Finite Group Databasebeta

← #13277499

Subgroups — #13277499

Order 1792.

2366 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D7×C4⋊C4C211yesmaximal, characteristic
2C2×#89744C211yesmaximal, characteristic, complemented
3C2×#89700C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
5C2×#89440C211yesmaximal, characteristic
6C2×#89440C211yesmaximal, characteristic
7C2×#89440C211yesmaximal, characteristic
8C7×#1436C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727174C211yesmaximal, characteristic, complemented
12#11727173C211yesmaximal, characteristic, complemented
13#11727165C211yesmaximal, characteristic, complemented
14#11727164C211yesmaximal, characteristic, complemented
15#11727159C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C2×D7×C4⋊C4—24no—
36C2×D7×C4⋊C4—24no—
37C2×D7×C4⋊C4—24no—
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
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89744—24no—
55C4×(C2×D7)⋊C4—24no—
56#89700—24no—
57#89440—24no—
58#89440—24no—
59#89440C418yescomplemented
60#14043—71nomaximal, Sylow
61C24×D7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
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—22no—
88C22×C4×D7—22no—
89C22×C4×D7—22no—
90C22×C4×D7—22no—
91C22×C4×D7—41no—
92C22×C4×D7—41no—
93C22×C4×D7—41no—
94C22×C4×D7—41no—
95C22×C4×D7C2×C414yes—
96C22×C4×D7D414yes—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4D414yes—
100C2×C42×C7—22no—
101C2×C42×C7—22no—
102C2×C42×C7—41no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—22no—
105C2×(C2×D7)⋊C4—22no—
106C2×(C2×D7)⋊C4—22no—
107C2×(C2×D7)⋊C4—22no—
108C2×(C2×D7)⋊C4—22no—
109C2×(C2×D7)⋊C4—22no—
110C2×(C2×D7)⋊C4C2×C414yes—
111C2×(C2×D7)⋊C4C2×C414yes—
112C2×(C2×D7)⋊C4D414yes—
113C2×(C2×D7)⋊C4Q814yes—
114C2×(C2×D7)⋊C4Q814yes—
115C2×C4⋊Dic7—22no—
116C2×C4⋊Dic7—22no—
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—41no—
124C2×C4⋊Dic7—41no—
125C2×C4⋊Dic7—41no—
126C2×C4⋊Dic7C2×C414yescomplemented
127C2×Dic7⋊C4—22no—
128C2×Dic7⋊C4—22no—
129C2×Dic7⋊C4—22no—
130C2×Dic7⋊C4—22no—
131C2×Dic7⋊C4—22no—
132C2×Dic7⋊C4—22no—
133C2×Dic7⋊C4—22no—
134C2×Dic7⋊C4—22no—
135C2×Dic7⋊C4—22no—
136C2×Dic7⋊C4—22no—
137C2×Dic7⋊C4—22no—
138C2×Dic7⋊C4—22no—
139C2×Dic7⋊C4—41no—
140C2×Dic7⋊C4C2×C414yescomplemented
141C2×Dic7⋊C4D414yes—
142C2×C4×Dic7—22no—
143C2×C4×Dic7—22no—
144C2×C4×Dic7—41no—
145D7×C4⋊C4—232no—
146C7×#95—22no—
147C7×#95—22no—
148C7×#95—22no—
149C7×#95—41no—
150C7×#95C2×C414yescomplemented
151C7⋊#95—22no—
152C7⋊#95—22no—
153C7⋊#95—22no—
154C7⋊#95—22no—
155C7⋊#95—22no—
156C7⋊#95—22no—
157C7⋊#95—22no—
158C7⋊#95—22no—
159C7⋊#95—22no—
160C7⋊#95—41no—
