Finite Group Databasebeta

← #13276853

Subgroups — #13276853

Order 1792.

1586 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×C22⋊C4×Dic7C211yesmaximal, characteristic
3C2×#89709C211yesmaximal, characteristic, complemented
4#11729323C211yesmaximal, characteristic, complemented
5#11729318C211yesmaximal, characteristic, complemented
6#11729302C211yesmaximal, characteristic
7#11729300C211yesmaximal, characteristic
8#11729299C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11729298C211yesmaximal, characteristic
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12#11727166C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14#11727155C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C7×#388C418yescomplemented
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
51C2×C7⋊#95C2211yescharacteristic
52C22⋊C4×Dic7—24no—
53#89709—24no—
54#13990—71nomaximal, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—22no—
63C23×Dic7—22no—
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—22no—
67C23×Dic7—41no—
68C23×Dic7—41no—
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C2×C7×C4⋊C4—41no—
78C2×C7×C4⋊C4—41no—
79C2×C7×C4⋊C4C2×C414yescomplemented
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—41no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4C2×C414yes—
87C2×C7×C22⋊C4C2×C414yes—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C42×C7C2×C414yescomplemented
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—41no—
100C2×C22⋊Dic7—41no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—41no—
103C2×C4⋊Dic7—41no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—41no—
111C2×C4×Dic7—41no—
112C2×C4×Dic7—41no—
113C7×#95C2×C414yescomplemented
114C7×#95C2×C414yescomplemented
115C7⋊#95—22no—
116C7⋊#95—22no—
117C7⋊#95—22no—
118C7⋊#95—22no—
119C7⋊#95—22no—
120C7⋊#95—22no—
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95—41no—
134C7⋊#95D414yes—
135C2×#388D711yescharacteristic
136C2×#383—71no—
137C2×C4×C22⋊C4—71no—
138#1445—71no—
139#1442—71no—
140#1440—71no—
141#1439—71no—
142#1437—71no—
143#1436—71no—
144#1436—71no—
145#1434—71no—
146#1434—71no—
147C22⋊#95—71no—
148C22⋊#95—71no—
149C4×#95—71no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7C22×C412yes—
163C24×C7#4112yes—
164C24×C7#4112yes—
165C24×C7C2411yescharacteristic
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×C7C22×C412yes—
201C22×C4×C7C22×C412yes—
202C22×C4×C7C22×C412yes—
203C22×C4×C7C22×C412yes—
204C22×C4×C7C22×C412yes—
205C22×C4×C7C22×C412yes—
206C22×C4×C7C2×D412yes—
207C22×C4×C7#4112yes—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—28no—
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×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—44no—
258C22×Dic7—44no—
259C22×Dic7—44no—
260C22×Dic7—44no—
261C22×Dic7—44no—
262C22×Dic7—44no—
263C22×Dic7C2×D412yes—
264C22×Dic7C2×D412yes—
265C22×Dic7#4112yes—
266C22×Dic7#4112yes—
267C22×Dic7#4112yes—
268C22×Dic7#4112yes—
269C22×Dic7#4112yes—
270C22×Dic7#4112yes—
271C7×C4⋊C4—44no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—44no—
275C42×C7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—44no—
278C22⋊Dic7—44no—
279C4⋊Dic7—44no—
280C4×Dic7—44no—
281C4×Dic7—44no—
282C4×Dic7—44no—
283C24×C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4C2×D711yescharacteristic
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4C2×D711yescharacteristic
290C22×C22⋊C4C2×D711yescharacteristic
291C22×C22⋊C4C2×D711yescharacteristic
292C22×C42—71no—
293C22×C42—71no—
294C22×C42—71no—
295C22×C42C2×D711yescharacteristic
296#388Dic718yescomplemented
297#383—144no—
298C4×C22⋊C4—144no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95C2×D711yescharacteristic
320C2×#95C2×D711yescharacteristic
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7#11714yes—
356C23×C7C23×C411yescharacteristic
357C23×C7C22×D411yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
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×C7H(5,𝔽2)11yescharacteristic
370C23×C72−1+411yescharacteristic
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—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
