Finite Group Databasebeta

← #13276167

Subgroups — #13276167

Order 1792.

2458 conjugacy classes of subgroups.

The subgroup lattice has 856 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×#89745C211yesmaximal, characteristic, complemented
5C2×#89714C212yesmaximal, complemented
6C2×#89700C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729301C212yesmaximal, complemented
9#11729301C212yesmaximal, complemented
10#11729298C212yesmaximal, 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×Dic7⋊C4C2212yes—
27C22×Dic7⋊C4C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C7×#390—24no—
31#89993—24no—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2211yescharacteristic
40#89745—24no—
41#89714—28no—
42#89700—24no—
43#13920—71nomaximal, Sylow
44C25×C7C2312yes—
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×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×Dic7—24no—
57C23×Dic7—24no—
58C23×Dic7—24no—
59C23×Dic7—24no—
60C23×Dic7—42no—
61C23×Dic7—42no—
62C23×Dic7C2×C418yes—
63C23×Dic7C2312yes—
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2312yes—
68C23×Dic7C2311yescharacteristic
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—42no—
77C2×C7×C22⋊C4—42no—
78C2×C42×C7—22no—
79C2×C42×C7—22no—
80C2×C42×C7—22no—
81C2×C22⋊Dic7—24no—
82C2×C22⋊Dic7—24no—
83C2×C22⋊Dic7—24no—
84C2×C22⋊Dic7—24no—
85C2×C22⋊Dic7—24no—
86C2×C22⋊Dic7—24no—
87C2×C22⋊Dic7—42no—
88C2×C22⋊Dic7—42no—
89C2×C22⋊Dic7C2×C418yes—
90D4×Dic7—232no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7C2×C414yes—
95C2×C4⋊Dic7D414yes—
96C2×C4⋊Dic7D414yes—
97C2×Dic7⋊C4—24no—
98C2×Dic7⋊C4—24no—
99C2×Dic7⋊C4—24no—
100C2×Dic7⋊C4—24no—
101C2×Dic7⋊C4—42no—
102C2×Dic7⋊C4—42no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7C2×C414yes—
109C7⋊#95—22no—
110C7⋊#95—24no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—22no—
114C7⋊#95—22no—
115C7⋊#95—42no—
116C7⋊#95D414yescomplemented
117C22×C4×D4—71no—
118C2×#390—71no—
119C2×#390D711yescharacteristic
120C2×#389—71no—
121C2×#389—71no—
122C2×#380—72no—
123#1439—72no—
124#1439—72no—
125C4⋊#95—71no—
126C22⋊#95—72no—
127C4×#95—71no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—22no—
140C24×C7C22×C414yes—
141C24×C7C2×D414yes—
142C24×C7C2×Q814yes—
143C24×C7C2411yescharacteristic
144C2×C7×D4—28no—
145C2×C7×D4—28no—
146C2×C7×D4—28no—
147C2×C7×D4—28no—
148C2×C7×D4—28no—
149C2×C7×D4—28no—
150C2×C7×D4C4⋊C4116yescomplemented
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—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—22no—
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×C7C22×C412yes—
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—21no—
180C22×Dic7—21no—
181C22×Dic7—22no—
182C22×Dic7—22no—
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—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—216no—
206C22×Dic7—216no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—48no—
215C22×Dic7—48no—
216C22×Dic7—48no—
217C22×Dic7—48no—
218C22×Dic7—48no—
219C22×Dic7C22×C412yes—
220C22×Dic7C22×C414yes—
221C22×Dic7C22×C412yes—
222C22×Dic7C2×D412yes—
223C22×Dic7C2×D414yes—
224C22×Dic7C2×D414yes—
225C22×Dic7C2×D412yes—
226C22×Dic7#4112yes—
227C22×Dic7#4112yes—
228C7×C4⋊C4—44no—
229C7×C22⋊C4—48no—
230C7×C22⋊C4—48no—
231C42×C7—44no—
232C22⋊Dic7—216no—
233C22⋊Dic7—48no—
234C22⋊Dic7—48no—
235C4⋊Dic7—44no—
236C4⋊Dic7C22⋊C4116yescomplemented
237Dic7⋊C4—48no—
238Dic7⋊C4—48no—
239C4×Dic7—28no—
240C4×Dic7—44no—
241C23×D4C2×D711yescharacteristic
