Finite Group Databasebeta

← #13276928

Subgroups — #13276928

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6509C211yesmaximal, characteristic
2C2×C7×#391C211yesmaximal, characteristic, complemented
3C2×#90002C211yesmaximal, characteristic, complemented
4C2×#89759C211yesmaximal, characteristic
5C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
6C2×#89700C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
8#11727182C212yesmaximal
9#11727175C212yesmaximal, complemented
10#11727162C212yesmaximal
11Dic7⋊#95C212yesmaximal, complemented
12C23×C7×Q8C2211yescharacteristic
13C23×C4×D7C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C2×#6509—24no—
17C2×#6509—24no—
18C2×#6509C418yescomplemented
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2212yes—
26C22×Dic7⋊C4C2212yes—
27C22×C4×Dic7C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29C7×#391—24no—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32#90002—24no—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2212yes—
40#89759—24no—
41C4⋊C4×Dic7—24no—
42C4×(C2×D7)⋊C4—24no—
43#89700—24no—
44#13997—71nomaximal, Sylow
45C24×D7C2311yescharacteristic
46C22×C7×Q8—22no—
47C22×C7×Q8—22no—
48C22×C7×Q8—22no—
49C22×C7×Q8—22no—
50C22×C7×Q8—22no—
51C22×C7×Q8—22no—
52C22×C7×Q8C2×C414yes—
53C23×C4×C7C2312yes—
54C23×C4×C7C2312yes—
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×Dic7C2312yes—
59C23×Dic7C2311yescharacteristic
60C23×Dic7C2311yescharacteristic
61C23×Dic7C2312yes—
62C23×Dic7C2311yescharacteristic
63C22×C4×D7—22no—
64C22×C4×D7—22no—
65C22×C4×D7—22no—
66C22×C4×D7—22no—
67C22×C4×D7—22no—
68C22×C4×D7—22no—
69C22×C4×D7C2×C414yes—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4D414yes—
73C2×C42×C7—22no—
74C2×C42×C7—22no—
75C2×C42×C7—22no—
76#6509—232no—
77C2×(C2×D7)⋊C4—22no—
78C2×(C2×D7)⋊C4—22no—
79C2×(C2×D7)⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—24no—
82C2×(C2×D7)⋊C4—24no—
83C2×(C2×D7)⋊C4—22no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—24no—
86C2×(C2×D7)⋊C4—42no—
87C2×(C2×D7)⋊C4C2×C418yes—
88C2×(C2×D7)⋊C4Q814yescomplemented
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7C2×C414yes—
93C2×C4⋊Dic7D414yes—
94C2×C4⋊Dic7D414yes—
95C2×Dic7⋊C4—24no—
96C2×Dic7⋊C4—24no—
97C2×Dic7⋊C4—24no—
98C2×Dic7⋊C4—24no—
99C2×Dic7⋊C4—42no—
100C2×Dic7⋊C4C2×C418yes—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—24no—
104C2×C4×Dic7—24no—
105C2×C4×Dic7—42no—
106C2×C4×Dic7D414yes—
107C7×#95—24no—
108C7×#95—24no—
109C7⋊#95—24no—
110C7⋊#95—24no—
111C7⋊#95—22no—
112C7⋊#95—22no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C22×C22⋊Q8—71no—
117C2×#391—71no—
118C2×#391D711yescharacteristic, complemented
119C2×#389—71no—
120C2×#380—71no—
121C2×C4×C4⋊C4—71no—
122C2×C4×C22⋊C4—71no—
123#1445—72no—
124#1439—72no—
125#1437—72no—
126C4⋊#95—72no—
127C24×C7C2411yescharacteristic
128C23×D7—21no—
129C23×D7—21no—
130C23×D7—21no—
131C23×D7—21no—
132C23×D7—21no—
133C23×D7—21no—
134C23×D7—21no—
135C23×D7—21no—
136C23×D7—21no—
137C23×D7—21no—
138C23×D7—21no—
139C23×D7—21no—
140C23×D7C22×C412yes—
141C23×D7C2×Q812yes—
142C23×D7#4112yes—
143C2×C7×Q8—28no—
144C2×C7×Q8—28no—
145C2×C7×Q8—28no—
