Finite Group Databasebeta

← #13277495

Subgroups — #13277495

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×#89761C211yesmaximal, characteristic
3C2×#89757C211yesmaximal, characteristic, complemented
4C2×#89440C211yesmaximal, characteristic
5C2×#89440C211yesmaximal, characteristic
6C2×#89419C211yesmaximal, characteristic, complemented
7C2×#89438C211yesmaximal, characteristic
8C7×#1441C211yesmaximal, characteristic, complemented
9#11729322C211yesmaximal, characteristic, complemented
10(C2×D7)⋊#95C211yesmaximal, characteristic
11(C2×D7)⋊#95C211yesmaximal, characteristic
12#11727174C211yesmaximal, characteristic, complemented
13#11727163C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
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#89761C418yescomplemented
55#89757—24no—
56#89440—24no—
57#89440—24no—
58#89438—24no—
59#89419—24no—
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⋊C4—22no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4C2×C414yescomplemented
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—41no—
123C2×C4⋊Dic7D414yes—
124C2×Dic7⋊C4—22no—
125C2×Dic7⋊C4—22no—
126C2×Dic7⋊C4—22no—
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—41no—
135C2×Dic7⋊C4—41no—
136C2×Dic7⋊C4—41no—
137C2×Dic7⋊C4C2×C414yescomplemented
138C2×Dic7⋊C4D414yes—
139C2×C4×Dic7—22no—
140C2×C4×Dic7—22no—
141C2×C4×Dic7—22no—
142C2×C4×Dic7—22no—
143C2×C4×Dic7—41no—
144C2×C4×Dic7—41no—
145D7×C4⋊C4—232no—
146C7×#95—22no—
147C7×#95—22no—
148C7×#95—22no—
149C7×#95—22no—
150C7×#95—22no—
151C7⋊#95—22no—
152C7⋊#95—22no—
153C7⋊#95—22no—
154C7⋊#95—22no—
155C7⋊#95—22no—
156C7⋊#95—22no—
157C7⋊#95—22no—
158C7⋊#95—41no—
159C7⋊#95—41no—
160C7⋊#95C2×C414yescomplemented
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#1441D711yescharacteristic, complemented
173#1436—71no—
174#1436—71no—
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×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7C22×C412yes—
233C22×C4×C7C22×C412yes—
234C22×C4×C7C22×C412yes—
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×Dic7C22×C412yes—
280C22×Dic7C22×C412yes—
281C22×Dic7C22×C412yes—
282C22×Dic7C2×D412yes—
283C22×Dic7C2×D412yes—
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—
313C7×C4⋊C4—28no—
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—44no—
320C4⋊Dic7—44no—
321Dic7⋊C4—28no—
322Dic7⋊C4—28no—
323Dic7⋊C4—28no—
324Dic7⋊C4—44no—
325Dic7⋊C4—44no—
326C4×Dic7—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—144no—
340C22×C4⋊C4—144no—
341C22×C4⋊C4—144no—
342C22×C4⋊C4C2×D711yescharacteristic
343C22×C4⋊C4C2×D711yescharacteristic
344C22×C22⋊C4—71no—
345C22×C22⋊C4—71no—
346C22×C22⋊C4—71no—
347C22×C22⋊C4—71no—
348C22×C42—71no—
349C22×C42—71no—
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—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
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×C7—41no—
469C2×C4×C7C2×C4⋊C414yescomplemented
470C2×C4×C7C4×D414yes—
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—22no—
496C2×Dic7—22no—
497C2×Dic7—22no—
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×Dic7C2×C4⋊C414yescomplemented
518C2×Dic7C4×D414yes—
519C2×Dic7#12014yes—
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—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—74no—
565C2×C4⋊C4—74no—
566C2×C4⋊C4—74no—
567C2×C4⋊C4—1432no—
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⋊C4C4×D714yescomplemented
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—142no—
603C2×C42—142no—
604C2×C42—142no—
605C2×C42—142no—
606C2×C42—281no—
607C2×C42—281no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—74no—
614#95—74no—
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#95—281no—
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—42no—
677C4×C7—42no—
678C4×C7—42no—
679C4×C7—42no—
680C4×C7—81no—
681Dic7—24no—
682Dic7—24no—
683Dic7—24no—
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—21no—
742C22×C4—21no—
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—72no—
752C22×C4—72no—
753C22×C4—72no—
754C22×C4—72no—
755C22×C4—148no—
756C22×C4—148no—
757C22×C4—148no—
758C22×C4—148no—
759C22×C4—148no—
760C22×C4—148no—
761C22×C4—148no—
762C22×C4—148no—
763C22×C4—148no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—141no—