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—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7C4×D414yes—
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—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—416no—
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—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7#12614yes—
470C25C22×D711yescharacteristic
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—142no—
480C23×C4—142no—
481C23×C4—142no—
482C23×C4—142no—
483C23×C4—142no—
484C23×C4—281no—
485C23×C4—281no—
486C23×C4C22×D711yescharacteristic
487C23×C4C22×D711yescharacteristic
488C23×C4C22×D711yescharacteristic
489C23×C4C22×D711yescharacteristic
490C23×C4C22×D711yescharacteristic
491C23×C4C22×D711yescharacteristic
492C2×C4⋊C4—41no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4—281no—
496C2×C4⋊C4—281no—
497C2×C4⋊C4C2×Dic714yescomplemented
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—142no—
505C2×C22⋊C4—142no—
506C2×C22⋊C4—142no—
507C2×C22⋊C4—142no—
508C2×C22⋊C4—142no—
509C2×C22⋊C4—142no—
510C2×C22⋊C4—142no—
511C2×C22⋊C4—281no—
512C2×C22⋊C4—281no—
513C2×C22⋊C4C2×Dic714yes—
514C2×C22⋊C4C2×Dic714yes—
515C2×C22⋊C4C2×Dic714yes—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—142no—
519C2×C42—142no—
520C2×C42—142no—
521C2×C42—142no—
522C2×C42—142no—
523C2×C42—142no—
524C2×C42—281no—
525C2×C42—281no—
526C2×C42—281no—
527C2×C42C2×Dic714yescomplemented
528#95—74no—
529#95—142no—
530#95—142no—
531#95—142no—
532#95—142no—
533#95—142no—
534#95—142no—
535#95—142no—
536#95—142no—
537#95—142no—
538#95—142no—
539#95—142no—
540#95—142no—
541#95—142no—
542#95—142no—
543#95—281no—
544#95—281no—
545#95—281no—
546#95—281no—
547#95—281no—
548#95C2×Dic714yescomplemented
549#95C2×Dic714yescomplemented
550C22×C7—24no—
551C22×C7—24no—
552C22×C7—24no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7C2×#11711yescharacteristic
566C22×C7C2×C4×D411yescharacteristic
567C22×C7C4×#4111yescharacteristic
568C22×C7C4×#4111yescharacteristic
569C22×C7C4×#4111yescharacteristic
570C22×C7#51811yescharacteristic
571C22×C7#52011yescharacteristic
572C22×C7#52511yescharacteristic
573C22×C7#52511yescharacteristic
574C22×C7C2×#12611yescharacteristic
575C22×C7#52911yescharacteristic
576C22×C7#52911yescharacteristic
577C22×C7#52911yescharacteristic
578C22×C7#52911yescharacteristic
579C22×C7#52911yescharacteristic
580C22×C7#53811yescharacteristic
581C22×C7#53811yescharacteristic
582C22×C7#54211yescharacteristic
583C22×C7#54211yescharacteristic
584C22×C7#54611yescharacteristic
585C22×C7#54611yescharacteristic
586C22×C7#54711yescharacteristic
587C22×C7#55011yescharacteristic
588C22×C7#55111yescharacteristic
589C22×C7#55111yescharacteristic
590C22×C7#55111yescharacteristic
591C22×C7#55111yescharacteristic
592C22×C7#55111yescharacteristic
593C22×C7#55211yescharacteristic
594C22×C7#55211yescharacteristic
595C22×C7#55211yescharacteristic
596C22×C7#55311yescharacteristic
597C22×C7#55311yescharacteristic
598C22×C7#55311yescharacteristic
599C22×C7#55511yescharacteristic
600C4×C7—24no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7—42no—
606Dic7—24no—
607Dic7—42no—
608Dic7—42no—
609Dic7—42no—
610Dic7—42no—
611Dic7—42no—
612Dic7—81no—
613Dic7—81no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24#115712yes—
627C24#115712yes—
628C24C22×Dic712yes—
629C24C23×D711yescharacteristic
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—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—141no—
673C22×C4—141no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—148no—
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—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—284no—
722C22×C4—284no—
723C22×C4—284no—
724C22×C4—284no—
725C22×C4—284no—
726C22×C4—284no—
727C22×C4D4×D712yes—
728C22×C4#115912yes—
729C22×C4C22×Dic712yes—
730C22×C4C22×Dic712yes—
731C22×C4C22×Dic712yes—
732C22×C4C22×Dic712yes—
733C22×C4C22×Dic712yes—
734C22×C4C22×Dic712yes—
735C4⋊C4—44no—
736C4⋊C4—284no—
737C22⋊C4—28no—
738C22⋊C4—28no—
739C22⋊C4—44no—
740C22⋊C4—148no—
741C22⋊C4—284no—
742C22⋊C4—284no—
743C42—28no—
744C42—284no—
745C42—284no—
746C42—284no—
747C2×C7—44no—
748C2×C7#229011yescharacteristic
