Finite Group Databasebeta

← #13277187

Subgroups — #13277187

Order 1792.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C2×#89993C211yesmaximal, characteristic
3C2×#89993C211yesmaximal, characteristic
4C2×#89982C212yesmaximal, complemented
5C2×#89745C211yesmaximal, characteristic, complemented
6C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
7#11729881C212yesmaximal, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729301C212yesmaximal, complemented
10#11729301C212yesmaximal, complemented
11#11729289C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2212yes—
14C2×C4×C7×D4—24no—
15C2×C4×C7×D4—24no—
16C2×C4×C7×D4—24no—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C42×C7C2211yescharacteristic
20C22×C22⋊Dic7C2212yes—
21C22×C22⋊Dic7C2212yes—
22C22×C22⋊Dic7C2212yes—
23C22×C22⋊Dic7C2212yes—
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2212yes—
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31#89993—24no—
32#89993C418yescomplemented
33#89982—28no—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41#89745—24no—
42C4×Dic7⋊C4—24no—
43#14018—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×C7—24no—
53C23×C4×C7—24no—
54C23×C4×C7—24no—
55C23×C4×C7—24no—
56C23×C4×C7—24no—
57C23×C4×C7—42no—
58C23×C4×C7—42no—
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2312yes—
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×Dic7C2312yes—
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2312yes—
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C4×C7×D4—232no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4D414yes—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C42×C7—22no—
77C2×C42×C7—22no—
78C2×C42×C7D414yes—
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⋊Dic7—42no—
88C2×C22⋊Dic7—42no—
89C2×C22⋊Dic7C2×C418yescomplemented
90C2×C22⋊Dic7C2×C418yescomplemented
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7—22no—
95C2×C4⋊Dic7—22no—
96C2×C4⋊Dic7C2×C414yescomplemented
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—22no—
99C2×Dic7⋊C4—22no—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—24no—
103C2×Dic7⋊C4—24no—
104C2×Dic7⋊C4—42no—
105C2×Dic7⋊C4D414yescomplemented
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7C2×C414yescomplemented
112C7⋊#95—22no—
113C7⋊#95—22no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C7⋊#95—24no—
117C7⋊#95—42no—
118C7⋊#95—42no—
119C22×C4×D4D711yescharacteristic
120C2×#390—71no—
121C2×#390—71no—
122C2×#389—71no—
123C2×#385—72no—
124C2×C4×C4⋊C4—71no—
125#1439—72no—
126#1439—72no—
127C4⋊#95—71no—
128C4⋊#95—71no—
129C22⋊#95—72no—
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×C7—22no—
141C24×C7—22no—
142C24×C7C22×C414yes—
143C24×C7C2×D414yes—
144C24×C7C2×Q814yes—
145C24×C7C2411yescharacteristic
146C2×C7×D4—28no—
147C2×C7×D4—28no—
148C2×C7×D4—28no—
149C2×C7×D4—28no—
150C2×C7×D4—28no—
151C2×C7×D4—28no—
152C2×C7×D4C4⋊C4116yescomplemented
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—216no—
158C22×C4×C7—22no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—21no—
170C22×C4×C7—48no—
171C22×C4×C7—48no—
172C22×C4×C7—48no—
173C22×C4×C7—48no—
174C22×C4×C7—48no—
175C22×C4×C7—48no—
176C22×C4×C7C22×C412yes—
177C22×C4×C7C2×D412yes—
178C22×C4×C7C2×D414yes—
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×D412yes—
182C22×C4×C7C2×D412yes—
183C22×C4×C7C2×D412yes—
184C22×C4×C7C2×Q812yes—
185C22×C4×C7#4112yes—
186C22×C4×C7#4112yes—
187C22×C4×C7#4112yes—
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—22no—
197C22×Dic7—22no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—21no—
207C22×Dic7—22no—
208C22×Dic7—21no—
209C22×Dic7—22no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7C22×C412yes—
224C22×Dic7C22×C414yes—
225C22×Dic7C22×C412yes—
226C22×Dic7C2×D412yes—
227C22×Dic7C2×D412yes—
228C22×Dic7#4112yes—