161C7⋊#95C2×C414yescomplemented
162C23×C4⋊C4—71no—
163C2×#389—71no—
164C2×#389—71no—
165C2×#385—71no—
166C2×#385—71no—
167C2×#385—71no—
168C2×C4×C22⋊C4—71no—
169#1444—71no—
170#1444—71no—
171#1441—71no—
172#1441—71no—
173#1436—71no—
174#1436D711yescharacteristic, complemented
175C22⋊#95—71no—
176C22⋊#95—71no—
177C24×C7C2411yescharacteristic
178C23×D7—21no—
179C23×D7—21no—
180C23×D7—21no—
181C23×D7—21no—
182C23×D7—21no—
183C23×D7—21no—
184C23×D7—21no—
185C23×D7—21no—
186C23×D7C22×C412yes—
187C23×D7C2×D412yes—
188C23×D7C2×D412yes—
189C23×D7C2×Q812yes—
190C23×D7C2×Q812yes—
191C23×D7#4112yes—
192C23×D7#4112yes—
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×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7C22×C412yes—
231C22×C4×C7C22×C412yes—
232C22×C4×C7C22×C412yes—
233C22×C4×C7C2×D412yes—
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2×D412yes—
236C22×C4×C7C2×D412yes—
237C22×C4×C7C2×D412yes—
238C22×C4×C7C2×D412yes—
239C22×C4×C7C2×Q812yes—
240C22×C4×C7C2×Q812yes—
241C22×C4×C7#4112yes—
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×Dic7—21no—
274C22×Dic7—21no—
275C22×Dic7—21no—
276C22×Dic7—21no—
277C22×Dic7—21no—
278C22×Dic7—21no—
279C22×Dic7—21no—
280C22×Dic7—21no—
281C22×Dic7C22×C412yes—
282C22×Dic7C22×C412yes—
283C22×Dic7C22×C412yes—
284C22×Dic7C2×D412yes—
285C22×Dic7C2×D412yes—
286C22×Dic7C2×D412yes—
287C22×Dic7C2×D412yes—
288C22×Dic7C2×Q812yes—
289C22×Dic7C2×Q812yes—
290C22×Dic7#4112yes—
291C2×C4×D7—28no—
292C2×C4×D7—28no—
293C2×C4×D7—28no—
294C2×C4×D7—28no—
295C2×C4×D7—28no—
296C2×C4×D7—28no—
297C2×C4×D7—28no—
298C2×C4×D7—28no—
299C2×C4×D7—28no—
300C2×C4×D7—28no—
301C2×C4×D7—44no—
302C2×C4×D7—44no—
303C2×C4×D7—44no—
304C2×C4×D7—44no—
305C2×C4×D7—44no—
306C2×C4×D7—44no—
307C2×C4×D7—44no—
308C2×C4×D7—44no—
309C2×C4×D7—44no—
310C2×C4×D7—44no—
311C2×C4×D7—44no—
312C7×C4⋊C4—28no—
313C42×C7—44no—
314(C2×D7)⋊C4—28no—
315(C2×D7)⋊C4—28no—
316(C2×D7)⋊C4—44no—
317(C2×D7)⋊C4C4⋊C4116yescomplemented
318C4⋊Dic7—28no—
319C4⋊Dic7—28no—
320C4⋊Dic7—44no—
321C4⋊Dic7—44no—
322Dic7⋊C4—28no—
323Dic7⋊C4—28no—
324Dic7⋊C4—28no—
325Dic7⋊C4—44no—
326Dic7⋊C4—44no—
327C4×Dic7—44no—
328C24×C4—71no—
329C24×C4—71no—
330C24×C4—71no—
331C22×C4⋊C4—71no—
332C22×C4⋊C4—71no—
333C22×C4⋊C4—71no—
334C22×C4⋊C4—71no—
335C22×C4⋊C4—71no—
336C22×C4⋊C4—71no—
337C22×C4⋊C4—71no—
338C22×C4⋊C4—71no—
339C22×C4⋊C4—71no—
340C22×C4⋊C4—144no—
341C22×C4⋊C4—144no—
342C22×C4⋊C4—144no—
343C22×C4⋊C4C2×D711yescharacteristic
344C22×C22⋊C4—71no—
345C22×C22⋊C4—71no—
346C22×C22⋊C4—71no—
347C22×C22⋊C4—71no—
348C22×C42—71no—
349C22×C42C2×D711yescharacteristic
350#389—144no—
351#389—144no—
352#385—78no—
353#385—144no—
