Finite Group Databasebeta

← #13276129

Subgroups — #13276129

Order 1792.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic7C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic
3C2×#89993C211yesmaximal, characteristic
4C2×#89715C212yesmaximal, complemented
5#11729317C211yesmaximal, characteristic, complemented
6#11729317C211yesmaximal, characteristic, complemented
7#11729303C212yesmaximal, complemented
8#11729303C212yesmaximal, complemented
9#11729298C212yesmaximal, complemented
10#11729289C211yesmaximal, characteristic, complemented
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×Dic7C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C7×C22⋊C4C2212yes—
17C22×C42×C7C2211yescharacteristic
18C22×C22⋊Dic7C2212yes—
19C22×C22⋊Dic7C2212yes—
20C22×C22⋊Dic7C2212yes—
21C2×D4×Dic7—24no—
22C2×D4×Dic7—24no—
23C2×D4×Dic7C418yescomplemented
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C7×#390—24no—
29#89993—24no—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2211yescharacteristic
40#89715—28no—
41#13916—71nomaximal, Sylow
42C25×C7C2312yes—
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4C2×C414yes—
48C22×C7×D4D414yes—
49C22×C7×D4D414yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×Dic7—24no—
55C23×Dic7—24no—
56C23×Dic7—24no—
57C23×Dic7—24no—
58C23×Dic7—42no—
59C23×Dic7—42no—
60C23×Dic7C2×C418yes—
61C23×Dic7C2312yes—
62C23×Dic7C2311yescharacteristic
63C23×Dic7C2312yes—
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C22⋊C4—24no—
71C2×C7×C22⋊C4—24no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—42no—
75C2×C7×C22⋊C4—42no—
76C2×C42×C7—22no—
77C2×C42×C7—22no—
78C2×C42×C7—22no—
79C2×C22⋊Dic7—24no—
80C2×C22⋊Dic7—24no—
81C2×C22⋊Dic7—24no—
82C2×C22⋊Dic7—24no—
83C2×C22⋊Dic7—24no—
84C2×C22⋊Dic7—24no—
85C2×C22⋊Dic7—42no—
86C2×C22⋊Dic7—42no—
87C2×C22⋊Dic7C2×C418yes—
88D4×Dic7—232no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7C2×C414yes—
95C2×C4×Dic7—22no—
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—22no—
100C2×C4×Dic7C2×C414yes—
101C7⋊#95—24no—
102C7⋊#95—22no—
103C7⋊#95—24no—
104C7⋊#95—24no—
105C7⋊#95—22no—
106C7⋊#95—22no—
107C7⋊#95—42no—
108C7⋊#95—42no—
109C7⋊#95—42no—
110C7⋊#95D414yescomplemented
111C22×C4×D4—71no—
112C2×#390—71no—
113C2×#390D711yescharacteristic
114C2×#381—72no—
115#1440—72no—
116#1440—72no—
117C4⋊#95—71no—
118C4⋊#95—71no—
119C4⋊#95—71no—
120C22⋊#95—72no—
121C4×#95—71no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7C22×C414yes—
135C24×C7C2×D414yes—
136C24×C7C2×D414yes—
137C24×C7C2411yescharacteristic
138C2×C7×D4—28no—
139C2×C7×D4—28no—
140C2×C7×D4—28no—
141C2×C7×D4—28no—
142C2×C7×D4—28no—
143C2×C7×D4—28no—
144C2×C7×D4C22⋊C4116yes—
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—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7C22×C412yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7#4112yes—
169C22×C4×C7#4112yes—
170C22×C4×C7#4112yes—
171C22×C4×C7#4112yes—
172C22×C4×C7#4112yes—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—216no—
178C22×Dic7—22no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—22no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—216no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—48no—
211C22×Dic7—48no—
212C22×Dic7—48no—
213C22×Dic7—48no—
214C22×Dic7—48no—
215C22×Dic7C22×C412yes—
216C22×Dic7C22×C414yes—
217C22×Dic7C22×C412yes—
218C22×Dic7C2×D412yes—
219C22×Dic7C2×D412yes—
220C22×Dic7#4112yes—
221C22×Dic7#4112yes—
222C7×C4⋊C4—44no—
223C7×C22⋊C4—48no—
224C7×C22⋊C4—48no—
225C42×C7—44no—
226C22⋊Dic7—216no—
227C22⋊Dic7—48no—
228C22⋊Dic7—48no—
229C4⋊Dic7—28no—
230C4⋊Dic7—44no—
231C4×Dic7—28no—