229C22×Dic7#4112yes—
230C7×C4⋊C4—28no—
231C7×C22⋊C4—216no—
232C42×C7—28no—
233C22⋊Dic7—216no—
234C22⋊Dic7—48no—
235C22⋊Dic7—48no—
236C22⋊Dic7—48no—
237C4⋊Dic7—28no—
238C4⋊Dic7—44no—
239Dic7⋊C4—28no—
240Dic7⋊C4—28no—
241Dic7⋊C4—48no—
242C4×Dic7—28no—
243C4×Dic7—44no—
244C23×D4C2×D711yescharacteristic
245C24×C4C2×D712yes—
246C2×C4×D4—24no—
247C2×C4×D4—24no—
248C2×C4×D4—24no—
249C22×C4⋊C4—71no—
250C22×C4⋊C4—71no—
251C22×C4⋊C4—71no—
252C22×C4⋊C4—71no—
253C22×C4⋊C4—72no—
254C22×C4⋊C4C2×D711yescharacteristic
255C22×C22⋊C4—72no—
256C22×C22⋊C4—72no—
257C22×C22⋊C4—72no—
258C22×C22⋊C4—72no—
259C22×C22⋊C4C2×D712yes—
260C22×C42—71no—
261C22×C42—71no—
262C22×C42C2×D711yescharacteristic
263#390—78no—
264#390—144no—
265#389—144no—
266#385—148no—
267C4×C4⋊C4—144no—
268C2×#95—71no—
269C2×#95—72no—
270C2×#95—72no—
271C2×#95—72no—
272C2×#95—71no—
273C2×#95—72no—
274C2×#95—72no—
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—24no—
291C23×C7—24no—
292C23×C7—24no—
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×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7C2×C4⋊C418yes—
310C23×C7C23×C411yescharacteristic
311C23×C7C22×D411yescharacteristic
312C23×C7C22×D411yescharacteristic
313C23×C7C22×D411yescharacteristic
314C23×C7C22×D411yescharacteristic
315C23×C7C22×Q811yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7C2×#4111yescharacteristic
319C23×C7C2×#4111yescharacteristic
320C23×C7C2×#4111yescharacteristic
321C23×C7H(5,𝔽2)11yescharacteristic
322C23×C7H(5,𝔽2)11yescharacteristic
323C23×C7H(5,𝔽2)11yescharacteristic
324C23×C72−1+411yescharacteristic
325C7×D4—232no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—24no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—24no—
337C2×C4×C7—24no—
338C2×C4×C7—432no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—41no—
343C2×C4×C7—42no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7C2×C4⋊C414yes—
348C2×C4×C7C4×D414yes—
349C2×C4×C7C4×D414yes—
350C2×C4×C7#12014yes—
351C2×C4×C7#12114yes—
352C2×C4×C7C22⋊Q814yes—
353C2×C4×C7C22⋊Q814yes—
354C2×C4×C7#12314yes—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—24no—
363C2×Dic7—24no—
364C2×Dic7—22no—
365C2×Dic7—24no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
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—42no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—41no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7C4×D414yescomplemented
397C25C22×D712yes—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—22no—
402C22×D4Dic1414yes—
403C22×D4C4×D714yes—
404C22×D4C22⋊D714yes—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—71no—
413C23×C4—71no—
414C23×C4—72no—
415C23×C4—71no—
416C23×C4—71no—
417C23×C4—72no—
418C23×C4C22×D711yescharacteristic
419C23×C4C22×D712yes—
420C23×C4C22×D711yescharacteristic
421C23×C4C22×D711yescharacteristic
422C4×D4—232no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—74no—
426C2×C4⋊C4—74no—
427C2×C4⋊C4—142no—
428C2×C4⋊C4—142no—
429C2×C4⋊C4—142no—
430C2×C4⋊C4—142no—
431C2×C4⋊C4—142no—
432C2×C4⋊C4—142no—
433C2×C4⋊C4—142no—
434C2×C4⋊C4—144no—
435C2×C4⋊C4—142no—
436C2×C4⋊C4—142no—
437C2×C4⋊C4—144no—
438C2×C4⋊C4—142no—
439C2×C4⋊C4—282no—
440C2×C4⋊C4C22⋊D714yes—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—78no—
445C2×C22⋊C4—78no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—144no—
449C2×C22⋊C4—144no—
450C2×C22⋊C4—144no—
451C2×C22⋊C4—144no—
452C2×C22⋊C4—282no—
453C2×C22⋊C4—282no—
454C2×C22⋊C4—282no—
455C2×C22⋊C4—282no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—74no—
459C2×C42—142no—
460C2×C42—142no—
461C2×C42—142no—
462C2×C42—142no—
463C2×C42—142no—
464C2×C42C22⋊D714yes—
465#95—144no—
466#95—144no—
467#95—142no—
468#95—142no—
469#95—144no—
470#95—282no—
471#95—282no—
472C22×C7—28no—
473C22×C7—28no—
474C22×C7—28no—
475C22×C7—44no—
476C22×C7—44no—
