Finite Group Databasebeta

← #13275747

Subgroups — #13275747

Order 1792.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C2×#89984C211yesmaximal, characteristic
4C2×#89723C212yesmaximal
5C2×#89707C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
7#11729300C212yesmaximal
8#11729289C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727166C212yesmaximal, complemented
11#11727161C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C22⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2212yes—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×C4⋊Dic7C2212yes—
22C22×C4⋊Dic7C2212yes—
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4×Dic7C2212yes—
26C4×C7×C22⋊C4C418yescomplemented
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
29#89984—24no—
30#89984—24no—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89723—28no—
39#89707—24no—
40C4×C4⋊Dic7—24no—
41#13876—71nomaximal, Sylow
42C25×C7C2311yescharacteristic
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7C2×C414yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×Dic7C2312yes—
57C23×Dic7C2312yes—
58C23×Dic7C2312yes—
59C23×Dic7C2312yes—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4—22no—
62C2×C7×C22⋊C4C2×C414yes—
63C2×C7×C22⋊C4C2×C414yes—
64C2×C7×C22⋊C4D414yes—
65C2×C7×C22⋊C4Q814yes—
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7—22no—
69C2×C42×C7—22no—
70C2×C42×C7C2×C414yes—
71C2×C42×C7C2×C414yes—
72C2×C22⋊Dic7—24no—
73C2×C22⋊Dic7—24no—
74C2×C22⋊Dic7—24no—
75C2×C22⋊Dic7—24no—
76C2×C22⋊Dic7—42no—
77C2×C22⋊Dic7—42no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—24no—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—24no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—24no—
91C2×C4⋊Dic7—24no—
92C2×C4⋊Dic7—42no—
93C2×C4⋊Dic7—42no—
94C2×C4⋊Dic7D414yes—
95C2×C4⋊Dic7D414yes—
96C2×C4×Dic7—24no—
97C2×C4×Dic7—24no—
98C2×C4×Dic7—42no—
99C7×#95C2×C414yes—
100C7×#95C2×C414yes—
101C7⋊#95—24no—
102C7⋊#95—24no—
103C7⋊#95—24no—
104C7⋊#95—24no—
105C7⋊#95—24no—
106C7⋊#95—24no—
107C7⋊#95—42no—
108C2×#388—72no—
109C2×#384—71no—
110C2×#380—71no—
111C2×#380—71no—
112C2×C4×C4⋊C4—71no—
113C2×C4×C22⋊C4D711yescharacteristic
114#1442—72no—
115#1439—72no—
116#1436—72no—
117C4⋊#95—71no—
118C4⋊#95—71no—
119C24×C7—21no—
120C24×C7—21no—
121C24×C7—21no—
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—21no—
131C24×C7C22×C412yes—
132C24×C7C2×D412yes—
133C24×C7C2×Q812yes—
134C24×C7C2411yescharacteristic
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
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—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—28no—
160C22×C4×C7—28no—
161C22×C4×C7—28no—
162C22×C4×C7—44no—
163C22×C4×C7—44no—
164C22×C4×C7—44no—
165C22×C4×C7—44no—
166C22×C4×C7C22×C412yes—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C22×C412yes—
170C22×C4×C7C22×C412yes—
171C22×C4×C7C22×C412yes—
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2×D412yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7C2×D412yes—
176C22×C4×C7C2×Q812yes—
177C22×C4×C7C2×Q812yes—
178C22×C4×C7#4112yes—
179C22×C4×C7#4112yes—
180C22×C4×C7#4112yes—
181C22×C4×C7#4112yes—
182C22×C4×C7#4112yes—
183C22×C4×C7#4112yes—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
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×Dic7C2×D414yes—
211C22×Dic7C2×D414yes—
212C7×C22⋊C4—28no—
213C7×C22⋊C4C4⋊C4116yescomplemented
214C42×C7—28no—
