Finite Group Databasebeta

← #13259076

Subgroups — #13259076

Order 1792.

1518 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6455C211yesmaximal, characteristic
2C22×(C2×D7)⋊C8C211yesmaximal, characteristic
3C2×#89759C211yesmaximal, characteristic
4C2×C7×#340C211yesmaximal, characteristic, complemented
5C2×#89346C211yesmaximal, characteristic, complemented
6C2×#89324C211yesmaximal, characteristic, complemented
7C2×#89324C211yesmaximal, characteristic, complemented
8C23×C4×D7C2211yescharacteristic
9C23×C7×C8C2211yescharacteristic
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×(C2×D7)⋊C4—21no—
13C22×(C2×D7)⋊C4—21no—
14C22×C4⋊Dic7C2211yescharacteristic
15C22×C4⋊Dic7C2211yescharacteristic
16C22×C4×Dic7—21no—
17C23×C7⋊C8C2211yescharacteristic
18C2×#6455—22no—
19C2×#6455—22no—
20C2×#6455—22no—
21C2×#6455—22no—
22C2×#6455—22no—
23C2×#6455C414yescomplemented
24C2×C7⋊#95—21no—
25C2×(C2×D7)⋊C8—22no—
26C2×(C2×D7)⋊C8—22no—
27C2×(C2×D7)⋊C8C414yescomplemented
28#89759—22no—
29#89759C414yescomplemented
30C7×#340—22no—
31#89346—22no—
32#89324—22no—
33#89324—22no—
34#10731—71nomaximal, Sylow
35C24×D7D411yescharacteristic
36C23×C4×C7—21no—
37C23×C4×C7—21no—
38C23×C4×C7C2311yescharacteristic
39C23×Dic7—21no—
40C23×Dic7—21no—
41C23×Dic7D411yescharacteristic
42C22×C4×D7—21no—
43C22×C4×D7—21no—
44C22×C4×D7—21no—
45C22×C4×D7—21no—
46C22×C4×D7—21no—
47C22×C4×D7—21no—
48C22×C4×D7—21no—
49C22×C4×D7—21no—
50C22×C4×D7C2×C412yes—
51C22×C4×D7C2×C412yes—
52C22×C4×D7C2×C412yes—
53C22×C4×D7D412yes—
54C22×C4×D7D412yes—
55C22×C4×D7Q812yes—
56C22×C7×C8—21no—
57C22×C7×C8—21no—
58C22×C7×C8—21no—
59C22×C7×C8—21no—
60C22×C7×C8—21no—
61C22×C7×C8—21no—
62C22×C7×C8C2×C412yes—
63C2×C7×C4⋊C4—21no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4C2×C412yes—
72C2×C7×C4⋊C4C2×C412yes—
73C2×C7×C4⋊C4D412yes—
74C2×C7×C4⋊C4D412yes—
75C2×(C2×D7)⋊C4—24no—
76C2×(C2×D7)⋊C4—24no—
77C2×(C2×D7)⋊C4—24no—
78C2×(C2×D7)⋊C4—24no—
79C2×(C2×D7)⋊C4—42no—
80C2×(C2×D7)⋊C4—42no—
81C2×C4⋊Dic7—21no—
82C2×C4⋊Dic7—21no—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7—21no—
85C2×C4⋊Dic7—21no—
86C2×C4⋊Dic7—21no—
87C2×C4⋊Dic7—21no—
88C2×C4⋊Dic7—21no—
89C2×C4⋊Dic7C2×C412yes—
90C2×C4⋊Dic7C2×C412yes—
91C2×C4⋊Dic7D412yes—
92C2×C4⋊Dic7D412yes—
93C2×C4×Dic7—24no—
94C2×C4×Dic7—24no—
95C2×C4×Dic7—24no—
96C22×C7⋊C8—21no—
97C22×C7⋊C8—21no—
98C22×C7⋊C8—21no—
99C22×C7⋊C8—21no—
100C22×C7⋊C8—21no—
101C22×C7⋊C8—21no—
102C22×C7⋊C8C2×C412yes—
103#6455—28no—
104#6455—28no—
105#6455—28no—
106#6455—28no—
107C7⋊#95—24no—
108(C2×D7)⋊C8—28no—
109C22×#117—71no—
110C22×C22⋊C8—71no—
111C2×#380—71no—
112C2×#340—71no—
113C2×#340—71no—
114C2×#340—71no—
