Finite Group Databasebeta

← #13285397

Subgroups — #13285397

Order 1792.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#398C211yesmaximal, characteristic, complemented
2C2×#89761C211yesmaximal, characteristic
3C2×#89761C211yesmaximal, characteristic
4C2×#89761C211yesmaximal, characteristic
5C2×#89759C211yesmaximal, characteristic
6C2×D7×#95C211yesmaximal, characteristic
7#11729322C211yesmaximal, characteristic, complemented
8#11729321C211yesmaximal, characteristic, complemented
9#11729320C211yesmaximal, characteristic, complemented
10#11729320C211yesmaximal, characteristic, complemented
11(C2×D7)⋊#95C211yesmaximal, characteristic
12(C2×D7)⋊#95C211yesmaximal, characteristic
13#11727175C211yesmaximal, characteristic, complemented
14#11727166C211yesmaximal, characteristic, complemented
15#11727165C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C7×#398—24no—
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
51C2×C7⋊#95C2211yescharacteristic
52#89761—24no—
53#89761—24no—
54#89761—24no—
55#89759—24no—
56D7×#95—24no—
57#14736—71nomaximal, Sylow
58C24×D7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
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×D7—41no—
92C22×C4×D7—41no—
93C22×C4×D7Q814yes—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—22no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—41no—
103C2×C7×C4⋊C4—41no—
104C2×C7×C4⋊C4—41no—
105C2×C7×C4⋊C4—41no—
106C2×(C2×D7)⋊C4—22no—
107C2×(C2×D7)⋊C4—22no—
108C2×(C2×D7)⋊C4—22no—
109C2×(C2×D7)⋊C4—22no—
110C2×(C2×D7)⋊C4—22no—
111C2×(C2×D7)⋊C4—22no—
112C2×(C2×D7)⋊C4—22no—
113C2×(C2×D7)⋊C4—22no—
114C2×(C2×D7)⋊C4—22no—
115C2×(C2×D7)⋊C4D414yes—
116C2×(C2×D7)⋊C4D414yes—
117C2×(C2×D7)⋊C4Q814yes—
118C2×C4⋊Dic7—22no—
119C2×C4⋊Dic7—22no—
120C2×C4⋊Dic7—41no—
121C2×Dic7⋊C4—22no—
122C2×Dic7⋊C4—22no—
123C2×Dic7⋊C4—22no—
124C2×Dic7⋊C4—22no—
125C2×Dic7⋊C4—22no—
126C2×Dic7⋊C4—22no—
127C2×Dic7⋊C4—41no—
128C2×Dic7⋊C4—41no—
129C2×Dic7⋊C4—41no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95D414yes—
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—22no—
145C7⋊#95—22no—
146C7⋊#95—41no—
147C7⋊#95—41no—
148C7⋊#95—41no—
149C7⋊#95—41no—
150C2×#398D711yescharacteristic, complemented
151C2×#385—71no—
152C2×#385—71no—
153C2×#385—71no—
154C2×#380—71no—
155C22×#95—71no—
156#1445—71no—
157#1444—71no—
158#1442—71no—
159#1442—71no—
160#1441—71no—
161#1441—71no—
162#1441—71no—
163C22⋊#95—71no—
164C22⋊#95—71no—
165C24×C7C2411yescharacteristic
166C23×D7—21no—
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7C2×D412yes—
175C23×D7C2×D412yes—
176C23×D7C2×Q812yes—
177C23×D7C2×Q812yes—
178C23×D7#4112yes—
179C23×D7#4112yes—
180C23×D7#4112yes—
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×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7C2×D412yes—
223C22×C4×C7C2×D412yes—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×Q812yes—
228C22×C4×C7C2×Q812yes—
229C22×C4×C7#4112yes—
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×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7C2×D412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7C2×Q812yes—
