Finite Group Databasebeta

← #13276871

Subgroups — #13276871

Order 1792.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
2C2×#89440C211yesmaximal, characteristic
3C2×#89436C211yesmaximal, characteristic
4C2×#89436C211yesmaximal, characteristic
5C2×D7×#95C211yesmaximal, characteristic
6C7×#1434C211yesmaximal, characteristic, complemented
7#11729288C211yesmaximal, characteristic, complemented
8(C2×D7)⋊#95C211yesmaximal, characteristic
9(C2×D7)⋊#95C211yesmaximal, characteristic
10#11727172C211yesmaximal, characteristic, complemented
11#11727171C211yesmaximal, characteristic, complemented
12#11727168C211yesmaximal, characteristic, complemented
13#11727166C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
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
51C4×(C2×D7)⋊C4—24no—
52#89440—24no—
53#89436—24no—
54#89436C418yescomplemented
55D7×#95—24no—
56#13992—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C22×C4×D7—22no—
73C22×C4×D7—22no—
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×D7C2×C414yes—
92C22×C4×D7D414yes—
93C2×C42×C7—22no—
94C2×C42×C7—22no—
95C2×C42×C7—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—22no—
104C2×(C2×D7)⋊C4—22no—
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—41no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—41no—
114C2×C4×Dic7—22no—
115C2×C4×Dic7—41no—
116C2×C4×Dic7—41no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—22no—
122C7×#95C2×C414yescomplemented
123C7⋊#95—22no—
124C7⋊#95—22no—
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—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95C2×C414yescomplemented
139C7⋊#95C2×C414yescomplemented
140C7⋊#95C2×C414yescomplemented
141C2×#385—71no—
142C2×#381—71no—
143C2×#381—71no—
144C2×C4×C22⋊C4—71no—
145C22×#95—71no—
146#1443—71no—
147#1443—71no—
148#1442—71no—
149#1442—71no—
150#1436—71no—
151#1436—71no—
152#1434—71no—
153#1434D711yescharacteristic, complemented
154C22⋊#95—71no—
155C22⋊#95—71no—
156C24×C7C2411yescharacteristic
157C23×D7—21no—
158C23×D7—21no—
159C23×D7—21no—
160C23×D7—21no—
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7C22×C412yes—
166C23×D7C2×D412yes—
167C23×D7C2×D412yes—
168C23×D7#4112yes—
169C23×D7#4112yes—
170C23×D7#4112yes—
171C23×D7#4112yes—
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×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C22×C412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7#4112yes—
219C22×C4×C7#4112yes—
220C22×C4×C7#4112yes—
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—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7C22×C412yes—
265C22×Dic7C22×C412yes—
266C22×Dic7C22×C412yes—
267C22×Dic7C2×D412yes—
268C22×Dic7C2×D412yes—
269C22×Dic7#4112yes—
270C2×C4×D7—28no—
271C2×C4×D7—28no—
272C2×C4×D7—28no—
273C2×C4×D7—28no—
274C2×C4×D7—28no—
275C2×C4×D7—28no—
276C2×C4×D7—44no—
277C2×C4×D7—44no—
278C2×C4×D7—44no—
279C2×C4×D7—44no—
280C2×C4×D7—44no—
281C2×C4×D7—44no—
282C2×C4×D7—44no—
283C2×C4×D7—44no—
284C2×C4×D7—44no—
285C2×C4×D7—44no—
286C2×C4×D7—44no—
287C2×C4×D7—44no—
288C2×C4×D7—44no—
289C2×C4×D7—44no—
290C2×C4×D7—44no—
291C42×C7—44no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—28no—
295(C2×D7)⋊C4—44no—
296C4⋊Dic7—44no—
297Dic7⋊C4—44no—
298C4×Dic7—44no—
299C24×C4—71no—
300C24×C4—71no—
301C24×C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C42—71no—
309C22×C42C2×D711yescharacteristic
310#385—144no—
311#381—78no—
312#381—144no—
313C4×C22⋊C4—144no—
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×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—144no—
333C2×#95C2×D711yescharacteristic
334C2×#95C2×D711yescharacteristic
335C2×#95C2×D711yescharacteristic
336C2×#95C2×D711yescharacteristic
337C2×#95C2×D711yescharacteristic
338C2×#95C2×D711yescharacteristic
339C23×C7C23×C411yescharacteristic
340C23×C7C22×D411yescharacteristic
341C23×C7C22×D411yescharacteristic
342C23×C7C2×#4111yescharacteristic
343C23×C7C2×#4111yescharacteristic
344C23×C7C2×#4111yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7C2×#4111yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C7H(5,𝔽2)11yescharacteristic
352C23×C72−1+411yescharacteristic
353C23×C72−1+411yescharacteristic
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
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—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7#11714yes—
383C22×D7C4×D414yes—
384C22×D7C4×D414yes—
385C22×D7#12114yes—
386C22×D7#12314yes—
387C22×D7#12414yes—
388C22×D7#12614yes—
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—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—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×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#12314yes—