115C2×#340D711yescharacteristic, complemented
116C24×C7C2×D411yescharacteristic
117C23×D7—21no—
118C23×D7—21no—
119C23×D7—21no—
120C23×D7—21no—
121C23×D7—21no—
122C23×D7—21no—
123C23×D7—21no—
124C23×D7—21no—
125C23×D7—21no—
126C23×D7—21no—
127C23×D7—21no—
128C23×D7—21no—
129C23×D7C22⋊C412yes—
130C23×D7C22⋊C412yes—
131C23×D7C4⋊C412yes—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—41no—
137C22×C4×C7—41no—
138C22×C4×C7—41no—
139C22×C4×C7—41no—
140C22×C4×C7—41no—
141C22×C4×C7—41no—
142C22×C4×C7—41no—
143C22×C4×C7—41no—
144C22×C4×C7—41no—
145C22×C4×C7—41no—
146C22×C4×C7C22×C411yescharacteristic
147C22×C4×C7C22×C411yescharacteristic
148C22×C4×C7C22×C411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×Q811yescharacteristic
156C22×C4×C7#4111yescharacteristic
157C22×C4×C7#4111yescharacteristic
158C22×C4×C7#4111yescharacteristic
159C22×C4×C7#4111yescharacteristic
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7—41no—
169C22×Dic7—41no—
170C22×Dic7—41no—
171C22×Dic7—41no—
172C22×Dic7—41no—
173C22×Dic7—41no—
174C22×Dic7—41no—
175C22×Dic7—41no—
176C22×Dic7—41no—
177C22×Dic7—41no—
178C22×Dic7C22⋊C412yes—
179C22×Dic7C22⋊C412yes—
180C22×Dic7C4⋊C412yes—
181C2×C4×D7—22no—
182C2×C4×D7—22no—
183C2×C4×D7—22no—
184C2×C4×D7—22no—
185C2×C4×D7—22no—
186C2×C4×D7—22no—
187C2×C4×D7—22no—
188C2×C4×D7—22no—
189C2×C4×D7—22no—
190C2×C4×D7—22no—
191C2×C4×D7—22no—
192C2×C4×D7—22no—
193C2×C4×D7—22no—
194C2×C4×D7—22no—
195C2×C4×D7—22no—
196C2×C4×D7—22no—
197C2×C4×D7—22no—
198C2×C4×D7—22no—
199C2×C4×D7—22no—
200C2×C4×D7—22no—
201C2×C4×D7—22no—
202C2×C4×D7—22no—
203C2×C4×D7—22no—
204C2×C4×D7—22no—
205C2×C4×D7C4214yes—
206C2×C4×D7C22⋊C414yes—
207C2×C4×D7C4⋊C414yes—
208C2×C4×D7C4⋊C414yes—
209C2×C7×C8—22no—
210C2×C7×C8—22no—
211C2×C7×C8—22no—
212C2×C7×C8—41no—
213C2×C7×C8—41no—
214C2×C7×C8—41no—
215C2×C7×C8—41no—
216C7×C4⋊C4—22no—
217C7×C4⋊C4—22no—
218C7×C4⋊C4—22no—
219C7×C4⋊C4—22no—
220C7×C4⋊C4—22no—
221C7×C4⋊C4—41no—
222C7×C4⋊C4—41no—
223C7×C4⋊C4C22⋊C414yescomplemented
224(C2×D7)⋊C4—216no—
225(C2×D7)⋊C4—48no—
226C4⋊Dic7—22no—
227C4⋊Dic7—22no—
228C4⋊Dic7—22no—
229C4⋊Dic7—22no—
230C4⋊Dic7—22no—
231C4⋊Dic7—41no—
232C4⋊Dic7—41no—
233C4⋊Dic7C22⋊C414yescomplemented
234C4×Dic7—216no—
235C2×C7⋊C8—22no—
236C2×C7⋊C8—22no—
237C2×C7⋊C8—22no—
238C2×C7⋊C8—41no—
239C2×C7⋊C8—41no—
240C2×C7⋊C8—41no—
241C2×C7⋊C8—41no—
242C24×C4—71no—
243C23×C8—71no—
244C23×C8C2×D711yescharacteristic
245C2×#117—74no—
246C2×#117—142no—
247C2×#117—142no—
248C2×#117—142no—
249C2×#117—142no—
250C2×#117—142no—
251C22×C4⋊C4—71no—
252C22×C4⋊C4—71no—
253C22×C4⋊C4C2×D711yescharacteristic
254C22×C4⋊C4C2×D711yescharacteristic