215C42×C7—28no—
216C22⋊Dic7—48no—
217C22⋊Dic7—48no—
218C4⋊Dic7—28no—
219C4⋊Dic7—28no—
220C4⋊Dic7—48no—
221C4⋊Dic7—48no—
222C4⋊Dic7—44no—
223C4⋊Dic7—44no—
224C4×Dic7—48no—
225C24×C4C2×D711yescharacteristic
226C22×C4⋊C4—71no—
227C22×C4⋊C4—71no—
228C22×C4⋊C4—71no—
229C22×C4⋊C4—71no—
230C22×C4⋊C4—72no—
231C22×C4⋊C4—72no—
232C22×C22⋊C4—72no—
233C22×C22⋊C4—72no—
234C22×C22⋊C4C2×D711yescharacteristic
235C22×C22⋊C4C2×D711yescharacteristic
236C22×C42—72no—
237C22×C42C2×D711yescharacteristic
238C22×C42C2×D711yescharacteristic
239#388—148no—
240#384—144no—
241#380—144no—
242#380—144no—
243C4×C4⋊C4—144no—
244C4×C22⋊C4Dic718yescomplemented
245C2×#95—72no—
246C2×#95—72no—
247C2×#95—72no—
248C2×#95—72no—
249C2×#95—72no—
250C2×#95—72no—
251C2×#95—72no—
252C2×#95C2×D711yescharacteristic
253C2×#95C2×D711yescharacteristic
254C23×C7—22no—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—22no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7C2×C4⋊C414yes—
289C23×C7C23×C411yescharacteristic
290C23×C7C22×D411yescharacteristic
291C23×C7C22×D411yescharacteristic
292C23×C7C22×D411yescharacteristic
293C23×C7C22×Q811yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7C2×#4111yescharacteristic
296C23×C7C2×#4111yescharacteristic
297C23×C7C2×#4111yescharacteristic
298C23×C7C2×#4111yescharacteristic
299C23×C7C2×#4111yescharacteristic
300C23×C7H(5,𝔽2)11yescharacteristic
301C23×C7H(5,𝔽2)11yescharacteristic
302C23×C72−1+411yescharacteristic
303C23×C72−1+411yescharacteristic
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
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—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—416no—
337C2×C4×C7C2×C4⋊C414yes—
338C2×C4×C7C2×C4⋊C414yes—
339C2×C4×C7#11714yes—
340C2×C4×C7#11714yes—
341C2×C4×C7C4×D414yes—
342C2×C4×C7C4×D414yes—
343C2×C4×C7#12114yes—
344C2×C4×C7#12314yes—
345C2×C4×C7#12414yes—
346C2×C4×C7#12614yes—
347C2×Dic7—24no—
348C2×Dic7—24no—
349C2×Dic7—24no—
350C2×Dic7—24no—
351C2×Dic7—24no—
352C2×Dic7—24no—
353C2×Dic7—42no—
354C2×Dic7—42no—
355C2×Dic7—42no—
356C2×Dic7—42no—
357C2×Dic7—42no—
358C2×Dic7—42no—
359C2×Dic7—42no—
360C2×Dic7—42no—
361C2×Dic7—42no—
362C2×Dic7—42no—
363C2×Dic7—42no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C25C22×D711yescharacteristic
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—72no—
383C23×C4—72no—
384C23×C4—72no—
385C23×C4—72no—
386C23×C4C2×Dic714yes—
387C23×C4C22×D711yescharacteristic
388C23×C4C22×D711yescharacteristic
389C23×C4C22×D711yescharacteristic
390C23×C4C22×D711yescharacteristic
391C23×C4C22×D711yescharacteristic
392C23×C4C22×D711yescharacteristic
393C2×C4⋊C4—74no—
394C2×C4⋊C4—74no—
395C2×C4⋊C4—142no—
396C2×C4⋊C4—142no—
397C2×C4⋊C4—142no—
398C2×C4⋊C4—142no—
399C2×C4⋊C4—144no—
400C2×C4⋊C4—144no—
401C2×C4⋊C4—144no—
402C2×C4⋊C4—144no—
403C2×C4⋊C4—142no—
404C2×C4⋊C4—142no—
405C2×C4⋊C4—142no—
406C2×C4⋊C4—142no—
407C2×C4⋊C4—142no—
408C2×C4⋊C4—142no—
409C2×C4⋊C4—282no—
410C2×C4⋊C4—282no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—144no—
414C2×C22⋊C4—144no—
415C2×C22⋊C4—144no—
416C2×C22⋊C4—144no—
417C2×C22⋊C4—282no—
418C2×C22⋊C4—282no—
419C2×C22⋊C4Dic1414yes—
420C2×C22⋊C4D2814yes—
421C2×C22⋊C4C2×Dic714yes—
422C2×C22⋊C4C2×Dic714yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—144no—
428C2×C42—144no—
429C2×C42—282no—
430C2×C42C2×Dic714yes—
431C2×C42C2×Dic714yes—
432#95—144no—
433#95—144no—
434#95—144no—
435#95—144no—
