Finite Group Databasebeta

← #13276923

Subgroups — #13276923

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6441C211yesmaximal, characteristic
2C2×#89744C211yesmaximal, characteristic, complemented
3C2×#89714C211yesmaximal, characteristic
4C2×C22⋊C4×Dic7C211yesmaximal, characteristic
5C2×#89418C211yesmaximal, characteristic, complemented
6C2×#89418C211yesmaximal, characteristic, complemented
7C2×#89421C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic
9#11729317C211yesmaximal, characteristic, complemented
10#11729301C211yesmaximal, characteristic
11#11729299C211yesmaximal, characteristic
12#11729299C211yesmaximal, characteristic
13#11727176C211yesmaximal, characteristic, complemented
14#11727175C211yesmaximal, characteristic, complemented
15Dic7⋊#95C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C23×Dic14C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C2×#6441—24no—
36C2×#6441—24no—
37C2×#6441C418yescomplemented
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—
55#89714—24no—
56C22⋊C4×Dic7—24no—
57#89421—24no—
58#89418—24no—
59#89418—24no—
60#13997—71nomaximal, Sylow
61C25×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—22no—
71C23×Dic7—22no—
72C23×Dic7—22no—
73C23×Dic7—22no—
74C23×Dic7C2×C414yes—
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C22×Dic14—22no—
84C22×Dic14—22no—
85C22×Dic14—22no—
86C22×Dic14—22no—
87C22×Dic14—22no—
88C22×Dic14—22no—
89C22×Dic14C2×C414yes—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—41no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—22no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—41no—
101C2×C7×C22⋊C4C2×C414yes—
102C2×C22⋊Dic7—22no—
103C2×C22⋊Dic7—22no—
104C2×C22⋊Dic7—22no—
105C2×C22⋊Dic7—22no—
106C2×C22⋊Dic7—22no—
107C2×C22⋊Dic7—22no—
108C2×C22⋊Dic7—41no—
109C2×C22⋊Dic7C2×C414yes—
110C2×C22⋊Dic7Q814yescomplemented
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7—22no—
113C2×C4⋊Dic7C2×C414yes—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4—22no—
122C2×Dic7⋊C4—22no—
123C2×Dic7⋊C4—41no—
124C2×Dic7⋊C4C2×C414yes—
125C2×Dic7⋊C4C2×C414yes—
126C2×Dic7⋊C4D414yes—
127C2×Dic7⋊C4D414yes—
128C2×Dic7⋊C4D414yes—
129C2×C4×Dic7—22no—
130C2×C4×Dic7—22no—
131C2×C4×Dic7—22no—
132C2×C4×Dic7—22no—
133C2×C4×Dic7—22no—
134C2×C4×Dic7—22no—
135C2×C4×Dic7—22no—
136C2×C4×Dic7—22no—
137C2×C4×Dic7—22no—
138C2×C4×Dic7—41no—
139C2×C4×Dic7—41no—
140C2×C4×Dic7D414yes—
141#6441—232no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7⋊#95—22no—
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—
158C22×C22⋊Q8—71no—
159C2×#391—71no—
160C2×#391—71no—
161C2×#389—71no—
162C2×#380—71no—
163C2×C4×C4⋊C4—71no—
164C2×C4×C22⋊C4—71no—
165#1445—71no—
166#1445—71no—
167#1439—71no—
168#1439D711yescharacteristic
169#1437—71no—
170#1437—71no—
171C4⋊#95—71no—
172C4⋊#95—71no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—21no—
179C24×C7—21no—
180C24×C7—21no—
181C24×C7—21no—
182C24×C7—21no—
183C24×C7—21no—
184C24×C7—21no—
185C24×C7C22×C412yes—
186C24×C7C2×Q812yes—
187C24×C7#4112yes—
188C24×C7C2411yescharacteristic
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×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×D412yes—