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—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
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×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—
487C4×D7—416no—
488C4×D7—416no—
489C4×D7—416no—
490C25—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—71no—
496C23×C4—71no—
497C23×C4—74no—
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×C4—142no—
507C23×C4—142no—
508C23×C4—142no—
509C23×C4—142no—
510C23×C4—142no—
511C23×C4—142no—
512C23×C4—142no—
513C23×C4—142no—
514C23×C4—142no—
515C23×C4—281no—
516C23×C4—281no—
517C23×C4—281no—
518C23×C4—281no—
519C23×C4C22×D711yescharacteristic
520C23×C4C22×D711yescharacteristic
521C23×C4C22×D711yescharacteristic
522C23×C4C22×D711yescharacteristic
523C23×C4C22×D711yescharacteristic
524C23×C4C22×D711yescharacteristic
525C23×C4C22×D711yescharacteristic
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—142no—
530C2×C4⋊C4—281no—
531C2×C4⋊C4—281no—
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×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—142no—
548C2×C42—281no—
549C2×C42—281no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—74no—
556#95—74no—
557#95—74no—
558#95—142no—
559#95—142no—
560#95—142no—
561#95—142no—
562#95—142no—
563#95—142no—
564#95—142no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—281no—
570#95—281no—
571#95—281no—
572#95—281no—
573#95C4×D714yescomplemented
574C22×C7C2×#11711yescharacteristic
575C22×C7C2×C4×D411yescharacteristic
576C22×C7C2×C4×D411yescharacteristic
577C22×C7C4×#4111yescharacteristic
578C22×C7C4×#4111yescharacteristic
579C22×C7#52011yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7C2×#12111yescharacteristic
582C22×C7C2×#12311yescharacteristic
583C22×C7C2×#12311yescharacteristic
584C22×C7#52511yescharacteristic
585C22×C7C2×#12411yescharacteristic
586C22×C7C2×#12611yescharacteristic
587C22×C7#52911yescharacteristic
588C22×C7#52911yescharacteristic
589C22×C7#53411yescharacteristic
590C22×C7#53611yescharacteristic
591C22×C7#53911yescharacteristic
592C22×C7#53911yescharacteristic
593C22×C7#54611yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54711yescharacteristic
596C22×C7#54711yescharacteristic
597C22×C7#55111yescharacteristic
598C22×C7#55111yescharacteristic
599C22×C7#55111yescharacteristic
600C22×C7#55111yescharacteristic
601C22×C7#55111yescharacteristic
602C22×C7#55111yescharacteristic
603C22×C7#55211yescharacteristic
604C22×C7#55211yescharacteristic
605C22×C7#55211yescharacteristic
606C22×C7#55211yescharacteristic
607C22×C7#55211yescharacteristic
608C22×C7#55211yescharacteristic
609C2×D7—24no—
610C2×D7—24no—
611C2×D7—24no—
612C2×D7—24no—
613C2×D7—24no—
614C2×D7—24no—
615C2×D7—24no—
616C2×D7—24no—
617C2×D7—24no—
618C2×D7—24no—
619C2×D7—24no—
620C2×D7—24no—
621C2×D7—24no—
622C2×D7—24no—
623C2×D7#38818yes—
624C4×C7—24no—
625C4×C7—42no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—81no—
631Dic7—42no—
632Dic7—42no—
633Dic7—42no—
634Dic7—42no—
635Dic7—42no—
636Dic7—42no—
637Dic7—81no—
638C24—72no—
639C24—72no—
640C24—72no—
641C24—72no—
642C24—72no—
643C24—72no—
644C24—72no—
645C24—141no—
646C24—141no—
647C24—141no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—141no—
653C24C23×D711yescharacteristic
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—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—72no—
696C22×C4—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—72no—
700C22×C4—72no—
701C22×C4—148no—
702C22×C4—148no—
703C22×C4—148no—
704C22×C4—148no—
705C22×C4—148no—
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—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—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—148no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—284no—
751C22×C4—284no—
752C22×C4—284no—
753C22×C4—284no—
754C22×C4—284no—
755C22×C4—284no—
756C22×C4—284no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4—284no—
760C22×C4—284no—
761C22×C4—284no—
762C22×C4—284no—
763C22×C4—284no—
764C22×C4—284no—
765C22×C4C2×C4×D712yes—
766C22×C4C2×C4×D712yes—
767C22×C4C2×C4×D712yes—
768C22×C4#115712yes—
769C22×C4#115712yes—
770C22×C4D4×D712yes—
771C22×C4D4×D712yes—
772C22×C4#115912yes—
773C4⋊C4—284no—
774C4⋊C4—284no—
775C22⋊C4—148no—
776C22⋊C4—148no—
777C22⋊C4—148no—
778C22⋊C4—284no—
779C42—44no—
780C42—284no—
781C2×C7C2×#38811yescharacteristic
782C2×C7C4×#12311yescharacteristic
783C2×C7#232211yescharacteristic
784C2×C7#234311yescharacteristic