436#95—144no—
437#95—144no—
438#95—282no—
439#95C2×Dic714yes—
440#95C2×Dic714yes—
441C22×C7—24no—
442C22×C7—24no—
443C22×C7—24no—
444C22×C7—42no—
445C22×C7—42no—
446C22×C7—42no—
447C22×C7—42no—
448C22×C7—42no—
449C22×C7—42no—
450C22×C7—42no—
451C22×C7—42no—
452C22×C7—42no—
453C22×C7—42no—
454C22×C7—42no—
455C22×C7—42no—
456C22×C7C22×C4⋊C411yescharacteristic
457C22×C7C2×#11711yescharacteristic
458C22×C7C2×#11711yescharacteristic
459C22×C7C2×C4×D411yescharacteristic
460C22×C7C2×C4×D411yescharacteristic
461C22×C7#52011yescharacteristic
462C22×C7#52011yescharacteristic
463C22×C7C2×#12111yescharacteristic
464C22×C7C2×#12311yescharacteristic
465C22×C7C2×#12411yescharacteristic
466C22×C7C2×#12611yescharacteristic
467C22×C7#53211yescharacteristic
468C22×C7#53211yescharacteristic
469C22×C7#53311yescharacteristic
470C22×C7#53311yescharacteristic
471C22×C7#54011yescharacteristic
472C22×C7#54111yescharacteristic
473C22×C7#54211yescharacteristic
474C22×C7#54211yescharacteristic
475C22×C7D4211yescharacteristic
476C22×C7D4211yescharacteristic
477C22×C7#54611yescharacteristic
478C22×C7#54711yescharacteristic
479C22×C7#54711yescharacteristic
480C22×C7#54711yescharacteristic
481C22×C7#54811yescharacteristic
482C22×C7D4×Q811yescharacteristic
483C22×C7D4×Q811yescharacteristic
484C22×C7#55011yescharacteristic
485C22×C7#55211yescharacteristic
486C22×C7#55311yescharacteristic
487C22×C7#55411yescharacteristic
488C22×C7#55411yescharacteristic
489C22×C7#55511yescharacteristic
490C22×C7#55611yescharacteristic
491C4×C7—24no—
492C4×C7—24no—
493C4×C7—24no—
494C4×C7—42no—
495C4×C7—42no—
496C4×C7#38818yescomplemented
497Dic7—44no—
498Dic7—44no—
499Dic7—82no—
500Dic7—82no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24C2×Dic1412yes—
514C24C2×D2812yes—
515C24C22×Dic712yes—
516C24C23×D711yescharacteristic
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—74no—
549C22×C4—74no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4C2×Dic1412yes—
577C22×C4C2×Dic1412yes—
578C22×C4C2×D2812yes—
579C22×C4C2×D2812yes—
580C22×C4#115712yes—
581C22×C4#115712yes—
582C22×C4#115712yes—
583C22×C4#115712yes—
584C22×C4D4×D712yes—
585C22×C4D4×D712yes—
586C22×C4#115912yes—
587C22×C4#115912yes—
588C22×C4C22×Dic712yes—
589C22×C4C22×Dic712yes—
590C22×C4C22×Dic712yes—
591C22×C4C22×Dic712yes—
592C22×C4C22×Dic712yes—
593C22×C4C22×Dic712yes—
594C4⋊C4—148no—
595C4⋊C4—148no—
596C4⋊C4—288no—
597C4⋊C4—288no—
598C4⋊C4—284no—
599C4⋊C4—284no—
600C22⋊C4—28no—
601C22⋊C4—288no—
602C22⋊C4—288no—
603C22⋊C4C4⋊Dic7116yescomplemented
604C42—28no—
605C42—28no—
606C42—288no—
607C2×C7—44no—
608C2×C7#228511yescharacteristic
609C2×C7C2×#38811yescharacteristic
610C2×C7#231411yescharacteristic
611C2×C7D4×C4⋊C411yescharacteristic
612C2×C7D4×C4⋊C411yescharacteristic
613C2×C7#235211yescharacteristic
614C2×C7#235411yescharacteristic
615C2×C7#242211yescharacteristic
616C2×C7#242311yescharacteristic
617C2×C7#242811yescharacteristic
618C2×C7#242911yescharacteristic
619C2×C7#249111yescharacteristic
620C2×C7#249211yescharacteristic
621C2×C7#249611yescharacteristic
622C2×C7#249711yescharacteristic
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23C2×C4⋊Dic714yes—
658C23C22×Dic1411yescharacteristic
659C23C22×D2811yescharacteristic
660C23C2×#115711yescharacteristic
661C23C2×#115711yescharacteristic
662C23C2×#115711yescharacteristic
663C23C2×#115711yescharacteristic
664C23C2×D4×D711yescharacteristic