230C22×C4×C7#4112yes—
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—28no—
264C22×Dic7—28no—
265C22×Dic7—28no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7—44no—
274C22×Dic7—44no—
275C22×Dic7—44no—
276C22×Dic7—44no—
277C22×Dic7C22×C412yes—
278C22×Dic7C22×C412yes—
279C22×Dic7C22×C412yes—
280C22×Dic7C22×C412yes—
281C22×Dic7C2×D412yes—
282C22×Dic7C2×D412yes—
283C22×Dic7C2×D412yes—
284C22×Dic7C2×D412yes—
285C22×Dic7C2×D412yes—
286C22×Dic7C2×D412yes—
287C22×Dic7C2×D412yes—
288C22×Dic7C2×D412yes—
289C22×Dic7C2×Q812yes—
290C22×Dic7C2×Q812yes—
291C22×Dic7#4112yes—
292C22×Dic7#4112yes—
293C22×Dic7#4112yes—
294C2×Dic14—28no—
295C2×Dic14—28no—
296C2×Dic14—28no—
297C2×Dic14—44no—
298C2×Dic14—44no—
299C2×Dic14—44no—
300C2×Dic14—44no—
301C7×C4⋊C4—44no—
302C7×C22⋊C4—28no—
303C7×C22⋊C4—28no—
304C7×C22⋊C4—44no—
305C22⋊Dic7—28no—
306C22⋊Dic7—28no—
307C22⋊Dic7—44no—
308C4⋊Dic7—28no—
309Dic7⋊C4—28no—
310Dic7⋊C4—28no—
311Dic7⋊C4—44no—
312Dic7⋊C4—44no—
313Dic7⋊C4C22⋊C4116yescomplemented
314C4×Dic7—28no—
315C4×Dic7—44no—
316C4×Dic7—44no—
317C4×Dic7—44no—
318C23×Q8—71no—
319C24×C4—71no—
320C2×C22⋊Q8—78no—
321C2×C22⋊Q8—144no—
322C2×C22⋊Q8—144no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326C22×C4⋊C4—71no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4—71no—
329C22×C4⋊C4C2×D711yescharacteristic
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4C2×D711yescharacteristic
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C42—71no—
337C22×C42—71no—
338C22×C42—71no—
339C22×C42—71no—
340#391—144no—
341#391—144no—
342#389—144no—
343#380—144no—
344C4×C4⋊C4—144no—
345C4×C22⋊C4—144no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—71no—
357C2×#95—71no—
358C2×#95—71no—
359C2×#95C2×D711yescharacteristic
360C2×#95C2×D711yescharacteristic
361C2×#95C2×D711yescharacteristic
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—41no—
381C23×C7—41no—
382C23×C7—41no—
383C23×C7—41no—
384C23×C7—41no—
385C23×C7—41no—
386C23×C7—41no—
387C23×C7—41no—
388C23×C7—41no—
389C23×C7—41no—
390C23×C7—41no—
391C23×C7—41no—
392C23×C7—41no—
393C23×C7—41no—
394C23×C7—41no—
395C23×C7—41no—
396C23×C7C4×Q814yes—
397C23×C7C23×C411yescharacteristic
398C23×C7C22×D411yescharacteristic
399C23×C7C22×D411yescharacteristic
400C23×C7C22×D411yescharacteristic
401C23×C7C22×D411yescharacteristic
402C23×C7C22×Q811yescharacteristic
403C23×C7C2×#4111yescharacteristic
404C23×C7C2×#4111yescharacteristic
405C23×C7C2×#4111yescharacteristic
406C23×C7C2×#4111yescharacteristic
407C23×C7C2×#4111yescharacteristic
408C23×C7H(5,𝔽2)11yescharacteristic
409C23×C72−1+411yescharacteristic
410C23×C72−1+411yescharacteristic
411C23×C72−1+411yescharacteristic
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—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
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×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7C2×C22⋊C414yes—
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—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
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—416no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C2×Dic7—41no—
502C2×Dic7C2×C22⋊C414yes—
503C2×Dic7C2×C22⋊C414yes—
