Finite Group Databasebeta

← #13276407

Subgroups — #13276407

Order 1792.

1486 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89438C211yesmaximal, characteristic
2C7×#1434C211yesmaximal, characteristic, complemented
3#11729291C211yesmaximal, characteristic
4C4×C7⋊#95C211yesmaximal, characteristic, complemented
5#11727183C211yesmaximal, characteristic
6#11727183C211yesmaximal, characteristic
7(C2×D7)⋊#95C211yesmaximal, characteristic
8(C2×D7)⋊#95C211yesmaximal, characteristic
9#11727172C211yesmaximal, characteristic, complemented
10#11727171C211yesmaximal, characteristic, complemented
11#11727162C211yesmaximal, characteristic
12#11727157C211yesmaximal, characteristic, complemented
13#11727156C211yesmaximal, characteristic, complemented
14#11727155C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7⋊#95C2211yescharacteristic
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
51#89438C418yescomplemented
52#13947—71nomaximal, Sylow
53C24×D7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×Dic7C2311yescharacteristic
62C23×Dic7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C22×C4×D7—22no—
69C22×C4×D7—22no—
70C22×C4×D7—41no—
71C22×C4×D7—41no—
72C22×C4×D7—41no—
73C22×C4×D7—41no—
74C22×C4×D7C2×C414yes—
75C2×C42×C7—22no—
76C2×C42×C7—22no—
77C2×C42×C7—41no—
78C2×(C2×D7)⋊C4—22no—
79C2×(C2×D7)⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×(C2×D7)⋊C4—22no—
85C2×(C2×D7)⋊C4—22no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—22no—
89C2×(C2×D7)⋊C4—22no—
90C2×(C2×D7)⋊C4—41no—
91C2×(C2×D7)⋊C4—41no—
92C2×(C2×D7)⋊C4—41no—
93C2×(C2×D7)⋊C4—41no—
94C2×(C2×D7)⋊C4C2×C414yes—
95C2×(C2×D7)⋊C4C2×C414yes—
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—41no—
99C2×C4×Dic7—41no—
100C2×C4×Dic7—41no—
101C2×C4×Dic7—41no—
102C2×C4×Dic7—41no—
103C2×C4×Dic7C2×C414yes—
104C2×C4×Dic7C2×C414yes—
105C7×#95—22no—
106C7×#95—22no—
107C7×#95—41no—
108C7×#95—41no—
109C7×#95—41no—
110C7×#95C2×C414yes—
111C7⋊#95—22no—
112C7⋊#95—22no—
113C7⋊#95—22no—
114C7⋊#95—22no—
115C7⋊#95—22no—
116C7⋊#95—22no—
117C7⋊#95—22no—
118C7⋊#95—22no—
119C7⋊#95—22no—
120C7⋊#95—22no—
121C7⋊#95—41no—
122C7⋊#95—41no—
123C7⋊#95—41no—
124C7⋊#95—41no—
125C7⋊#95—41no—
126C7⋊#95—41no—
127C7⋊#95—41no—
128C7⋊#95C2×C414yes—
129C2×C4×C22⋊C4—71no—
130#1443—71no—
131#1443—71no—
132#1440—71no—
133#1440—71no—
134#1437—71no—
135#1437—71no—
136#1434—71no—
137#1434—71no—
138#1434—71no—
139#1434—71no—
140#1434D711yescharacteristic, complemented
141C22⋊#95—71no—
142C22⋊#95—71no—
143C4×#95—71no—
144C24×C7C2411yescharacteristic
145C23×D7—21no—
146C23×D7—21no—
147C23×D7—21no—
148C23×D7—21no—
149C23×D7—21no—
150C23×D7—21no—
151C23×D7—21no—
152C23×D7—21no—
153C23×D7—21no—
154C23×D7—21no—
155C23×D7—21no—
156C23×D7—21no—
157C23×D7C22×C412yes—
158C23×D7#4112yes—
159C23×D7#4112yes—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
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×C7C22×C412yes—
203C22×C4×C7C22×C412yes—
204C22×C4×C7C22×C412yes—
205C22×C4×C7#4112yes—
206C22×C4×C7#4112yes—
207C22×C4×C7#4112yes—
208C22×C4×C7#4112yes—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
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×Dic7C22×C412yes—
252C22×Dic7C22×C412yes—
253C22×Dic7C22×C412yes—
254C22×Dic7#4112yes—
255C22×Dic7#4112yes—
256C22×Dic7#4112yes—
257C22×Dic7#4112yes—
258C2×C4×D7—28no—
259C2×C4×D7—44no—
260C2×C4×D7—44no—
261C2×C4×D7—44no—
262C2×C4×D7—44no—
263C2×C4×D7—44no—
264C2×C4×D7—44no—
265C42×C7—44no—
266(C2×D7)⋊C4—28no—
267(C2×D7)⋊C4—28no—
268(C2×D7)⋊C4—44no—
269(C2×D7)⋊C4—44no—
270(C2×D7)⋊C4—44no—
271(C2×D7)⋊C4—44no—
272C4×Dic7—44no—
273C4×Dic7—44no—