146C2×C7×Q8—44no—
147C2×C7×Q8—44no—
148C2×C7×Q8—44no—
149C2×C7×Q8—44no—
150C22×C4×C7—21no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—22no—
158C22×C4×C7—21no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—21no—
170C22×C4×C7—22no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7C22×C414yes—
175C22×C4×C7C22×C412yes—
176C22×C4×C7C2×D414yes—
177C22×C4×C7C2×D412yes—
178C22×C4×C7C2×D412yes—
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×Q812yes—
182C22×C4×C7#4112yes—
183C22×C4×C7#4112yes—
184C22×C4×C7#4112yes—
185C22×Dic7—21no—
186C22×Dic7—22no—
187C22×Dic7—21no—
188C22×Dic7—22no—
189C22×Dic7—21no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7C22×C412yes—
213C22×Dic7C22×C414yes—
214C22×Dic7C2×D412yes—
215C22×Dic7C2×D414yes—
216C22×Dic7C2×D414yes—
217C22×Dic7C2×D412yes—
218C22×Dic7C2×Q812yes—
219C22×Dic7#4112yes—
220C2×C4×D7—28no—
221C2×C4×D7—28no—
222C2×C4×D7—28no—
223C2×C4×D7—44no—
224C2×C4×D7—44no—
225C2×C4×D7—44no—
226C2×C4×D7—44no—
227C7×C4⋊C4—28no—
228C42×C7—44no—
229(C2×D7)⋊C4—28no—
230(C2×D7)⋊C4—216no—
231(C2×D7)⋊C4—28no—
232(C2×D7)⋊C4—48no—
233C4⋊Dic7—44no—
234C4⋊Dic7C22⋊C4116yescomplemented
235Dic7⋊C4—216no—
236Dic7⋊C4—48no—
237C4×Dic7—28no—
238C4×Dic7—48no—
239C23×Q8C2×D711yescharacteristic
240C24×C4—71no—
241C2×C22⋊Q8—78no—
242C2×C22⋊Q8—144no—
243C2×C22⋊Q8—144no—
244C22×C4⋊C4—71no—
245C22×C4⋊C4—72no—
246C22×C4⋊C4—71no—
247C22×C4⋊C4—72no—
248C22×C4⋊C4C2×D711yescharacteristic
249C22×C22⋊C4—72no—
250C22×C22⋊C4—71no—
251C22×C22⋊C4—71no—
252C22×C22⋊C4—72no—
253C22×C42—71no—
254C22×C42—72no—
255C22×C42C2×D711yescharacteristic
256#391—24no—
257#391—144no—
258#389—144no—
259#380—144no—
260C4×C4⋊C4—144no—
261C4×C22⋊C4—144no—
262C2×#95—71no—
263C2×#95—72no—
264C2×#95—72no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—71no—
269C2×#95C2×D712yes—
270C2×#95C2×D712yes—
271C23×C7C23×C411yescharacteristic
272C23×C7C22×D411yescharacteristic
273C23×C7C22×D411yescharacteristic
274C23×C7C22×D411yescharacteristic
275C23×C7C22×D411yescharacteristic
276C23×C7C22×Q811yescharacteristic
277C23×C7C2×#4111yescharacteristic
278C23×C7C2×#4111yescharacteristic
279C23×C7C2×#4111yescharacteristic
280C23×C7C2×#4111yescharacteristic
281C23×C7C2×#4111yescharacteristic
282C23×C7H(5,𝔽2)11yescharacteristic
283C23×C72−1+411yescharacteristic
284C23×C72−1+411yescharacteristic
285C23×C72−1+411yescharacteristic
286C22×D7—22no—
287C22×D7—22no—
288C22×D7—22no—
289C22×D7—22no—
290C22×D7—22no—
291C22×D7—22no—
292C22×D7—22no—
293C22×D7—22no—
294C22×D7—22no—
295C22×D7—22no—
296C22×D7—22no—
297C22×D7—22no—
298C22×D7—22no—
299C22×D7—22no—
300C22×D7—22no—
301C22×D7—22no—
302C22×D7—22no—
303C22×D7—22no—
304C22×D7—41no—
305C22×D7—41no—
306C22×D7—41no—
307C22×D7—41no—
308C22×D7—41no—
309C22×D7—41no—
310C22×D7—41no—
311C22×D7—41no—
312C22×D7—41no—
313C22×D7—41no—
314C22×D7—41no—
315C22×D7—41no—
316C22×D7—41no—
317C22×D7—41no—
318C22×D7—41no—
319C22×D7—41no—
320C22×D7C4×Q814yes—
321C7×Q8—416no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—24no—
330C2×C4×C7—24no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—42no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—42no—
349C2×C4×C7—41no—
