Finite Group Databasebeta

← #13277169

Subgroups — #13277169

Order 1792.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C22×C7×#95C211yesmaximal, characteristic, complemented
3C2×#89985C211yesmaximal, characteristic
4C2×#89985C211yesmaximal, characteristic
5C2×#89982C211yesmaximal, characteristic, complemented
6#11729881C211yesmaximal, characteristic, complemented
7#11729881C211yesmaximal, characteristic, complemented
8#11727182C212yesmaximal, complemented
9(C2×D7)⋊#95C212yesmaximal, complemented
10#11727168C212yesmaximal, complemented
11#11727160C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C23×C22⋊D7C2211yescharacteristic
16C23×C4×D7C2211yescharacteristic
17C22×C22⋊Dic7C2211yescharacteristic
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C22⋊Dic7C2211yescharacteristic
20C2×C4×C22⋊D7—24no—
21C2×C4×C22⋊D7—24no—
22C2×C4×C22⋊D7—24no—
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2212yes—
25C22×(C2×D7)⋊C4C2212yes—
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29C2×C7×#95—24no—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32#89985—24no—
33#89985C418yescomplemented
34#89982—24no—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42#14016—71nomaximal, Sylow
43C25×C7C2311yescharacteristic
44C24×D7C2311yescharacteristic
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—24no—
51C23×C4×C7—24no—
52C23×C4×C7—22no—
53C23×C4×C7—22no—
54C23×C4×C7—42no—
55C23×C4×C7—42no—
56C23×C4×C7—42no—
57C23×C4×C7—42no—
58C23×C4×C7C2×C414yescomplemented
59C23×C4×C7D414yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2312yes—
63C23×C4×C7C2311yescharacteristic
64C22×C22⋊D7—22no—
65C22×C22⋊D7—22no—
66C22×C22⋊D7—22no—
67C22×C22⋊D7—22no—
68C22×C22⋊D7C2×C414yes—
69C22×C22⋊D7D414yes—
70C22×C22⋊D7Q814yes—
71C23×Dic7C2312yes—
72C23×Dic7C2312yes—
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C22×C4×D7—22no—
77C22×C4×D7—22no—
78C22×C4×D7—22no—
79C22×C4×D7—24no—
80C22×C4×D7—42no—
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7—22no—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7C2×C414yescomplemented
89C2×C22⋊Dic7D414yes—
90C4×C22⋊D7—232no—
91C2×(C2×D7)⋊C4—22no—
92C2×(C2×D7)⋊C4—22no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—24no—
95C2×(C2×D7)⋊C4—24no—
96C2×(C2×D7)⋊C4—42no—
97C2×(C2×D7)⋊C4—42no—
98C2×(C2×D7)⋊C4—42no—
99C2×(C2×D7)⋊C4C2×C418yescomplemented
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4—24no—
105C2×Dic7⋊C4—42no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C7×#95—24no—
110C7×#95—24no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—42no—
115C7⋊#95—42no—
116C7⋊#95—42no—
117C7⋊#95C2×C418yescomplemented
118C22×C4×D4—71no—
119C2×#386—71no—
120C2×#386—71no—
121C2×#385—71no—
122C22×#95D711yescharacteristic, complemented
123#1442—72no—
124#1439—72no—
125#1436—72no—
126C22⋊#95—72no—
127C22⋊#95—71no—
128C22⋊#95—71no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7C22×C412yes—
134C24×C7C2×D412yes—
135C24×C7C2×D412yes—
136C24×C7C2×D412yes—
137C24×C7C2×Q812yes—
138C24×C7#4112yes—
139C24×C7#4112yes—
140C24×C7C2411yescharacteristic
141C23×D7—21no—
142C23×D7—21no—
143C23×D7—22no—
144C23×D7—22no—
145C23×D7—21no—
146C23×D7—21no—
147C23×D7—22no—
148C23×D7—22no—
149C23×D7C22×C412yes—
150C23×D7C2×D412yes—
151C23×D7C2×Q812yes—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—22no—
155C22×C4×C7—28no—
156C22×C4×C7—28no—
157C22×C4×C7—28no—
158C22×C4×C7—22no—
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—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—28no—
175C22×C4×C7—48no—
176C22×C4×C7—44no—
177C22×C4×C7—48no—