242C24×C4—72no—
243C2×C4×D4—78no—
244C2×C4×D4—144no—
245C2×C4×D4—144no—
246C22×C4⋊C4—71no—
247C22×C4⋊C4—71no—
248C22×C4⋊C4—72no—
249C22×C4⋊C4—72no—
250C22×C4⋊C4C2×D711yescharacteristic
251C22×C22⋊C4—72no—
252C22×C22⋊C4—72no—
253C22×C22⋊C4—72no—
254C22×C22⋊C4C2×D712yes—
255C22×C22⋊C4C2×D712yes—
256C22×C42—71no—
257C22×C42—71no—
258C22×C42C2×D711yescharacteristic
259#390—24no—
260#390—144no—
261#389—144no—
262#389—144no—
263#380—148no—
264C2×#95—71no—
265C2×#95—71no—
266C2×#95—71no—
267C2×#95—71no—
268C2×#95—72no—
269C2×#95—72no—
270C2×#95—72no—
271C2×#95—72no—
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—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—24no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7—42no—
297C23×C7—42no—
298C23×C7—42no—
299C23×C7—42no—
300C23×C7—42no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7C2×C4⋊C418yes—
307C23×C7C23×C411yescharacteristic
308C23×C7C22×D411yescharacteristic
309C23×C7C22×D411yescharacteristic
310C23×C7C22×D411yescharacteristic
311C23×C7C22×D411yescharacteristic
312C23×C7C22×Q811yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7H(5,𝔽2)11yescharacteristic
319C23×C7H(5,𝔽2)11yescharacteristic
320C23×C7H(5,𝔽2)11yescharacteristic
321C23×C72−1+411yescharacteristic
322C7×D4—232no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
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—41no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—42no—
344C2×C4×C7C2×C22⋊C414yes—
345C2×C4×C7C2×C4⋊C414yes—
346C2×C4×C7#11714yes—
347C2×C4×C7#12114yes—
348C2×C4×C7#12114yes—
349C2×C4×C7C22⋊Q814yes—
350C2×C4×C7C22⋊Q814yes—
351C2×Dic7—22no—
352C2×Dic7—24no—
353C2×Dic7—22no—
354C2×Dic7—24no—
355C2×Dic7—24no—
356C2×Dic7—24no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—24no—
362C2×Dic7—24no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—432no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7C2×C22⋊C418yes—
393C2×Dic7C4×D414yes—
394C25C22×D712yes—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—22no—
399C22×D4Dic1414yes—
400C22×D4C4×D714yes—
401C22×D4C22⋊D714yes—
402C23×C4—72no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—78no—
408C23×C4—72no—
409C23×C4—144no—
410C23×C4—144no—
411C23×C4—144no—
412C23×C4—144no—
413C23×C4—282no—
414C23×C4—282no—
415C23×C4C22×D712yes—
416C23×C4C22×D711yescharacteristic
417C23×C4C22×D711yescharacteristic
418C23×C4C22×D711yescharacteristic
419C4×D4—1432no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—74no—
424C2×C4⋊C4—74no—
425C2×C4⋊C4—74no—
426C2×C4⋊C4—144no—
427C2×C4⋊C4—144no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—144no—
430C2×C4⋊C4—142no—
431C2×C4⋊C4—142no—
432C2×C4⋊C4—142no—
433C2×C4⋊C4—282no—
434C2×C4⋊C4—282no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—78no—
442C2×C22⋊C4—144no—
443C2×C22⋊C4—144no—
444C2×C22⋊C4—144no—
445C2×C22⋊C4—144no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—282no—
449C2×C22⋊C4—282no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—74no—
454C2×C42—142no—
455C2×C42—142no—
456C2×C42—142no—
457C2×C42—142no—
458C2×C42—142no—
459#95—74no—
460#95—142no—
461#95—142no—
462#95—144no—
463#95—144no—
464#95—144no—
465#95—142no—
466#95—282no—
467C22×C7—28no—
468C22×C7—28no—
469C22×C7—28no—
470C22×C7—44no—
471C22×C7—44no—
472C22×C7—44no—
473C22×C7—44no—
474C22×C7—44no—
475C22×C7—44no—
476C22×C7—44no—
477C22×C7—44no—
478C22×C7—44no—
479C22×C7—44no—
480C22×C7—44no—
481C22×C7—44no—
482C22×C7C22×C22⋊C411yescharacteristic