350C2×C4×C7C2×C22⋊C414yes—
351C2×C4×C7C4×D414yes—
352C2×C4×C7C4×D414yes—
353C2×C4×C7#12114yes—
354C2×C4×C7#12114yes—
355C2×C4×C7#12414yes—
356C2×C4×C7#12714yes—
357C2×Dic7—24no—
358C2×Dic7—24no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—24no—
363C2×Dic7—24no—
364C2×Dic7—24no—
365C2×Dic7—24no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7C2×C22⋊C418yes—
391C2×Dic7C22⋊Q814yescomplemented
392C4×D7—416no—
393C25—71no—
394C22×Q8—22no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8C4×D714yes—
401C23×C4—72no—
402C23×C4—71no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—74no—
406C23×C4—72no—
407C23×C4—142no—
408C23×C4—142no—
409C23×C4—142no—
410C23×C4—142no—
411C23×C4—142no—
412C23×C4—142no—
413C23×C4C22×D712yes—
414C23×C4C22×D711yescharacteristic
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D712yes—
417C23×C4C22×D711yescharacteristic
418C22⋊Q8—1432no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—74no—
422C2×C4⋊C4—74no—
423C2×C4⋊C4—74no—
424C2×C4⋊C4—78no—
425C2×C4⋊C4—144no—
426C2×C4⋊C4—144no—
427C2×C4⋊C4—144no—
428C2×C4⋊C4—142no—
429C2×C4⋊C4—142no—
430C2×C4⋊C4—144no—
431C2×C4⋊C4—142no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4C22⋊D714yes—
434C2×C22⋊C4—78no—
435C2×C22⋊C4—74no—
436C2×C22⋊C4—144no—
437C2×C22⋊C4—144no—
438C2×C22⋊C4—142no—
439C2×C22⋊C4—142no—
440C2×C22⋊C4—142no—
441C2×C22⋊C4—142no—
442C2×C22⋊C4—142no—
443C2×C22⋊C4—144no—
444C2×C22⋊C4—144no—
445C2×C22⋊C4—282no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—74no—
450C2×C42—142no—
451C2×C42—142no—
452C2×C42—144no—
453C2×C42—144no—
454C2×C42—282no—
455#95—24no—
456#95—24no—
457#95—142no—
458#95—142no—
459#95—144no—
460#95—144no—
461#95—144no—
462#95—144no—
463#95—144no—
464C22×C7C22×C22⋊C411yescharacteristic
465C22×C7C2×C4×D411yescharacteristic
466C22×C7C2×C4×D411yescharacteristic
467C22×C7C2×C4×Q811yescharacteristic
468C22×C7C4×#4111yescharacteristic
469C22×C7#51911yescharacteristic
470C22×C7#52011yescharacteristic
471C22×C7C2×#12111yescharacteristic
472C22×C7C2×#12111yescharacteristic
473C22×C7C2×C22⋊Q811yescharacteristic
474C22×C7#52511yescharacteristic
475C22×C7C2×#12411yescharacteristic
476C22×C7#52911yescharacteristic
477C22×C7C2×#12711yescharacteristic
478C22×C7#53311yescharacteristic
479C22×C7#53611yescharacteristic
480C22×C7#53711yescharacteristic
481C22×C7#54111yescharacteristic
482C22×C7#54211yescharacteristic
483C22×C7#54611yescharacteristic
484C22×C7#54611yescharacteristic
485C22×C7#54611yescharacteristic
486C22×C7#54711yescharacteristic
487C22×C7#54711yescharacteristic
488C22×C7#54711yescharacteristic
489C22×C7#54811yescharacteristic
490C22×C7#54811yescharacteristic
491C22×C7#54811yescharacteristic
492C22×C7D4×Q811yescharacteristic
493C22×C7D4×Q811yescharacteristic
494C22×C7D4×Q811yescharacteristic
495C22×C7#55211yescharacteristic
496C22×C7#55211yescharacteristic
497C22×C7#55411yescharacteristic
498C22×C7#55611yescharacteristic
499C2×D7—24no—
500C2×D7—24no—
501C2×D7—24no—
502C2×D7—42no—
503C2×D7—42no—
504C2×D7—42no—
505C2×D7—42no—
506C2×D7—42no—
507C2×D7—42no—
508C2×D7—42no—
509C2×D7—42no—
510C2×D7—42no—
511C2×D7—42no—
512C2×D7—42no—
