Finite Group Databasebeta

← #13360495

Subgroups — #13360495

Order 1792.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×#121C211yesmaximal, characteristic, complemented
2C2×#89811C211yesmaximal, characteristic
3C2×#89786C211yesmaximal, characteristic, complemented
4C4×#6493C211yesmaximal, characteristic, complemented
5C2×C4×#1136C211yesmaximal, characteristic, complemented
6#11729436C211yesmaximal, characteristic, complemented
7#11729363C211yesmaximal, characteristic, complemented
8#11727401C211yesmaximal, characteristic, complemented
9#11727398C211yesmaximal, characteristic, complemented
10#11727372C211yesmaximal, characteristic, complemented
11#11727369C211yesmaximal, characteristic, complemented
12#11727271C211yesmaximal, characteristic, complemented
13#11727267C211yesmaximal, characteristic, complemented
14#11727235C211yesmaximal, characteristic, complemented
15#11727228C211yesmaximal, characteristic, complemented
16C2×C7×#121C2211yescharacteristic
17C2×C4×C7×D4—21no—
18C2×C4×C7×D4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×#1141C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×C4×C22⋊D7—21no—
23C22×#1136C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25C2×C4×D28C2211yescharacteristic
26C7×#390C2211yescharacteristic
27C7×#389C2211yescharacteristic
28C7×#388—21no—
29C7×#386—21no—
30C7×#380C2211yescharacteristic
31C4×C7×C4⋊C4C2211yescharacteristic
32C4×C7×C22⋊C4—21no—
33C2×#6406C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36#89985—21no—
37#89984C2211yescharacteristic
38#89811C418yescomplemented
39#89786—24no—
40C2×#6383C2211yescharacteristic
41C2×#6383C2211yescharacteristic
42C2×#6383C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C2×#6382C2211yescharacteristic
45C2×#6381C2211yescharacteristic
46#89712—21no—
47#89711C2211yescharacteristic
48C4×(C2×D7)⋊C4—21no—
49C4×C4⋊Dic7C2211yescharacteristic
50#89700C2211yescharacteristic
51C4×#1136—24no—
52C2×#6377C2211yescharacteristic
53C2×#6377C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×C4×C7⋊C8C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#21538—71nomaximal, Sylow
63C22×C7×D4—21no—
64C22×C7×D4C2311yescharacteristic
65C23×C4×C7—21no—
66C23×C4×C7D411yescharacteristic
67C23×C4×C7D411yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C22×C22⋊D7—21no—
70C22×D28C2311yescharacteristic
71C22×C4×D7—21no—
72C7×#121—22no—
73C7×#121C2×C414yescomplemented
74C4×C7×D4—22no—
75C4×C7×D4—22no—
76C4×C7×D4—44no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C22⋊C4—21no—
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—21no—
89C2×C42×C7D411yescharacteristic
90C2×C42×C7D411yescharacteristic
91C2×C42×C7C2311yescharacteristic
92C2×C42×C7C2311yescharacteristic
93C2×C22⋊Dic7—21no—
94C2×#1141—22no—
95C2×#1141—22no—
96C2×#1141C2×C414yescomplemented
97#6493—22no—
98#6493C2×C414yescomplemented
99C4×C22⋊D7—44no—
100C2×(C2×D7)⋊C4—21no—
101C2×(C2×D7)⋊C4—21no—
102C2×(C2×D7)⋊C4—21no—
103C2×(C2×D7)⋊C4—21no—
104C2×C4⋊Dic7C2311yescharacteristic
105C2×C4⋊Dic7C2311yescharacteristic
106C2×C4⋊Dic7C2311yescharacteristic
107C2×Dic7⋊C4—21no—
108C2×C4×Dic7—21no—
109C2×#1136—22no—
110C2×#1136—22no—
111C2×#1136—22no—
112C2×#1136—22no—
113C2×#1136—22no—
114C2×#1136C2×C414yescomplemented
115C22×C7⋊C8C2311yescharacteristic
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C22×C7⋊C8C2311yescharacteristic
119C4×D28—22no—
120C4×D28—22no—
121C7×#95—21no—
122C7×#95—21no—
123C7×#95—21no—
124#6406—22no—
125#6406—22no—
126#6406C2×C414yescomplemented