504C2×Dic7C4×D414yes—
505C2×Dic7C4×D414yes—
506C2×Dic7#12114yes—
507C2×Dic7#12114yes—
508C2×Dic7C22⋊Q814yescomplemented
509C2×Dic7#12414yes—
510C2×Dic7#12714yes—
511Dic14—416no—
512C25C22×D711yescharacteristic
513C22×Q8—74no—
514C22×Q8—142no—
515C22×Q8—142no—
516C22×Q8—142no—
517C22×Q8—142no—
518C22×Q8—142no—
519C22×Q8—142no—
520C23×C4—71no—
521C23×C4—71no—
522C23×C4—71no—
523C23×C4—74no—
524C23×C4—71no—
525C23×C4—71no—
526C23×C4—71no—
527C23×C4—71no—
528C23×C4—71no—
529C23×C4—142no—
530C23×C4—142no—
531C23×C4—142no—
532C23×C4—142no—
533C23×C4—142no—
534C23×C4—142no—
535C23×C4C22×D711yescharacteristic
536C23×C4C22×D711yescharacteristic
537C23×C4C22×D711yescharacteristic
538C23×C4C22×D711yescharacteristic
539C23×C4C22×D711yescharacteristic
540C23×C4C22×D711yescharacteristic
541C22⋊Q8—1432no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—74no—
546C2×C4⋊C4—74no—
547C2×C4⋊C4—74no—
548C2×C4⋊C4—74no—
549C2×C4⋊C4—74no—
550C2×C4⋊C4—74no—
551C2×C4⋊C4—142no—
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—142no—
561C2×C4⋊C4—142no—
562C2×C4⋊C4—281no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—74no—
572C2×C22⋊C4—74no—
573C2×C22⋊C4—142no—
574C2×C22⋊C4—142no—
575C2×C22⋊C4—142no—
576C2×C22⋊C4—142no—
577C2×C22⋊C4—142no—
578C2×C22⋊C4—142no—
579C2×C22⋊C4—281no—
580C2×C22⋊C4C4×D714yes—
581C2×C42—74no—
582C2×C42—142no—
583C2×C42—142no—
584C2×C42—142no—
585C2×C42—142no—
586C2×C42—142no—
587C2×C42—142no—
588C2×C42—142no—
589C2×C42—142no—
590C2×C42—142no—
591C2×C42—281no—
592C2×C42—281no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—142no—
597#95—142no—
598#95—142no—
599#95—142no—
600#95—142no—
601#95—142no—
602#95—142no—
603#95—142no—
604#95—142no—
605#95—142no—
606#95—142no—
607#95—142no—
608#95—142no—
609C22×C7—24no—
610C22×C7—24no—
611C22×C7—24no—
612C22×C7—42no—
613C22×C7—42no—
614C22×C7—42no—
615C22×C7—42no—
616C22×C7—42no—
617C22×C7—42no—
618C22×C7—42no—
619C22×C7—42no—
620C22×C7—42no—
621C22×C7—42no—
622C22×C7—42no—
623C22×C7—42no—
624C22×C7C22×C22⋊C411yescharacteristic
625C22×C7C2×C4×D411yescharacteristic
626C22×C7C2×C4×D411yescharacteristic
627C22×C7C2×C4×Q811yescharacteristic
628C22×C7C4×#4111yescharacteristic
629C22×C7#51911yescharacteristic
630C22×C7#52011yescharacteristic
631C22×C7C2×#12111yescharacteristic
632C22×C7C2×#12111yescharacteristic
633C22×C7C2×C22⋊Q811yescharacteristic
634C22×C7#52511yescharacteristic
635C22×C7C2×#12411yescharacteristic
636C22×C7#52911yescharacteristic
637C22×C7C2×#12711yescharacteristic
638C22×C7#53311yescharacteristic
639C22×C7#53611yescharacteristic
640C22×C7#53711yescharacteristic
641C22×C7#54111yescharacteristic
642C22×C7#54211yescharacteristic
643C22×C7#54611yescharacteristic
644C22×C7#54611yescharacteristic
645C22×C7#54611yescharacteristic
646C22×C7#54711yescharacteristic
647C22×C7#54711yescharacteristic
648C22×C7#54711yescharacteristic
649C22×C7#54811yescharacteristic
650C22×C7#54811yescharacteristic
651C22×C7#54811yescharacteristic
652C22×C7D4×Q811yescharacteristic
653C22×C7D4×Q811yescharacteristic
654C22×C7D4×Q811yescharacteristic
655C22×C7#55211yescharacteristic
656C22×C7#55211yescharacteristic
657C22×C7#55411yescharacteristic
658C22×C7#55611yescharacteristic