513C2×D7—42no—
514C4×C7—44no—
515C4×C7—42no—
516C4×C7—42no—
517C4×C7—44no—
518C4×C7#39018yes—
519Dic7—28no—
520Dic7—24no—
521Dic7—42no—
522Dic7—42no—
523Dic7—82no—
524C24—72no—
525C24—72no—
526C24—72no—
527C24—141no—
528C24—141no—
529C24—141no—
530C24—141no—
531C24—141no—
532C24—141no—
533C24—141no—
534C24—141no—
535C24—141no—
536C24—141no—
537C24—141no—
538C24—141no—
539C24C23×D711yescharacteristic
540C2×Q8—28no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—44no—
544C2×Q8—44no—
545C2×Q8—44no—
546C2×Q8—44no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—74no—
572C22×C4—72no—
573C22×C4—74no—
574C22×C4—74no—
575C22×C4—72no—
576C22×C4—72no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—141no—
584C22×C4—142no—
585C22×C4—141no—
586C22×C4—142no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—148no—
600C22×C4—148no—
601C22×C4—148no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—284no—
610C22×C4—284no—
611C22×C4—284no—
612C22×C4—284no—
613C22×C4C2×C4×D714yes—
614C22×C4C2×C4×D712yes—
615C22×C4#115712yes—
616C22×C4D4×D712yes—
617C22×C4D4×D712yes—
618C22×C4D4×D712yes—
619C22×C4#115912yes—
620C22×C4Q8×D712yes—
621C22×C4#116112yes—
622C22×C4C2×C22⋊D714yes—
623C22×C4C2×C22⋊D712yes—
624C4⋊C4—28no—
625C4⋊C4—716no—
626C4⋊C4—1416no—
627C4⋊C4—288no—
628C4⋊C4—284no—
629C22⋊C4—148no—
630C22⋊C4—1416no—
631C22⋊C4—148no—
632C22⋊C4—288no—
633C42—44no—
634C42—148no—
635C42—288no—
636C2×C7C2×#39011yescharacteristic
637C2×C7C4×C22⋊Q811yescharacteristic
638C2×C7#232311yescharacteristic
639C2×C7#233911yescharacteristic
640C2×C7Q8×C22⋊C411yescharacteristic
641C2×C7#236011yescharacteristic
642C2×C7#236211yescharacteristic
643C2×C7#241511yescharacteristic
644C2×C7#241711yescharacteristic
645C2×C7#242711yescharacteristic
646C2×C7#242911yescharacteristic
647C2×C7#248911yescharacteristic
648C2×C7#249211yescharacteristic
649C2×C7#254011yescharacteristic
650C2×C7#254211yescharacteristic
651D7—44no—
652C23—74no—
653C23—142no—
654C23—142no—
655C23—142no—
656C23—142no—
657C23—142no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—281no—
672C23—281no—
673C23—281no—
674C23—281no—
675C23—281no—
676C23—281no—
677C23—281no—
678C23—281no—
679C23—281no—
680C23—281no—
681C23—281no—
682C23—281no—
683C23—281no—
684C23—281no—
685C23—281no—
686C23—281no—
687C23C22×C4×D711yescharacteristic
688C23C2×#115711yescharacteristic
689C23C2×D4×D711yescharacteristic
690C23C2×D4×D711yescharacteristic
691C23C2×D4×D711yescharacteristic
692C23C2×#115911yescharacteristic
693C23C2×Q8×D711yescharacteristic
694C23C2×#116111yescharacteristic
695C23#655111yescharacteristic
696C23#655111yescharacteristic
697C23D7×#4111yescharacteristic
698C23D7×#4111yescharacteristic
699C23#655311yescharacteristic
700C23#655411yescharacteristic
701C23C22×C22⋊D711yescharacteristic
702Q8—416no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—78no—
732C2×C4—74no—
733C2×C4—144no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—144no—
737C2×C4—144no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—144no—
742C2×C4—144no—
743C2×C4—142no—
744C2×C4—144no—
745C2×C4—142no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—281no—