127C7⋊#95—21no—
128C7⋊#95—21no—
129C7⋊#95—21no—
130#6383—22no—
131#6383—22no—
132#6383C2×C414yescomplemented
133#6382—22no—
134#6382C2×C414yescomplemented
135#6381—22no—
136#6377—22no—
137#6377D414yescomplemented
138C4×C7⋊C8—22no—
139C4×C7⋊C8—22no—
140C2×#469—71no—
141C2×#442—71no—
142C2×C4×M16—71no—
143C4×#121—71no—
144C4×#121D711yescharacteristic, complemented
145#1970—71no—
146#1941—71no—
147#1934—71no—
148#1934—71no—
149#1895—71no—
150#1895—71no—
151#1809—71no—
152#1776—71no—
153#1762—71no—
154#1762—71no—
155C24×C7—21no—
156C24×C7C2×D411yescharacteristic
157C23×D7—21no—
158C2×C7×D4—24no—
159C2×C7×D4—21no—
160C2×C7×D4—21no—
161C2×C7×D4—21no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4—42no—
165C2×C7×D4—42no—
166C2×C7×D4C22×C412yes—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—41no—
179C22×C4×C7—41no—
180C22×C4×C7—42no—
181C22×C4×C7—42no—
182C22×C4×C7—42no—
183C22×C4×C7C22×C412yes—
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7#4112yes—
190C22×C4×C7C2411yescharacteristic
191C2×C22⋊D7—24no—
192C2×C22⋊D7—42no—
193C2×C22⋊D7—42no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C2×D28—21no—
198C2×D28—21no—
199C2×D28—21no—
200C2×D28—21no—
201C2×D28—21no—
202C2×D28C22×C412yes—
203C2×C4×D7—42no—
204C2×C4×D7—42no—
205C2×C4×D7—42no—
206C7×C4⋊C4—21no—
207C7×C4⋊C4—21no—
208C7×C4⋊C4—21no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4—21no—
211C7×C4⋊C4—42no—
212C7×C4⋊C4C22×C412yes—
213C7×C22⋊C4—24no—
214C7×C22⋊C4—42no—
215C7×C22⋊C4—42no—
216C7×C22⋊C4—42no—
217C7×C22⋊C4—42no—
218C42×C7—22no—
219C42×C7—22no—
220C42×C7—21no—
221C42×C7—21no—
222C42×C7—42no—
223C42×C7C2×D412yes—
224C42×C7#4112yes—
225C22⋊Dic7—42no—
226#1141—28no—
227(C2×D7)⋊C4—24no—
228(C2×D7)⋊C4—42no—
229(C2×D7)⋊C4—42no—
230(C2×D7)⋊C4—42no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7C22×C412yes—
237Dic7⋊C4—42no—
238C4×Dic7—42no—
239#1136—28no—
240#1136—28no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8C22×C412yes—
248C2×C7⋊C8C22×C412yes—
249C2×C7⋊C8C2×D412yes—
250C2×C7⋊C8C2×D412yes—
251C2×C7⋊C8#4112yes—
252C2×C7⋊C8#4112yes—
253C22×D8—71no—
254C22×M16—71no—
255C22×M16—71no—
256C2×#121—71no—
257C2×#121C2×D711yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4—71no—
260C2×C4×D4—141no—
261C2×C4×D4C2×D711yescharacteristic
262C22×C42C2×D711yescharacteristic
263#469—78no—
264#442—144no—
265C2×#107—71no—
266C2×#106—71no—
267C2×#106—71no—
268C2×#102—71no—
269C2×#102—71no—
270C2×#102—71no—
271C2×#102—71no—
272C2×#102—71no—
273C2×#102—71no—
274C4×M16—144no—
275C2×#97—71no—
276C2×#97—71no—
277C2×C4×C8—71no—
278C2×C4×C8—71no—
279#390—71no—
280#390C2×D711yescharacteristic
281#389—71no—
282#389C2×D711yescharacteristic
283#388—21no—
284#388—141no—
285#386—21no—
286#386—141no—
287#380—71no—
288#380C2×D711yescharacteristic
289C4×C4⋊C4—71no—
290C4×C4⋊C4C2×D711yescharacteristic
291C4×C22⋊C4—21no—
292C4×C22⋊C4—141no—
293#340—71no—
294#340—71no—
295#340—71no—
296#340—71no—
297#340—71no—
298#340—71no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—22no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7C4×D412yes—
313C23×C7C22×D411yescharacteristic
314C22×D7—22no—
315C22×D7—41no—
316C22×D7—41no—
317C22×D7—41no—
318C22×D7—41no—
319C22×D7—41no—
320C22×D7—41no—
321C7×D4—22no—
322C7×D4—22no—
323C7×D4—48no—
324C7×D4—41no—
325C7×D4—41no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—44no—
342C2×C4×C7—44no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—84no—
352C2×C4×C7C4×D412yes—
353C2×C4×C7#12112yes—