659C4×C7—24no—
660C4×C7—42no—
661C4×C7—42no—
662C4×C7—42no—
663C4×C7—42no—
664C4×C7—81no—
665Dic7—24no—
666Dic7—24no—
667Dic7—42no—
668Dic7—42no—
669Dic7—42no—
670Dic7—42no—
671Dic7—81no—
672Dic7#39018yes—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24C2×C4×D712yes—
686C24#115912yes—
687C24Q8×D712yes—
688C24C23×D711yescharacteristic
689C2×Q8—148no—
690C2×Q8—148no—
691C2×Q8—148no—
692C2×Q8—284no—
693C2×Q8—284no—
694C2×Q8—284no—
695C2×Q8—284no—
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—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—72no—
732C22×C4—72no—
733C22×C4—72no—
734C22×C4—72no—
735C22×C4—72no—
736C22×C4—72no—
737C22×C4—72no—
738C22×C4—72no—
739C22×C4—72no—
740C22×C4—72no—
741C22×C4—72no—
742C22×C4—72no—
743C22×C4—72no—
744C22×C4—72no—
745C22×C4—72no—
746C22×C4—72no—
747C22×C4—72no—
748C22×C4—148no—
749C22×C4—148no—
750C22×C4—148no—
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—141no—
763C22×C4—141no—
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—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—284no—
791C22×C4—284no—
792C22×C4—284no—
793C22×C4—284no—
794C22×C4C2×C4×D712yes—
795C22×C4C2×C4×D712yes—
796C22×C4D4×D712yes—
797C22×C4D4×D712yes—
798C22×C4D4×D712yes—
799C22×C4D4×D712yes—
800C22×C4#115912yes—
801C4⋊C4—44no—
802C4⋊C4—716no—
803C4⋊C4—148no—
804C4⋊C4—148no—
805C4⋊C4—148no—
806C4⋊C4—284no—
807C4⋊C4—284no—
808C22⋊C4—28no—
809C22⋊C4—28no—
810C22⋊C4—44no—
811C22⋊C4—148no—
812C22⋊C4—148no—
813C22⋊C4—284no—
814C42—148no—
815C42—284no—
816C42—284no—
817C42—284no—
818C2×C7—44no—
819C2×C7C2×#39011yescharacteristic
820C2×C7C4×C22⋊Q811yescharacteristic
821C2×C7#232311yescharacteristic
822C2×C7#233911yescharacteristic
823C2×C7Q8×C22⋊C411yescharacteristic
824C2×C7#236011yescharacteristic
825C2×C7#236211yescharacteristic
826C2×C7#241511yescharacteristic
827C2×C7#241711yescharacteristic
828C2×C7#242711yescharacteristic
829C2×C7#242911yescharacteristic
830C2×C7#248911yescharacteristic
831C2×C7#249211yescharacteristic
832C2×C7#254011yescharacteristic
833C2×C7#254211yescharacteristic
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23#645014yes—
869C23C22×C4×D711yescharacteristic
870C23C2×D4×D711yescharacteristic
871C23C2×D4×D711yescharacteristic
872C23C2×D4×D711yescharacteristic
873C23C2×D4×D711yescharacteristic
874C23C2×#115911yescharacteristic
875C23C2×#115911yescharacteristic
876C23#654811yescharacteristic
877C23C2×Q8×D711yescharacteristic
878C23D7×#4111yescharacteristic
879C23D7×#4111yescharacteristic
880C23D7×#4111yescharacteristic
881C23#655411yescharacteristic
882C23#655411yescharacteristic
883C23#655411yescharacteristic
884Q8—2816no—
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—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
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—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—74no—
927C2×C4—74no—
928C2×C4—74no—
929C2×C4—74no—
930C2×C4—74no—
931C2×C4—74no—
932C2×C4—74no—
933C2×C4—74no—
934C2×C4—74no—
935C2×C4—142no—
936C2×C4—142no—
937C2×C4—142no—
938C2×C4—142no—
939C2×C4—142no—
940C2×C4—142no—
941C2×C4—142no—
942C2×C4—142no—
943C2×C4—142no—
944C2×C4—142no—
945C2×C4—142no—
946C2×C4—142no—