483C22×C7C22×C4⋊C411yescharacteristic
484C22×C7C2×#11711yescharacteristic
485C22×C7C2×C4×D411yescharacteristic
486C22×C7C4×#4111yescharacteristic
487C22×C7#51811yescharacteristic
488C22×C7#52011yescharacteristic
489C22×C7C2×#12111yescharacteristic
490C22×C7C2×#12111yescharacteristic
491C22×C7C2×C22⋊Q811yescharacteristic
492C22×C7C2×C22⋊Q811yescharacteristic
493C22×C7#52911yescharacteristic
494C22×C7#52911yescharacteristic
495C22×C7#53211yescharacteristic
496C22×C7#53211yescharacteristic
497C22×C7#54011yescharacteristic
498C22×C7#54011yescharacteristic
499C22×C7#54211yescharacteristic
500C22×C7#54211yescharacteristic
501C22×C7D4211yescharacteristic
502C22×C7D4211yescharacteristic
503C22×C7D4211yescharacteristic
504C22×C7#54611yescharacteristic
505C22×C7#54611yescharacteristic
506C22×C7#54611yescharacteristic
507C22×C7#54611yescharacteristic
508C22×C7#54711yescharacteristic
509C22×C7#54811yescharacteristic
510C22×C7#54811yescharacteristic
511C22×C7D4×Q811yescharacteristic
512C22×C7#55011yescharacteristic
513C22×C7#55011yescharacteristic
514C22×C7#55411yescharacteristic
515C22×C7#55411yescharacteristic
516C22×C7#55411yescharacteristic
517C4×C7—42no—
518C4×C7—42no—
519C4×C7—82no—
520C4×C7#38018yescomplemented
521Dic7—24no—
522Dic7—28no—
523Dic7—42no—
524Dic7—42no—
525Dic7—42no—
526Dic7—82no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24C2×Dic1414yes—
540C24C2×C4×D714yes—
541C24C2×C22⋊D714yes—
542C24C23×D711yescharacteristic
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4Dic7⋊C4116yescomplemented
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
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—72no—
570C22×C4—74no—
571C22×C4—72no—
572C22×C4—74no—
573C22×C4—74no—
574C22×C4—72no—
575C22×C4—72no—
576C22×C4—72no—
577C22×C4—72no—
578C22×C4—1416no—
579C22×C4—1416no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—141no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—288no—
614C22×C4—288no—
615C22×C4—288no—
616C22×C4—288no—
617C22×C4—288no—
618C22×C4C2×Dic1412yes—
619C22×C4C2×C4×D712yes—
620C22×C4D4×D712yes—
621C22×C4D4×D712yes—
622C22×C4D4×D712yes—
623C22×C4#115912yes—
624C22×C4#115912yes—
625C22×C4#115912yes—
626C22×C4C2×C22⋊D712yes—
627C4⋊C4—44no—
628C4⋊C4—716no—
629C4⋊C4—288no—
630C4⋊C4—288no—
631C4⋊C4—284no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—1416no—
635C22⋊C4—288no—
636C22⋊C4—288no—
637C42—44no—
638C42—148no—
639C42—284no—
640C2×C7—48no—
641C2×C7C2×#38011yescharacteristic
642C2×C7#229311yescharacteristic
643C2×C7#231911yescharacteristic
644C2×C7D4×C22⋊C411yescharacteristic
645C2×C7#234111yescharacteristic
646C2×C7D4×C4⋊C411yescharacteristic
647C2×C7#234911yescharacteristic
648C2×C7#242711yescharacteristic
649C2×C7#242711yescharacteristic
650C2×C7#242811yescharacteristic
651C2×C7#242811yescharacteristic
652C2×C7#245211yescharacteristic
653C2×C7#245211yescharacteristic
654C2×C7#245411yescharacteristic
655C2×C7#245411yescharacteristic
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23C2×Dic7⋊C418yes—
691C23C22×Dic1411yescharacteristic
692C23C22×C4×D711yescharacteristic
693C23C2×D4×D711yescharacteristic
694C23C2×D4×D711yescharacteristic
695C23C2×D4×D711yescharacteristic
696C23C2×#115911yescharacteristic
697C23C2×#115911yescharacteristic
698C23C2×#115911yescharacteristic
699C23#654811yescharacteristic
700C23#654811yescharacteristic
701C23D7×#4111yescharacteristic
702C23D7×#4111yescharacteristic
703C23#655311yescharacteristic
704C23#655411yescharacteristic