255C22×C22⋊C4—141no—
256C22×C22⋊C4—141no—
257C22×C42—141no—
258C2×C22⋊C8—74no—
259C2×C22⋊C8—142no—
260C2×C22⋊C8—142no—
261#380—74no—
262#380—142no—
263C2×#95—141no—
264#340—22no—
265#340—142no—
266#340—142no—
267#340—142no—
268C23×C7C2×C22⋊C411yescharacteristic
269C23×C7C2×C22⋊C411yescharacteristic
270C23×C7C2×C4⋊C411yescharacteristic
271C23×C7#12011yescharacteristic
272C23×C7#12011yescharacteristic
273C23×C7#12311yescharacteristic
274C23×C7#12311yescharacteristic
275C23×C7#13511yescharacteristic
276C23×C7#13511yescharacteristic
277C23×C7#13511yescharacteristic
278C23×C7#13511yescharacteristic
279C23×C7AGL(1,ℤ/8)11yescharacteristic
280C23×C7AGL(1,ℤ/8)11yescharacteristic
281C23×C7#13711yescharacteristic
282C23×C7#13711yescharacteristic
283C22×D7—22no—
284C22×D7—22no—
285C22×D7—22no—
286C22×D7—22no—
287C22×D7—22no—
288C22×D7—22no—
289C22×D7—22no—
290C22×D7—22no—
291C22×D7—22no—
292C22×D7—22no—
293C22×D7—22no—
294C22×D7—22no—
295C22×D7—22no—
296C22×D7—22no—
297C22×D7—22no—
298C22×D7—22no—
299C22×D7—22no—
300C22×D7—22no—
301C22×D7—41no—
302C22×D7—41no—
303C22×D7—41no—
304C22×D7—41no—
305C22×D7—41no—
306C22×D7—41no—
307C22×D7—41no—
308C22×D7—41no—
309C22×D7—41no—
310C22×D7—41no—
311C22×D7—41no—
312C22×D7—41no—
313C22×D7—41no—
314C22×D7—41no—
315C22×D7—41no—
316C22×D7—41no—
317C22×D7#9514yes—
318C2×C4×C7—24no—
319C2×C4×C7—42no—
320C2×C4×C7—42no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—81no—
329C2×C4×C7—81no—
330C2×C4×C7—81no—
331C2×C4×C7—81no—
332C2×C4×C7C2×C4211yescharacteristic
333C2×C4×C7C2×C22⋊C411yescharacteristic
334C2×C4×C7C2×C22⋊C411yescharacteristic
335C2×C4×C7C2×C22⋊C411yescharacteristic
336C2×C4×C7C2×C4⋊C411yescharacteristic
337C2×C4×C7C2×C4⋊C411yescharacteristic
338C2×C4×C7#11711yescharacteristic
339C2×C4×C7#11711yescharacteristic
340C2×C4×C7C4×D411yescharacteristic
341C2×C4×C7C4×D411yescharacteristic
342C2×C4×C7C4×D411yescharacteristic
343C2×C4×C7C4×D411yescharacteristic
344C2×C4×C7C4×D411yescharacteristic
345C2×C4×C7C4×D411yescharacteristic
346C2×C4×C7C4×D411yescharacteristic
347C2×C4×C7C4×D411yescharacteristic
348C2×C4×C7#12011yescharacteristic
349C2×C4×C7#12011yescharacteristic
350C2×C4×C7#12111yescharacteristic
351C2×C4×C7#12111yescharacteristic
352C2×C4×C7#12111yescharacteristic
353C2×C4×C7#12111yescharacteristic
354C2×C4×C7C22⋊Q811yescharacteristic
355C2×C4×C7C22⋊Q811yescharacteristic
356C2×C4×C7C22⋊Q811yescharacteristic
357C2×C4×C7C22⋊Q811yescharacteristic
358C2×C4×C7#12311yescharacteristic
359C2×C4×C7#12311yescharacteristic
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—24no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C2×Dic7—42no—
