Finite Group Databasebeta

← #13277105

Subgroups — #13277105

Order 1792.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89718C211yesmaximal, characteristic
2C2×#89714C211yesmaximal, characteristic
3C2×C22⋊C4×Dic7C211yesmaximal, characteristic
4C2×#89419C211yesmaximal, characteristic, complemented
5C2×#89427C211yesmaximal, characteristic, complemented
6C7×#1437C211yesmaximal, characteristic
7#11729301C211yesmaximal, characteristic
8#11729300C211yesmaximal, characteristic
9#11729299C211yesmaximal, characteristic
10#11729290C211yesmaximal, characteristic, complemented
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12#11727168C211yesmaximal, characteristic, complemented
13#11727163C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
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#89718C418yescomplemented
52#89714—24no—
53C22⋊C4×Dic7—24no—
54#89427—24no—
55#89419—24no—
56#14011—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—41no—
69C23×Dic7—41no—
70C23×Dic7C2×C414yes—
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—41no—
84C2×C7×C22⋊C4—41no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4C2×C414yes—
87C2×C7×C22⋊C4Q814yes—
88C2×C42×C7—22no—
89C2×C42×C7—41no—
90C2×C42×C7—41no—
91C2×C22⋊Dic7—22no—
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—41no—
99C2×C22⋊Dic7C2×C414yes—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—41no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—41no—
114C2×Dic7⋊C4—41no—
115C2×Dic7⋊C4—41no—
116C2×Dic7⋊C4C2×C414yes—
117C2×Dic7⋊C4C2×C414yes—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—41no—
125C2×C4×Dic7—41no—
126C2×C4×Dic7—41no—
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—41no—
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—41no—
140C7⋊#95—41no—
141C7⋊#95C2×C414yes—
142C7⋊#95C2×C414yes—
143C7⋊#95D414yes—
144C7⋊#95D414yes—
145C2×#389—71no—
146C2×#387—71no—
147C2×#385—71no—
148C2×#380—71no—
149C2×C4×C22⋊C4—71no—
150#1442—71no—
151#1441—71no—
152#1439—71no—
153#1439—71no—
154#1437—71no—
155#1437D711yescharacteristic
156#1436—71no—
157#1436—71no—
158#1436—71no—
159C4×#95—71no—
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×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7C22×C412yes—
173C24×C7C2×Q812yes—
174C24×C7#4112yes—
175C24×C7C2411yescharacteristic
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×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×Q812yes—
216C22×C4×C7C2×Q812yes—
217C22×C4×C7#4112yes—
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—28no—
255C22×Dic7—28no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—44no—
264C22×Dic7—44no—
265C22×Dic7—44no—
266C22×Dic7—44no—
267C22×Dic7—44no—
268C22×Dic7C22×C412yes—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C2×D412yes—
273C22×Dic7C2×D412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7C2×D412yes—
276C22×Dic7#4112yes—
277C22×Dic7#4112yes—
278C22×Dic7#4112yes—
279C22×Dic7#4112yes—
280C22×Dic7#4112yes—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—44no—
283C7×C22⋊C4—44no—
284C42×C7—44no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—44no—
288C4⋊Dic7—44no—
289Dic7⋊C4—28no—
290Dic7⋊C4—28no—
291Dic7⋊C4—44no—
292Dic7⋊C4—44no—
293Dic7⋊C4—44no—
294C4×Dic7—44no—
295C4×Dic7—44no—
296C4×Dic7—44no—
297C24×C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4C2×D711yescharacteristic
308C22×C22⋊C4C2×D711yescharacteristic
309C22×C22⋊C4C2×D711yescharacteristic
310C22×C42—71no—
311C22×C42—71no—
312C22×C42—71no—
313C22×C42C2×D711yescharacteristic
314#389—144no—
315#387—144no—
316#385—78no—
317#380—144no—
318C4×C22⋊C4—144no—
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—71no—
333C2×#95—71no—
334C2×#95C2×D711yescharacteristic
335C2×#95C2×D711yescharacteristic
336C2×#95C2×D711yescharacteristic
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—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
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—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7C4×Q814yes—
372C23×C7C23×C411yescharacteristic
373C23×C7C22×D411yescharacteristic
374C23×C7C22×D411yescharacteristic
375C23×C7C22×Q811yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7C2×#4111yescharacteristic
380C23×C7C2×#4111yescharacteristic
381C23×C7C2×#4111yescharacteristic