354#385—144no—
355C4×C22⋊C4—144no—
356C2×#95—71no—
357C2×#95—71no—
358C2×#95—71no—
359C2×#95—71no—
360C2×#95—71no—
361C2×#95—71no—
362C2×#95—71no—
363C2×#95—71no—
364C2×#95—71no—
365C2×#95—71no—
366C2×#95—71no—
367C2×#95C2×D711yescharacteristic
368C2×#95C2×D711yescharacteristic
369C2×#95C2×D711yescharacteristic
370C2×#95C2×D711yescharacteristic
371C2×#95C2×D711yescharacteristic
372C23×C7C23×C411yescharacteristic
373C23×C7C22×D411yescharacteristic
374C23×C7C22×D411yescharacteristic
375C23×C7C22×D411yescharacteristic
376C23×C7C22×D411yescharacteristic
377C23×C7C22×Q811yescharacteristic
378C23×C7C22×Q811yescharacteristic
379C23×C7C2×#4111yescharacteristic
380C23×C7C2×#4111yescharacteristic
381C23×C7C2×#4111yescharacteristic
382C23×C7C2×#4111yescharacteristic
383C23×C7H(5,𝔽2)11yescharacteristic
384C23×C7H(5,𝔽2)11yescharacteristic
385C23×C72−1+411yescharacteristic
386C23×C72−1+411yescharacteristic
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—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—22no—
404C22×D7—22no—
405C22×D7—22no—
406C22×D7—22no—
407C22×D7—22no—
408C22×D7—22no—
409C22×D7—22no—
410C22×D7—22no—
411C22×D7—22no—
412C22×D7—22no—
413C22×D7—22no—
414C22×D7—22no—
415C22×D7C2×C4⋊C414yes—
416C22×D7C4×D414yes—
417C22×D7C4×Q814yes—
418C22×D7#12114yes—
419C22×D7C22⋊Q814yes—
420C22×D7#12514yes—
421C22×D7C4⋊Q814yes—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7C2×C4⋊C414yescomplemented
469C2×C4×C7C4×D414yes—
470C2×C4×C7#12014yes—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—22no—
483C2×Dic7—22no—
484C2×Dic7—22no—
485C2×Dic7—22no—
486C2×Dic7—22no—
487C2×Dic7—22no—
488C2×Dic7—22no—
489C2×Dic7—22no—
490C2×Dic7—22no—
491C2×Dic7—22no—
492C2×Dic7—22no—
493C2×Dic7—22no—
494C2×Dic7—22no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C2×Dic7—41no—
502C2×Dic7—41no—
503C2×Dic7—41no—
504C2×Dic7—41no—
505C2×Dic7—41no—
506C2×Dic7—41no—
507C2×Dic7—41no—
508C2×Dic7—41no—
509C2×Dic7—41no—
510C2×Dic7—41no—
511C2×Dic7—41no—
512C2×Dic7—41no—
513C2×Dic7—41no—
514C2×Dic7—41no—
515C2×Dic7—41no—
516C2×Dic7—41no—
517C2×Dic7—41no—
518C2×Dic7C2×C4⋊C414yescomplemented
519C2×Dic7C4×D414yes—
520C4×D7—232no—
521C4×D7—416no—
522C4×D7—416no—
523C25—71no—
524C23×C4—71no—
525C23×C4—71no—
526C23×C4—71no—
527C23×C4—71no—
528C23×C4—71no—
529C23×C4—71no—
530C23×C4—74no—
531C23×C4—74no—
532C23×C4—71no—
533C23×C4—142no—
534C23×C4—142no—
535C23×C4—142no—
536C23×C4—142no—
537C23×C4—142no—
538C23×C4—142no—
539C23×C4—142no—
540C23×C4—142no—
541C23×C4—142no—
542C23×C4—142no—
543C23×C4—142no—
544C23×C4—142no—
545C23×C4—142no—
546C23×C4—142no—
547C23×C4—142no—
548C23×C4—281no—