178C22×C4×C7—48no—
179C22×C4×C7—48no—
180C22×C4×C7—48no—
181C22×C4×C7—44no—
182C22×C4×C7—44no—
183C22×C4×C7—44no—
184C22×C4×C7—48no—
185C22×C4×C7—44no—
186C22×C4×C7C22×C414yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7#4114yes—
190C22×C4×C7#4114yes—
191C2×C22⋊D7—28no—
192C2×C22⋊D7—28no—
193C2×C22⋊D7—28no—
194C2×C22⋊D7—28no—
195C2×C22⋊D7—28no—
196C2×C22⋊D7—28no—
197C2×C22⋊D7C4⋊C4116yescomplemented
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—22no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7C22×C414yes—
224C22×Dic7C22×C412yes—
225C22×Dic7C2×D412yes—
226C22×Dic7C2×D412yes—
227C22×Dic7C2×D412yes—
228C22×Dic7C2×Q812yes—
229C2×C4×D7—28no—
230C2×C4×D7—48no—
231C2×C4×D7—48no—
232C2×C4×D7—44no—
233C2×C4×D7—44no—
234C22⋊Dic7—28no—
235C22⋊Dic7—28no—
236C22⋊Dic7—44no—
237(C2×D7)⋊C4—28no—
238(C2×D7)⋊C4—48no—
239(C2×D7)⋊C4—48no—
240Dic7⋊C4—28no—
241Dic7⋊C4—48no—
242C4×Dic7—28no—
243C23×D4—71no—
244C24×C4—71no—
245C24×C4C2×D711yescharacteristic
246C24×C4C2×D711yescharacteristic
247C24×C4C2×D711yescharacteristic
248C2×C4×D4—144no—
249C2×C4×D4—144no—
250C2×C4×D4—144no—
251C22×C4⋊C4—71no—
252C22×C4⋊C4—72no—
253C22×C22⋊C4—71no—
254C22×C22⋊C4—71no—
255C22×C22⋊C4—72no—
256C22×C22⋊C4—71no—
257C22×C22⋊C4—71no—
258C22×C22⋊C4—72no—
259C22×C42—71no—
260#386—78no—
261#386—144no—
262#385—144no—
263C2×#95—24no—
264C2×#95—72no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—72no—
269C2×#95—72no—
270C2×#95—72no—
271C2×#95C2×D712yes—
272C2×#95C2×D712yes—
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—24no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—24no—
281C23×C7—24no—
282C23×C7—24no—
283C23×C7—24no—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—24no—
288C23×C7—24no—
289C23×C7C2×C4⋊C414yes—
290C23×C7C4×D414yes—
291C23×C7C4×D414yes—
292C23×C7#12014yes—
293C23×C7C22⋊Q814yes—
294C23×C7C22⋊Q814yes—
295C23×C7#12314yes—
296C23×C7C23×C411yescharacteristic
297C23×C7C22×D411yescharacteristic
298C23×C7C22×D411yescharacteristic
299C23×C7C22×D411yescharacteristic
300C23×C7C22×Q811yescharacteristic
301C23×C7C2×#4111yescharacteristic
302C23×C7C2×#4112yes—
303C23×C7C2×#4112yes—
304C23×C7C2×#4111yescharacteristic
305C23×C7H(5,𝔽2)12yes—
306C23×C7H(5,𝔽2)12yes—
307C22×D7—22no—
308C22×D7—22no—
309C22×D7—24no—
310C22×D7—24no—
311C22×D7—22no—
312C22×D7—22no—
313C22×D7—22no—
314C22×D7—22no—
315C22×D7—24no—
316C22×D7—24no—
317C22×D7—24no—
318C22×D7—24no—
319C22×D7—41no—
320C22×D7—41no—
321C22×D7—42no—
322C22×D7—41no—
323C22×D7—41no—
324C22×D7—42no—
325C22×D7—42no—
326C22×D7—42no—
327C22×D7—42no—
328C22×D7—42no—
329C22×D7C2×C4⋊C414yes—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—24no—
333C2×C4×C7—24no—
334C2×C4×C7—24no—
335C2×C4×C7—24no—
336C2×C4×C7—24no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—24no—
340C2×C4×C7—22no—
341C2×C4×C7—24no—
342C2×C4×C7—24no—
343C2×C4×C7—416no—
344C2×C4×C7—416no—
345C2×C4×C7—416no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7#12314yes—
357C22⋊D7—232no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—24no—
365C2×Dic7—24no—
366C2×Dic7—24no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—24no—
370C2×Dic7—24no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7—42no—
381C2×Dic7—42no—
382C2×Dic7—42no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7C2×C4⋊C414yes—
389C4×D7—416no—
390C25—71no—
391C25C22×D711yescharacteristic
392C22×D4—74no—
393C22×D4—74no—
394C22×D4—74no—
395C22×D4—142no—
396C22×D4—142no—
397C22×D4—142no—
398C22×D4—142no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—71no—
413C23×C4—71no—
