Finite Group Databasebeta

← #13275893

Subgroups — #13275893

Order 1792.

1746 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×C7×#388C211yesmaximal, characteristic
2C2×#89723C211yesmaximal, characteristic
3C2×#89714C211yesmaximal, characteristic
4C2×C22⋊C4×Dic7C211yesmaximal, characteristic
5C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
6#11729322C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729301C211yesmaximal, characteristic
9#11729301C211yesmaximal, characteristic
10#11729298C211yesmaximal, characteristic
11#11729290C211yesmaximal, characteristic, complemented
12#11727174C211yesmaximal, characteristic, complemented
13#11727160C211yesmaximal, characteristic, complemented
14#11727157C211yesmaximal, characteristic, complemented
15#11727157C211yesmaximal, 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×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C7×#388—24no—
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
52#89723—24no—
53#89714—24no—
54C22⋊C4×Dic7C418yescomplemented
55C4×Dic7⋊C4—24no—
56#13891—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×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—41no—
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⋊C4—41no—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C7×C22⋊C4D414yes—
90C2×C7×C22⋊C4Q814yes—
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—41no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—22no—
100C2×C22⋊Dic7—41no—
101C2×C22⋊Dic7—41no—
102C2×C22⋊Dic7C2×C414yes—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—41no—
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—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—41no—
117C2×Dic7⋊C4—41no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—41no—
123C2×C4×Dic7—41no—
124C2×C4×Dic7—41no—
125C2×C4×Dic7C2×C414yes—
126C2×C4×Dic7C2×C414yes—
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—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95C2×C414yes—
143C7⋊#95C2×C414yes—
144C7⋊#95D414yes—
145C2×#388—71no—
146C2×#388D711yescharacteristic
147C2×#380—71no—
148C2×C4×C4⋊C4—71no—
149C2×C4×C22⋊C4—71no—
150#1444—71no—
151#1444—71no—
152#1439—71no—
153#1439—71no—
154#1436—71no—
155#1436—71no—
156C4⋊#95—71no—
157#1434—71no—
158#1434—71no—
159C22⋊#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×D412yes—
174C24×C7C2×Q812yes—
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×C7C22×C412yes—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C2×D412yes—
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—28no—
249C22×Dic7—28no—
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×Dic7—44no—
265C22×Dic7—44no—
266C22×Dic7—44no—
267C22×Dic7—44no—
268C22×Dic7—44no—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C2×D412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7#4112yes—
276C22×Dic7#4112yes—
277C22×Dic7#4112yes—
278C22×Dic7#4112yes—
279C22×Dic7#4112yes—
280C22×Dic7#4112yes—
281C7×C4⋊C4—44no—
282C7×C22⋊C4—44no—
283C7×C22⋊C4—44no—
284C7×C22⋊C4C4⋊C4116yescomplemented
285C42×C7—44no—
286C22⋊Dic7—28no—
287C22⋊Dic7—44no—
288C22⋊Dic7—44no—
289C4⋊Dic7—44no—
290Dic7⋊C4—28no—
291Dic7⋊C4—28no—
292Dic7⋊C4—44no—
293Dic7⋊C4—44no—
294C4×Dic7—28no—
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⋊C4C2×D711yescharacteristic
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#388—24no—
315#388—144no—
316#380—144no—
317C4×C4⋊C4—144no—
318C4×C22⋊C4—78no—
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×#95—71no—
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×C7C2×C4⋊C414yes—
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×C7C2×C4⋊C414yes—