376C2×Dic7—81no—
377C2×Dic7—81no—
378C2×Dic7—81no—
379C2×Dic7—81no—
380C2×Dic7#9514yes—
381C4×D7—24no—
382C4×D7—24no—
383C4×D7—24no—
384C4×D7—24no—
385C4×D7—24no—
386C4×D7—24no—
387C4×D7—24no—
388C4×D7—24no—
389C7×C8—42no—
390C7⋊C8—42no—
391C25—71no—
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—71no—
395C23×C4—72no—
396C23×C4—72no—
397C23×C4—72no—
398C23×C4—72no—
399C23×C4—72no—
400C23×C4—72no—
401C23×C4—141no—
402C23×C4—141no—
403C23×C4—141no—
404C23×C4—141no—
405C23×C4—141no—
406C23×C4—141no—
407C23×C4—141no—
408C23×C4—141no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4C22×D711yescharacteristic
412C22×C8—21no—
413C22×C8—21no—
414C22×C8—21no—
415C22×C8—21no—
416C22×C8—21no—
417C22×C8—21no—
418C22×C8—72no—
419C22×C8—141no—
420C22×C8—141no—
421C22×C8—141no—
422C22×C8—141no—
423C22×C8—141no—
424C22×C8—141no—
425C22×C8C4×D712yes—
426#117—148no—
427#117—148no—
428#117—148no—
429#117—148no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—72no—
439C2×C4⋊C4—72no—
440C2×C4⋊C4—72no—
441C2×C4⋊C4—72no—
442C2×C4⋊C4—141no—
443C2×C4⋊C4—141no—
444C2×C4⋊C4—141no—
445C2×C4⋊C4—141no—
446C2×C4⋊C4—141no—
447C2×C4⋊C4—141no—
448C2×C4⋊C4—141no—
449C2×C4⋊C4—141no—
450C2×C4⋊C4C4×D712yes—
451C2×C4⋊C4C4×D712yes—
452C2×C4⋊C4D2812yes—
453C2×C4⋊C4C22⋊D712yes—
454C2×C22⋊C4—144no—
455C2×C22⋊C4—144no—
456C2×C22⋊C4—144no—
457C2×C22⋊C4—144no—
458C2×C22⋊C4—282no—
459C2×C22⋊C4—282no—
460C2×C42—144no—
461C2×C42—144no—
462C2×C42—144no—
463C22⋊C8—148no—
464#95—144no—
465C22×C7C2×#9511yescharacteristic
466C22×C7#37911yescharacteristic
467C22×C7#38111yescharacteristic
468C22×C7#38511yescharacteristic
469C22×C7#38511yescharacteristic
470C22×C7#38611yescharacteristic
471C22×C7#38611yescharacteristic
472C22×C7#41611yescharacteristic
473C22×C7#41611yescharacteristic
474C22×C7#41611yescharacteristic
475C22×C7#41611yescharacteristic
476C22×C7#41711yescharacteristic
477C22×C7#41711yescharacteristic
478C22×C7#41811yescharacteristic
479C22×C7#41911yescharacteristic
480C22×C7#42711yescharacteristic
481C22×C7#42711yescharacteristic
482C22×C7#42811yescharacteristic
483C22×C7#42811yescharacteristic
484C22×C7#44911yescharacteristic
485C22×C7#44911yescharacteristic
486C22×C7#44911yescharacteristic
487C22×C7#44911yescharacteristic
488C22×C7#45211yescharacteristic
489C22×C7#45211yescharacteristic
490C22×C7#45211yescharacteristic
491C22×C7#45211yescharacteristic
492C22×C7#48211yescharacteristic
493C22×C7#48211yescharacteristic
494C22×C7#48211yescharacteristic
495C22×C7#48211yescharacteristic
496C22×C7#48511yescharacteristic
497C22×C7#48511yescharacteristic
498C22×C7#48511yescharacteristic
499C22×C7#48511yescharacteristic
