristic
586C22×C7#52011yescharacteristic
587C22×C7C2×#12011yescharacteristic
588C22×C7#52511yescharacteristic
589C22×C7#52511yescharacteristic
590C22×C7#52511yescharacteristic
591C22×C7#52511yescharacteristic
592C22×C7#52511yescharacteristic
593C22×C7#52911yescharacteristic
594C22×C7#52911yescharacteristic
595C22×C7#53611yescharacteristic
596C22×C7#53711yescharacteristic
597C22×C7#54111yescharacteristic
598C22×C7#54211yescharacteristic
599C22×C7#54611yescharacteristic
600C22×C7#54711yescharacteristic
601C22×C7#54711yescharacteristic
602C22×C7#54711yescharacteristic
603C22×C7#54711yescharacteristic
604C22×C7#54711yescharacteristic
605C22×C7#54811yescharacteristic
606C22×C7#55011yescharacteristic
607C22×C7#55111yescharacteristic
608C22×C7#55211yescharacteristic
609C22×C7#55211yescharacteristic
610C22×C7#55211yescharacteristic
611C22×C7#55211yescharacteristic
612C22×C7#55511yescharacteristic
613C22×C7#55611yescharacteristic
614C22×C7#55611yescharacteristic
615C2×D7—24no—
616C2×D7—24no—
617C2×D7—24no—
618C2×D7—42no—
619C2×D7—42no—
620C2×D7—42no—
621C2×D7—42no—
622C2×D7—42no—
623C2×D7—42no—
624C2×D7—42no—
625C2×D7—42no—
626C2×D7—42no—
627C2×D7—42no—
628C2×D7—42no—
629C2×D7—42no—
630C4×C7—24no—
631C4×C7—24no—
632C4×C7—42no—
633C4×C7—42no—
634C4×C7—42no—
635C4×C7—42no—
636C4×C7—81no—
637Dic7—24no—
638Dic7—24no—
639Dic7—42no—
640Dic7—42no—
641Dic7—42no—
642Dic7—42no—
643Dic7—81no—
644C24—72no—
645C24—72no—
646C24—72no—
647C24—141no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—141no—
653C24—141no—
654C24—141no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24—141no—
659C24C23×D711yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
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—72no—
700C22×C4—72no—
701C22×C4—72no—
702C22×C4—72no—
703C22×C4—72no—
704C22×C4—72no—
705C22×C4—72no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—148no—
710C22×C4—148no—
711C22×C4—148no—
712C22×C4—148no—
713C22×C4—148no—
714C22×C4—148no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—148no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4—141no—
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×C4C2×C4×D712yes—
756C22×C4C2×C4×D712yes—
757C22×C4C2×C4×D712yes—
758C22×C4#115712yes—
759C22×C4D4×D712yes—
760C22×C4D4×D712yes—
761C22×C4#116112yes—
762C22×C4C2×C22⋊D712yes—
763C22×C4C2×C22⋊D712yes—
764C22×C4C2×C22⋊D712yes—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—148no—
768C4⋊C4—148no—
769C4⋊C4—148no—
770C4⋊C4—284no—
771C22⋊C4—148no—
772C22⋊C4—148no—
773C22⋊C4—148no—
774C22⋊C4—148no—
775C22⋊C4—284no—
776C22⋊C4—284no—
777C42—44no—
778C42—148no—
779C42—148no—
780C42—148no—
781C2×C7#229011yescharacteristic
782C2×C7C4×#12011yescharacteristic
783C2×C7#232311yescharacteristic
784C2×C7#234411yescharacteristic
785C2×C7#235411yescharacteristic
786C2×C7#235911yescharacteristic
787C2×C7#236211yescharacteristic
788C2×C7#240611yescharacteristic
789C2×C7#240711yescharacteristic
790C2×C7#247411yescharacteristic
791C2×C7#247511yescharacteristic
792C2×C7#247811yescharacteristic
793C2×C7#247911yescharacteristic
794C2×C7#259911yescharacteristic
795C2×C7#260911yescharacteristic
796D7—44no—
797C23—74no—
798C23—142no—
799C23—142no—
800C23—142no—
801C23—142no—
802C23—142no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—142no—
812C23—142no—
813C23—142no—
814C23—142no—
815C23—142no—
816C23—281no—
817C23—281no—
818C23—281no—
819C23—281no—
820C23—281no—
821C23—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23—281no—
827C23—281no—
828C23—281no—
829C23—281no—
830C23—281no—
831C23—281no—
832C23C22×C4×D711yescharacteristic
833C23C2×#115711yescharacteristic
834C23C2×D4×D711yescharacteristic
835C23C2×D4×D711yescharacteristic
836C23C2×#116111yescharacteristic