428C2×C4×C7C2×C4⋊C414yes—
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—416no—
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#11714yes—
484C2×Dic7#11714yes—
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—74no—
494C23×C4—71no—
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—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—41no—
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—142no—
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—74no—
533C2×C22⋊C4—142no—
534C2×C22⋊C4—142no—
535C2×C22⋊C4—142no—
536C2×C22⋊C4—142no—
537C2×C22⋊C4—142no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—281no—
540C2×C22⋊C4—281no—
541C2×C22⋊C4Dic1414yes—
542C2×C22⋊C4C4×D714yes—
543C2×C22⋊C4C22⋊D714yes—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—41no—
547C2×C42—74no—
548C2×C42—74no—
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—74no—
559#95—74no—
560#95—74no—
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—142no—
570#95—281no—
571#95—281no—
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×C7C22×C4⋊C411yescharacteristic
590C22×C7C2×#11711yescharacteristic
591C22×C7C2×#11711yescharacteristic
592C22×C7C2×C4×D411yescharacteristic
593C22×C7C4×#4111yescharacteristic
594C22×C7#51811yescharacteristic
595C22×C7#52011yescharacteristic
596C22×C7#52511yescharacteristic
597C22×C7#52511yescharacteristic
598C22×C7#52911yescharacteristic
599C22×C7#52911yescharacteristic
600C22×C7#53211yescharacteristic
601C22×C7#53211yescharacteristic
602C22×C7#53311yescharacteristic
603C22×C7#53311yescharacteristic
604C22×C7#54011yescharacteristic
605C22×C7#54011yescharacteristic
606C22×C7#54211yescharacteristic
607C22×C7#54211yescharacteristic
608C22×C7D4211yescharacteristic
609C22×C7#54611yescharacteristic
610C22×C7#54611yescharacteristic
611C22×C7#54611yescharacteristic
612C22×C7#54611yescharacteristic
613C22×C7#54711yescharacteristic
614C22×C7D4×Q811yescharacteristic
615C22×C7#55111yescharacteristic
616C22×C7#55111yescharacteristic
617C22×C7#55311yescharacteristic
618C22×C7#55311yescharacteristic
619C22×C7#55411yescharacteristic
620C22×C7#55411yescharacteristic
621C22×C7#55411yescharacteristic
622C22×C7#55611yescharacteristic
623C22×C7#55611yescharacteristic
624C4×C7—24no—
625C4×C7—24no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—81no—
629C4×C7—81no—
630Dic7—24no—
631Dic7—24no—
632Dic7—24no—
633Dic7—42no—
634Dic7—42no—
635Dic7—42no—
636Dic7—81no—
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—
652C24C2×C22⋊D712yes—
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—72no—
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—148no—
701C22×C4—148no—
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—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—284no—
747C22×C4—284no—
748C22×C4—284no—
749C22×C4—284no—
750C22×C4—284no—
751C22×C4C2×Dic1412yes—
752C22×C4C2×Dic1412yes—
753C22×C4C2×C4×D712yes—
754C22×C4C2×C4×D712yes—
755C22×C4D4×D712yes—
756C22×C4#115912yes—
757C22×C4C2×C22⋊D712yes—
758C22×C4C2×C22⋊D712yes—
759C4⋊C4—44no—
760C4⋊C4—148no—
761C4⋊C4—148no—
762C4⋊C4—284no—
763C4⋊C4—284no—
764C4⋊C4—284no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C22⋊C4—148no—
768C22⋊C4—284no—
769C22⋊C4—284no—
770C22⋊C4Dic7⋊C4116yescomplemented
771C42—44no—
772C42—148no—
773C42—284no—
774C42—284no—
775C2×C7—44no—
776C2×C7#228511yescharacteristic
777C2×C7#229011yescharacteristic
778C2×C7#231911yescharacteristic
779C2×C7#234211yescharacteristic
780C2×C7#234711yescharacteristic
781C2×C7D4×C4⋊C411yescharacteristic
782C2×C7#234911yescharacteristic
783C2×C7#246411yescharacteristic
784C2×C7#246411yescharacteristic
