Finite Group Databasebeta

← #13276890

Subgroups — #13276890

Order 1792.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89717C211yesmaximal, characteristic
2C2×#89723C211yesmaximal, characteristic
3C2×#89714C211yesmaximal, characteristic
4C2×#89714C211yesmaximal, characteristic
5C2×C22⋊C4×Dic7C211yesmaximal, characteristic
6C2×#89419C211yesmaximal, characteristic, complemented
7C2×#89421C211yesmaximal, characteristic, complemented
8C7×#1440C211yesmaximal, characteristic
9#11729303C211yesmaximal, characteristic
10#11727169C211yesmaximal, characteristic, complemented
11#11727167C211yesmaximal, characteristic, complemented
12Dic7⋊#95C211yesmaximal, characteristic, complemented
13Dic7⋊#95C211yesmaximal, characteristic, complemented
14#11727157C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, 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×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
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#89723—24no—
52#89717—24no—
53#89714—24no—
54#89714C418yescomplemented
55C22⋊C4×Dic7—24no—
56#89421—24no—
57#89419—24no—
58#13994—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×Dic7—22no—
67C23×Dic7—22no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—22no—
71C23×Dic7—22no—
72C23×Dic7C2×C414yes—
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
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—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—41no—
89C2×C7×C22⋊C4C2×C414yes—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—41no—
97C2×C22⋊Dic7C2×C414yes—
98C2×C22⋊Dic7D414yes—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—41no—
102C2×Dic7⋊C4—22no—
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⋊C4C2×C414yes—
115C2×Dic7⋊C4C2×C414yes—
116C2×Dic7⋊C4D414yes—
117C2×C4×Dic7—22no—
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—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—22no—
128C2×C4×Dic7D414yes—
129C7×#95—22no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—41no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—41no—
145C7⋊#95C2×C414yes—
146C7⋊#95C2×C414yes—
147C2×#389—71no—
148C2×#388—71no—
149C2×#388—71no—
150C2×#380—71no—
151C2×#380—71no—
152C2×C4×C4⋊C4—71no—
153C2×C4×C22⋊C4—71no—
154#1442—71no—
155#1442—71no—
156#1440—71no—
157#1440D711yescharacteristic
158C4⋊#95—71no—
159C4⋊#95—71no—
160#1434—71no—
161#1434—71no—
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×C7—21no—
173C24×C7—21no—
174C24×C7C22×C412yes—
175C24×C7C2×D412yes—
176C24×C7#4112yes—
177C24×C7C2411yescharacteristic
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×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7C22×C412yes—
216C22×C4×C7C22×C412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7#4112yes—
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—28no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
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×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7#4112yes—
279C22×Dic7#4112yes—
280C22×Dic7#4112yes—
281C22×Dic7#4112yes—
282C22×Dic7#4112yes—
283C7×C22⋊C4—28no—
284C7×C22⋊C4—28no—
285C7×C22⋊C4—44no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—44no—
289C4⋊Dic7—44no—
290Dic7⋊C4—28no—
291Dic7⋊C4—28no—
292Dic7⋊C4—28no—
293Dic7⋊C4—44no—
294Dic7⋊C4—44no—
295C4×Dic7—28no—
296C4×Dic7—44no—
297C4×Dic7—44no—
298C4×Dic7—44no—
299C24×C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4C2×D711yescharacteristic
310C22×C22⋊C4C2×D711yescharacteristic
311C22×C22⋊C4C2×D711yescharacteristic
312C22×C42—71no—
313C22×C42—71no—
314C22×C42—71no—
315C22×C42—71no—
316#389—144no—
317#388—144no—
318#388—144no—
319#380—78no—
320#380—144no—
321C4×C4⋊C4—144no—
322C4×C22⋊C4—144no—
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×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95C2×D711yescharacteristic
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
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—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
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×C7—41no—
372C23×C7—41no—
373C23×C7—41no—
374C23×C7—41no—
375C23×C7C4×D414yes—
376C23×C7C23×C411yescharacteristic
377C23×C7C22×D411yescharacteristic
378C23×C7C22×D411yescharacteristic
379C23×C7C22×D411yescharacteristic
380C23×C7C2×#4111yescharacteristic
381C23×C7C2×#4111yescharacteristic
382C23×C7C2×#4111yescharacteristic