477C22×C7—44no—
478C22×C7—44no—
479C22×C7—44no—
480C22×C7—44no—
481C22×C7—44no—
482C22×C7—44no—
483C22×C7—44no—
484C22×C7—44no—
485C22×C7—44no—
486C22×C7—44no—
487C22×C7C22×C4⋊C411yescharacteristic
488C22×C7C2×C4×D411yescharacteristic
489C22×C7C2×C4×D411yescharacteristic
490C22×C7C2×C4×D411yescharacteristic
491C22×C7C4×#4111yescharacteristic
492C22×C7#51811yescharacteristic
493C22×C7#52011yescharacteristic
494C22×C7C2×#12011yescharacteristic
495C22×C7C2×#12111yescharacteristic
496C22×C7C2×C22⋊Q811yescharacteristic
497C22×C7C2×C22⋊Q811yescharacteristic
498C22×C7C2×#12311yescharacteristic
499C22×C7#52511yescharacteristic
500C22×C7#52911yescharacteristic
501C22×C7#53211yescharacteristic
502C22×C7#53511yescharacteristic
503C22×C7#53711yescharacteristic
504C22×C7#54011yescharacteristic
505C22×C7#54211yescharacteristic
506C22×C7D4211yescharacteristic
507C22×C7D4211yescharacteristic
508C22×C7#54611yescharacteristic
509C22×C7#54611yescharacteristic
510C22×C7#54611yescharacteristic
511C22×C7#54711yescharacteristic
512C22×C7#54811yescharacteristic
513C22×C7D4×Q811yescharacteristic
514C22×C7#55011yescharacteristic
515C22×C7#55011yescharacteristic
516C22×C7#55411yescharacteristic
517C22×C7#55411yescharacteristic
518C22×C7#55411yescharacteristic
519C22×C7#55611yescharacteristic
520C22×C7#55911yescharacteristic
521C22×C7#55911yescharacteristic
522C4×C7—24no—
523C4×C7—42no—
524C4×C7—44no—
525C4×C7#38518yescomplemented
526Dic7—24no—
527Dic7—42no—
528Dic7—44no—
529Dic7—42no—
530Dic7—42no—
531Dic7—82no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C2×Dic1414yes—
545C24C2×C4×D714yes—
546C24C2×C22⋊D714yes—
547C24C23×D711yescharacteristic
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4Dic7⋊C4116yescomplemented
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—216no—
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—22no—
571C22×C4—22no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—72no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—72no—
582C22×C4—74no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—142no—
597C22×C4—141no—
598C22×C4—142no—
599C22×C4—141no—
600C22×C4—142no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—141no—
608C22×C4—141no—
609C22×C4—142no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4C2×Dic1412yes—
621C22×C4C2×C4×D712yes—
622C22×C4#115712yes—
623C22×C4#115712yes—
624C22×C4D4×D712yes—
625C22×C4#115912yes—
626C22×C4C2×C22⋊D712yes—
627C22×C4C2×C22⋊D714yes—
628C22×C4C2×C22⋊D712yes—
629C22×C4C2×C22⋊D712yes—
630C22×C4C2×C22⋊D712yes—
631C22×C4C2×C22⋊D712yes—
632C4⋊C4—28no—
633C4⋊C4—148no—
634C4⋊C4—148no—
635C4⋊C4—148no—
636C4⋊C4—288no—
637C4⋊C4—284no—
638C22⋊C4—216no—
639C22⋊C4—1416no—
640C22⋊C4—288no—
641C22⋊C4—288no—
642C22⋊C4—288no—
643C42—28no—
644C42—148no—
645C42—284no—
646C2×C7—48no—
647C2×C7C2×#38511yescharacteristic
648C2×C7C4×#12111yescharacteristic
649C2×C7#232411yescharacteristic
650C2×C7D4×C4⋊C411yescharacteristic
651C2×C7#234911yescharacteristic
652C2×C7#236611yescharacteristic
653C2×C7#236711yescharacteristic
654C2×C7#240711yescharacteristic
655C2×C7#240811yescharacteristic
656C2×C7#244511yescharacteristic
657C2×C7#244711yescharacteristic
658C2×C7#245211yescharacteristic
659C2×C7#245411yescharacteristic
660C2×C7#253811yescharacteristic
661C2×C7#258011yescharacteristic
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—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23C2×Dic7⋊C418yes—
697C23C22×Dic1411yescharacteristic
698C23C22×C4×D711yescharacteristic
699C23C2×#115711yescharacteristic
700C23C2×#115711yescharacteristic
701C23C2×D4×D711yescharacteristic
702C23C2×#115911yescharacteristic
703C23#654811yescharacteristic
704C23#654811yescharacteristic
705C23D7×#4111yescharacteristic
706C23D7×#4111yescharacteristic
707C23#655311yescharacteristic
708C23#655411yescharacteristic