749C2×C7C4×#12611yescharacteristic
750C2×C7#233711yescharacteristic
751C2×C7#234311yescharacteristic
752C2×C7#235311yescharacteristic
753C2×C7#235911yescharacteristic
754C2×C7#236311yescharacteristic
755C2×C7#246711yescharacteristic
756C2×C7#246811yescharacteristic
757C2×C7#247911yescharacteristic
758C2×C7#248011yescharacteristic
759C2×C7#249511yescharacteristic
760C2×C7#251511yescharacteristic
761C2×C7#257211yescharacteristic
762C2×C7#257811yescharacteristic
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23#648914yes—
798C23C2×#115711yescharacteristic
799C23C2×#115711yescharacteristic
800C23C2×D4×D711yescharacteristic
801C23C2×#115911yescharacteristic
802C23#654811yescharacteristic
803C23#654811yescharacteristic
804C23D7×#4111yescharacteristic
805C23D7×#4111yescharacteristic
806C23D7×#4111yescharacteristic
807C23D7×#4111yescharacteristic
808C23D7×#4111yescharacteristic
809C23D7×#4111yescharacteristic
810C23#655311yescharacteristic
811C23#655411yescharacteristic
812C23C23×Dic711yescharacteristic
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
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—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—74no—
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—142no—
865C2×C4—142no—
866C2×C4—142no—
867C2×C4—142no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—2816no—
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—281no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4D4×Dic714yes—
912C7#1399011yescharacteristic, complemented, Sylow
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22#9021811yescharacteristic
929C22#9021811yescharacteristic
930C22#9022211yescharacteristic
931C22#9022211yescharacteristic
932C22#9022911yescharacteristic
933C22#9022911yescharacteristic
934C22#9023111yescharacteristic
935C22#9023111yescharacteristic
936C22#9023811yescharacteristic
937C22#9023811yescharacteristic
938C22#9024711yescharacteristic
939C22#9024711yescharacteristic
940C22#9029011yescharacteristic
941C22#9030311yescharacteristic
942C22#9030511yescharacteristic
943C22#9030711yescharacteristic
944C22#9034111yescharacteristic
945C22#9034511yescharacteristic
946C22#9034611yescharacteristic
947C22#9034911yescharacteristic
948C22#9036011yescharacteristic
949C22#9036011yescharacteristic
950C22#9036911yescharacteristic
951C22#9036911yescharacteristic
952C22D7×#12611yescharacteristic
953C22#9039711yescharacteristic
954C22#9039711yescharacteristic
955C22#9039711yescharacteristic
956C22C2×#648911yescharacteristic
957C22C2×D4×Dic711yescharacteristic
958C22#9048911yescharacteristic
959C22#41×Dic711yescharacteristic
960C22#41×Dic711yescharacteristic
961C22#41×Dic711yescharacteristic
962C22#9051811yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—144no—
970C4—282no—
971C4—282no—
972C4—282no—
973C4—282no—
974C4—282no—
975C4—561no—
976C4—561no—
977C2—44no—
978C2#1173296311yescharacteristic
979C2#1173298111yescharacteristic
980C2#1173298411yescharacteristic
981C2#1173299411yescharacteristic
982C2#1173300111yescharacteristic
983C2#1173330411yescharacteristic
984C2#1173333611yescharacteristic
985C2#1173333811yescharacteristic
986C2#1173968211yescharacteristic
987C2#1173976311yescharacteristic
988C2#1173978111yescharacteristic
989C2#1174008211yescharacteristic
990C2#1174028311yescharacteristic
991C2#1174039911yescharacteristic
992C2Dic7×#12611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#13990
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×#89709C2semidirect
4. #11729323C2semidirect
5. #11729318C2semidirect
11. C4×C7⋊#95C2semidirect
12. #11727166C2semidirect
13. #11727161C2semidirect
14. #11727155C2semidirect
15. #11727155C2semidirect
29. C7×#388C4semidirect
79. C2×C7×C4⋊C4C2×C4semidirect
91. C2×C42×C7C2×C4semidirect
113. C7×#95C2×C4semidirect
114. C7×#95C2×C4semidirect
296. #388Dic7semidirect
497. C2×C4⋊C4C2×Dic7semidirect
527. C2×C42C2×Dic7semidirect
548. #95C2×Dic7semidirect
549. #95C2×Dic7semidirect
912. C7#13990semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C22⋊C4×Dic72
C2×#897092
#117293232
#117293182
#117293022
#117293002
#117292992
#117292982
C4×C7⋊#952
#117271662
#117271612
#117271552
#139907