500C2×D7—24no—
501C2×D7—24no—
502C2×D7—24no—
503C2×D7—42no—
504C2×D7—42no—
505C2×D7—42no—
506C2×D7—42no—
507C2×D7—42no—
508C2×D7—42no—
509C2×D7—42no—
510C2×D7—42no—
511C2×D7—42no—
512C2×D7—42no—
513C2×D7—42no—
514C2×D7—42no—
515C4×C7—44no—
516C4×C7—82no—
517C4×C7C4×C22⋊C411yescharacteristic
518C4×C7C4×C22⋊C411yescharacteristic
519C4×C7#38011yescharacteristic
520C4×C7#38011yescharacteristic
521C4×C7#38511yescharacteristic
522C4×C7#38511yescharacteristic
523C4×C7#38611yescharacteristic
524C4×C7#38611yescharacteristic
525Dic7—24no—
526Dic7—44no—
527Dic7—82no—
528C24—72no—
529C24—72no—
530C24—72no—
531C24—141no—
532C24—141no—
533C24—141no—
534C24—141no—
535C24—141no—
536C24—141no—
537C24—141no—
538C24—141no—
539C24—141no—
540C24—141no—
541C24—141no—
542C24—141no—
543C24D4×D711yescharacteristic
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—74no—
562C22×C4—74no—
563C22×C4—74no—
564C22×C4—74no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
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—281no—
598C22×C4—281no—
599C22×C4—281no—
600C22×C4—281no—
601C22×C4—281no—
602C22×C4—281no—
603C22×C4—281no—
604C22×C4—281no—
605C22×C4—281no—
606C22×C4—281no—
607C22×C4C2×C4×D711yescharacteristic
608C22×C4C2×C4×D711yescharacteristic
609C22×C4C2×C4×D711yescharacteristic
610C22×C4C2×D2811yescharacteristic
611C22×C4#115711yescharacteristic
612C22×C4#115711yescharacteristic
613C22×C4D4×D711yescharacteristic
614C22×C4D4×D711yescharacteristic
615C22×C4D4×D711yescharacteristic
616C22×C4D4×D711yescharacteristic
617C22×C4#115911yescharacteristic
618C22×C4Q8×D711yescharacteristic
619C22×C4#116111yescharacteristic
620C22×C4C2×C22⋊D711yescharacteristic
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—142no—
629C2×C8—142no—
630C2×C8—142no—
631C2×C8—281no—
632C2×C8—281no—
633C2×C8—281no—
634C2×C8—281no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—74no—
643C4⋊C4—142no—
644C4⋊C4—142no—
645C4⋊C4—142no—
646C4⋊C4—142no—
647C4⋊C4—142no—
648C4⋊C4—281no—
649C4⋊C4—281no—
650C4⋊C4(C2×D7)⋊C414yescomplemented
651C22⋊C4—1416no—
652C22⋊C4—288no—
653C42—1416no—
654C2×C7C22⋊#9511yescharacteristic
655C2×C7#173511yescharacteristic
656C2×C7#173611yescharacteristic
657C2×C7#178811yescharacteristic
658C2×C7#178811yescharacteristic
659C2×C7#182511yescharacteristic
660C2×C7#182511yescharacteristic
661C2×C7#185411yescharacteristic
662C2×C7#185411yescharacteristic
663C2×C7#185411yescharacteristic
664C2×C7#185411yescharacteristic
665C2×C7#187311yescharacteristic
666C2×C7#187311yescharacteristic
667C2×C7#187511yescharacteristic
668C2×C7#187511yescharacteristic
669D7—44no—
670C23—74no—