549C23×C4—281no—
550C23×C4—281no—
551C23×C4—281no—
552C23×C4C22×D711yescharacteristic
553C23×C4C22×D711yescharacteristic
554C23×C4C22×D711yescharacteristic
555C23×C4C22×D711yescharacteristic
556C23×C4C22×D711yescharacteristic
557C23×C4C22×D711yescharacteristic
558C23×C4C22×D711yescharacteristic
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—74no—
562C2×C4⋊C4—74no—
563C2×C4⋊C4—74no—
564C2×C4⋊C4—1432no—
565C2×C4⋊C4—142no—
566C2×C4⋊C4—142no—
567C2×C4⋊C4—142no—
568C2×C4⋊C4—142no—
569C2×C4⋊C4—142no—
570C2×C4⋊C4—142no—
571C2×C4⋊C4—142no—
572C2×C4⋊C4—142no—
573C2×C4⋊C4—142no—
574C2×C4⋊C4—142no—
575C2×C4⋊C4—142no—
576C2×C4⋊C4—142no—
577C2×C4⋊C4—142no—
578C2×C4⋊C4—142no—
579C2×C4⋊C4—142no—
580C2×C4⋊C4—142no—
581C2×C4⋊C4—142no—
582C2×C4⋊C4—142no—
583C2×C4⋊C4—142no—
584C2×C4⋊C4—142no—
585C2×C4⋊C4—281no—
586C2×C4⋊C4—281no—
587C2×C4⋊C4—281no—
588C2×C4⋊C4—281no—
589C2×C4⋊C4D2814yes—
590C2×C22⋊C4—74no—
591C2×C22⋊C4—74no—
592C2×C22⋊C4—74no—
593C2×C22⋊C4—74no—
594C2×C22⋊C4—74no—
595C2×C22⋊C4—142no—
596C2×C22⋊C4—142no—
597C2×C22⋊C4—142no—
598C2×C22⋊C4—142no—
599C2×C22⋊C4—142no—
600C2×C22⋊C4—142no—
601C2×C22⋊C4—142no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—41no—
605C2×C42—142no—
606C2×C42—142no—
607C2×C42—281no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—74no—
613#95—142no—
614#95—142no—
615#95—142no—
616#95—142no—
617#95—142no—
618#95—142no—
619#95—142no—
620#95—142no—
621#95—142no—
622#95—281no—
623#95C4×D714yescomplemented
624C22×C7C22×C4⋊C411yescharacteristic
625C22×C7C2×C4×D411yescharacteristic
626C22×C7C2×C4×D411yescharacteristic
627C22×C7C2×C4×D411yescharacteristic
628C22×C7C2×C4×Q811yescharacteristic
629C22×C7#52011yescharacteristic
630C22×C7#52011yescharacteristic
631C22×C7C2×#12011yescharacteristic
632C22×C7C2×#12111yescharacteristic
633C22×C7C2×C22⋊Q811yescharacteristic
634C22×C7#52511yescharacteristic
635C22×C7#52511yescharacteristic
636C22×C7#52511yescharacteristic
637C22×C7C2×#12511yescharacteristic
638C22×C7C2×C4⋊Q811yescharacteristic
639C22×C7#53411yescharacteristic
640C22×C7#53611yescharacteristic
641C22×C7#53911yescharacteristic
642C22×C7#53911yescharacteristic
643C22×C7D4211yescharacteristic
644C22×C7D4211yescharacteristic
645C22×C7#54611yescharacteristic
646C22×C7#54611yescharacteristic
647C22×C7#54711yescharacteristic
648C22×C7#54711yescharacteristic
649C22×C7D4×Q811yescharacteristic
650C22×C7D4×Q811yescharacteristic
651C22×C7D4×Q811yescharacteristic
652C22×C7D4×Q811yescharacteristic
653C22×C7#55211yescharacteristic
654C22×C7#55211yescharacteristic
655C22×C7#55411yescharacteristic
656C22×C7#55411yescharacteristic
657C22×C7#55411yescharacteristic
