Finite Group Databasebeta

← #13277165

Subgroups — #13277165

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×C7×D4C211yesmaximal, characteristic
2C2×#89992C211yesmaximal, characteristic
3C2×#89992C211yesmaximal, characteristic
4C22×C7⋊#95C211yesmaximal, characteristic, complemented
5C2×#89718C211yesmaximal, characteristic, complemented
6#11729881C212yesmaximal, complemented
7#11729881C211yesmaximal, characteristic, complemented
8#11729321C212yesmaximal, complemented
9#11729301C212yesmaximal, complemented
10#11729298C211yesmaximal, characteristic, complemented
11#11729290C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×Dic7C2211yescharacteristic
16C24×Dic7C2211yescharacteristic
17C2×C4×C7×D4—24no—
18C2×C4×C7×D4—24no—
19C2×C4×C7×D4—24no—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2212yes—
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2212yes—
28C22×Dic7⋊C4C2212yes—
29#89992—24no—
30#89992C418yescomplemented
31C2×C7⋊#95—24no—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41#89718—24no—
42#14016—71nomaximal, Sylow
43C25×C7C2311yescharacteristic
44C25×C7C2311yescharacteristic
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4C2×C414yes—
50C22×C7×D4D414yes—
51C22×C7×D4Q814yes—
52C23×C4×C7—22no—
53C23×C4×C7—22no—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—22no—
57C23×C4×C7—24no—
58C23×C4×C7—24no—
59C23×C4×C7—42no—
60C23×C4×C7—42no—
61C23×C4×C7D414yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7—22no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—24no—
71C23×Dic7—22no—
72C23×Dic7—22no—
73C23×Dic7—42no—
74C23×Dic7—42no—
75C23×Dic7—42no—
76C23×Dic7C2×C414yescomplemented
77C23×Dic7C2312yes—
78C23×Dic7C2312yes—
79C23×Dic7C2312yes—
80C23×Dic7C2312yes—
81C4×C7×D4—232no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4D414yes—
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—24no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—22no—
100C2×C22⋊Dic7—24no—
101C2×C22⋊Dic7—42no—
102C2×C22⋊Dic7—42no—
103C2×C22⋊Dic7—42no—
104C2×C22⋊Dic7C2×C414yescomplemented
105C2×C22⋊Dic7C2×C418yescomplemented
106C2×Dic7⋊C4—24no—
107C2×Dic7⋊C4—24no—
108C2×Dic7⋊C4—42no—
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×D4D711yescharacteristic
119C2×#386—71no—
120C2×#386—71no—
121C2×#385—71no—
122C22×#95—71no—
123#1442—72no—
124#1439—72no—
125#1436—72no—
126C22⋊#95—71no—
127C22⋊#95—72no—
128C22⋊#95—71no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—22no—
140C24×C7—22no—
141C24×C7C22×C412yes—
142C24×C7C22×C412yes—
143C24×C7C2×D412yes—
144C24×C7C2×D412yes—
145C24×C7C2×D412yes—
146C24×C7C2×D412yes—
147C24×C7C2×Q812yes—
148C24×C7C2×Q812yes—
149C24×C7#4112yes—
150C24×C7#4112yes—
151C24×C7C2411yescharacteristic
152C2×C7×D4—28no—
153C2×C7×D4—28no—
154C2×C7×D4—28no—
155C2×C7×D4—28no—
156C2×C7×D4—28no—
157C2×C7×D4—28no—
158C2×C7×D4C4⋊C4116yescomplemented
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—22no—
166C22×C4×C7—28no—
167C22×C4×C7—28no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—28no—
181C22×C4×C7—44no—
182C22×C4×C7—48no—
183C22×C4×C7—48no—
184C22×C4×C7—48no—
185C22×C4×C7—48no—
186C22×C4×C7—44no—
187C22×C4×C7—44no—
188C22×C4×C7C22×C412yes—