665C23C2×D4×D711yescharacteristic
666C23C2×#115911yescharacteristic
667C23C2×#115911yescharacteristic
668C23#655311yescharacteristic
669C23#655311yescharacteristic
670C23#655411yescharacteristic
671C23#655411yescharacteristic
672C23C23×Dic711yescharacteristic
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—416no—
706C2×C4—144no—
707C2×C4—144no—
708C2×C4—144no—
709C2×C4—144no—
710C2×C4—144no—
711C2×C4—144no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4—282no—
719C2×C4—282no—
720C2×C4—282no—
721C2×C4—282no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—282no—
728C2×C4—282no—
729C2×C4—282no—
730C2×C4—282no—
731C2×C4—282no—
732C2×C4—282no—
733C2×C4—282no—
734C2×C4#644214yes—
735C2×C4#644614yes—
736C2×C4#644714yes—
737C2×C4#644814yes—
738C2×C4C2×C4⋊Dic714yes—
739C2×C4C2×C4⋊Dic714yes—
740C2×C4#648914yes—
741C2×C4#648914yes—
742C2×C4D4×Dic714yes—
743C2×C4D4×Dic714yes—
744C7#1387611yescharacteristic, complemented, Sylow
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22#9016111yescharacteristic
761C22#9016111yescharacteristic
762C22#9016811yescharacteristic
763C22#9016811yescharacteristic
764C22C2×#644211yescharacteristic
765C22C2×#644611yescharacteristic
766C22C2×#644711yescharacteristic
767C22C2×#644811yescharacteristic
768C22#9020911yescharacteristic
769C22#9022511yescharacteristic
770C22#9022511yescharacteristic
771C22#9022611yescharacteristic
772C22D4×Dic1411yescharacteristic
773C22D4×Dic1411yescharacteristic
774C22#9023211yescharacteristic
775C22#9023311yescharacteristic
776C22#9023411yescharacteristic
777C22#9023411yescharacteristic
778C22D4×D2811yescharacteristic
779C22D4×D2811yescharacteristic
780C22#9024111yescharacteristic
781C22#9024211yescharacteristic
782C22#9024311yescharacteristic
783C22#9024411yescharacteristic
784C22#9024611yescharacteristic
785C22#9024611yescharacteristic
786C22#9025411yescharacteristic
787C22#9025611yescharacteristic
788C22C22×C4⋊Dic711yescharacteristic
789C22C2×#648911yescharacteristic
790C22C2×#648911yescharacteristic
791C22C2×D4×Dic711yescharacteristic
792C22C2×D4×Dic711yescharacteristic
793C22#9051811yescharacteristic
794C22#9051811yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—284no—
801C4—284no—
802C4—562no—
803C4—562no—
804C4#8972318yescomplemented
805C2—44no—
806C2#1173092911yescharacteristic
807C2#1173093211yescharacteristic
808C2#1173093311yescharacteristic
809C2#1173095211yescharacteristic
810C2#1173095311yescharacteristic
811C2#1173095711yescharacteristic
812C2#1173095811yescharacteristic
813C2#1173103011yescharacteristic
814C2#1173950711yescharacteristic
815C2C2×#8972311yescharacteristic
816C2#1173967611yescharacteristic
817C2D4×C4⋊Dic711yescharacteristic
818C2D4×C4⋊Dic711yescharacteristic
819C2#1173978011yescharacteristic
820C2#1173978211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#13876
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C2×#89707C2semidirect
6. C2×C4×C4⋊Dic7C2semidirect
8. #11729289C2semidirect
9. #11729289C2semidirect
10. #11727166C2semidirect
11. #11727161C2semidirect
26. C4×C7×C22⋊C4C4semidirect
213. C7×C22⋊C4C4⋊C4semidirect
244. C4×C22⋊C4Dic7semidirect
496. C4×C7#388semidirect
603. C22⋊C4C4⋊Dic7semidirect
744. C7#13876semidirect
804. C4#89723semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#899842
C2×#897232
C2×#897072
C2×C4×C4⋊Dic72
#117293002
#117292892
#117271662
#117271612
#138767