709C23C22×C22⋊D711yescharacteristic
710C23C22×C22⋊D711yescharacteristic
711C23C22×C22⋊D711yescharacteristic
712D4—232no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—432no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—74no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—144no—
743C2×C4—144no—
744C2×C4—142no—
745C2×C4—142no—
746C2×C4—144no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—282no—
754C2×C4—281no—
755C2×C4—281no—
756C2×C4—281no—
757C2×C4—281no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4—281no—
761C2×C4—281no—
762C2×C4—281no—
763C2×C4—281no—
764C2×C4—281no—
765C2×C4—281no—
766C2×C4—282no—
767C2×C4—281no—
768C2×C4—281no—
769C2×C4—282no—
770C2×C4—282no—
771C2×C4—282no—
772C2×C4—282no—
773C2×C4—282no—
774C2×C4—282no—
775C2×C4—282no—
776C2×C4C2×Dic7⋊C414yes—
777C2×C4#648714yes—
778C2×C4#648714yes—
779C2×C4C4×C22⋊D714yes—
780C2×C4C4×C22⋊D714yes—
781C2×C4#649214yes—
782C2×C4#650114yes—
783C2×C4#651614yes—
784C7#1401811yescharacteristic, complemented, Sylow
785C22—28no—
786C22—28no—
787C22—28no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22C4×#115911yescharacteristic
801C22D4×Dic1411yescharacteristic
802C22#9023011yescharacteristic
803C22#9023011yescharacteristic
804C22#9023311yescharacteristic
805C22#9023411yescharacteristic
806C22C4×D4×D711yescharacteristic
807C22#9023611yescharacteristic
808C22#9023711yescharacteristic
809C22#9023911yescharacteristic
810C22#9024411yescharacteristic
811C22#9024811yescharacteristic
812C22#9025011yescharacteristic
813C22#9025011yescharacteristic
814C22#9025211yescharacteristic
815C22#9025311yescharacteristic
816C22C22×Dic7⋊C411yescharacteristic
817C22C2×#648711yescharacteristic
818C22C2×#648711yescharacteristic
819C22C2×C4×C22⋊D711yescharacteristic
820C22C2×C4×C22⋊D711yescharacteristic
821C22C2×#649211yescharacteristic
822C22C2×#650111yescharacteristic
823C22D4×C22⋊D711yescharacteristic
824C22D4×C22⋊D711yescharacteristic
825C22#9049611yescharacteristic
826C22#9049711yescharacteristic
827C22#9049711yescharacteristic
828C22#9051511yescharacteristic
829C22#9051911yescharacteristic
830C22#9052011yescharacteristic
831C22#9052211yescharacteristic
832C22#9052411yescharacteristic
833C22#9052511yescharacteristic
834C22C2×#651611yescharacteristic
835C4—24no—
836C4—44no—
837C4—42no—
838C4—144no—
839C4—282no—
840C4—282no—
841C4—284no—
842C4—282no—
843C4—562no—
844C4#8998218yescomplemented
845C2—48no—
846C2D4×Dic7⋊C411yescharacteristic
847C2#1173977911yescharacteristic
848C2#1173978811yescharacteristic
849C2#1173978911yescharacteristic
850C2#1173980311yescharacteristic
851C2#1173980411yescharacteristic
852C2#1173980711yescharacteristic
853C2#1173980811yescharacteristic
854C2#1173982111yescharacteristic
855C2#1173983311yescharacteristic
856C2C4×#650111yescharacteristic
857C2#1173984111yescharacteristic
858C2C2×#8998211yescharacteristic
859C2#1174149811yescharacteristic
860C2#1174154211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C4×C7×D4C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC22×C4×D4D7
hypocenterC7#14018
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
4. C2×#89982C2semidirect
5. C2×#89745C2semidirect
6. C2×C4×Dic7⋊C4C2semidirect
7. #11729881C2semidirect
8. #11729317C2semidirect
9. #11729301C2semidirect
10. #11729301C2semidirect
11. #11729289C2semidirect
32. #89993C4semidirect
89. C2×C22⋊Dic7C2×C4semidirect
90. C2×C22⋊Dic7C2×C4semidirect
96. C2×C4⋊Dic7C2×C4semidirect
105. C2×Dic7⋊C4D4semidirect
111. C2×C4×Dic7C2×C4semidirect
152. C2×C7×D4C4⋊C4semidirect
396. C2×Dic7C4×D4semidirect
525. C4×C7#385semidirect
554. C2×D4Dic7⋊C4semidirect
784. C7#14018semidirect
844. C4#89982semidirect

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×#899932
C2×#899822
C2×#897452
C2×C4×Dic7⋊C42
#117298812
#117293172
#117293012
#117292892
#140187