414C23×C4—72no—
415C23×C4—71no—
416C23×C4—72no—
417C23×C4—142no—
418C23×C4—142no—
419C23×C4—142no—
420C23×C4—144no—
421C23×C4—282no—
422C23×C4C4×D714yescomplemented
423C23×C4C22⋊D714yes—
424C23×C4C22×D712yes—
425C23×C4C22×D712yes—
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C4×D4—1432no—
429C2×C4⋊C4—142no—
430C2×C4⋊C4—142no—
431C2×C4⋊C4—142no—
432C2×C4⋊C4—144no—
433C2×C4⋊C4—144no—
434C2×C4⋊C4—282no—
435C2×C22⋊C4—74no—
436C2×C22⋊C4—74no—
437C2×C22⋊C4—78no—
438C2×C22⋊C4—142no—
439C2×C22⋊C4—142no—
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—142no—
447C2×C22⋊C4—142no—
448C2×C22⋊C4—142no—
449C2×C22⋊C4—144no—
450C2×C22⋊C4—282no—
451C2×C22⋊C4—282no—
452C2×C22⋊C4—282no—
453C2×C42—142no—
454C2×C42—142no—
455C2×C42—142no—
456#95—24no—
457#95—24no—
458#95—78no—
459#95—144no—
460#95—144no—
461#95—144no—
462#95—282no—
463#95—282no—
464#95—282no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—28no—
468C22×C7—28no—
469C22×C7—24no—
470C22×C7—24no—
471C22×C7—28no—
472C22×C7—28no—
473C22×C7—24no—
474C22×C7—24no—
475C22×C7#38518yes—
476C22×C7C22×C4⋊C411yescharacteristic
477C22×C7C2×C4×D411yescharacteristic
478C22×C7C2×C4×D411yescharacteristic
479C22×C7C4×#4112yes—
480C22×C7#51812yes—
481C22×C7C2×#12011yescharacteristic
482C22×C7C2×C22⋊Q811yescharacteristic
483C22×C7C2×C22⋊Q811yescharacteristic
484C22×C7C2×#12311yescharacteristic
485C22×C7C2×#12311yescharacteristic
486C22×C7#52511yescharacteristic
487C22×C7#52912yes—
488C22×C7#53411yescharacteristic
489C22×C7#53511yescharacteristic
490C22×C7#53812yes—
491C22×C7#54612yes—
492C22×C7#54612yes—
493C22×C7#54612yes—
494C22×C7#54612yes—
495C22×C7#55312yes—
496C22×C7#55312yes—
497C22×C7#55412yes—
498C22×C7#55412yes—
499C2×D7—28no—
500C2×D7—24no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—44no—
504C2×D7—42no—
505C2×D7—42no—
506C2×D7—44no—
507C2×D7—44no—
508C2×D7—42no—
509C2×D7—42no—
510C4×C7—24no—
511C4×C7—44no—
512C4×C7—44no—
513C4×C7—42no—
514Dic7—24no—
515Dic7—44no—
516Dic7—42no—
517Dic7—42no—
518Dic7—82no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—72no—
524C24—72no—
525C24—72no—
526C24—142no—
527C24—142no—
528C24—141no—
529C24—141no—
530C24—142no—
531C24—142no—
532C24—141no—
533C24—141no—
534C24C2×C4×D712yes—
535C24#115712yes—
536C24D4×D712yes—
537C24D4×D712yes—
538C24Q8×D712yes—
539C24#116112yes—
540C24C2×C22⋊D712yes—
541C24C23×D711yescharacteristic
542C2×D4—716no—
543C2×D4—148no—
544C2×D4—148no—
545C2×D4—148no—
546C2×D4—148no—
547C2×D4—148no—
548C2×D4—148no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—28no—
572C22×C4—48no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—74no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—148no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—141no—
607C22×C4—141no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—288no—
616C22×C4—288no—
617C22×C4—284no—
618C22×C4—284no—
619C22×C4C2×C4×D714yes—
620C22×C4#115714yes—
621C22×C4#115714yes—
622C22×C4C2×C22⋊D712yes—
623C22×C4C2×C22⋊D712yes—
624C4⋊C4—148no—
625C4⋊C4—288no—
626C22⋊C4—148no—
627C22⋊C4—148no—
628C22⋊C4—148no—
629C22⋊C4—288no—
630C22⋊C4—288no—
631C22⋊C4—284no—
632C42—148no—
633C2×C7—28no—
634C2×C7C2×#38511yescharacteristic
635C2×C7C4×#12311yescharacteristic
636C2×C7#232111yescharacteristic
637C2×C7#234912yes—
638C2×C7#236412yes—
639C2×C7#240411yescharacteristic
640C2×C7#240511yescharacteristic
641C2×C7#244412yes—
642C2×C7#245012yes—
643C2×C7#248711yescharacteristic
644C2×C7#257911yescharacteristic
645D7—44no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—74no—
663C23—144no—
664C23—144no—
665C23—144no—
