Finite Group Databasebeta

← #13276591

Subgroups — #13276591

Order 1792.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6460C211yesmaximal, characteristic
2C22×C4×Dic14C211yesmaximal, characteristic, complemented
3C2×#89759C211yesmaximal, characteristic
4C2×#89746C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
6C7×C4⋊#95C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11727182C212yesmaximal
9#11727165C212yesmaximal, complemented
10#11727162C212yesmaximal
11#11727161C212yesmaximal, complemented
12C23×C4×D7C2211yescharacteristic
13C23×Dic14C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×(C2×D7)⋊C4C2211yescharacteristic
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×C4⋊Dic7C2212yes—
22C22×C4⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4C2212yes—
24C22×C4×Dic7C2212yes—
25C22×C4×Dic7C2211yescharacteristic
26C2×#6460—24no—
27C2×#6460—24no—
28C2×#6460C418yescomplemented
29C2×C4×Dic14—24no—
30C2×C4×Dic14—24no—
31C2×C4×Dic14—24no—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2212yes—
41#89759—24no—
42#89746—24no—
43C4×(C2×D7)⋊C4—24no—
44#13969—71nomaximal, Sylow
45C24×D7C2311yescharacteristic
46C23×C4×C7C2312yes—
47C23×C4×C7C2312yes—
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2312yes—
53C23×Dic7C2311yescharacteristic
54C23×Dic7C2311yescharacteristic
55C23×Dic7C2312yes—
56C22×C4×D7—22no—
57C22×C4×D7—22no—
58C22×C4×D7—22no—
59C22×C4×D7—22no—
60C22×C4×D7—22no—
61C22×C4×D7—22no—
62C22×C4×D7C2×C414yes—
63C22×Dic14—22no—
64C22×Dic14—22no—
65C22×Dic14—22no—
66C22×Dic14—22no—
67C22×Dic14C2×C414yes—
68C22×Dic14D414yes—
69C22×Dic14D414yes—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4C2×C414yes—
76C2×C42×C7—22no—
77C2×C42×C7—22no—
78C2×C42×C7D414yes—
79C2×(C2×D7)⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—24no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—22no—
86C2×(C2×D7)⋊C4—24no—
87C2×(C2×D7)⋊C4—24no—
88C2×(C2×D7)⋊C4—42no—
89C2×(C2×D7)⋊C4C2×C418yes—
90C2×(C2×D7)⋊C4Q814yescomplemented
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×C4⋊Dic7—24no—
94C2×C4⋊Dic7—24no—
95C2×C4⋊Dic7C2×C418yes—
96C2×C4⋊Dic7D414yes—
97C2×Dic7⋊C4—24no—
98C2×Dic7⋊C4—24no—
99C2×Dic7⋊C4—24no—
100C2×C4×Dic7—24no—
101C2×C4×Dic7—24no—
102C2×C4×Dic7—24no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106#6460—232no—
107C4×Dic14—232no—
108C7×#95—24no—
109C7×#95—42no—
110C7⋊#95—22no—
111C7⋊#95—22no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C7⋊#95—42no—
117C22×C22⋊Q8—71no—
118C22×C4×Q8—71no—
119C2×#391—71no—
120C2×#380—71no—
121C2×C4×C22⋊C4—71no—
122#1441—72no—
123#1439—72no—
124#1437—72no—
125#1436—72no—
126C4⋊#95—71no—
127C4⋊#95D711yescharacteristic, complemented
128C24×C7C2411yescharacteristic
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×D7—21no—
141C23×D7C22×C412yes—
142C23×D7C2×Q812yes—
143C23×D7#4112yes—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—22no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7C22×C414yes—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2×D412yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7C2×Q812yes—
176C22×C4×C7#4112yes—
177C22×C4×C7#4112yes—
178C22×C4×C7#4112yes—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—22no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—22no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7C22×C412yes—
208C22×Dic7C22×C414yes—
209C22×Dic7C2×D414yes—
210C22×Dic7C2×D414yes—
211C22×Dic7C2×D414yes—
212C22×Dic7C2×Q812yes—
213C22×Dic7#4112yes—
214C2×C4×D7—28no—
215C2×C4×D7—28no—
216C2×C4×D7—28no—
217C2×C4×D7—44no—
218C2×C4×D7—44no—
219C2×C4×D7—44no—
220C2×C4×D7—44no—
221C2×Dic14—28no—
222C2×Dic14—28no—
223C2×Dic14—28no—
224C2×Dic14—28no—
225C2×Dic14—28no—
226C2×Dic14—28no—
227C2×Dic14C22⋊C4116yescomplemented
228C7×C4⋊C4—28no—
