Finite Group Databasebeta

← #13276782

Subgroups — #13276782

Order 1792.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89723C211yesmaximal, characteristic
2C2×#89718C211yesmaximal, characteristic
3C2×C22⋊C4×Dic7C211yesmaximal, characteristic
4C2×#89425C211yesmaximal, characteristic, complemented
5C2×#89422C211yesmaximal, characteristic, complemented
6C7×#1440C211yesmaximal, characteristic
7#11729301C211yesmaximal, characteristic
8#11729299C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11727172C211yesmaximal, characteristic, complemented
11#11727165C211yesmaximal, characteristic, complemented
12#11727160C211yesmaximal, characteristic, complemented
13#11727160C211yesmaximal, characteristic, complemented
14#11727157C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
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#89723C418yescomplemented
52#89718—24no—
53C22⋊C4×Dic7—24no—
54#89425—24no—
55#89422—24no—
56#13986—71nomaximal, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—22no—
67C23×Dic7—22no—
68C23×Dic7—22no—
69C23×Dic7—41no—
70C23×Dic7—41no—
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—41no—
87C2×C7×C22⋊C4C2×C414yes—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—41no—
95C2×C22⋊Dic7C2×C414yes—
96C2×C22⋊Dic7C2×C414yes—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7C2×C414yescomplemented
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—41no—
108C2×Dic7⋊C4—41no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—22no—
113C2×C4×Dic7—22no—
114C2×C4×Dic7—22no—
115C2×C4×Dic7—22no—
116C2×C4×Dic7—22no—
117C2×C4×Dic7—41no—
118C2×C4×Dic7—41no—
119C2×C4×Dic7—41no—
120C2×C4×Dic7C2×C414yescomplemented
121C7×#95—22no—
122C7×#95—22no—
123C7×#95—22no—
124C7×#95—41no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95C2×C414yescomplemented
138C7⋊#95C2×C414yescomplemented
139C7⋊#95D414yes—
140C7⋊#95D414yes—
141C2×#388—71no—
142C2×#387—71no—
143C2×#385—71no—
144C2×#382—71no—
145C2×C4×C22⋊C4—71no—
146#1443—71no—
147#1441—71no—
148#1440D711yescharacteristic
149#1439—71no—
150#1437—71no—
151#1436—71no—
152#1436—71no—
153#1434—71no—
154C22⋊#95—71no—
155C4×#95—71no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7C22×C412yes—
169C24×C7#4112yes—
170C24×C7#4112yes—
171C24×C7C2411yescharacteristic
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×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×C7C22×C412yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7#4112yes—
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—28no—
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—21no—
258C22×Dic7—44no—
259C22×Dic7—44no—
260C22×Dic7—44no—
261C22×Dic7—44no—
262C22×Dic7—44no—
263C22×Dic7—44no—
264C22×Dic7C22×C412yes—
265C22×Dic7C22×C412yes—
266C22×Dic7C22×C412yes—
267C22×Dic7C22×C412yes—
268C22×Dic7C2×D412yes—
269C22×Dic7C2×D412yes—
270C22×Dic7C2×D412yes—
271C22×Dic7C2×D412yes—
272C22×Dic7#4112yes—
273C22×Dic7#4112yes—
274C22×Dic7#4112yes—
275C22×Dic7#4112yes—
276C22×Dic7#4112yes—
277C7×C22⋊C4—28no—
278C7×C22⋊C4—28no—
279C7×C22⋊C4—44no—
280C22⋊Dic7—28no—
281C22⋊Dic7—28no—
282C22⋊Dic7—44no—
283C4⋊Dic7—28no—
284Dic7⋊C4—44no—
285Dic7⋊C4—44no—
286Dic7⋊C4—44no—
287C4×Dic7—28no—
288C4×Dic7—44no—
289C4×Dic7—44no—
290C4×Dic7—44no—
291C24×C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C22⋊C4C2×D711yescharacteristic
302C22×C42—71no—
303C22×C42—71no—
304C22×C42—71no—
305C22×C42—71no—
306#388—78no—
307#387—144no—
308#385—144no—
309#382—144no—
310C4×C22⋊C4—144no—
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×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95C2×D711yescharacteristic
328C2×#95C2×D711yescharacteristic
329C2×#95C2×D711yescharacteristic
330C2×#95C2×D711yescharacteristic
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—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7#11714yes—
366C23×C7C23×C411yescharacteristic
367C23×C7C22×D411yescharacteristic
368C23×C7C22×D411yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7H(5,𝔽2)11yescharacteristic
378C23×C7H(5,𝔽2)11yescharacteristic
379C23×C72−1+411yescharacteristic
380C23×C72−1+411yescharacteristic
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—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
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×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