232C4×Dic7—44no—
233C23×D4C2×D711yescharacteristic
234C24×C4—72no—
235C2×C4×D4—78no—
236C2×C4×D4—144no—
237C2×C4×D4—144no—
238C22×C4⋊C4—71no—
239C22×C4⋊C4—71no—
240C22×C4⋊C4C2×D711yescharacteristic
241C22×C22⋊C4—72no—
242C22×C22⋊C4—72no—
243C22×C22⋊C4—72no—
244C22×C22⋊C4C2×D712yes—
245C22×C22⋊C4C2×D712yes—
246C22×C42—71no—
247C22×C42—71no—
248C22×C42C2×D711yescharacteristic
249#390—24no—
250#390—144no—
251#381—148no—
252C2×#95—71no—
253C2×#95—71no—
254C2×#95—71no—
255C2×#95—71no—
256C2×#95—72no—
257C2×#95—72no—
258C2×#95—72no—
259C2×#95—72no—
260C2×#95—72no—
261C2×#95—72no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—24no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—24no—
271C23×C7—24no—
272C23×C7—24no—
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—24no—
276C23×C7—24no—
277C23×C7—24no—
278C23×C7—24no—
279C23×C7—24no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7—42no—
283C23×C7—42no—
284C23×C7—42no—
285C23×C7—42no—
286C23×C7—42no—
287C23×C7—42no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7C2×C22⋊C418yes—
297C23×C7C23×C411yescharacteristic
298C23×C7C22×D411yescharacteristic
299C23×C7C22×D411yescharacteristic
300C23×C7C22×D411yescharacteristic
301C23×C7C2×#4111yescharacteristic
302C23×C7C2×#4111yescharacteristic
303C23×C7C2×#4111yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C23×C7C2×#4111yescharacteristic
306C23×C7C2×#4111yescharacteristic
307C23×C7C2×#4111yescharacteristic
308C23×C7H(5,𝔽2)11yescharacteristic
309C23×C7H(5,𝔽2)11yescharacteristic
310C23×C7H(5,𝔽2)11yescharacteristic
311C23×C72−1+411yescharacteristic
312C7×D4—232no—
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—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7C2×C22⋊C414yes—
335C2×C4×C7#11714yes—
336C2×C4×C7#11714yes—
337C2×C4×C7#12314yes—
338C2×C4×C7#12314yes—
339C2×C4×C7#12314yes—
340C2×C4×C7#12314yes—
341C2×Dic7—22no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—22no—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—24no—
349C2×Dic7—24no—
350C2×Dic7—22no—
351C2×Dic7—24no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—432no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—42no—
365C2×Dic7—42no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—42no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7—42no—
381C2×Dic7—42no—
382C2×Dic7—42no—
383C2×Dic7C4×D414yes—
384C25C22×D712yes—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4C4×D714yes—
390C22×D4D2814yes—
391C22×D4C22⋊D714yes—
392C23×C4—71no—
393C23×C4—71no—
394C23×C4—71no—
395C23×C4—71no—
396C23×C4—72no—
397C23×C4—78no—
398C23×C4—72no—
399C23×C4—144no—
400C23×C4—144no—
401C23×C4—144no—
402C23×C4—144no—
403C23×C4—282no—
404C23×C4—282no—
405C23×C4C22×D712yes—
406C23×C4C22×D711yescharacteristic
407C23×C4C22×D711yescharacteristic
408C23×C4C22×D711yescharacteristic
409C4×D4—1432no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—74no—
414C2×C4⋊C4—142no—
415C2×C4⋊C4—142no—
416C2×C4⋊C4—142no—
417C2×C4⋊C4—142no—
418C2×C4⋊C4—142no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—78no—
426C2×C22⋊C4—144no—
427C2×C22⋊C4—144no—
428C2×C22⋊C4—144no—
429C2×C22⋊C4—144no—
430C2×C22⋊C4—144no—
431C2×C22⋊C4—144no—
432C2×C22⋊C4—282no—
433C2×C22⋊C4—282no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—74no—
438C2×C42—142no—
439C2×C42—142no—
440C2×C42—142no—
441C2×C42—142no—
442C2×C42—142no—
443#95—74no—
444#95—142no—
445#95—142no—
446#95—144no—
447#95—144no—
448#95—144no—
449#95—142no—
450#95—282no—
451#95—282no—
452#95—282no—
453C22×C7—28no—
454C22×C7—28no—
455C22×C7—28no—
456C22×C7—44no—
457C22×C7—44no—
458C22×C7—44no—
459C22×C7—44no—