229C7×C4⋊C4—44no—
230C42×C7—28no—
231(C2×D7)⋊C4—28no—
232(C2×D7)⋊C4—28no—
233(C2×D7)⋊C4—216no—
234(C2×D7)⋊C4—48no—
235C4⋊Dic7—28no—
236C4⋊Dic7—216no—
237Dic7⋊C4—216no—
238C4×Dic7—216no—
239C4×Dic7—44no—
240C23×Q8—71no—
241C24×C4—71no—
242C2×C22⋊Q8—78no—
243C2×C22⋊Q8—144no—
244C2×C22⋊Q8—144no—
245C2×C4×Q8—144no—
246C2×C4×Q8—144no—
247C2×C4×Q8—144no—
248C22×C4⋊C4—71no—
249C22×C4⋊C4—72no—
250C22×C4⋊C4—72no—
251C22×C4⋊C4C2×D711yescharacteristic
252C22×C4⋊C4C2×D711yescharacteristic
253C22×C22⋊C4—72no—
254C22×C22⋊C4—71no—
255C22×C22⋊C4—71no—
256C22×C22⋊C4—72no—
257C22×C42—72no—
258C22×C42—71no—
259C22×C42C2×D711yescharacteristic
260#391—144no—
261#380—144no—
262C4×C22⋊C4—144no—
263C2×#95—72no—
264C2×#95—71no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—71no—
269C2×#95—72no—
270C2×#95C2×D712yes—
271C2×#95C2×D712yes—
272C23×C7C23×C411yescharacteristic
273C23×C7C22×D411yescharacteristic
274C23×C7C22×D411yescharacteristic
275C23×C7C22×D411yescharacteristic
276C23×C7C22×D411yescharacteristic
277C23×C7C22×Q811yescharacteristic
278C23×C7C2×#4111yescharacteristic
279C23×C7C2×#4111yescharacteristic
280C23×C7C2×#4111yescharacteristic
281C23×C7C2×#4111yescharacteristic
282C23×C7C2×#4111yescharacteristic
283C23×C7H(5,𝔽2)11yescharacteristic
284C23×C72−1+411yescharacteristic
285C23×C72−1+411yescharacteristic
286C23×C72−1+411yescharacteristic
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—22no—
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×D7—41no—
321C22×D7C4×Q814yescomplemented
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—24no—
329C2×C4×C7—24no—
330C2×C4×C7—24no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—41no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—41no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7—42no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7C2×C22⋊C414yes—
350C2×C4×C7C4×D414yes—
351C2×C4×C7C4×D414yes—
352C2×C4×C7#12014yes—
353C2×C4×C7#12114yes—
354C2×C4×C7#12114yes—
355C2×C4×C7C22⋊Q814yescomplemented
356C2×C4×C7#12314yes—
357C2×Dic7—24no—
358C2×Dic7—24no—
359C2×Dic7—24no—
360C2×Dic7—24no—
361C2×Dic7—24no—
362C2×Dic7—24no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—24no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—24no—
370C2×Dic7—24no—
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—42no—
382C2×Dic7—41no—
383C2×Dic7—42no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7—42no—
387C2×Dic7—41no—
388C2×Dic7—42no—
389C2×Dic7—41no—
390C2×Dic7—41no—
391C2×Dic7C2×C22⋊C418yes—
392C4×D7—416no—
393Dic14—232no—
394C25—71no—
395C22×Q8—74no—
396C22×Q8—74no—
397C22×Q8—74no—
398C22×Q8—142no—
399C22×Q8—142no—
400C22×Q8—142no—
401C22×Q8—142no—
402C23×C4—72no—
403C23×C4—72no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—74no—
408C23×C4—142no—
409C23×C4—142no—
410C23×C4—142no—
411C23×C4—142no—
412C23×C4—142no—
413C23×C4—142no—
414C23×C4C22×D712yes—
415C23×C4C22×D712yes—
416C23×C4C22×D711yescharacteristic
417C23×C4C22×D711yescharacteristic
418C23×C4C22×D711yescharacteristic
419C22⋊Q8—1432no—
420C4×Q8—1432no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—78no—
427C2×C4⋊C4—74no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—144no—
430C2×C4⋊C4—144no—
431C2×C4⋊C4—144no—
432C2×C4⋊C4—144no—
433C2×C4⋊C4—142no—
434C2×C4⋊C4—142no—
435C2×C4⋊C4C4×D714yes—
436C2×C22⋊C4—78no—
437C2×C22⋊C4—74no—
438C2×C22⋊C4—144no—
439C2×C22⋊C4—144no—
440C2×C22⋊C4—142no—
441C2×C22⋊C4—142no—
442C2×C22⋊C4—142no—
443C2×C22⋊C4—142no—
444C2×C22⋊C4—142no—
445C2×C22⋊C4—144no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—282no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—144no—
451C2×C42—144no—
452C2×C42—144no—
453C2×C42—142no—
454C2×C42—142no—
455C2×C42—142no—
456C2×C42D2814yes—
457#95—24no—
458#95—42no—
459#95—144no—
460#95—144no—