189C22×C4×C7C2×D412yes—
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2×D412yes—
192C22×C4×C7C2×D412yes—
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2×Q812yes—
195C22×C4×C7#4114yes—
196C22×Dic7—28no—
197C22×Dic7—28no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
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×Dic7—48no—
224C22×Dic7—48no—
225C22×Dic7—48no—
226C22×Dic7—44no—
227C22×Dic7—44no—
228C22×Dic7—44no—
229C22×Dic7—48no—
230C22×Dic7—44no—
231C22×Dic7C22×C414yes—
232C22×Dic7C22×C414yes—
233C22×Dic7#4114yes—
234C7×C4⋊C4—28no—
235C7×C22⋊C4—28no—
236C7×C22⋊C4—28no—
237C42×C7—28no—
238C22⋊Dic7—28no—
239C22⋊Dic7—48no—
240C22⋊Dic7—48no—
241C22⋊Dic7—44no—
242Dic7⋊C4—48no—
243C23×D4C2×D711yescharacteristic
244C24×C4—71no—
245C24×C4—71no—
246C24×C4C2×D711yescharacteristic
247C24×C4C2×D711yescharacteristic
248C2×C4×D4—24no—
249C2×C4×D4—24no—
250C2×C4×D4—24no—
251C22×C4⋊C4—72no—
252C22×C4⋊C4C2×D711yescharacteristic
253C22×C22⋊C4—71no—
254C22×C22⋊C4—72no—
255C22×C22⋊C4—71no—
256C22×C22⋊C4—72no—
257C22×C22⋊C4C2×D711yescharacteristic
258C22×C22⋊C4C2×D711yescharacteristic
259C22×C42C2×D711yescharacteristic
260#386—78no—
261#386—144no—
262#385—144no—
263C2×#95—72no—
264C2×#95—72no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—72no—
269C2×#95—72no—
270C2×#95—72no—
271C2×#95—72no—
272C2×#95—144no—
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×C7—22no—
290C23×C7—22no—
291C23×C7—24no—
292C23×C7—24no—
293C23×C7—22no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—24no—
300C23×C7—24no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—42no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7C2×C4⋊C414yes—
312C23×C7C2×C4⋊C414yes—
313C23×C7C4×D414yes—
314C23×C7C4×D414yes—
315C23×C7#12014yes—
316C23×C7C22⋊Q814yes—
317C23×C7C22⋊Q814yes—
318C23×C7#12314yes—
319C23×C7C23×C411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D411yescharacteristic
322C23×C7C22×D411yescharacteristic
323C23×C7C22×Q811yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C7H(5,𝔽2)12yes—
330C7×D4—232no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—24no—
347C2×C4×C7—24no—
348C2×C4×C7—416no—
349C2×C4×C7—416no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7C2×C4⋊C414yes—
359C2×C4×C7#12314yes—
360C2×Dic7—24no—
361C2×Dic7—24no—
362C2×Dic7—24no—
363C2×Dic7—24no—
364C2×Dic7—24no—
365C2×Dic7—24no—
366C2×Dic7—24no—
367C2×Dic7—24no—
368C2×Dic7—24no—
369C2×Dic7—416no—
370C2×Dic7—416no—
371C2×Dic7—42no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
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×Dic7—42no—
389C2×Dic7—42no—
390C25C22×D711yescharacteristic
391C25C22×D711yescharacteristic
392C22×D4—22no—
393C22×D4—22no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4Dic1414yes—
397C22×D4C4×D714yes—
398C22×D4C22⋊D714yes—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—24no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—72no—
409C23×C4—72no—
410C23×C4—72no—
411C23×C4—74no—
412C23×C4—72no—
413C23×C4—144no—
414C23×C4—142no—
415C23×C4—142no—
416C23×C4—142no—
417C23×C4—142no—
418C23×C4—142no—
419C23×C4—282no—
420C23×C4—282no—
421C23×C4—282no—
422C23×C4C22⋊D714yes—
423C23×C4C22×D711yescharacteristic