460C22×C7—44no—
461C22×C7—44no—
462C22×C7—44no—
463C22×C7—44no—
464C22×C7—44no—
465C22×C7—44no—
466C22×C7—44no—
467C22×C7—44no—
468C22×C7C22×C22⋊C411yescharacteristic
469C22×C7C2×#11711yescharacteristic
470C22×C7C2×#11711yescharacteristic
471C22×C7C2×C4×D411yescharacteristic
472C22×C7C4×#4111yescharacteristic
473C22×C7#51811yescharacteristic
474C22×C7#52011yescharacteristic
475C22×C7C2×#12311yescharacteristic
476C22×C7C2×#12311yescharacteristic
477C22×C7C2×#12311yescharacteristic
478C22×C7C2×#12311yescharacteristic
479C22×C7#52911yescharacteristic
480C22×C7#52911yescharacteristic
481C22×C7#53211yescharacteristic
482C22×C7#53211yescharacteristic
483C22×C7#54011yescharacteristic
484C22×C7#54011yescharacteristic
485C22×C7#54211yescharacteristic
486C22×C7#54211yescharacteristic
487C22×C7D4211yescharacteristic
488C22×C7D4211yescharacteristic
489C22×C7#54611yescharacteristic
490C22×C7#54611yescharacteristic
491C22×C7#54611yescharacteristic
492C22×C7#54611yescharacteristic
493C22×C7#54711yescharacteristic
494C22×C7#54711yescharacteristic
495C22×C7#54711yescharacteristic
496C22×C7#55011yescharacteristic
497C22×C7#55311yescharacteristic
498C22×C7#55311yescharacteristic
499C22×C7#55511yescharacteristic
500C22×C7#55611yescharacteristic
501C22×C7#55911yescharacteristic
502C22×C7#55911yescharacteristic
503C4×C7—42no—
504C4×C7—42no—
505C4×C7—82no—
506C4×C7#38118yescomplemented
507Dic7—24no—
508Dic7—44no—
509Dic7—42no—
510Dic7—42no—
511Dic7—42no—
512Dic7—82no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24C2×C4×D714yes—
526C24C2×D2814yes—
527C24C2×C22⋊D714yes—
528C24C23×D711yescharacteristic
529C2×D4—28no—
530C2×D4—28no—
531C2×D4—28no—
532C2×D4—28no—
533C2×D4—28no—
534C2×D4—28no—
535C2×D4(C2×D7)⋊C4116yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—72no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—74no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—1416no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—1416no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—142no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
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—288no—
600C22×C4—288no—
601C22×C4—288no—
602C22×C4—288no—
603C22×C4—288no—
604C22×C4C2×C4×D712yes—
605C22×C4C2×D2812yes—
606C22×C4D4×D712yes—
607C22×C4#115912yes—
608C22×C4#115912yes—
609C22×C4#115912yes—
610C22×C4#115912yes—
611C22×C4#115912yes—
612C22×C4C2×C22⋊D712yes—
613C4⋊C4—44no—
614C4⋊C4—148no—
615C4⋊C4—284no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—1416no—
619C22⋊C4—288no—
620C22⋊C4—288no—
621C42—44no—
622C42—148no—
623C42—284no—
624C2×C7—48no—
625C2×C7C2×#38111yescharacteristic
626C2×C7#229311yescharacteristic
627C2×C7#231911yescharacteristic
628C2×C7D4×C22⋊C411yescharacteristic
629C2×C7#233911yescharacteristic
630C2×C7#235411yescharacteristic
631C2×C7#235711yescharacteristic
632C2×C7#242011yescharacteristic
633C2×C7#242011yescharacteristic
634C2×C7#242211yescharacteristic
635C2×C7#242211yescharacteristic
636C2×C7#244511yescharacteristic
637C2×C7#244511yescharacteristic
638C2×C7#244711yescharacteristic
639C2×C7#244711yescharacteristic
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
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—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23C2×(C2×D7)⋊C418yes—
675C23C22×C4×D711yescharacteristic
676C23C22×D2811yescharacteristic
677C23C2×D4×D711yescharacteristic
678C23C2×#115911yescharacteristic
679C23C2×#115911yescharacteristic
680C23C2×#115911yescharacteristic
681C23C2×#115911yescharacteristic
682C23C2×#115911yescharacteristic
683C23#654811yescharacteristic