382C23×C7C2×#4111yescharacteristic
383C23×C7H(5,𝔽2)11yescharacteristic
384C23×C7H(5,𝔽2)11yescharacteristic
385C23×C7H(5,𝔽2)11yescharacteristic
386C23×C72−1+411yescharacteristic
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—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—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×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7C22⋊Q814yes—
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—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—416no—
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#11714yes—
484C2×Dic7C4×D414yes—
485C2×Dic7C4×D414yes—
486C25C22×D711yescharacteristic
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—74no—
495C23×C4—71no—
496C23×C4—142no—
497C23×C4—142no—
498C23×C4—142no—
499C23×C4—142no—
500C23×C4—281no—
501C23×C4—281no—
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—142no—
511C2×C4⋊C4—142no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—142no—
514C2×C4⋊C4—142no—
515C2×C4⋊C4—142no—
516C2×C4⋊C4—142no—
517C2×C4⋊C4—142no—
518C2×C4⋊C4—142no—
519C2×C4⋊C4—142no—
520C2×C4⋊C4—142no—
521C2×C4⋊C4—142no—
522C2×C4⋊C4—281no—
523C2×C4⋊C4—281no—
524C2×C4⋊C4—281no—
525C2×C4⋊C4—281no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—142no—
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—281no—
542C2×C22⋊C4Dic1414yes—
543C2×C22⋊C4C4×D714yes—
544C2×C42—22no—
545C2×C42—41no—
546C2×C42—41no—
547C2×C42—142no—
548C2×C42—142no—
549C2×C42—142no—
550C2×C42—142no—
551C2×C42—142no—
552C2×C42—142no—
553C2×C42—281no—
554C2×C42—281no—
555C2×C42—281no—
556#95—22no—
557#95—22no—
558#95—41no—
559#95—74no—
560#95—74no—
561#95—74no—
562#95—74no—
563#95—142no—
564#95—142no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—142no—
570#95—142no—
571#95—142no—
572#95—281no—
573#95—281no—
574C22×C7—24no—
575C22×C7—24no—
576C22×C7—24no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7—42no—
582C22×C7—42no—
583C22×C7—42no—
584C22×C7—42no—
585C22×C7—42no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7C2×#11711yescharacteristic
590C22×C7C2×C4×D411yescharacteristic
591C22×C7C2×C4×D411yescharacteristic
592C22×C7C2×C4×Q811yescharacteristic
593C22×C7C4×#4111yescharacteristic
594C22×C7#51811yescharacteristic
595C22×C7#52011yescharacteristic
596C22×C7C2×C22⋊Q811yescharacteristic
597C22×C7#52511yescharacteristic
598C22×C7#52911yescharacteristic
599C22×C7#52911yescharacteristic
600C22×C7#52911yescharacteristic
601C22×C7#53211yescharacteristic
602C22×C7#53211yescharacteristic
603C22×C7#53311yescharacteristic
604C22×C7#53811yescharacteristic
605C22×C7#53911yescharacteristic
606C22×C7#54011yescharacteristic
607C22×C7#54211yescharacteristic
608C22×C7D4211yescharacteristic
609C22×C7#54611yescharacteristic
610C22×C7#54611yescharacteristic
611C22×C7#54611yescharacteristic
612C22×C7#54611yescharacteristic
613C22×C7#54811yescharacteristic
614C22×C7D4×Q811yescharacteristic
615C22×C7#55111yescharacteristic
616C22×C7#55211yescharacteristic
617C22×C7#55211yescharacteristic
618C22×C7#55311yescharacteristic
619C22×C7#55311yescharacteristic
620C22×C7#55311yescharacteristic
621C22×C7#55411yescharacteristic
622C22×C7#55411yescharacteristic
623C22×C7#55411yescharacteristic
624C4×C7—24no—
625C4×C7—42no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—81no—
630Dic7—24no—
631Dic7—24no—
632Dic7—24no—
633Dic7—42no—
634Dic7—42no—
635Dic7—42no—
636Dic7—42no—
637Dic7—81no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24C2×Dic1412yes—
651C24C2×C4×D712yes—
652C24#115712yes—
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—72no—
690C22×C4—72no—
691C22×C4—72no—
692C22×C4—72no—
693C22×C4—72no—
694C22×C4—72no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—72no—
700C22×C4—72no—
701C22×C4—72no—
702C22×C4—148no—
703C22×C4—148no—
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—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—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—284no—
748C22×C4—284no—
749C22×C4—284no—
750C22×C4—284no—
751C22×C4—284no—
752C22×C4C2×Dic1412yes—
753C22×C4C2×Dic1412yes—
754C22×C4C2×C4×D712yes—
755C22×C4C2×C4×D712yes—
756C22×C4D4×D712yes—
757C22×C4D4×D712yes—
758C22×C4#115912yes—
759C4⋊C4—148no—
760C4⋊C4—148no—
761C4⋊C4—284no—
762C4⋊C4—284no—
763C4⋊C4—284no—