383C23×C7C2×#4111yescharacteristic
384C23×C7C2×#4111yescharacteristic
385C23×C7C2×#4111yescharacteristic
386C23×C7C2×#4111yescharacteristic
387C23×C7H(5,𝔽2)11yescharacteristic
388C23×C72−1+411yescharacteristic
389C23×C72−1+411yescharacteristic
390C23×C72−1+411yescharacteristic
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—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×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
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—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—416no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7#11714yes—
483C2×Dic7C4×D414yes—
484C2×Dic7C4×D414yes—
485C2×Dic7#12114yes—
486C2×Dic7#12114yes—
487C2×Dic7#12314yes—
488C2×Dic7#12414yes—
489C2×Dic7#12614yes—
490C25C22×D711yescharacteristic
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—74no—
494C23×C4—71no—
495C23×C4—71no—
496C23×C4—71no—
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—142no—
501C23×C4—142no—
502C23×C4—142no—
503C23×C4—142no—
504C23×C4—142no—
505C23×C4—142no—
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C23×C4C22×D711yescharacteristic
509C23×C4C22×D711yescharacteristic
510C23×C4C22×D711yescharacteristic
511C23×C4C22×D711yescharacteristic
512C2×C4⋊C4—74no—
513C2×C4⋊C4—74no—
514C2×C4⋊C4—74no—
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—142no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—281no—
529C2×C4⋊C4—281no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—74no—
539C2×C22⋊C4—74no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—281no—
547C2×C22⋊C4C4×D714yes—
548C2×C42—74no—
549C2×C42—142no—
550C2×C42—142no—
551C2×C42—142no—
552C2×C42—142no—
553C2×C42—142no—
554C2×C42—142no—
555C2×C42—142no—
556C2×C42—142no—
557C2×C42—142no—
558C2×C42—142no—
559C2×C42—142no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—41no—
564#95—74no—
565#95—74no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—142no—
570#95—142no—
571#95—142no—
572#95—142no—
573#95—142no—
574#95—142no—
575#95—142no—
576#95—142no—
577#95—281no—
578C22×C7—24no—
579C22×C7—24no—
580C22×C7—24no—
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×C7—42no—
590C22×C7—42no—
591C22×C7—42no—
592C22×C7—42no—
593C22×C7C2×#11711yescharacteristic
594C22×C7C2×C4×D411yescharacteristic
595C22×C7C2×C4×D411yescharacteristic
596C22×C7C2×C4×D411yescharacteristic
597C22×C7C4×#4111yescharacteristic
598C22×C7#51911yescharacteristic
599C22×C7#52011yescharacteristic
600C22×C7C2×#12111yescharacteristic
601C22×C7C2×#12111yescharacteristic
602C22×C7C2×#12311yescharacteristic
603C22×C7#52511yescharacteristic
604C22×C7C2×#12411yescharacteristic
605C22×C7C2×#12611yescharacteristic
606C22×C7#52911yescharacteristic
607C22×C7#53211yescharacteristic
608C22×C7#53611yescharacteristic
609C22×C7#53711yescharacteristic
610C22×C7#54111yescharacteristic
611C22×C7#54211yescharacteristic
612C22×C7D4211yescharacteristic
613C22×C7#54711yescharacteristic
614C22×C7#54711yescharacteristic
615C22×C7#54711yescharacteristic
616C22×C7#54711yescharacteristic
617C22×C7#54811yescharacteristic
618C22×C7#54811yescharacteristic
619C22×C7#55211yescharacteristic
620C22×C7#55211yescharacteristic
621C22×C7#55211yescharacteristic
622C22×C7#55211yescharacteristic
623C22×C7#55211yescharacteristic
624C22×C7#55311yescharacteristic
625C22×C7#55511yescharacteristic
626C22×C7#55511yescharacteristic
627C22×C7#55611yescharacteristic
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—42no—
631C4×C7—42no—
632C4×C7—42no—
633C4×C7—81no—
634Dic7—24no—
635Dic7—42no—
636Dic7—42no—
637Dic7—42no—
638Dic7—42no—
639Dic7—42no—
640Dic7—81no—
641Dic7#38818yescomplemented
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24C2×C4×D712yes—
655C24D4×D712yes—
656C24#115912yes—
657C24C23×D711yescharacteristic
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—72no—
702C22×C4—72no—
703C22×C4—72no—
704C22×C4—72no—
705C22×C4—72no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—72no—
710C22×C4—148no—
711C22×C4—148no—
712C22×C4—148no—
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—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—284no—
755C22×C4—284no—
756C22×C4—284no—
757C22×C4—284no—
758C22×C4C2×C4×D712yes—
759C22×C4C2×C4×D712yes—
760C22×C4D4×D712yes—
761C22×C4D4×D712yes—
762C22×C4#115912yes—
763C4⋊C4—148no—
764C4⋊C4—148no—
765C4⋊C4—148no—
766C4⋊C4—284no—
767C4⋊C4—284no—