837C23#655111yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23D7×#4111yescharacteristic
841C23D7×#4111yescharacteristic
842C23D7×#4111yescharacteristic
843C23#655311yescharacteristic
844C23#655411yescharacteristic
845C23#655411yescharacteristic
846C23C22×C22⋊D711yescharacteristic
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—74no—
895C2×C4—74no—
896C2×C4—1432no—
897C2×C4—142no—
898C2×C4—142no—
899C2×C4—142no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—142no—
917C2×C4—142no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4—281no—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4—281no—
927C2×C4—281no—
928C2×C4—281no—
929C2×C4—281no—
930C2×C4—281no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4—281no—
939C2×C4—281no—
940C2×C4—281no—
941C2×C4—281no—
942C2×C4—281no—
943C2×C4—281no—
944C2×C4C4×C22⋊D714yes—
945C2×C4#650014yes—
946C7#1406311yescharacteristic, complemented, Sylow
947C22—144no—
948C22—144no—
949C22—144no—
950C22—282no—
951C22—282no—
952C22—282no—
953C22—282no—
954C22—282no—
955C22—282no—
956C22—282no—
957C22—282no—
958C22—282no—
959C22—282no—
960C22—282no—
961C22—282no—
962C22D7×#11711yescharacteristic
963C22#9021411yescharacteristic
964C22#9022311yescharacteristic
965C22#9022411yescharacteristic
966C22C4×D4×D711yescharacteristic
967C22C4×D4×D711yescharacteristic
968C22#9023811yescharacteristic
969C22#9023811yescharacteristic
970C22#9026311yescharacteristic
971C22C4×#116111yescharacteristic
972C22#9027211yescharacteristic
973C22#9027511yescharacteristic
974C22#9031811yescharacteristic
975C22#9032011yescharacteristic
976C22#9032111yescharacteristic
977C22#9032211yescharacteristic
978C22#9033911yescharacteristic
979C22#9034611yescharacteristic
980C22#9034611yescharacteristic
981C22#9034711yescharacteristic
982C22#9038211yescharacteristic
983C22#9038411yescharacteristic
984C22#9038511yescharacteristic
985C22#9038711yescharacteristic
986C22#9039611yescharacteristic
987C22#9039711yescharacteristic
988C22#9039911yescharacteristic
989C22#9040111yescharacteristic
990C22C2×C4×C22⋊D711yescharacteristic
991C22C2×#650011yescharacteristic
992C22#9050811yescharacteristic
993C22#9051511yescharacteristic
994C22#9051511yescharacteristic
995C22#9051911yescharacteristic
996C22#9052511yescharacteristic
997C4—24no—
998C4—24no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—144no—
1005C4—144no—
1006C4—282no—
1007C4—282no—
1008C4—282no—
1009C4—282no—
1010C4—561no—
1011C2—284no—
1012C2#1173238211yescharacteristic
1013C2#1173239211yescharacteristic
1014C2#1173240611yescharacteristic
1015C2#1173245511yescharacteristic
1016C2#1173246011yescharacteristic
1017C2#1173257011yescharacteristic
1018C2#1173275311yescharacteristic
1019C2#1173282011yescharacteristic
1020C2#1173968611yescharacteristic
1021C2C4×#650011yescharacteristic
1022C2#1173990911yescharacteristic
1023C2#1174025711yescharacteristic
1024C2#1174028611yescharacteristic
1025C2#1174047811yescharacteristic
1026C2#1174052511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#387C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#387D7
hypocenterC7#14063
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C2×C7×#387C2semidirect
5. C2×C4×Dic7⋊C4C2semidirect
6. #11729319C2semidirect
7. #11729318C2semidirect
11. #11727174C2semidirect
13. #11727160C2semidirect
14. #11727160C2semidirect
15. #11727156C2semidirect
55. #89761C4semidirect
150. C2×#387D7semidirect
488. C2×Dic7#117semidirect
946. C7#14063semidirect

Maximal subgroups

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

subgroupindex
C22×#64552
C2×C7×#3872
C2×#897612
C2×#897122
C2×C4×Dic7⋊C42
#117293192
#117293182
#117271832
#117271822
(C2×D7)⋊#952
#117271742
#117271622
#117271602
#117271562
#140637