671C23—142no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—142no—
678C23—142no—
679C23—142no—
680C23—142no—
681C23—142no—
682C23—142no—
683C23—142no—
684C23—142no—
685C23—142no—
686C23—142no—
687C23—142no—
688C23—142no—
689C23—281no—
690C23—281no—
691C23—281no—
692C23—281no—
693C23—281no—
694C23—281no—
695C23—281no—
696C23—281no—
697C23—281no—
698C23—281no—
699C23—281no—
700C23—281no—
701C23—281no—
702C23—281no—
703C23—281no—
704C23—281no—
705C23D7×C22⋊C411yescharacteristic
706C23D7×C22⋊C411yescharacteristic
707C23#644511yescharacteristic
708C23#644611yescharacteristic
709C23D7×C4⋊C411yescharacteristic
710C23#645711yescharacteristic
711C23#647411yescharacteristic
712C23#647511yescharacteristic
713C23#647711yescharacteristic
714C23#647811yescharacteristic
715C23#647911yescharacteristic
716C23#647911yescharacteristic
717C23#648111yescharacteristic
718C23#648211yescharacteristic
719C23#650011yescharacteristic
720C2×C4—24no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—74no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—144no—
742C2×C4—144no—
743C2×C4—144no—
744C2×C4—144no—
745C2×C4—144no—
746C2×C4—144no—
747C2×C4—144no—
748C2×C4—144no—
749C2×C4—144no—
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—561no—
760C2×C4—561no—
761C2×C4—561no—
762C2×C4—561no—
763C2×C4C42×D711yescharacteristic
764C2×C4#643511yescharacteristic
765C2×C4C4×D2811yescharacteristic
766C2×C4C4×D2811yescharacteristic
767C2×C4D7×C22⋊C411yescharacteristic
768C2×C4D7×C22⋊C411yescharacteristic
769C2×C4(C22⋊D7)⋊C411yescharacteristic
770C2×C4(C22⋊D7)⋊C411yescharacteristic
771C2×C4#644511yescharacteristic
772C2×C4#644611yescharacteristic
773C2×C4#644711yescharacteristic
774C2×C4#644711yescharacteristic
775C2×C4D7×C4⋊C411yescharacteristic
776C2×C4D7×C4⋊C411yescharacteristic
777C2×C4#645511yescharacteristic
778C2×C4#645611yescharacteristic
779C2×C4#645611yescharacteristic
780C2×C4#645711yescharacteristic
781C2×C4#645811yescharacteristic
782C2×C4#645911yescharacteristic
783C2×C4#645911yescharacteristic
784C2×C4#646011yescharacteristic
785C2×C4C2×(C2×D7)⋊C411yescharacteristic
786C2×C4C4×C22⋊D711yescharacteristic
787C2×C4C4×C22⋊D711yescharacteristic
788C2×C4#650011yescharacteristic
789C2×C4#650111yescharacteristic
790C2×C4#650911yescharacteristic
791C8—42no—
792C8—282no—
793C7#1073111yescharacteristic, complemented, Sylow
794C22—144no—
795C22—144no—
796C22—144no—
797C22—282no—
798C22—282no—
799C22—282no—
800C22—282no—
801C22—282no—
802C22—282no—
803C22—282no—
804C22—282no—
805C22—282no—
806C22—282no—
807C22—282no—
808C22—282no—
809C22D7×#9511yescharacteristic
810C22#8943611yescharacteristic