947C2×C4—142no—
948C2×C4—142no—
949C2×C4—142no—
950C2×C4—142no—
951C2×C4—142no—
952C2×C4—142no—
953C2×C4—142no—
954C2×C4—142no—
955C2×C4—142no—
956C2×C4—142no—
957C2×C4—142no—
958C2×C4—142no—
959C2×C4—2816no—
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—281no—
974C2×C4—281no—
975C2×C4—281no—
976C2×C4—281no—
977C2×C4—281no—
978C2×C4—281no—
979C2×C4—281no—
980C2×C4—281no—
981C2×C4—281no—
982C2×C4—281no—
983C2×C4D7×C22⋊C414yes—
984C7#1399711yescharacteristic, complemented, Sylow
985C22—24no—
986C22—24no—
987C22—24no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22C2×D7×C22⋊C411yescharacteristic
1001C22C2×#645011yescharacteristic
1002C22#9020711yescharacteristic
1003C22C4×#115911yescharacteristic
1004C22C4×D4×D711yescharacteristic
1005C22C4×D4×D711yescharacteristic
1006C22#9023711yescharacteristic
1007C22#9027711yescharacteristic
1008C22#9028211yescharacteristic
1009C22#9028211yescharacteristic
1010C22#9028911yescharacteristic
1011C22#9028911yescharacteristic
1012C22#9028911yescharacteristic
1013C22D7×#12111yescharacteristic
1014C22D7×#12111yescharacteristic
1015C22#9029911yescharacteristic
1016C22#9030111yescharacteristic
1017C22#9030211yescharacteristic
1018C22#9031311yescharacteristic
1019C22D7×C22⋊Q811yescharacteristic
1020C22#9032311yescharacteristic
1021C22#9032311yescharacteristic
1022C22#9032311yescharacteristic
1023C22#9032711yescharacteristic
1024C22#9033911yescharacteristic
1025C22#9034011yescharacteristic
1026C22#9034111yescharacteristic
1027C22#9034611yescharacteristic
1028C22#9034611yescharacteristic
1029C22#9036011yescharacteristic
1030C22#9036211yescharacteristic
1031C22D7×#12411yescharacteristic
1032C22#9039211yescharacteristic
1033C22#9039911yescharacteristic
1034C22D7×#12711yescharacteristic
1035C4—24no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—78no—
1041C4—81no—
1042C4—144no—
1043C4—144no—
1044C4—282no—
1045C4—282no—
1046C4—282no—
1047C4—282no—
1048C4—561no—
1049C2—44no—
1050C2#1173132111yescharacteristic
1051C2#1173182611yescharacteristic
1052C2#1173184111yescharacteristic
1053C2#1173211711yescharacteristic
1054C2#1173290511yescharacteristic
1055C2#1173292411yescharacteristic
1056C2D7×#39011yescharacteristic
1057C2#1173413211yescharacteristic
1058C2#1173423811yescharacteristic
1059C2#1173434211yescharacteristic
1060C2#1173434711yescharacteristic
1061C2#1173473011yescharacteristic
1062C2#1173473211yescharacteristic
1063C2#1173493111yescharacteristic
1064C2#1173548211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1439C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1439D7
hypocenterC7#13997
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#89744C2semidirect
5. C2×#89418C2semidirect
6. C2×#89418C2semidirect
7. C2×#89421C2semidirect
9. #11729317C2semidirect
13. #11727176C2semidirect
14. #11727175C2semidirect
15. Dic7⋊#95C2semidirect
37. C2×#6441C4semidirect
110. C2×C22⋊Dic7Q8semidirect
313. Dic7⋊C4C22⋊C4semidirect
508. C2×Dic7C22⋊Q8semidirect
984. C7#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#64412
C2×#897442
C2×#897142
C2×C22⋊C4×Dic72
C2×#894182
C2×#894212
C7×#14392
#117293172
#117293012
#117292992
#117271762
#117271752
Dic7⋊#952
#139977