785C2×C7#234311yescharacteristic
786C2×C7#235911yescharacteristic
787C2×C7#235911yescharacteristic
788C2×C7#248311yescharacteristic
789C2×C7#248411yescharacteristic
790C2×C7#248611yescharacteristic
791C2×C7#248811yescharacteristic
792C2×C7#248811yescharacteristic
793C2×C7#249311yescharacteristic
794C2×C7#249311yescharacteristic
795C2×C7#253411yescharacteristic
796D7—28no—
797C23—74no—
798C23—74no—
799C23—74no—
800C23—74no—
801C23—74no—
802C23—74no—
803C23—74no—
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—142no—
817C23—142no—
818C23—142no—
819C23—142no—
820C23—142no—
821C23—142no—
822C23—142no—
823C23—142no—
824C23—142no—
825C23—142no—
826C23—142no—
827C23—142no—
828C23—142no—
829C23—142no—
830C23—142no—
831C23—142no—
832C23C22×C4×D711yescharacteristic
833C23C2×#115711yescharacteristic
834C23C2×#115711yescharacteristic
835C23C2×D4×D711yescharacteristic
836C23C2×D4×D711yescharacteristic
837C23C2×#115911yescharacteristic
838C23#655111yescharacteristic
839C23D7×#4111yescharacteristic
840C23D7×#4111yescharacteristic
841C23D7×#4111yescharacteristic
842C23D7×#4111yescharacteristic
843C23D7×#4111yescharacteristic
844C23#655311yescharacteristic
845C23#655311yescharacteristic
846C23#655411yescharacteristic
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—41no—
869C2×C4—41no—
870C2×C4—41no—
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—41no—
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—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—2816no—
914C2×C4—2816no—
915C2×C4—2816no—
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—
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×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4#644614yes—
948C7#1399211yescharacteristic, complemented, Sylow
949C22—78no—
950C22—144no—
951C22—144no—
952C22—144no—
953C22—144no—
954C22—144no—
955C22—144no—
956C22—144no—
957C22—144no—
958C22—144no—
959C22—144no—
960C22—144no—
961C22—144no—
962C22—144no—
963C22—144no—
964C22C4×#115711yescharacteristic
965C22C2×#644611yescharacteristic
966C22#9019811yescharacteristic
967C22D7×#11711yescharacteristic
968C22#9021411yescharacteristic
969C22#9021811yescharacteristic
970C22#9021811yescharacteristic
971C22#9021811yescharacteristic
972C22#9021911yescharacteristic
973C22#9022011yescharacteristic
974C22#9022011yescharacteristic
975C22C4×#115911yescharacteristic
976C22C4×D4×D711yescharacteristic
977C22C4×D4×D711yescharacteristic
978C22#9023811yescharacteristic
979C22#9024111yescharacteristic
980C22#9024811yescharacteristic
981C22#9026511yescharacteristic
982C22#9027211yescharacteristic
983C22D7×#12111yescharacteristic
984C22#9030211yescharacteristic
985C22#9031911yescharacteristic
986C22#9033011yescharacteristic
987C22D7×#12311yescharacteristic
988C22#9034411yescharacteristic
989C22#9034911yescharacteristic
990C22#9034911yescharacteristic
991C22D7×#12411yescharacteristic
992C22#9036711yescharacteristic
993C22#9038311yescharacteristic
994C22#9038411yescharacteristic
995C22D7×#12611yescharacteristic
996C22#9039611yescharacteristic
997C22#9039811yescharacteristic
998C22#9039911yescharacteristic
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—81no—
1006C4—282no—
1007C4—282no—
1008C4—282no—
1009C4—282no—
1010C4—282no—
1011C4—282no—
1012C4—561no—
1013C2—148no—
1014C2#1173086111yescharacteristic
1015C2C4×#644611yescharacteristic
1016C2#1173121711yescharacteristic
1017C2#1173135611yescharacteristic
1018C2#1173157511yescharacteristic
1019C2#1173167811yescharacteristic
1020C2#1173174511yescharacteristic
1021C2#1173274211yescharacteristic
1022C2#1173274811yescharacteristic
1023C2#1173278011yescharacteristic
1024C2#1173278211yescharacteristic
1025C2D7×#38811yescharacteristic
1026C2#1173328311yescharacteristic
1027C2#1173331311yescharacteristic
1028C2#1173332611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1434C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1434D7
hypocenterC7#13992
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
6. C7×#1434C2semidirect
7. #11729288C2semidirect
10. #11727172C2semidirect
11. #11727171C2semidirect
12. #11727168C2semidirect
13. #11727166C2semidirect
14. #11727161C2semidirect
15. #11727160C2semidirect
54. #89436C4semidirect
122. C7×#95C2×C4semidirect
138. C7⋊#95C2×C4semidirect
139. C7⋊#95C2×C4semidirect
140. C7⋊#95C2×C4semidirect
153. #1434D7semidirect
573. #95C4×D7semidirect
948. C7#13992semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D7)⋊C42
C2×#894402
C2×#894362
C2×D7×#952
C7×#14342
#117292882
(C2×D7)⋊#952
#117271722
#117271712
#117271682
#117271662
#117271612
#117271602
#139927