658C22×C7#55411yescharacteristic
659C2×D7—24no—
660C2×D7—24no—
661C2×D7—24no—
662C2×D7—24no—
663C2×D7—24no—
664C2×D7—24no—
665C2×D7—24no—
666C2×D7—24no—
667C2×D7—24no—
668C2×D7—24no—
669C2×D7—24no—
670C2×D7—24no—
671C2×D7—24no—
672C2×D7—24no—
673C2×D7#38918yescomplemented
674C4×C7—24no—
675C4×C7—24no—
676C4×C7—24no—
677C4×C7—42no—
678C4×C7—42no—
679C4×C7—42no—
680C4×C7—81no—
681Dic7—24no—
682Dic7—24no—
683Dic7—42no—
684Dic7—42no—
685Dic7—42no—
686Dic7—42no—
687Dic7—81no—
688C24—72no—
689C24—72no—
690C24—72no—
691C24—72no—
692C24—72no—
693C24—72no—
694C24—72no—
695C24—141no—
696C24—141no—
697C24—141no—
698C24—141no—
699C24—141no—
700C24—141no—
701C24—141no—
702C24—141no—
703C24C23×D711yescharacteristic
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—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—72no—
742C22×C4—72no—
743C22×C4—72no—
744C22×C4—72no—
745C22×C4—72no—
746C22×C4—72no—
747C22×C4—72no—
748C22×C4—72no—
749C22×C4—72no—
750C22×C4—72no—
751C22×C4—148no—
752C22×C4—148no—
753C22×C4—148no—
754C22×C4—148no—
755C22×C4—148no—
756C22×C4—148no—
757C22×C4—148no—
758C22×C4—148no—
759C22×C4—141no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—148no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—141no—
773C22×C4—141no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—141no—
779C22×C4—141no—
780C22×C4—141no—
781C22×C4—141no—
782C22×C4—141no—
783C22×C4—141no—
784C22×C4—141no—
785C22×C4—141no—
786C22×C4—141no—
787C22×C4—141no—
788C22×C4—141no—
789C22×C4—141no—
790C22×C4—141no—
791C22×C4—141no—
792C22×C4—148no—
793C22×C4—141no—
794C22×C4—141no—
795C22×C4—141no—
796C22×C4—141no—
797C22×C4—141no—
798C22×C4—141no—
799C22×C4—141no—
800C22×C4—284no—
801C22×C4—284no—
802C22×C4—284no—
803C22×C4—284no—
804C22×C4—284no—
805C22×C4—284no—
806C22×C4—284no—
807C22×C4—284no—
808C22×C4—284no—
809C22×C4—284no—
810C22×C4—284no—
811C22×C4C2×C4×D712yes—
812C22×C4C2×C4×D712yes—
813C22×C4C2×C4×D712yes—
814C22×C4C2×D2812yes—
815C22×C4C2×D2812yes—
816C22×C4C2×D2812yes—
817C22×C4#115712yes—
818C22×C4D4×D712yes—
819C22×C4D4×D712yes—
820C22×C4D4×D712yes—
821C22×C4Q8×D712yes—
822C22×C4Q8×D712yes—
823C4⋊C4—28no—
824C4⋊C4—148no—
825C4⋊C4—148no—
826C4⋊C4—148no—
827C4⋊C4—148no—
828C4⋊C4—148no—
829C4⋊C4—284no—
830C4⋊C4—284no—
831C4⋊C4—284no—
832C4⋊C4—284no—
833C22⋊C4—716no—
834C22⋊C4—148no—
835C22⋊C4—148no—
836C22⋊C4—284no—
837C42—44no—
838C42—284no—
839C2×C7C2×#38911yescharacteristic
840C2×C7C4×#12011yescharacteristic
841C2×C7#232211yescharacteristic
842C2×C7D4×C4⋊C411yescharacteristic
843C2×C7D4×C4⋊C411yescharacteristic
844C2×C7#236011yescharacteristic
845C2×C7#236011yescharacteristic