764C4⋊C4—284no—
765C22⋊C4—28no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—148no—
769C22⋊C4—148no—
770C22⋊C4—284no—
771C42—44no—
772C42—284no—
773C42—284no—
774C42—284no—
775C2×C7—44no—
776C2×C7#229311yescharacteristic
777C2×C7C4×C22⋊Q811yescharacteristic
778C2×C7#233511yescharacteristic
779C2×C7#234511yescharacteristic
780C2×C7#235211yescharacteristic
781C2×C7#235811yescharacteristic
782C2×C7#236011yescharacteristic
783C2×C7#245011yescharacteristic
784C2×C7#245211yescharacteristic
785C2×C7#246011yescharacteristic
786C2×C7#246411yescharacteristic
787C2×C7#252211yescharacteristic
788C2×C7#253011yescharacteristic
789C2×C7#255611yescharacteristic
790C2×C7#255911yescharacteristic
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C4×Dic1414yes—
826C23C22×Dic1411yescharacteristic
827C23C22×C4×D711yescharacteristic
828C23C2×#115711yescharacteristic
829C23C2×D4×D711yescharacteristic
830C23C2×D4×D711yescharacteristic
831C23C2×#115911yescharacteristic
832C23#654811yescharacteristic
833C23#654811yescharacteristic
834C23#654811yescharacteristic
835C23D7×#4111yescharacteristic
836C23D7×#4111yescharacteristic
837C23D7×#4111yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23#655411yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
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—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—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—74no—
883C2×C4—74no—
884C2×C4—74no—
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—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—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#644114yes—
940C7#1401111yescharacteristic, complemented, Sylow
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C4×Dic1411yescharacteristic
957C22C2×#644111yescharacteristic
958C22#9017711yescharacteristic
959C22#9018111yescharacteristic
960C22#9020811yescharacteristic
961C22D7×#11711yescharacteristic
962C22#9022211yescharacteristic
963C22C4×#115911yescharacteristic
964C22D4×Dic1411yescharacteristic
965C22#9022911yescharacteristic
966C22#9023011yescharacteristic
967C22#9023011yescharacteristic
968C22#9023011yescharacteristic
969C22#9023111yescharacteristic
970C22#9023111yescharacteristic
971C22C4×D4×D711yescharacteristic
972C22C4×D4×D711yescharacteristic
973C22#9023711yescharacteristic
974C22#9023811yescharacteristic
975C22#9028411yescharacteristic
976C22#9028711yescharacteristic
977C22#9029411yescharacteristic
978C22#9030111yescharacteristic
979C22#9030111yescharacteristic
980C22#9030111yescharacteristic
981C22#9030611yescharacteristic
982C22#9034011yescharacteristic
983C22#9035111yescharacteristic
984C22#9035211yescharacteristic
985C22#9035911yescharacteristic
986C22#9036811yescharacteristic
987C22#9037011yescharacteristic
988C22#9039711yescharacteristic
989C22#9039911yescharacteristic
990C22#9040811yescharacteristic
991C4—24no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—81no—
997C4—144no—
998C4—144no—
999C4—144no—
1000C4—282no—
1001C4—282no—
1002C4—282no—
1003C4—282no—
1004C4—561no—
1005C2—44no—
1006C2C4×#644111yescharacteristic
1007C2#1173090311yescharacteristic
1008C2#1173091111yescharacteristic
1009C2#1173211511yescharacteristic
1010C2#1173215711yescharacteristic
1011C2#1173220511yescharacteristic
1012C2#1173289511yescharacteristic
1013C2#1173295511yescharacteristic
1014C2#1173301311yescharacteristic
1015C2#1173302811yescharacteristic
1016C2#1173304411yescharacteristic
1017C2#1173327911yescharacteristic
1018C2#1173376811yescharacteristic
1019C2#1173387711yescharacteristic
1020C2#1173389211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1437C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1437D7
hypocenterC7#14011
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×#89419C2semidirect
5. C2×#89427C2semidirect
10. #11729290C2semidirect
11. C4×C7⋊#95C2semidirect
12. #11727168C2semidirect
13. #11727163C2semidirect
14. #11727160C2semidirect
15. #11727160C2semidirect
51. #89718C4semidirect
940. C7#14011semidirect

Maximal subgroups

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

subgroupindex
C2×#897182
C2×#897142
C2×C22⋊C4×Dic72
C2×#894192
C2×#894272
C7×#14372
#117293012
#117293002
#117292992
#117292902
C4×C7⋊#952
#117271682
#117271632
#117271602
#140117