274C4×Dic7—44no—
275C24×C4—71no—
276C22×C22⋊C4—71no—
277C22×C22⋊C4—71no—
278C22×C22⋊C4—71no—
279C22×C22⋊C4—71no—
280C22×C22⋊C4—71no—
281C22×C22⋊C4—71no—
282C22×C42—71no—
283C22×C42—71no—
284C22×C42—71no—
285C22×C42C2×D711yescharacteristic
286C4×C22⋊C4—78no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95C2×D711yescharacteristic
306C2×#95C2×D711yescharacteristic
307C2×#95C2×D711yescharacteristic
308C2×#95C2×D711yescharacteristic
309C2×#95C2×D711yescharacteristic
310C2×#95C2×D711yescharacteristic
311C23×C7C23×C411yescharacteristic
312C23×C7C2×#4111yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7C2×#4111yescharacteristic
319C23×C7C2×#4111yescharacteristic
320C23×C7C2×#4111yescharacteristic
321C23×C7C2×#4111yescharacteristic
322C23×C7H(5,𝔽2)11yescharacteristic
323C23×C7H(5,𝔽2)11yescharacteristic
324C23×C7H(5,𝔽2)11yescharacteristic
325C23×C7H(5,𝔽2)11yescharacteristic
326C22×D7—22no—
327C22×D7—22no—
328C22×D7—22no—
329C22×D7—22no—
330C22×D7—22no—
331C22×D7—22no—
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—22no—
342C22×D7—22no—
343C22×D7—22no—
344C22×D7—41no—
345C22×D7—41no—
346C22×D7—41no—
347C22×D7—41no—
348C22×D7—41no—
349C22×D7—41no—
350C22×D7—41no—
351C22×D7—41no—
352C22×D7—41no—
353C22×D7—41no—
354C22×D7—41no—
355C22×D7—41no—
356C22×D7—41no—
357C22×D7—41no—
358C22×D7—41no—
359C22×D7—41no—
360C22×D7#11714yes—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7#11714yes—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—41no—
440C2×Dic7—41no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—41no—
445C2×Dic7—41no—
446C2×Dic7—41no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—41no—
450C2×Dic7—41no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7#11714yes—
459C4×D7—416no—
460C25—71no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—74no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—142no—
470C23×C4—142no—
471C23×C4—281no—
472C23×C4—281no—
473C23×C4—281no—
474C23×C4—281no—
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4—142no—
485C2×C22⋊C4—142no—
486C2×C22⋊C4—142no—
487C2×C22⋊C4—142no—
488C2×C22⋊C4—142no—
489C2×C22⋊C4—142no—
490C2×C22⋊C4—142no—
491C2×C22⋊C4—142no—
492C2×C22⋊C4—142no—
493C2×C22⋊C4—142no—
494C2×C22⋊C4—142no—
495C2×C22⋊C4—142no—
496C2×C22⋊C4—281no—
497C2×C22⋊C4—281no—
498C2×C22⋊C4—281no—
499C2×C22⋊C4—281no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—41no—
503C2×C42—74no—
504C2×C42—74no—
505C2×C42—142no—
506C2×C42—142no—
507C2×C42—281no—
508C2×C42—281no—
509C2×C42—281no—
510C2×C42—281no—
511C2×C42—281no—
512#95—22no—
513#95—22no—
514#95—41no—
515#95—41no—
516#95—41no—
517#95—74no—
518#95—142no—
519#95—142no—
520#95—142no—
521#95—142no—
522#95—142no—
523#95—142no—
524#95—142no—
525#95—142no—
526#95—142no—
527#95—142no—
528#95—281no—
529#95—281no—
530#95—281no—
531#95—281no—
532#95—281no—
533#95—281no—
534#95—281no—
535#95C4×D714yes—
536C22×C7C2×#11711yescharacteristic
537C22×C7C2×#11711yescharacteristic
538C22×C7C2×#11711yescharacteristic
539C22×C7C4×#4111yescharacteristic
540C22×C7C4×#4111yescharacteristic
541C22×C7#51811yescharacteristic
542C22×C7#51811yescharacteristic
543C22×C7#52911yescharacteristic
544C22×C7#52911yescharacteristic
545C22×C7#52911yescharacteristic
546C22×C7#52911yescharacteristic
547C22×C7#52911yescharacteristic
548C22×C7#52911yescharacteristic
549C22×C7#52911yescharacteristic
550C22×C7#52911yescharacteristic
551C22×C7#53811yescharacteristic
552C22×C7#53811yescharacteristic
553C22×C7#53811yescharacteristic
554C22×C7#53811yescharacteristic
555C22×C7#55111yescharacteristic
556C22×C7#55111yescharacteristic