276C22×Dic7C2×Q812yes—
277C22×Dic7#4112yes—
278C22×Dic7#4112yes—
279C2×C4×D7—28no—
280C2×C4×D7—28no—
281C2×C4×D7—28no—
282C2×C4×D7—28no—
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—
291C2×C4×D7—44no—
292C2×C4×D7—44no—
293C2×C4×D7—44no—
294C2×C4×D7—44no—
295C2×C4×D7—44no—
296C2×C4×D7—44no—
297C2×C4×D7—44no—
298C2×C4×D7—44no—
299C2×C4×D7—44no—
300C7×C4⋊C4—44no—
301C7×C4⋊C4—44no—
302C7×C4⋊C4—44no—
303C7×C4⋊C4—44no—
304(C2×D7)⋊C4—28no—
305(C2×D7)⋊C4—28no—
306(C2×D7)⋊C4—28no—
307(C2×D7)⋊C4—44no—
308C4⋊Dic7—44no—
309Dic7⋊C4—44no—
310Dic7⋊C4—44no—
311Dic7⋊C4—44no—
312C24×C4—71no—
313C24×C4—71no—
314C24×C4—71no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4C2×D711yescharacteristic
320C22×C4⋊C4C2×D711yescharacteristic
321C22×C4⋊C4C2×D711yescharacteristic
322C22×C4⋊C4C2×D711yescharacteristic
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327#398—24no—
328#385—144no—
329#385—144no—
330#385—144no—
331#380—144no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C2×#95—144no—
350C2×#95C2×D711yescharacteristic
351C2×#95C2×D711yescharacteristic
352C2×#95C2×D711yescharacteristic
353C23×C7C22×D411yescharacteristic
354C23×C7C22×D411yescharacteristic
355C23×C7C22×D411yescharacteristic
356C23×C7C22×Q811yescharacteristic
357C23×C7C22×Q811yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7C2×#4111yescharacteristic
363C23×C7C2×#4111yescharacteristic
364C23×C7H(5,𝔽2)11yescharacteristic
365C23×C7H(5,𝔽2)11yescharacteristic
366C23×C7H(5,𝔽2)11yescharacteristic
367C23×C72−1+411yescharacteristic
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—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—22no—
389C22×D7—22no—
390C22×D7—22no—
391C22×D7—22no—
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7#12114yes—
397C22×D7C22⋊Q814yes—
398C22×D7C22⋊Q814yes—
399C22×D7#12314yes—
400C22×D7#12514yes—
401C22×D7#12514yes—
402C22×D7C4⋊Q814yes—
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—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
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—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7C22⋊Q814yes—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
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—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7—41no—
494C2×Dic7—41no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C4×D7—416no—
502C4×D7—416no—
503C4×D7—416no—
504C25—71no—
505C23×C4—71no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—71no—
511C23×C4—74no—
512C23×C4—71no—
513C23×C4—142no—
514C23×C4—142no—
515C23×C4—142no—
516C23×C4—142no—
517C23×C4—142no—
518C23×C4—142no—
519C23×C4—142no—
520C23×C4—142no—
521C23×C4—142no—
522C23×C4—142no—
523C23×C4—142no—
524C23×C4—142no—
525C23×C4—142no—
526C23×C4—142no—
527C23×C4—281no—
528C23×C4—281no—
529C23×C4—281no—
530C23×C4—281no—
531C23×C4—281no—
532C23×C4—281no—
533C23×C4C22×D711yescharacteristic
534C23×C4C22×D711yescharacteristic
535C23×C4C22×D711yescharacteristic
536C23×C4C22×D711yescharacteristic