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×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—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
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—416no—
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—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7C4×D414yes—
478C2×Dic7C4×D414yes—
479C2×Dic7#12414yes—
480C25C22×D711yescharacteristic
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—142no—
490C23×C4—142no—
491C23×C4—142no—
492C23×C4—142no—
493C23×C4—142no—
494C23×C4—281no—
495C23×C4—281no—
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C23×C4C22×D711yescharacteristic
501C23×C4C22×D711yescharacteristic
502C2×C4⋊C4—74no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—142no—
506C2×C4⋊C4—142no—
507C2×C4⋊C4—142no—
508C2×C4⋊C4—142no—
509C2×C4⋊C4—142no—
510C2×C4⋊C4—142no—
511C2×C4⋊C4—142no—
512C2×C4⋊C4—281no—
513C2×C4⋊C4—281no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—142no—
525C2×C22⋊C4—142no—
526C2×C22⋊C4—142no—
527C2×C22⋊C4—142no—
528C2×C22⋊C4—142no—
529C2×C22⋊C4—142no—
530C2×C22⋊C4—281no—
531C2×C22⋊C4C4×D714yes—
532C2×C42—74no—
533C2×C42—142no—
534C2×C42—142no—
535C2×C42—142no—
536C2×C42—142no—
537C2×C42—142no—
538C2×C42—142no—
539C2×C42—142no—
540C2×C42—142no—
541C2×C42—281no—
542C2×C42—281no—
543C2×C42—281no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—41no—
548#95—74no—
549#95—74no—
550#95—74no—
551#95—74no—
552#95—142no—
553#95—142no—
554#95—142no—
555#95—142no—
556#95—142no—
557#95—142no—
558#95—142no—
559#95—142no—
560#95—142no—
561#95—142no—
562#95—281no—
563#95—281no—
564C22×C7—24no—
565C22×C7—24no—
566C22×C7—24no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7C2×#11711yescharacteristic
580C22×C7C2×C4×D411yescharacteristic
581C22×C7C2×C4×D411yescharacteristic
582C22×C7C4×#4111yescharacteristic
583C22×C7C4×#4111yescharacteristic
584C22×C7#52011yescharacteristic
585C22×C7#52011yescharacteristic
586C22×C7#52511yescharacteristic
587C22×C7#52511yescharacteristic
588C22×C7C2×#12411yescharacteristic
589C22×C7#52911yescharacteristic
590C22×C7#52911yescharacteristic
591C22×C7#52911yescharacteristic
592C22×C7#52911yescharacteristic
593C22×C7#53211yescharacteristic
594C22×C7#53811yescharacteristic
595C22×C7#53911yescharacteristic
596C22×C7#54111yescharacteristic
597C22×C7#54211yescharacteristic
598C22×C7D4211yescharacteristic
599C22×C7#54611yescharacteristic
600C22×C7#54611yescharacteristic
601C22×C7#54711yescharacteristic
602C22×C7#54711yescharacteristic
603C22×C7#54811yescharacteristic
604C22×C7#54811yescharacteristic
605C22×C7#55111yescharacteristic
606C22×C7#55111yescharacteristic
607C22×C7#55111yescharacteristic
608C22×C7#55211yescharacteristic
609C22×C7#55211yescharacteristic
610C22×C7#55211yescharacteristic
611C22×C7#55211yescharacteristic
612C22×C7#55311yescharacteristic
613C22×C7#55311yescharacteristic
614C4×C7—42no—
615C4×C7—42no—
616C4×C7—42no—
617C4×C7—42no—
618C4×C7—42no—
619C4×C7—81no—
620Dic7—24no—
621Dic7—24no—
622Dic7—24no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626Dic7—42no—
627Dic7—81no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C2×C4×D712yes—
641C24#115912yes—
642C24#115912yes—
643C24C23×D711yescharacteristic
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—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—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—72no—
689C22×C4—72no—
690C22×C4—72no—
691C22×C4—72no—
692C22×C4—72no—
693C22×C4—72no—
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—148no—
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—141no—
722C22×C4—141no—
723C22×C4—141no—
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—284no—
739C22×C4—284no—
740C22×C4—284no—
741C22×C4—284no—
742C22×C4—284no—
743C22×C4—284no—
744C22×C4C2×C4×D712yes—
745C22×C4C2×C4×D712yes—
746C22×C4D4×D712yes—
747C22×C4D4×D712yes—
748C22×C4#115912yes—
749C4⋊C4—148no—
750C4⋊C4—284no—
751C4⋊C4—284no—
752C4⋊C4—284no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—44no—
756C22⋊C4—148no—
757C22⋊C4—148no—
758C22⋊C4—284no—
759C42—148no—
760C42—284no—
761C42—284no—
762C42—284no—
763C2×C7—44no—
764C2×C7#229011yescharacteristic
765C2×C7C4×#12411yescharacteristic
766C2×C7#233411yescharacteristic