684C23#654811yescharacteristic
685C23D7×#4111yescharacteristic
686C23D7×#4111yescharacteristic
687C23#655311yescharacteristic
688C23#655411yescharacteristic
689C23C22×C22⋊D711yescharacteristic
690D4—232no—
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—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—74no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—144no—
723C2×C4—142no—
724C2×C4—144no—
725C2×C4—144no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—2832no—
732C2×C4—281no—
733C2×C4—281no—
734C2×C4—281no—
735C2×C4—281no—
736C2×C4—282no—
737C2×C4—282no—
738C2×C4—281no—
739C2×C4—281no—
740C2×C4—281no—
741C2×C4—282no—
742C2×C4—281no—
743C2×C4—281no—
744C2×C4—281no—
745C2×C4—282no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4—282no—
749C2×C4—282no—
750C2×C4—282no—
751C2×C4—282no—
752C2×C4—282no—
753C2×C4—282no—
754C2×C4—282no—
755C2×C4#644014yes—
756C2×C4#644014yes—
757C2×C4#644914yes—
758C2×C4#644914yes—
759C2×C4C2×(C2×D7)⋊C414yes—
760C2×C4#649814yes—
761C2×C4#649814yes—
762C7#1391611yescharacteristic, complemented, Sylow
763C22—28no—
764C22—28no—
765C22—28no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22C2×#644011yescharacteristic
779C22C2×#644011yescharacteristic
780C22C2×#644911yescharacteristic
781C22C2×#644911yescharacteristic
782C22C4×#115911yescharacteristic
783C22C4×D4×D711yescharacteristic
784C22#9023611yescharacteristic
785C22#9023711yescharacteristic
786C22D4×D2811yescharacteristic
787C22#9024511yescharacteristic
788C22#9024511yescharacteristic
789C22#9024611yescharacteristic
790C22#9028711yescharacteristic
791C22#9029111yescharacteristic
792C22#9029411yescharacteristic
793C22#9030211yescharacteristic
794C22#9030511yescharacteristic
795C22#9030711yescharacteristic
796C22#9030911yescharacteristic
797C22#9031011yescharacteristic
798C22#9036211yescharacteristic
799C22#9037111yescharacteristic
800C22#9037211yescharacteristic
801C22#9037311yescharacteristic
802C22#9040411yescharacteristic
803C22#9040711yescharacteristic
804C22#9040911yescharacteristic
805C22#9041011yescharacteristic
806C22C22×(C2×D7)⋊C411yescharacteristic
807C22C2×#649811yescharacteristic
808C22C2×#649811yescharacteristic
809C22D4×C22⋊D711yescharacteristic
810C22#9049711yescharacteristic
811C22#9051511yescharacteristic
812C22#9052011yescharacteristic
813C4—42no—
814C4—42no—
815C4—82no—
816C4—144no—
817C4—282no—
818C4—282no—
819C4—282no—
820C4—284no—
821C4—562no—
822C4#8971518yescomplemented
823C2—48no—
824C2#1173373411yescharacteristic
825C2#1173374011yescharacteristic
826C2#1173374711yescharacteristic
827C2#1173374811yescharacteristic
828C2#1173376211yescharacteristic
829C2#1173376411yescharacteristic
830C2#1173388511yescharacteristic
831C2#1173388611yescharacteristic
832C2C2×#8971511yescharacteristic
833C2#1173977511yescharacteristic
834C2D4×(C2×D7)⋊C411yescharacteristic
835C2#1174008811yescharacteristic
836C2#1174008911yescharacteristic
837C2#1174040711yescharacteristic
838C2#1174062111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#390C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#390D7
hypocenterC7#13916
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#89715C2semidirect
5. #11729317C2semidirect
6. #11729317C2semidirect
7. #11729303C2semidirect
8. #11729303C2semidirect
9. #11729298C2semidirect
10. #11729289C2semidirect
11. C4×C7⋊#95C2semidirect
23. C2×D4×Dic7C4semidirect
110. C7⋊#95D4semidirect
506. C4×C7#381semidirect
762. C7#13916semidirect
822. C4#89715semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic72
C2×C7×#3902
C2×#899932
C2×#897152
#117293172
#117293032
#117292982
#117292892
C4×C7⋊#952
#139167