785C2×C7#246511yescharacteristic
786C2×C7#246511yescharacteristic
787C2×C7#252111yescharacteristic
788C2×C7#252111yescharacteristic
789C2×C7#252211yescharacteristic
790C2×C7#252211yescharacteristic
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—
825C23C2×Dic7⋊C414yes—
826C23C22×Dic1411yescharacteristic
827C23C22×C4×D711yescharacteristic
828C23C2×D4×D711yescharacteristic
829C23C2×#115911yescharacteristic
830C23#654811yescharacteristic
831C23#654811yescharacteristic
832C23D7×#4111yescharacteristic
833C23D7×#4111yescharacteristic
834C23D7×#4111yescharacteristic
835C23D7×#4111yescharacteristic
836C23D7×#4111yescharacteristic
837C23D7×#4111yescharacteristic
838C23#655311yescharacteristic
839C23#655411yescharacteristic
840C23C22×C22⋊D711yescharacteristic
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—74no—
882C2×C4—74no—
883C2×C4—74no—
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—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—2816no—
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—
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×C4C2×Dic7⋊C414yes—
939C2×C4C2×Dic7⋊C414yes—
940C7#1389111yescharacteristic, 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—
956C22#9020811yescharacteristic
957C22#9020811yescharacteristic
958C22D7×#11711yescharacteristic
959C22D7×#11711yescharacteristic
960C22C4×#115911yescharacteristic
961C22D4×Dic1411yescharacteristic
962C22#9023011yescharacteristic
963C22#9023011yescharacteristic
964C22#9023411yescharacteristic
965C22C4×D4×D711yescharacteristic
966C22#9023611yescharacteristic
967C22#9023711yescharacteristic
968C22#9029211yescharacteristic
969C22#9029711yescharacteristic
970C22#9030311yescharacteristic
971C22#9030611yescharacteristic
972C22#9034511yescharacteristic
973C22#9034711yescharacteristic
974C22#9035211yescharacteristic
975C22#9035411yescharacteristic
976C22#9036011yescharacteristic
977C22#9036211yescharacteristic
978C22#9037011yescharacteristic
979C22#9037111yescharacteristic
980C22#9039311yescharacteristic
981C22#9039611yescharacteristic
982C22#9039711yescharacteristic
983C22#9040111yescharacteristic
984C22C22×Dic7⋊C411yescharacteristic
985C22D4×C22⋊D711yescharacteristic
986C22#9049711yescharacteristic
987C22#9051511yescharacteristic
988C22#9052011yescharacteristic
989C22#9052311yescharacteristic
990C22#9052311yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—144no—
998C4—144no—
999C4—144no—
1000C4—282no—
1001C4—282no—
1002C4—282no—
1003C4—561no—
1004C4—561no—
1005C2—44no—
1006C2#1173289411yescharacteristic
1007C2#1173290311yescharacteristic
1008C2#1173291911yescharacteristic
1009C2#1173295911yescharacteristic
1010C2#1173296011yescharacteristic
1011C2#1173301211yescharacteristic
1012C2#1173301311yescharacteristic
1013C2#1173327711yescharacteristic
1014C2#1173966911yescharacteristic
1015C2D4×Dic7⋊C411yescharacteristic
1016C2#1173977911yescharacteristic
1017C2#1174010411yescharacteristic
1018C2#1174029811yescharacteristic
1019C2#1174041311yescharacteristic
1020C2#1174053111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#13891
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. C2×C4×Dic7⋊C4C2semidirect
6. #11729322C2semidirect
7. #11729317C2semidirect
11. #11729290C2semidirect
12. #11727174C2semidirect
13. #11727160C2semidirect
14. #11727157C2semidirect
15. #11727157C2semidirect
54. C22⋊C4×Dic7C4semidirect
284. C7×C22⋊C4C4⋊C4semidirect
770. C22⋊C4Dic7⋊C4semidirect
940. C7#13891semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×#897232
C2×#897142
C2×C22⋊C4×Dic72
C2×C4×Dic7⋊C42
#117293222
#117293172
#117293012
#117292982
#117292902
#117271742
#117271602
#117271572
#138917