537C23×C4C22×D711yescharacteristic
538C23×C4C22×D711yescharacteristic
539C23×C4C22×D711yescharacteristic
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—142no—
553C2×C4⋊C4—142no—
554C2×C4⋊C4—142no—
555C2×C4⋊C4—142no—
556C2×C4⋊C4—142no—
557C2×C4⋊C4—142no—
558C2×C4⋊C4—142no—
559C2×C4⋊C4—142no—
560C2×C4⋊C4—281no—
561C2×C4⋊C4—281no—
562C2×C4⋊C4—281no—
563C2×C4⋊C4—281no—
564C2×C22⋊C4—74no—
565C2×C22⋊C4—74no—
566C2×C22⋊C4—74no—
567C2×C22⋊C4—142no—
568C2×C22⋊C4—142no—
569C2×C22⋊C4—142no—
570C2×C22⋊C4—142no—
571C2×C22⋊C4—142no—
572C2×C22⋊C4—142no—
573C2×C22⋊C4—142no—
574C2×C22⋊C4—142no—
575C2×C22⋊C4—142no—
576#95—22no—
577#95—22no—
578#95—142no—
579#95—142no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—142no—
585#95—142no—
586#95—142no—
587#95—142no—
588#95—142no—
589#95—142no—
590#95—142no—
591#95—281no—
592#95—281no—
593#95—281no—
594#95—281no—
595#95C22⋊D714yes—
596C22×C7C2×#12111yescharacteristic
597C22×C7C2×C22⋊Q811yescharacteristic
598C22×C7C2×C22⋊Q811yescharacteristic
599C22×C7C2×C22⋊Q811yescharacteristic
600C22×C7C2×#12311yescharacteristic
601C22×C7#52511yescharacteristic
602C22×C7#52511yescharacteristic
603C22×C7C2×#12511yescharacteristic
604C22×C7C2×#12511yescharacteristic
605C22×C7#52911yescharacteristic
606C22×C7#52911yescharacteristic
607C22×C7C2×C4⋊Q811yescharacteristic
608C22×C7#53311yescharacteristic
609C22×C7#53811yescharacteristic
610C22×C7#53811yescharacteristic
611C22×C7#53911yescharacteristic
612C22×C7#53911yescharacteristic
613C22×C7#54311yescharacteristic
614C22×C7#54411yescharacteristic
615C22×C7D4211yescharacteristic
616C22×C7D4211yescharacteristic
617C22×C7#54611yescharacteristic
618C22×C7#54611yescharacteristic
619C22×C7#54611yescharacteristic
620C22×C7#54611yescharacteristic
621C22×C7#54611yescharacteristic
622C22×C7#54711yescharacteristic
623C22×C7#54711yescharacteristic
624C22×C7D4×Q811yescharacteristic
625C22×C7#55111yescharacteristic
626C22×C7#55111yescharacteristic
627C22×C7#55211yescharacteristic
628C22×C7#55411yescharacteristic
629C22×C7#55411yescharacteristic
630C22×C7#55411yescharacteristic
631C2×D7—24no—
632C2×D7—24no—
633C2×D7—24no—
634C2×D7—24no—
635C2×D7—24no—
636C2×D7—24no—
637C2×D7—24no—
638C2×D7—24no—
639C2×D7—24no—
640C2×D7—24no—
641C2×D7—24no—
642C2×D7—24no—
643C2×D7—24no—
644C2×D7—24no—
645C2×D7#39818yescomplemented
646C4×C7—24no—
647C4×C7—42no—
648C4×C7—42no—
649C4×C7—42no—
650C4×C7—42no—
651C4×C7—42no—
652C4×C7—81no—
653Dic7—42no—
654Dic7—42no—
655Dic7—42no—
656Dic7—42no—
657Dic7—42no—
658Dic7—42no—
659Dic7—81no—
660C24—72no—
661C24—72no—
662C24—72no—
663C24—72no—
664C24—72no—
665C24—72no—
666C24—72no—
667C24—141no—
668C24—141no—
669C24—141no—
670C24—141no—
671C24—141no—
672C24—141no—
673C24—141no—
674C24—141no—
675C24C23×D711yescharacteristic
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—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—72no—
718C22×C4—72no—
719C22×C4—72no—
720C22×C4—72no—
721C22×C4—72no—
722C22×C4—72no—
723C22×C4—148no—
724C22×C4—148no—
725C22×C4—148no—