461#95—144no—
462#95—144no—
463#95—142no—
464#95—142no—
465#95—282no—
466C22×C7C22×C22⋊C411yescharacteristic
467C22×C7C2×C4×D411yescharacteristic
468C22×C7C2×C4×D411yescharacteristic
469C22×C7C2×C4×Q811yescharacteristic
470C22×C7C4×#4111yescharacteristic
471C22×C7#51911yescharacteristic
472C22×C7#52011yescharacteristic
473C22×C7C2×#12011yescharacteristic
474C22×C7C2×#12111yescharacteristic
475C22×C7C2×#12111yescharacteristic
476C22×C7C2×C22⋊Q811yescharacteristic
477C22×C7C2×#12311yescharacteristic
478C22×C7#52511yescharacteristic
479C22×C7#52911yescharacteristic
480C22×C7#53311yescharacteristic
481C22×C7#53611yescharacteristic
482C22×C7#53711yescharacteristic
483C22×C7#54111yescharacteristic
484C22×C7#54211yescharacteristic
485C22×C7#54611yescharacteristic
486C22×C7#54711yescharacteristic
487C22×C7#54811yescharacteristic
488C22×C7#54811yescharacteristic
489C22×C7#54811yescharacteristic
490C22×C7#54811yescharacteristic
491C22×C7#54811yescharacteristic
492C22×C7D4×Q811yescharacteristic
493C22×C7D4×Q811yescharacteristic
494C22×C7D4×Q811yescharacteristic
495C22×C7#55011yescharacteristic
496C22×C7#55011yescharacteristic
497C22×C7#55211yescharacteristic
498C22×C7#55211yescharacteristic
499C22×C7#55411yescharacteristic
500C22×C7#55611yescharacteristic
501C2×D7—24no—
502C2×D7—24no—
503C2×D7—24no—
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—
514C2×D7—42no—
515C2×D7—42no—
516C4×C7—24no—
517C4×C7—44no—
518C4×C7—42no—
519C4×C7—82no—
520C4×C7#38618yes—
521Dic7—28no—
522Dic7—44no—
523Dic7—42no—
524Dic7—42no—
525Dic7—42no—
526C24—72no—
527C24—72no—
528C24—72no—
529C24—141no—
530C24—141no—
531C24—141no—
532C24—141no—
533C24—141no—
534C24—141no—
535C24—141no—
536C24—141no—
537C24—141no—
538C24—141no—
539C24—141no—
540C24—141no—
541C24C23×D711yescharacteristic
542C2×Q8—716no—
543C2×Q8—148no—
544C2×Q8—148no—
545C2×Q8—148no—
546C2×Q8—148no—
547C2×Q8—148no—
548C2×Q8—148no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—74no—
573C22×C4—74no—
574C22×C4—74no—
575C22×C4—72no—
576C22×C4—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—142no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—142no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—142no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—141no—
604C22×C4—142no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—148no—
608C22×C4—148no—
609C22×C4—148no—
610C22×C4—284no—
611C22×C4—284no—
612C22×C4—284no—
613C22×C4—284no—
614C22×C4C2×C4×D714yes—
615C22×C4C2×C4×D712yes—
616C22×C4C2×D2812yes—
617C22×C4C2×D2812yes—
618C22×C4C2×D2812yes—
619C22×C4#115712yes—
620C22×C4D4×D712yes—
621C22×C4D4×D712yes—
622C22×C4D4×D712yes—
623C22×C4#115912yes—
624C22×C4Q8×D712yes—
625C22×C4#116112yes—
626C4⋊C4—28no—
627C4⋊C4—44no—
628C4⋊C4—1416no—
629C4⋊C4—1416no—
630C4⋊C4—148no—
631C22⋊C4—1416no—
632C22⋊C4—148no—
633C22⋊C4—148no—
634C22⋊C4—288no—
635C42—28no—
636C42—1416no—
637C42—284no—
638C2×C7C2×#38611yescharacteristic
639C2×C7C4×C22⋊Q811yescharacteristic
640C2×C7#232311yescharacteristic
641C2×C7Q8×C22⋊C411yescharacteristic
642C2×C7#234111yescharacteristic
643C2×C7#236011yescharacteristic
644C2×C7#236211yescharacteristic
645C2×C7#240711yescharacteristic
646C2×C7#240911yescharacteristic
647C2×C7#242111yescharacteristic
648C2×C7#242311yescharacteristic
649C2×C7#242611yescharacteristic
650C2×C7#242911yescharacteristic
651C2×C7#253611yescharacteristic
652C2×C7#253811yescharacteristic
653D7—44no—
654C23—74no—
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—142no—
672C23—142no—
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—
687C23—281no—
688C23—281no—
689C23C22×C4×D711yescharacteristic
690C23C22×D2811yescharacteristic
691C23C2×#115711yescharacteristic
692C23C2×D4×D711yescharacteristic
693C23C2×D4×D711yescharacteristic