811C22#8943711yescharacteristic
812C22#8944011yescharacteristic
813C22#8954211yescharacteristic
814C22#8954311yescharacteristic
815C22#8954411yescharacteristic
816C22#8954411yescharacteristic
817C22#8955111yescharacteristic
818C22#8955311yescharacteristic
819C22#8955511yescharacteristic
820C22#8955611yescharacteristic
821C22#8957411yescharacteristic
822C22#8957511yescharacteristic
823C22#8957611yescharacteristic
824C22#8957611yescharacteristic
825C22#8958211yescharacteristic
826C22#8958311yescharacteristic
827C22#8958611yescharacteristic
828C22#8958711yescharacteristic
829C22#8963211yescharacteristic
830C22#8963311yescharacteristic
831C22#8963811yescharacteristic
832C22#8963911yescharacteristic
833C22#8965211yescharacteristic
834C22#8965311yescharacteristic
835C22#8965711yescharacteristic
836C22#8966011yescharacteristic
837C22#8972711yescharacteristic
838C22#8972811yescharacteristic
839C22#8976111yescharacteristic
840C22#8993011yescharacteristic
841C22#8994411yescharacteristic
842C22#8994511yescharacteristic
843C22#8995911yescharacteristic
844C4—44no—
845C4—82no—
846C4—144no—
847C4—284no—
848C4—562no—
849C4#8943711yescharacteristic
850C4#8943811yescharacteristic
851C4#8943911yescharacteristic
852C4#8944011yescharacteristic
853C4C4×(C2×D7)⋊C411yescharacteristic
854C4#8972811yescharacteristic
855C4#8975911yescharacteristic
856C4#8976111yescharacteristic
857C2—284no—
858C2#1172656711yescharacteristic
859C2#1172662011yescharacteristic
860C2#1172662111yescharacteristic
861C2#1172662711yescharacteristic
862C2#1172663011yescharacteristic
863C2#1172663111yescharacteristic
864C2#1172663311yescharacteristic
865C2#1172663511yescharacteristic
866C2(C2×D7)⋊#9511yescharacteristic
867C2#1172795311yescharacteristic
868C2#1172795511yescharacteristic
869C2#1172802111yescharacteristic
870C2#1172802311yescharacteristic
871C2#1172833411yescharacteristic
872C2#1172838711yescharacteristic
subgroupG/H
centerC24D4×D7
commutatorC2×C4×C7C2×C42
FrattiniC23×C4C22×D7
FittingC2×C7×#340C2
socleC24×C7C2×D4
prime radicalC24×D7D4
cosocleC23×C4×C7C23
hypercenterC2×#340D7
hypocenterC7#10731
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×C7×#340C2semidirect
5. C2×#89346C2semidirect
6. C2×#89324C2semidirect
7. C2×#89324C2semidirect
23. C2×#6455C4semidirect
27. C2×(C2×D7)⋊C8C4semidirect
29. #89759C4semidirect
115. C2×#340D7semidirect
223. C7×C4⋊C4C22⋊C4semidirect
233. C4⋊Dic7C22⋊C4semidirect
650. C4⋊C4(C2×D7)⋊C4semidirect
793. C7#10731semidirect

Maximal subgroups

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

subgroupindex
C22×#64552
C22×(C2×D7)⋊C82
C2×#897592
C2×C7×#3402
C2×#893462
C2×#893242
#107317