752C2×C4—281no—
753C2×C4—281no—
754C2×C4—281no—
755C2×C4—281no—
756C2×C4—281no—
757C2×C4—281no—
758C2×C4—281no—
759C2×C4—2816no—
760C2×C4—282no—
761C2×C4—282no—
762C2×C4—282no—
763C2×C4—282no—
764C2×C4—282no—
765C2×C4—282no—
766C2×C4—282no—
767C2×C4D7×C22⋊C414yes—
768C2×C4(C22⋊D7)⋊C414yes—
769C2×C4#644714yes—
770C2×C4#644814yes—
771C2×C4C4×C22⋊D714yes—
772C2×C4#650214yes—
773C2×C4#650314yes—
774C7#1399711yescharacteristic, complemented, Sylow
775C22—144no—
776C22—144no—
777C22—144no—
778C22—282no—
779C22—282no—
780C22—282no—
781C22—282no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—282no—
786C22—282no—
787C22—282no—
788C22—282no—
789C22—282no—
790C22C2×D7×C22⋊C411yescharacteristic
791C22C2×(C22⋊D7)⋊C411yescharacteristic
792C22C2×#644711yescharacteristic
793C22C2×#644811yescharacteristic
794C22C4×Q8×D711yescharacteristic
795C22#9026311yescharacteristic
796C22C4×#116111yescharacteristic
797C22#9026511yescharacteristic
798C22#9027011yescharacteristic
799C22#9027211yescharacteristic
800C22#9027211yescharacteristic
801C22#9027511yescharacteristic
802C22D7×C22⋊Q811yescharacteristic
803C22#9031811yescharacteristic
804C22#9031911yescharacteristic
805C22#9032011yescharacteristic
806C22#9032111yescharacteristic
807C22#9032211yescharacteristic
808C22#9032311yescharacteristic
809C22#9032411yescharacteristic
810C22#9036711yescharacteristic
811C22#9036811yescharacteristic
812C22#9037111yescharacteristic
813C22#9037311yescharacteristic
814C22#9041711yescharacteristic
815C22#9041811yescharacteristic
816C22#9041911yescharacteristic
817C22#9042211yescharacteristic
818C22C2×C4×C22⋊D711yescharacteristic
819C22C2×#650211yescharacteristic
820C22C2×#650311yescharacteristic
821C22Q8×C22⋊D711yescharacteristic
822C22#9050811yescharacteristic
823C22#9051511yescharacteristic
824C22#9052011yescharacteristic
825C4—44no—
826C4—42no—
827C4—42no—
828C4—44no—
829C4—148no—
830C4—144no—
831C4—282no—
832C4—282no—
833C4—562no—
834C4#8972918yes—
835C2—284no—
836C2#1173392411yescharacteristic
837C2#1173405611yescharacteristic
838C2#1173405811yescharacteristic
839C2#1173405911yescharacteristic
840C2#1173406511yescharacteristic
841C2#1173406611yescharacteristic
842C2#1173407611yescharacteristic
843C2#1173407811yescharacteristic
844C2C2×#8972911yescharacteristic
845C2#1173990911yescharacteristic
846C2#1173993511yescharacteristic
847C2#1174022411yescharacteristic
848C2#1174022511yescharacteristic
849C2#1174044111yescharacteristic
850C2#1174069911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#391C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#391D7
hypocenterC7#13997
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×C7×#391C2semidirect
3. C2×#90002C2semidirect
5. C2×C4⋊C4×Dic7C2semidirect
6. C2×#89700C2semidirect
9. #11727175C2semidirect
11. Dic7⋊#95C2semidirect
18. C2×#6509C4semidirect
88. C2×(C2×D7)⋊C4Q8semidirect
118. C2×#391D7semidirect
234. C4⋊Dic7C22⋊C4semidirect
391. C2×Dic7C22⋊Q8semidirect
774. C7#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#65092
C2×C7×#3912
C2×#900022
C2×#897592
C2×C4⋊C4×Dic72
C2×#897002
C2×C4×(C2×D7)⋊C42
#117271822
#117271752
#117271622
Dic7⋊#952
#139977