767C2×C7#234311yescharacteristic
768C2×C7#235211yescharacteristic
769C2×C7#235911yescharacteristic
770C2×C7#236111yescharacteristic
771C2×C7#246011yescharacteristic
772C2×C7#246111yescharacteristic
773C2×C7#247211yescharacteristic
774C2×C7#247511yescharacteristic
775C2×C7#248911yescharacteristic
776C2×C7#251511yescharacteristic
777C2×C7#255311yescharacteristic
778C2×C7#257611yescharacteristic
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23#644014yes—
814C23C22×C4×D711yescharacteristic
815C23C2×D4×D711yescharacteristic
816C23C2×D4×D711yescharacteristic
817C23C2×#115911yescharacteristic
818C23C2×#115911yescharacteristic
819C23C2×#115911yescharacteristic
820C23#654811yescharacteristic
821C23D7×#4111yescharacteristic
822C23D7×#4111yescharacteristic
823C23D7×#4111yescharacteristic
824C23D7×#4111yescharacteristic
825C23D7×#4111yescharacteristic
826C23#655311yescharacteristic
827C23#655411yescharacteristic
828C23#655411yescharacteristic
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
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—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—74no—
872C2×C4—74no—
873C2×C4—74no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—142no—
889C2×C4—142no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—142no—
893C2×C4—142no—
894C2×C4—142no—
895C2×C4—142no—
896C2×C4—142no—
897C2×C4—142no—
898C2×C4—142no—
899C2×C4—142no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—2816no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4—281no—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4—281no—
927C2×C4—281no—
928C7#1398611yescharacteristic, complemented, Sylow
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×#644011yescharacteristic
945C22#9021311yescharacteristic
946C22#9021411yescharacteristic
947C22C4×#115911yescharacteristic
948C22C4×D4×D711yescharacteristic
949C22C4×D4×D711yescharacteristic
950C22#9023711yescharacteristic
951C22#9027711yescharacteristic
952C22#9028211yescharacteristic
953C22#9028711yescharacteristic
954C22#9028911yescharacteristic
955C22#9029111yescharacteristic
956C22#9029211yescharacteristic
957C22#9029311yescharacteristic
958C22#9029711yescharacteristic
959C22#9030011yescharacteristic
960C22#9030311yescharacteristic
961C22#9034011yescharacteristic
962C22#9034011yescharacteristic
963C22#9034111yescharacteristic
964C22#9034111yescharacteristic
965C22#9034111yescharacteristic
966C22#9034611yescharacteristic
967C22#9034611yescharacteristic
968C22#9034811yescharacteristic
969C22#9034911yescharacteristic
970C22#9034911yescharacteristic
971C22D7×#12411yescharacteristic
972C22#9036811yescharacteristic
973C22#9037011yescharacteristic
974C22#9037311yescharacteristic
975C22#9039211yescharacteristic
976C22#9039711yescharacteristic
977C22#9039911yescharacteristic
978C22#9040011yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—144no—
986C4—144no—
987C4—144no—
988C4—282no—
989C4—282no—
990C4—282no—
991C4—282no—
992C4—561no—
993C2—44no—
994C2#1173150411yescharacteristic
995C2#1173210211yescharacteristic
996C2#1173211811yescharacteristic
997C2#1173289911yescharacteristic
998C2#1173291111yescharacteristic
999C2#1173292211yescharacteristic
1000C2#1173328211yescharacteristic
1001C2#1173435811yescharacteristic
1002C2#1173436011yescharacteristic
1003C2#1173437011yescharacteristic
1004C2#1173439211yescharacteristic
1005C2#1173492111yescharacteristic
1006C2#1173493111yescharacteristic
1007C2#1173494111yescharacteristic
1008C2#1173496611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1440C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1440D7
hypocenterC7#13986
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. C2×#89425C2semidirect
5. C2×#89422C2semidirect
10. #11727172C2semidirect
11. #11727165C2semidirect
12. #11727160C2semidirect
13. #11727160C2semidirect
14. #11727157C2semidirect
15. Dic7×#95C2semidirect
51. #89723C4semidirect
99. C2×C4⋊Dic7C2×C4semidirect
120. C2×C4×Dic7C2×C4semidirect
137. C7⋊#95C2×C4semidirect
138. C7⋊#95C2×C4semidirect
928. C7#13986semidirect

Maximal subgroups

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

subgroupindex
C2×#897232
C2×#897182
C2×C22⋊C4×Dic72
C2×#894252
C2×#894222
C7×#14402
#117293012
#117292992
#117292982
#117271722
#117271652
#117271602
#117271572
Dic7×#952
#139867