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C4×D4—232no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—144no—
433C2×C4⋊C4—144no—
434C2×C4⋊C4—282no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—74no—
441C2×C22⋊C4—78no—
442C2×C22⋊C4—142no—
443C2×C22⋊C4—142no—
444C2×C22⋊C4—144no—
445C2×C22⋊C4—142no—
446C2×C22⋊C4—142no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—142no—
449C2×C22⋊C4—282no—
450C2×C22⋊C4—282no—
451C2×C22⋊C4—282no—
452C2×C22⋊C4C22⋊D714yes—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456#95—78no—
457#95—144no—
458#95—144no—
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—28no—
476C22×C7—24no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—44no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—44no—
483C22×C7—44no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7#38518yes—
487C22×C7C22×C4⋊C411yescharacteristic
488C22×C7C2×C4×D411yescharacteristic
489C22×C7C2×C4×D411yescharacteristic
490C22×C7C4×#4112yes—
491C22×C7#51812yes—
492C22×C7C2×#12011yescharacteristic
493C22×C7C2×C22⋊Q811yescharacteristic
494C22×C7C2×C22⋊Q811yescharacteristic
495C22×C7C2×#12311yescharacteristic
496C22×C7C2×#12311yescharacteristic
497C22×C7#52511yescharacteristic
498C22×C7#52912yes—
499C22×C7#53411yescharacteristic
500C22×C7#53511yescharacteristic
501C22×C7#53812yes—
502C22×C7#54612yes—
503C22×C7#54612yes—
504C22×C7#54612yes—
505C22×C7#54612yes—
506C22×C7#55312yes—
507C22×C7#55312yes—
508C22×C7#55412yes—
509C22×C7#55412yes—
510C4×C7—24no—
511C4×C7—24no—
512C4×C7—42no—
513C4×C7—42no—
514C4×C7—42no—
515Dic7—44no—
516Dic7—44no—
517Dic7—44no—
518Dic7—82no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24C2×Dic1412yes—
532C24C2×Dic1412yes—
533C24C2×C4×D712yes—
534C24C2×C4×D712yes—
535C24#115712yes—
536C24#115712yes—
537C24C2×C22⋊D712yes—
538C24C2×C22⋊D712yes—
539C24C2×C22⋊D712yes—
540C24C2×C22⋊D712yes—
541C24C23×D711yescharacteristic
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4Dic7⋊C4116yescomplemented
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—28no—
571C22×C4—44no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—74no—
579C22×C4—74no—
580C22×C4—74no—
581C22×C4—148no—
582C22×C4—148no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—288no—
609C22×C4—288no—
610C22×C4—288no—
611C22×C4—284no—
612C22×C4—288no—
613C22×C4—284no—
614C22×C4—284no—
615C22×C4—284no—
616C22×C4C2×Dic1412yes—
617C22×C4C2×C4×D712yes—
618C22×C4#115914yes—
619C22×C4C2×C22⋊D712yes—
620C22×C4C2×C22⋊D712yes—
621C22×C4C2×C22⋊D712yes—
622C22×C4C2×C22⋊D712yes—
623C22×C4C2×C22⋊D712yes—
624C4⋊C4—28no—
625C4⋊C4—288no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—148no—
629C22⋊C4—288no—
630C22⋊C4—288no—
631C22⋊C4—284no—
632C42—28no—
633C2×C7—28no—
634C2×C7—44no—
635C2×C7C2×#38511yescharacteristic
636C2×C7C4×#12311yescharacteristic
637C2×C7#232111yescharacteristic
638C2×C7#234912yes—
639C2×C7#236412yes—
640C2×C7#240411yescharacteristic
641C2×C7#240511yescharacteristic
642C2×C7#244412yes—
643C2×C7#245012yes—
644C2×C7#248711yescharacteristic
645C2×C7#257911yescharacteristic
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23C2×Dic7⋊C414yes—
685C23C2×Dic7⋊C414yes—