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—148no—
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—141no—
793C22×C4—141no—
794C22×C4—141no—
795C22×C4—141no—
796C22×C4—141no—
797C22×C4—141no—
798C22×C4—141no—
799C22×C4—141no—
800C22×C4—141no—
801C22×C4—141no—
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×C4—284no—
812C22×C4—284no—
813C22×C4C2×C4×D712yes—
814C22×C4C2×C4×D712yes—
815C22×C4C2×C4×D712yes—
816C22×C4D4×D712yes—
817C22×C4D4×D712yes—
818C22×C4D4×D712yes—
819C22×C4D4×D712yes—
820C22×C4#115912yes—
821C22×C4Q8×D712yes—
822C22×C4Q8×D712yes—
823C4⋊C4—28no—
824C4⋊C4—28no—
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—284no—
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
891C23C2×D4×D711yescharacteristic
892C23C2×D4×D711yescharacteristic
893C23C2×D4×D711yescharacteristic
894C23C2×D4×D711yescharacteristic
895C23C2×#115911yescharacteristic
896C23C2×Q8×D711yescharacteristic
897C23C2×Q8×D711yescharacteristic
898C23#655111yescharacteristic
899C23D7×#4111yescharacteristic
900C23D7×#4111yescharacteristic
901C23D7×#4111yescharacteristic
902C23#655311yescharacteristic
903C23#655311yescharacteristic
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—41no—
930C2×C4—41no—
931C2×C4—41no—
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—41no—
952C2×C4—74no—
953C2×C4—74no—
954C2×C4—74no—
955C2×C4—1432no—
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—142no—
979C2×C4—142no—
980C2×C4—142no—
981C2×C4—142no—
982C2×C4—142no—
983C2×C4—2816no—
984C2×C4—2816no—
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×C4—281no—
1004C2×C4(C22⋊D7)⋊C414yes—
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×(C22⋊D7)⋊C411yescharacteristic
1023C22C2×D7×C4⋊C411yescharacteristic
1024C22#9021411yescharacteristic
1025C22C4×D4×D711yescharacteristic
1026C22C4×D4×D711yescharacteristic
1027C22C4×Q8×D711yescharacteristic
1028C22#9026511yescharacteristic
1029C22D7×#12011yescharacteristic
1030C22D7×#12111yescharacteristic
1031C22#9029711yescharacteristic
1032C22#9029711yescharacteristic
1033C22#9030011yescharacteristic
1034C22#9030011yescharacteristic
1035C22#9030211yescharacteristic
1036C22D7×C22⋊Q811yescharacteristic
1037C22#9031911yescharacteristic
1038C22#9032211yescharacteristic
1039C22#9032311yescharacteristic
1040C22#9032311yescharacteristic
1041C22#9032611yescharacteristic
1042C22#9032611yescharacteristic
1043C22#9033011yescharacteristic
1044C22#9034411yescharacteristic
1045C22#9034511yescharacteristic
1046C22#9034711yescharacteristic
1047C22#9036711yescharacteristic
1048C22D7×#12511yescharacteristic
1049C22#9038111yescharacteristic
1050C22#9038111yescharacteristic
1051C22#9038311yescharacteristic
1052C22#9039811yescharacteristic
1053C22#9039911yescharacteristic
1054C22D7×C4⋊Q811yescharacteristic
1055C22#9041811yescharacteristic
1056C22#9041811yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—144no—
1065C4—144no—
1066C4—144no—
1067C4—282no—
1068C4—282no—
1069C4—282no—
1070C4—561no—
1071C2—148no—
1072C2#1173145511yescharacteristic
1073C2#1173210411yescharacteristic
1074C2#1173241011yescharacteristic
1075C2#1173274211yescharacteristic
1076C2D7×#38911yescharacteristic
1077C2#1173364711yescharacteristic
1078C2#1173406011yescharacteristic
1079C2#1173455311yescharacteristic
1080C2#1173461811yescharacteristic
1081C2#1173486011yescharacteristic
1082C2#1173486411yescharacteristic
1083C2#1173520211yescharacteristic
1084C2#1173539711yescharacteristic
1085C2#1173540611yescharacteristic
1086C2#1173558611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1441D7
hypocenterC7#14043
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#89757C2semidirect
6. C2×#89419C2semidirect
8. C7×#1441C2semidirect
9. #11729322C2semidirect
12. #11727174C2semidirect
13. #11727163C2semidirect
14. #11727161C2semidirect
15. #11727160C2semidirect
54. #89761C4semidirect
102. C2×C7×C4⋊C4C2×C4semidirect
137. C2×Dic7⋊C4C2×C4semidirect
160. C7⋊#95C2×C4semidirect
161. C7⋊#95C2×C4semidirect
172. #1441D7semidirect
317. (C2×D7)⋊C4C4⋊C4semidirect
469. C2×C4×C7C2×C4⋊C4semidirect
517. C2×Dic7C2×C4⋊C4semidirect
589. C2×C4⋊C4C4×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×#897612
C2×#897572
C2×#894402
C2×#894192
C2×#894382
C7×#14412
#117293222
(C2×D7)⋊#952
#117271742
#117271632
#117271612
#117271602
#140437