557C22×C7#55111yescharacteristic
558C22×C7#55111yescharacteristic
559C22×C7#55111yescharacteristic
560C22×C7#55111yescharacteristic
561C22×C7#55311yescharacteristic
562C22×C7#55311yescharacteristic
563C22×C7#55311yescharacteristic
564C22×C7#55311yescharacteristic
565C22×C7#55311yescharacteristic
566C22×C7#55311yescharacteristic
567C22×C7#55311yescharacteristic
568C22×C7#55311yescharacteristic
569C22×C7#55911yescharacteristic
570C22×C7#55911yescharacteristic
571C2×D7—24no—
572C2×D7—24no—
573C2×D7—24no—
574C2×D7—42no—
575C2×D7—42no—
576C2×D7—42no—
577C2×D7—42no—
578C2×D7—42no—
579C2×D7—42no—
580C2×D7—42no—
581C2×D7—42no—
582C2×D7—42no—
583C2×D7—42no—
584C2×D7—42no—
585C2×D7—42no—
586C4×C7—24no—
587C4×C7—42no—
588C4×C7—42no—
589C4×C7—42no—
590C4×C7—42no—
591C4×C7—81no—
592C4×C7—81no—
593Dic7—24no—
594Dic7—42no—
595Dic7—42no—
596Dic7—42no—
597Dic7—42no—
598Dic7—81no—
599Dic7—81no—
600C24—72no—
601C24—72no—
602C24—72no—
603C24—141no—
604C24—141no—
605C24—141no—
606C24—141no—
607C24—141no—
608C24—141no—
609C24—141no—
610C24—141no—
611C24—141no—
612C24—141no—
613C24—141no—
614C24—141no—
615C24C23×D711yescharacteristic
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—72no—
659C22×C4—72no—
660C22×C4—72no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—148no—
666C22×C4—141no—
667C22×C4—141no—
668C22×C4—141no—
669C22×C4—141no—
670C22×C4—141no—
671C22×C4—141no—
672C22×C4—141no—
673C22×C4—141no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
678C22×C4—141no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4—141no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—141no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—284no—
709C22×C4—284no—
710C22×C4—284no—
711C22×C4—284no—
712C22×C4—284no—
713C22×C4—284no—
714C22×C4C2×C4×D712yes—
715C22×C4C2×C4×D712yes—
716C22×C4C2×C4×D712yes—
717C22×C4#115712yes—
718C22×C4#115712yes—
719C22×C4#115912yes—
720C22×C4#116112yes—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C22⋊C4—284no—
724C22⋊C4—284no—
725C22⋊C4—284no—
726C22⋊C4—284no—
727C42—44no—
728C42—284no—
729C42—284no—
730C42—284no—
731C2×C7#228311yescharacteristic
732C2×C7#229811yescharacteristic
733C2×C7#231211yescharacteristic
734C2×C7#235311yescharacteristic
735C2×C7#235311yescharacteristic
736C2×C7#235311yescharacteristic
737C2×C7#235711yescharacteristic
738C2×C7#257611yescharacteristic
739C2×C7#257611yescharacteristic
740C2×C7#257811yescharacteristic
741C2×C7#257811yescharacteristic
742C2×C7#259511yescharacteristic
743C2×C7#259511yescharacteristic
744C2×C7#259711yescharacteristic
745C2×C7#259711yescharacteristic
746D7—44no—
747C23—74no—
748C23—142no—
749C23—142no—
750C23—142no—
751C23—142no—
752C23—142no—
753C23—142no—
754C23—142no—
755C23—142no—
756C23—142no—
757C23—142no—
758C23—142no—
759C23—142no—
760C23—142no—
761C23—142no—
762C23—142no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—281no—
767C23—281no—
768C23—281no—
769C23—281no—
770C23—281no—
771C23—281no—
772C23—281no—
773C23—281no—
774C23—281no—
775C23—281no—
776C23—281no—
777C23—281no—
778C23—281no—
779C23—281no—
780C23—281no—
781C23—281no—
782C23C22×C4×D711yescharacteristic
783C23C2×#115711yescharacteristic
784C23C2×#115711yescharacteristic
785C23C2×#115911yescharacteristic
786C23#654811yescharacteristic
787C23#654811yescharacteristic
788C23C2×#116111yescharacteristic
789C23D7×#4111yescharacteristic
790C23D7×#4111yescharacteristic
791C23D7×#4111yescharacteristic
792C23D7×#4111yescharacteristic
793C23D7×#4111yescharacteristic
794C23D7×#4111yescharacteristic
795C23#655311yescharacteristic
796C23#655311yescharacteristic