846C2×C7#241011yescharacteristic
847C2×C7#241311yescharacteristic
848C2×C7#243411yescharacteristic
849C2×C7#244911yescharacteristic
850C2×C7#244911yescharacteristic
851C2×C7#247311yescharacteristic
852C2×C7#247311yescharacteristic
853C2×C7#258311yescharacteristic
854D7—28no—
855C23—74no—
856C23—74no—
857C23—74no—
858C23—74no—
859C23—74no—
860C23—74no—
861C23—74no—
862C23—142no—
863C23—142no—
864C23—142no—
865C23—142no—
866C23—142no—
867C23—142no—
868C23—142no—
869C23—142no—
870C23—142no—
871C23—142no—
872C23—142no—
873C23—142no—
874C23—142no—
875C23—142no—
876C23—142no—
877C23—142no—
878C23—142no—
879C23—142no—
880C23—142no—
881C23—142no—
882C23—142no—
883C23—142no—
884C23—142no—
885C23—142no—
886C23—142no—
887C23—142no—
888C23—142no—
889C23—142no—
890C23C22×C4×D711yescharacteristic
891C23C22×D2811yescharacteristic
892C23C2×#115711yescharacteristic
893C23C2×D4×D711yescharacteristic
894C23C2×D4×D711yescharacteristic
895C23C2×D4×D711yescharacteristic
896C23#654811yescharacteristic
897C23C2×Q8×D711yescharacteristic
898C23C2×Q8×D711yescharacteristic
899C23D7×#4111yescharacteristic
900C23D7×#4111yescharacteristic
901C23D7×#4111yescharacteristic
902C23#655311yescharacteristic
903C23#655411yescharacteristic
904C23#655411yescharacteristic
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—74no—
952C2×C4—74no—
953C2×C4—1432no—
954C2×C4—142no—
955C2×C4—142no—
956C2×C4—142no—
957C2×C4—142no—
958C2×C4—142no—
959C2×C4—142no—
960C2×C4—142no—
961C2×C4—142no—
962C2×C4—142no—
963C2×C4—142no—
964C2×C4—142no—
965C2×C4—142no—
966C2×C4—142no—
967C2×C4—142no—
968C2×C4—142no—
969C2×C4—142no—
970C2×C4—142no—
971C2×C4—142no—
972C2×C4—142no—
973C2×C4—142no—
974C2×C4—142no—
975C2×C4—142no—
976C2×C4—142no—
977C2×C4—142no—
978C2×C4—2816no—
979C2×C4—2816no—
980C2×C4—281no—
981C2×C4—281no—
982C2×C4—281no—
983C2×C4—281no—
984C2×C4—281no—
985C2×C4—281no—
986C2×C4—281no—
987C2×C4—281no—
988C2×C4—281no—
989C2×C4—281no—
990C2×C4—281no—
991C2×C4—281no—
992C2×C4—281no—
993C2×C4—281no—
994C2×C4—281no—
995C2×C4—281no—
996C2×C4—281no—
997C2×C4—281no—
998C2×C4—281no—
999C2×C4—281no—
1000C2×C4—281no—
1001C2×C4—281no—
1002C2×C4—281no—
1003C2×C4C4×D2814yes—
1004C2×C4#644514yes—
1005C2×C4D7×C4⋊C414yescomplemented
1006C7#1404311yescharacteristic, complemented, Sylow
1007C22—78no—
1008C22—144no—
1009C22—144no—
1010C22—144no—
1011C22—144no—
1012C22—144no—
1013C22—144no—
1014C22—144no—
1015C22—144no—
1016C22—144no—
1017C22—144no—
1018C22—144no—
1019C22—144no—
1020C22—144no—
1021C22—144no—
1022C22C2×C4×D2811yescharacteristic
1023C22C2×#644511yescharacteristic
1024C22C2×D7×C4⋊C411yescharacteristic