686C23#648714yes—
687C23#648714yes—
688C23C4×C22⋊D714yes—
689C23C4×C22⋊D714yes—
690C23#649214yes—
691C23#651614yes—
692C23C22×Dic1411yescharacteristic
693C23C22×C4×D711yescharacteristic
694C23C2×#115711yescharacteristic
695C23C2×#115711yescharacteristic
696C23C2×#115912yes—
697C23#654812yes—
698C23D7×#4112yes—
699C23#655312yes—
700C23C22×C22⋊D711yescharacteristic
701C23C22×C22⋊D711yescharacteristic
702C23C22×C22⋊D711yescharacteristic
703D4—232no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—416no—
722C2×C4—416no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—144no—
732C2×C4—144no—
733C2×C4—144no—
734C2×C4—144no—
735C2×C4—144no—
736C2×C4—144no—
737C2×C4—144no—
738C2×C4—144no—
739C2×C4—144no—
740C2×C4—2816no—
741C2×C4—2816no—
742C2×C4—282no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4—282no—
748C2×C4—282no—
749C2×C4—282no—
750C2×C4—282no—
751C2×C4—282no—
752C2×C4—282no—
753C2×C4—282no—
754C2×C4—282no—
755C2×C4—282no—
756C2×C4—282no—
757C2×C4—282no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4—282no—
761C2×C4C2×Dic7⋊C414yes—
762C2×C4#649814yes—
763C7#1401611yescharacteristic, complemented, Sylow
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—28no—
769C22—28no—
770C22—28no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—28no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22#8998218yes—
786C22C4×#115912yes—
787C22#9022912yes—
788C22#9023012yes—
789C22#9023112yes—
790C22#9023412yes—
791C22#9023612yes—
792C22#9025112yes—
793C22#9025612yes—
794C22C22×Dic7⋊C411yescharacteristic
795C22C2×#648711yescharacteristic
796C22C2×#648711yescharacteristic
797C22C2×C4×C22⋊D711yescharacteristic
798C22C2×C4×C22⋊D711yescharacteristic
799C22C2×#649211yescharacteristic
800C22C2×#649811yescharacteristic
801C22#9049511yescharacteristic
802C22#9049712yes—
803C22#9049712yes—
804C22#9051911yescharacteristic
805C22#9052012yes—
806C22#9052012yes—
807C22#9052111yescharacteristic
808C22C2×#651611yescharacteristic
809C4—24no—
810C4—24no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—284no—
815C4—284no—
816C4—284no—
817C4—562no—
818C2—28no—
819C2—44no—
820C2C4×#649811yescharacteristic
821C2#1173977912yes—
822C2#1173978712yes—
823C2#1173980212yes—
824C2#1173980612yes—
825C2#1173981911yescharacteristic
826C2#1173983211yescharacteristic
827C2#1173984011yescharacteristic
828C2C2×#8998211yescharacteristic
829C2#1174149211yescharacteristic
830C2#1174154111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C4×C7×D4C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC22×C4×D4D7
hypocenterC7#14016
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
4. C22×C7⋊#95C2semidirect
5. C2×#89718C2semidirect
6. #11729881C2semidirect
7. #11729881C2semidirect
8. #11729321C2semidirect
9. #11729301C2semidirect
10. #11729298C2semidirect
11. #11729290C2semidirect
30. #89992C4semidirect
76. C23×Dic7C2×C4semidirect
104. C2×C22⋊Dic7C2×C4semidirect
105. C2×C22⋊Dic7C2×C4semidirect
117. C7⋊#95C2×C4semidirect
158. C2×C7×D4C4⋊C4semidirect
548. C2×D4Dic7⋊C4semidirect
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×C7×D42
C2×#899922
C22×C7⋊#952
C2×#897182
#117298812
#117293212
#117293012
#117292982
#117292902
#140167