705C23C22×C22⋊D711yescharacteristic
706D4—232no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—78no—
729C2×C4—74no—
730C2×C4—144no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—144no—
734C2×C4—144no—
735C2×C4—142no—
736C2×C4—144no—
737C2×C4—142no—
738C2×C4—144no—
739C2×C4—142no—
740C2×C4—144no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—142no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—2832no—
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—281no—
762C2×C4—281no—
763C2×C4—281no—
764C2×C4—282no—
765C2×C4—282no—
766C2×C4—282no—
767C2×C4—282no—
768C2×C4—282no—
769C2×C4—282no—
770C2×C4—282no—
771C2×C4#644014yes—
772C2×C4#644114yes—
773C2×C4#644114yes—
774C2×C4D7×C22⋊C414yes—
775C2×C4C2×Dic7⋊C414yes—
776C2×C4#650214yes—
777C2×C4#650214yes—
778C7#1392011yescharacteristic, complemented, Sylow
779C22—28no—
780C22—28no—
781C22—28no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22C2×#644011yescharacteristic
795C22C2×#644111yescharacteristic
796C22C2×#644111yescharacteristic
797C22C2×D7×C22⋊C411yescharacteristic
798C22C4×#115911yescharacteristic
799C22D4×Dic1411yescharacteristic
800C22#9023011yescharacteristic
801C22#9023011yescharacteristic
802C22#9023411yescharacteristic
803C22C4×D4×D711yescharacteristic
804C22#9023611yescharacteristic
805C22#9023711yescharacteristic
806C22#9028711yescharacteristic
807C22#9028911yescharacteristic
808C22#9029011yescharacteristic
809C22#9029111yescharacteristic
810C22#9029411yescharacteristic
811C22#9030011yescharacteristic
812C22#9030311yescharacteristic
813C22#9031011yescharacteristic
814C22#9036711yescharacteristic
815C22#9036811yescharacteristic
816C22#9037111yescharacteristic
817C22#9037311yescharacteristic
818C22#9040711yescharacteristic
819C22#9040811yescharacteristic
820C22#9040911yescharacteristic
821C22#9041011yescharacteristic
822C22C22×Dic7⋊C411yescharacteristic
823C22D4×C22⋊D711yescharacteristic
824C22C2×#650211yescharacteristic
825C22C2×#650211yescharacteristic
826C22#9049711yescharacteristic
827C22#9051511yescharacteristic
828C22#9052011yescharacteristic
829C4—42no—
830C4—42no—
831C4—82no—
832C4—144no—
833C4—148no—
834C4—282no—
835C4—282no—
836C4—282no—
837C4—562no—
838C4#8971418yescomplemented
839C2—48no—
840C2#1173373411yescharacteristic
841C2#1173374011yescharacteristic
842C2#1173374611yescharacteristic
843C2#1173376711yescharacteristic
844C2#1173376811yescharacteristic
845C2#1173376911yescharacteristic
846C2#1173377011yescharacteristic
847C2#1173387611yescharacteristic
848C2C2×#8971411yescharacteristic
849C2D4×Dic7⋊C411yescharacteristic
850C2#1173977911yescharacteristic
851C2#1174009211yescharacteristic
852C2#1174009411yescharacteristic
853C2#1174044111yescharacteristic
854C2#1174063111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#390C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#390D7
hypocenterC7#13920
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#89745C2semidirect
5. C2×#89714C2semidirect
6. C2×#89700C2semidirect
7. #11729317C2semidirect
8. #11729301C2semidirect
9. #11729301C2semidirect
10. #11729298C2semidirect
11. C4×C7⋊#95C2semidirect
23. C2×D4×Dic7C4semidirect
116. C7⋊#95D4semidirect
150. C2×C7×D4C4⋊C4semidirect
236. C4⋊Dic7C22⋊C4semidirect
520. C4×C7#380semidirect
549. C2×D4Dic7⋊C4semidirect
778. C7#13920semidirect
838. C4#89714semidirect

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×#897452
C2×#897142
C2×#897002
#117293172
#117293012
#117292982
C4×C7⋊#952
#139207