768C4⋊C4—284no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—44no—
772C22⋊C4—148no—
773C22⋊C4—148no—
774C22⋊C4—284no—
775C42—148no—
776C42—284no—
777C42—284no—
778C42—284no—
779C2×C7—44no—
780C2×C7C2×#38811yescharacteristic
781C2×C7C4×#12111yescharacteristic
782C2×C7#232311yescharacteristic
783C2×C7#234411yescharacteristic
784C2×C7#234611yescharacteristic
785C2×C7#236111yescharacteristic
786C2×C7#236211yescharacteristic
787C2×C7#248511yescharacteristic
788C2×C7#248611yescharacteristic
789C2×C7#248911yescharacteristic
790C2×C7#249111yescharacteristic
791C2×C7#249511yescharacteristic
792C2×C7#249611yescharacteristic
793C2×C7#253611yescharacteristic
794C2×C7#253711yescharacteristic
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—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23(C22⋊D7)⋊C414yes—
830C23C22×C4×D711yescharacteristic
831C23C2×D4×D711yescharacteristic
832C23C2×D4×D711yescharacteristic
833C23C2×D4×D711yescharacteristic
834C23C2×#115911yescharacteristic
835C23C2×#115911yescharacteristic
836C23#654811yescharacteristic
837C23D7×#4111yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23D7×#4111yescharacteristic
841C23D7×#4111yescharacteristic
842C23#655411yescharacteristic
843C23#655411yescharacteristic
844C23#655411yescharacteristic
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—22no—
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—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—74no—
888C2×C4—74no—
889C2×C4—74no—
890C2×C4—74no—
891C2×C4—74no—
892C2×C4—74no—
893C2×C4—74no—
894C2×C4—74no—
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—142no—
916C2×C4—2816no—
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—
944C7#1399411yescharacteristic, complemented, Sylow
945C22—24no—
946C22—24no—
947C22—24no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22C2×(C22⋊D7)⋊C411yescharacteristic
961C22#9020711yescharacteristic
962C22D7×#11711yescharacteristic
963C22C4×#115911yescharacteristic
964C22C4×D4×D711yescharacteristic
965C22C4×D4×D711yescharacteristic
966C22#9023711yescharacteristic
967C22#9027711yescharacteristic
968C22#9028111yescharacteristic
969C22#9028711yescharacteristic
970C22#9028811yescharacteristic
971C22#9028911yescharacteristic
972C22#9028911yescharacteristic
973C22#9029211yescharacteristic
974C22D7×#12111yescharacteristic
975C22D7×#12111yescharacteristic
976C22#9030711yescharacteristic
977C22#9034011yescharacteristic
978C22#9034111yescharacteristic
979C22#9034111yescharacteristic
980C22#9034111yescharacteristic
981C22D7×#12311yescharacteristic
982C22#9034611yescharacteristic
983C22#9034611yescharacteristic
984C22#9034611yescharacteristic
985C22#9034611yescharacteristic
986C22#9035311yescharacteristic
987C22#9036111yescharacteristic
988C22#9036211yescharacteristic
989C22D7×#12411yescharacteristic
990C22#9036611yescharacteristic
991C22#9039211yescharacteristic
992C22D7×#12611yescharacteristic
993C22#9039911yescharacteristic
994C22#9039911yescharacteristic
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—78no—
1001C4—81no—
1002C4—144no—
1003C4—282no—
1004C4—282no—
1005C4—282no—
1006C4—282no—
1007C4—282no—
1008C4—561no—
1009C2—44no—
1010C2#1173150511yescharacteristic
1011C2#1173210511yescharacteristic
1012C2#1173212111yescharacteristic
1013C2#1173290411yescharacteristic
1014C2#1173291811yescharacteristic
1015C2#1173292411yescharacteristic
1016C2D7×#38811yescharacteristic
1017C2#1173437811yescharacteristic
1018C2#1173438011yescharacteristic
1019C2#1173438811yescharacteristic
1020C2#1173438911yescharacteristic
1021C2#1173493011yescharacteristic
1022C2#1173493111yescharacteristic
1023C2#1173493411yescharacteristic
1024C2#1173493511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1440C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1440D7
hypocenterC7#13994
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
6. C2×#89419C2semidirect
7. C2×#89421C2semidirect
10. #11727169C2semidirect
11. #11727167C2semidirect
12. Dic7⋊#95C2semidirect
13. Dic7⋊#95C2semidirect
14. #11727157C2semidirect
15. #11727155C2semidirect
54. #89714C4semidirect
641. Dic7#388semidirect
944. C7#13994semidirect

Maximal subgroups

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

subgroupindex
C2×#897172
C2×#897232
C2×#897142
C2×C22⋊C4×Dic72
C2×#894192
C2×#894212
C7×#14402
#117293032
#117271692
#117271672
Dic7⋊#952
#117271572
#117271552
#139947