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—74no—
846C2×C4—142no—
847C2×C4—142no—
848C2×C4—142no—
849C2×C4—142no—
850C2×C4—142no—
851C2×C4—142no—
852C2×C4—142no—
853C2×C4—142no—
854C2×C4—142no—
855C2×C4—142no—
856C2×C4—142no—
857C2×C4—142no—
858C2×C4—142no—
859C2×C4—142no—
860C2×C4—142no—
861C2×C4—142no—
862C2×C4—142no—
863C2×C4—142no—
864C2×C4—2816no—
865C2×C4—281no—
866C2×C4—281no—
867C2×C4—281no—
868C2×C4—281no—
869C2×C4—281no—
870C2×C4—281no—
871C2×C4—281no—
872C2×C4—281no—
873C2×C4—281no—
874C2×C4—281no—
875C2×C4—281no—
876C2×C4—281no—
877C2×C4—281no—
878C2×C4—281no—
879C2×C4—281no—
880C2×C4—281no—
881C2×C4—281no—
882C2×C4—281no—
883C2×C4—281no—
884C2×C4—281no—
885C2×C4—281no—
886C2×C4—281no—
887C2×C4—281no—
888C2×C4—281no—
889C2×C4—281no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—281no—
893C2×C4—281no—
894C2×C4—281no—
895C2×C4#643514yes—
896C7#1394711yescharacteristic, complemented, Sylow
897C22—144no—
898C22—144no—
899C22—144no—
900C22—282no—
901C22—282no—
902C22—282no—
903C22—282no—
904C22—282no—
905C22—282no—
906C22—282no—
907C22—282no—
908C22—282no—
909C22—282no—
910C22—282no—
911C22—282no—
912C22C2×#643511yescharacteristic
913C22#9018611yescharacteristic
914C22#9020511yescharacteristic
915C22D7×#11711yescharacteristic
916C22D7×#11711yescharacteristic
917C22#9021811yescharacteristic
918C22#9021911yescharacteristic
919C22#9021911yescharacteristic
920C22#9021911yescharacteristic
921C22#9021911yescharacteristic
922C22#9022111yescharacteristic
923C22C4×#115911yescharacteristic
924C22#9023111yescharacteristic
925C22#9023611yescharacteristic
926C22#9023611yescharacteristic
927C22#9025011yescharacteristic
928C22#9025611yescharacteristic
929C22C4×#116111yescharacteristic
930C22#9027611yescharacteristic
931C22#9030411yescharacteristic
932C22#9030511yescharacteristic
933C22#9031511yescharacteristic
934C22#9032811yescharacteristic
935C22#9034011yescharacteristic
936C22#9034811yescharacteristic
937C22#9034911yescharacteristic
938C22#9035211yescharacteristic
939C22#9036911yescharacteristic
940C22#9037011yescharacteristic
941C22#9038211yescharacteristic
942C22#9038611yescharacteristic
943C22#9039511yescharacteristic
944C22#9039611yescharacteristic
945C22#9039711yescharacteristic
946C22#9040011yescharacteristic
947C4—24no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—144no—
955C4—282no—
956C4—282no—
957C4—282no—
958C4—282no—
959C4—561no—
960C4—561no—
961C2—284no—
962C2#1173085811yescharacteristic
963C2#1173090711yescharacteristic
964C2#1173109111yescharacteristic
965C2#1173139311yescharacteristic
966C2#1173153211yescharacteristic
967C2#1173168711yescharacteristic
968C2#1173175111yescharacteristic
969C2#1173238411yescharacteristic
970C2#1173256311yescharacteristic
971C2#1173256811yescharacteristic
972C2#1173275111yescharacteristic
973C2#1173307411yescharacteristic
974C2#1173308411yescharacteristic
975C2#1173327011yescharacteristic
976C2#1173328011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1434C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1434D7
hypocenterC7#13947
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C7×#1434C2semidirect
4. C4×C7⋊#95C2semidirect
9. #11727172C2semidirect
10. #11727171C2semidirect
12. #11727157C2semidirect
13. #11727156C2semidirect
14. #11727155C2semidirect
15. #11727155C2semidirect
51. #89438C4semidirect
140. #1434D7semidirect
896. C7#13947semidirect

Maximal subgroups

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

subgroupindex
C2×#894382
C7×#14342
#117292912
C4×C7⋊#952
#117271832
(C2×D7)⋊#952
#117271722
#117271712
#117271622
#117271572
#117271562
#117271552
#139477