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—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—141no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—148no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—141no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—284no—
771C22×C4—284no—
772C22×C4—284no—
773C22×C4—284no—
774C22×C4—284no—
775C22×C4—284no—
776C22×C4—284no—
777C22×C4—284no—
778C22×C4—284no—
779C22×C4—284no—
780C22×C4—284no—
781C22×C4—284no—
782C22×C4—284no—
783C22×C4—284no—
784C22×C4—284no—
785C22×C4—284no—
786C22×C4—284no—
787C22×C4D4×D712yes—
788C22×C4D4×D712yes—
789C22×C4Q8×D712yes—
790C22×C4Q8×D712yes—
791C22×C4#116112yes—
792C22×C4C2×C22⋊D712yes—
793C22×C4C2×C22⋊D712yes—
794C22×C4C2×C22⋊D712yes—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—284no—
800C4⋊C4—284no—
801C4⋊C4—284no—
802C4⋊C4—284no—
803C22⋊C4—148no—
804C22⋊C4—148no—
805C22⋊C4—148no—
806C22⋊C4—284no—
807C2×C7C2×#39811yescharacteristic
808C2×C7#241811yescharacteristic
809C2×C7#241911yescharacteristic
810C2×C7#242411yescharacteristic
811C2×C7#242511yescharacteristic
812C2×C7#243711yescharacteristic
813C2×C7#243811yescharacteristic
814C2×C7#244011yescharacteristic
815C2×C7#244911yescharacteristic
816C2×C7#245011yescharacteristic
817C2×C7#247311yescharacteristic
818C2×C7#250511yescharacteristic
819C2×C7#254911yescharacteristic
820C2×C7#264611yescharacteristic
821C2×C7#285111yescharacteristic
822D7—28no—
823C23—74no—
824C23—74no—
825C23—74no—
826C23—74no—
827C23—74no—
828C23—74no—
829C23—74no—
830C23—142no—
831C23—142no—
832C23—142no—
833C23—142no—
834C23—142no—
835C23—142no—
836C23—142no—
837C23—142no—
838C23—142no—
839C23—142no—
840C23—142no—
841C23—142no—
842C23—142no—
843C23—142no—
844C23—142no—
845C23—142no—
846C23—142no—
847C23—142no—
848C23—142no—
849C23—142no—
850C23—142no—
851C23—142no—
852C23—142no—
853C23—142no—
854C23—142no—
855C23—142no—
856C23—142no—
857C23—142no—
858C23C2×D4×D711yescharacteristic
859C23C2×D4×D711yescharacteristic
860C23#654811yescharacteristic
861C23#654811yescharacteristic
862C23C2×Q8×D711yescharacteristic
863C23C2×Q8×D711yescharacteristic
864C23C2×#116111yescharacteristic
865C23#655111yescharacteristic
866C23D7×#4111yescharacteristic
867C23D7×#4111yescharacteristic
868C23D7×#4111yescharacteristic
869C23D7×#4111yescharacteristic
870C23D7×#4111yescharacteristic
871C23#655311yescharacteristic
872C23C22×C22⋊D711yescharacteristic
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—142no—
922C2×C4—142no—
923C2×C4—142no—
924C2×C4—142no—
925C2×C4—142no—
926C2×C4—142no—
927C2×C4—142no—
928C2×C4—142no—
929C2×C4—142no—
930C2×C4—142no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—142no—
935C2×C4—142no—
936C2×C4—142no—
937C2×C4—142no—
938C2×C4—142no—
939C2×C4—2816no—
940C2×C4—2816no—
941C2×C4—2816no—
942C2×C4—281no—
943C2×C4—281no—
944C2×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4—281no—
950C2×C4—281no—
951C2×C4—281no—
952C2×C4—281no—
953C2×C4—281no—
954C2×C4—281no—
955C2×C4—281no—
956C2×C4—281no—
957C2×C4—281no—
958C2×C4—281no—
959C2×C4—281no—