694C23C2×D4×D711yescharacteristic
695C23C2×#115911yescharacteristic
696C23#654811yescharacteristic
697C23C2×Q8×D711yescharacteristic
698C23C2×#116111yescharacteristic
699C23#655111yescharacteristic
700C23D7×#4111yescharacteristic
701C23D7×#4111yescharacteristic
702C23#655411yescharacteristic
703C23#655411yescharacteristic
704Q8—1432no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—78no—
733C2×C4—144no—
734C2×C4—144no—
735C2×C4—144no—
736C2×C4—144no—
737C2×C4—144no—
738C2×C4—144no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—144no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—144no—
750C2×C4—144no—
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—281no—
760C2×C4—281no—
761C2×C4—282no—
762C2×C4—281no—
763C2×C4—282no—
764C2×C4—281no—
765C2×C4—282no—
766C2×C4—282no—
767C2×C4—2816no—
768C2×C4C4×D2814yes—
769C2×C4D7×C22⋊C414yes—
770C2×C4#644514yes—
771C2×C4#644714yes—
772C2×C4#645614yes—
773C2×C4#645714yes—
774C2×C4#645814yes—
775C2×C4#646014yescomplemented
776C7#1396911yescharacteristic, complemented, Sylow
777C22—144no—
778C22—144no—
779C22—144no—
780C22—282no—
781C22—282no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—282no—
786C22—282no—
787C22—282no—
788C22—282no—
789C22—282no—
790C22—282no—
791C22—282no—
792C22C2×C4×D2811yescharacteristic
793C22C2×D7×C22⋊C411yescharacteristic
794C22C2×#644511yescharacteristic
795C22C2×#644711yescharacteristic
796C22C2×#645611yescharacteristic
797C22C2×#645711yescharacteristic
798C22C2×#645811yescharacteristic
799C22C2×#646011yescharacteristic
800C22#9020111yescharacteristic
801C22#9021511yescharacteristic
802C22#9021711yescharacteristic
803C22C4×#115911yescharacteristic
804C22#9023711yescharacteristic
805C22#9024811yescharacteristic
806C22#9025211yescharacteristic
807C22C4×Q8×D711yescharacteristic
808C22#9026311yescharacteristic
809C22#9026911yescharacteristic
810C22#9027411yescharacteristic
811C22#9028911yescharacteristic
812C22#9028911yescharacteristic
813C22#9029011yescharacteristic
814C22#9030311yescharacteristic
815C22#9032211yescharacteristic
816C22#9032311yescharacteristic
817C22#9032311yescharacteristic
818C22#9032411yescharacteristic
819C22#9036811yescharacteristic
820C22#9036811yescharacteristic
821C22#9038511yescharacteristic
822C22#9038511yescharacteristic
823C22#9040911yescharacteristic
824C22#9041811yescharacteristic
825C22#9042111yescharacteristic
826C22#9042311yescharacteristic
827C4—24no—
828C4—42no—
829C4—44no—
830C4—82no—
831C4—148no—
832C4—284no—
833C4—282no—
834C4—282no—
835C4—282no—
836C4#8943718yes—
837C2—284no—
838C2C2×#8943711yescharacteristic
839C2C4×#646011yescharacteristic
840C2#1173120711yescharacteristic
841C2#1173146011yescharacteristic
842C2#1173146211yescharacteristic
843C2#1173168511yescharacteristic
844C2#1173181411yescharacteristic
845C2#1173342911yescharacteristic
846C2#1173365011yescharacteristic
847C2#1173365911yescharacteristic
848C2#1173366111yescharacteristic
849C2#1173374611yescharacteristic
850C2#1173388811yescharacteristic
851C2#1173405911yescharacteristic
852C2#1173407011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC4⋊#95D7
hypocenterC7#13969
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic14C2semidirect
4. C2×#89746C2semidirect
6. C7×C4⋊#95C2semidirect
7. #11729317C2semidirect
9. #11727165C2semidirect
11. #11727161C2semidirect
28. C2×#6460C4semidirect
90. C2×(C2×D7)⋊C4Q8semidirect
127. C4⋊#95D7semidirect
227. C2×Dic14C22⋊C4semidirect
321. C22×D7C4×Q8semidirect
355. C2×C4×C7C22⋊Q8semidirect
775. C2×C4#6460semidirect
776. C7#13969semidirect

Maximal subgroups

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

subgroupindex
C22×#64602
C22×C4×Dic142
C2×#897592
C2×#897462
C2×C4×(C2×D7)⋊C42
C7×C4⋊#952
#117293172
#117271822
#117271652
#117271622
#117271612
#139697