666C23—144no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—144no—
671C23—144no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23—282no—
676C23—282no—
677C23—282no—
678C23—282no—
679C23—282no—
680C23—282no—
681C23—281no—
682C23—281no—
683C23—281no—
684C23—281no—
685C23D7×C4⋊C414yes—
686C23#645614yes—
687C23#645714yes—
688C23#645914yes—
689C23C4×C22⋊D714yes—
690C23#650014yes—
691C23#650914yes—
692C23C22×C4×D711yescharacteristic
693C23C2×#115712yes—
694C23C2×#115712yes—
695C23C2×#115711yescharacteristic
696C23C2×D4×D711yescharacteristic
697C23C2×D4×D711yescharacteristic
698C23#654812yes—
699C23#654812yes—
700C23C2×Q8×D711yescharacteristic
701C23C2×#116111yescharacteristic
702C23C22×C22⋊D711yescharacteristic
703D4—1432no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—416no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—74no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—144no—
738C2×C4—144no—
739C2×C4—144no—
740C2×C4—144no—
741C2×C4—144no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—2816no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4—282no—
748C2×C4—282no—
749C2×C4—282no—
750C2×C4—282no—
751C2×C4—281no—
752C2×C4—281no—
753C2×C4—281no—
754C2×C4—281no—
755C2×C4—282no—
756C2×C4—282no—
757C2×C4—282no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4—282no—
761C2×C4—282no—
762C2×C4#649214yes—
763C7#1401611yescharacteristic, complemented, Sylow
764C22—28no—
765C22—28no—
766C22—24no—
767C22—28no—
768C22—28no—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—148no—
775C22—144no—
776C22—284no—
777C22—284no—
778C22—282no—
779C22—284no—
780C22—282no—
781C22—282no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22#8976118yes—
786C22C4×#115712yes—
787C22#9017012yes—
788C22#9017712yes—
789C22#9018112yes—
790C22#9018112yes—
791C22#9018112yes—
792C22#9018112yes—
793C22#9018512yes—
794C22C2×D7×C4⋊C411yescharacteristic
795C22C2×#645611yescharacteristic
796C22C2×#645711yescharacteristic
797C22C2×#645911yescharacteristic
798C22#9020212yes—
799C22#9020212yes—
800C22#9020512yes—
801C22#9020512yes—
802C22C2×C4×C22⋊D711yescharacteristic
803C22C2×#649211yescharacteristic
804C22#9048211yescharacteristic
805C22C2×#650011yescharacteristic
806C22#9049511yescharacteristic
807C22#9049611yescharacteristic
808C22C2×#650911yescharacteristic
809C4—24no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—144no—
814C4—284no—
815C4—282no—
816C4—282no—
817C4—562no—
818C2—28no—
819C2—284no—
820C2#1173078312yes—
821C2#1173079612yes—
822C2#1173081412yes—
823C2#1173082212yes—
824C2C4×#649211yescharacteristic
825C2#1173954111yescharacteristic
826C2#1173957011yescharacteristic
827C2#1173957111yescharacteristic
828C2C2×#8976111yescharacteristic
829C2#1173964211yescharacteristic
830C2#1173964311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C7×#95C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22×#95D7
hypocenterC7#14016
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C22×C7×#95C2semidirect
5. C2×#89982C2semidirect
6. #11729881C2semidirect
7. #11729881C2semidirect
8. #11727182C2semidirect
9. (C2×D7)⋊#95C2semidirect
10. #11727168C2semidirect
11. #11727160C2semidirect
33. #89985C4semidirect
58. C23×C4×C7C2×C4semidirect
88. C2×C22⋊Dic7C2×C4semidirect
99. C2×(C2×D7)⋊C4C2×C4semidirect
117. C7⋊#95C2×C4semidirect
122. C22×#95D7semidirect
197. C2×C22⋊D7C4⋊C4semidirect
422. C23×C4C4×D7semidirect
763. C7#14016semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C22×C7×#952
C2×#899852
C2×#899822
#117298812
#117271822
(C2×D7)⋊#952
#117271682
#117271602
#140167