960C2×C4—281no—
961C2×C4—281no—
962C2×C4—281no—
963C2×C4—281no—
964C2×C4—281no—
965C2×C4—281no—
966C2×C4—281no—
967C2×C4—281no—
968C2×C4—281no—
969C2×C4—281no—
970C2×C4—281no—
971C2×C4—281no—
972C2×C4—281no—
973C2×C4#650914yes—
974C7#1473611yescharacteristic, complemented, Sylow
975C22—78no—
976C22—144no—
977C22—144no—
978C22—144no—
979C22—144no—
980C22—144no—
981C22—144no—
982C22—144no—
983C22—144no—
984C22—144no—
985C22—144no—
986C22—144no—
987C22—144no—
988C22—144no—
989C22—144no—
990C22D7×#12111yescharacteristic
991C22#9030111yescharacteristic
992C22#9030311yescharacteristic
993C22#9030411yescharacteristic
994C22D7×C22⋊Q811yescharacteristic
995C22D7×C22⋊Q811yescharacteristic
996C22#9032111yescharacteristic
997C22#9032211yescharacteristic
998C22#9032511yescharacteristic
999C22#9032711yescharacteristic
1000C22#9032811yescharacteristic
1001C22#9032911yescharacteristic
1002C22D7×#12311yescharacteristic
1003C22#9034511yescharacteristic
1004C22#9034811yescharacteristic
1005C22#9035011yescharacteristic
1006C22D7×#12511yescharacteristic
1007C22D7×#12511yescharacteristic
1008C22#9037911yescharacteristic
1009C22#9038111yescharacteristic
1010C22#9038211yescharacteristic
1011C22#9038211yescharacteristic
1012C22#9038311yescharacteristic
1013C22#9038411yescharacteristic
1014C22D7×C4⋊Q811yescharacteristic
1015C22#9041711yescharacteristic
1016C22#9042011yescharacteristic
1017C22#9042111yescharacteristic
1018C22D4×C22⋊D711yescharacteristic
1019C22D4×C22⋊D711yescharacteristic
1020C22C2×#650911yescharacteristic
1021C22Q8×C22⋊D711yescharacteristic
1022C22#9051911yescharacteristic
1023C22#9051911yescharacteristic
1024C22#9052011yescharacteristic
1025C4—24no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—81no—
1032C4—282no—
1033C4—282no—
1034C4—282no—
1035C4—282no—
1036C4—282no—
1037C4—282no—
1038C4—561no—
1039C2—148no—
1040C2D7×#39811yescharacteristic
1041C2#1173539211yescharacteristic
1042C2#1173539311yescharacteristic
1043C2#1173539511yescharacteristic
1044C2#1173539811yescharacteristic
1045C2#1173540111yescharacteristic
1046C2#1173540311yescharacteristic
1047C2#1173541011yescharacteristic
1048C2#1174015211yescharacteristic
1049C2#1174026111yescharacteristic
1050C2#1174026211yescharacteristic
1051C2#1174034111yescharacteristic
1052C2#1174047711yescharacteristic
1053C2#1174051711yescharacteristic
1054C2#1174067811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutator, socle, cosocleC24×C7C24
FittingC2×C7×#398C2
prime radicalC24×D7C23
hypercenterC2×#398D7
hypocenterC7#14736
LCSG ▷ C24×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C2×C7×#398C2semidirect
7. #11729322C2semidirect
8. #11729321C2semidirect
9. #11729320C2semidirect
10. #11729320C2semidirect
13. #11727175C2semidirect
14. #11727166C2semidirect
15. #11727165C2semidirect
150. C2×#398D7semidirect
645. C2×D7#398semidirect
974. C7#14736semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3982
C2×#897612
C2×#897592
C2×D7×#952
#117293222
#117293212
#117293202
(C2×D7)⋊#952
#117271752
#117271662
#117271652
#147367