1025C22#9020211yescharacteristic
1026C22#9021411yescharacteristic
1027C22#9021511yescharacteristic
1028C22#9022011yescharacteristic
1029C22C4×D4×D711yescharacteristic
1030C22C4×D4×D711yescharacteristic
1031C22#9023711yescharacteristic
1032C22#9023811yescharacteristic
1033C22#9023811yescharacteristic
1034C22D4×D2811yescharacteristic
1035C22#9024211yescharacteristic
1036C22#9024511yescharacteristic
1037C22C4×Q8×D711yescharacteristic
1038C22Q8×D2811yescharacteristic
1039C22Q8×D2811yescharacteristic
1040C22#9027011yescharacteristic
1041C22#9028111yescharacteristic
1042C22D7×#12111yescharacteristic
1043C22#9029611yescharacteristic
1044C22D7×C22⋊Q811yescharacteristic
1045C22#9032311yescharacteristic
1046C22#9032311yescharacteristic
1047C22#9032711yescharacteristic
1048C22#9034511yescharacteristic
1049C22#9034611yescharacteristic
1050C22#9035111yescharacteristic
1051C22#9036611yescharacteristic
1052C22D7×#12511yescharacteristic
1053C22#9038111yescharacteristic
1054C22#9039811yescharacteristic
1055C22#9039911yescharacteristic
1056C22D7×C4⋊Q811yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—144no—
1065C4—144no—
1066C4—282no—
1067C4—282no—
1068C4—282no—
1069C4—282no—
1070C4—561no—
1071C2—148no—
1072C2C4×#644511yescharacteristic
1073C2C4⋊C4×D2811yescharacteristic
1074C2#1173121811yescharacteristic
1075C2#1173183811yescharacteristic
1076C2#1173205411yescharacteristic
1077C2#1173233311yescharacteristic
1078C2#1173241011yescharacteristic
1079C2#1173245311yescharacteristic
1080C2#1173245411yescharacteristic
1081C2#1173276611yescharacteristic
1082C2#1173327311yescharacteristic
1083C2#1173328811yescharacteristic
1084C2D7×#38911yescharacteristic
1085C2#1173369211yescharacteristic
1086C2#1173394411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#14043
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#89744C2semidirect
3. C2×#89700C2semidirect
8. C7×#1436C2semidirect
11. #11727174C2semidirect
12. #11727173C2semidirect
13. #11727165C2semidirect
14. #11727164C2semidirect
15. #11727159C2semidirect
59. #89440C4semidirect
126. C2×C4⋊Dic7C2×C4semidirect
140. C2×Dic7⋊C4C2×C4semidirect
150. C7×#95C2×C4semidirect
161. C7⋊#95C2×C4semidirect
174. #1436D7semidirect
317. (C2×D7)⋊C4C4⋊C4semidirect
468. C2×C4×C7C2×C4⋊C4semidirect
518. C2×Dic7C2×C4⋊C4semidirect
623. #95C4×D7semidirect
673. C2×D7#389semidirect
1005. C2×C4D7×C4⋊C4semidirect
1006. C7#14043semidirect

Maximal subgroups

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

subgroupindex
C22×D7×C4⋊C42
C2×#897442
C2×#897002
C2×C4×(C2×D7)⋊C42
C2×#894402
C7×#14362
(C2×D7)⋊#952
#117271742
#117271732
#117271652
#117271642
#117271592
#140437