354C2×C4×C7#12112yes—
355C2×C4×C7AGL(1,ℤ/8)12yes—
356C2×C4×C7AGL(1,ℤ/8)12yes—
357C2×C4×C7C23×C411yescharacteristic
358C2×C4×C7C22×D411yescharacteristic
359C2×C4×C7C2×#4111yescharacteristic
360C2×C4×C7C2×#4111yescharacteristic
361C2×C4×C7C2×#4111yescharacteristic
362C2×C4×C7C2×#4111yescharacteristic
363C22⋊D7—48no—
364C2×Dic7—22no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373D28—22no—
374D28—22no—
375D28—41no—
376D28—41no—
377C4×D7—84no—
378C7⋊C8—22no—
379C7⋊C8—22no—
380C7⋊C8—22no—
381C7⋊C8C4×D414yescomplemented
382C22×D4—21no—
383C22×D4—71no—
384C22×D4—141no—
385C22×D4C22×D711yescharacteristic
386C23×C4—21no—
387C23×C4—141no—
388C23×C4C22⋊D711yescharacteristic
389C23×C4C22⋊D711yescharacteristic
390C23×C4C22×D711yescharacteristic
391C2×D8—74no—
392C2×D8—142no—
393C2×D8—142no—
394C2×M16—74no—
395C2×M16—142no—
396C2×M16—142no—
397C2×M16—142no—
398C2×M16—142no—
399C2×M16—142no—
400C22×C8—71no—
401C22×C8—71no—
402C22×C8—71no—
403C22×C8—71no—
404#121—22no—
405#121—74no—
406#121—142no—
407#121C4×D714yescomplemented
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—44no—
411C4×D4—142no—
412C4×D4—142no—
413C4×D4—284no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—141no—
419C2×C4⋊C4C22×D711yescharacteristic
420C2×C4⋊C4C22×D711yescharacteristic
421C2×C4⋊C4C22×D711yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—141no—
428C2×C22⋊C4—141no—
429C2×C22⋊C4—141no—
430C2×C22⋊C4—141no—
431C2×C22⋊C4—141no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—21no—
435C2×C42—141no—
436C2×C42C22⋊D711yescharacteristic
437C2×C42C22⋊D711yescharacteristic
438C2×C42C22×D711yescharacteristic
439C2×C42C22×D711yescharacteristic
440#107—142no—
441#106—74no—
442#106—142no—
443#102—74no—
444#102—74no—
445#102—142no—
446#102—142no—
447#102—142no—
448#102—142no—
449#97—74no—
450#97—142no—
451C4×C8—142no—
452C4×C8—142no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—141no—
457#95—141no—
458#95—141no—
459C22×C7—22no—
460C22×C7—22no—
461C22×C7—22no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—42no—
467C22×C7—42no—
468C22×C7—42no—
469C22×C7—81no—
470C22×C7—81no—
471C22×C7—81no—
472C22×C7—81no—
473C22×C7C2×C4×D411yescharacteristic
474C22×C7C2×#12111yescharacteristic
475C22×C7#53211yescharacteristic
476C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
477C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
478C22×C7#57511yescharacteristic
479C22×C7#57511yescharacteristic
480C2×D7—42no—
481C2×D7—42no—
482C2×D7—42no—
483C2×D7—81no—
484C2×D7—81no—
485C2×D7—81no—
486C2×D7—81no—
487C4×C7—22no—
488C4×C7—22no—
489C4×C7—22no—
490C4×C7—22no—
491C4×C7—22no—
492C4×C7—42no—
493C4×C7—81no—
494C4×C7—81no—
495C4×C7C2×C4×D411yescharacteristic
496C4×C7C4×#4111yescharacteristic
497C4×C7#52511yescharacteristic
498C4×C7#52911yescharacteristic
499Dic7—42no—
500Dic7—81no—
501Dic7—81no—
502C24—21no—
503C24—141no—
504C24C2×C22⋊D711yescharacteristic
505C2×D4—24no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—72no—
514C2×D4—144no—
515C2×D4—141no—
516C2×D4—141no—
517C2×D4—141no—
518C2×D4—141no—
519C2×D4—141no—
520C2×D4—282no—
521C2×D4—282no—
522C2×D4C2×C4×D712yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—141no—
540C22×C4—141no—
541C22×C4—141no—
542C22×C4—282no—
543C22×C4—282no—
544C22×C4—282no—
545C22×C4C2×C4×D712yes—
546C22×C4#115712yes—
547C22×C4C2×C22⋊D711yescharacteristic
548C22×C4C2×C22⋊D711yescharacteristic
549C22×C4C2×C22⋊D711yescharacteristic
550C22×C4C2×C22⋊D711yescharacteristic
551C22×C4C2×C22⋊D711yescharacteristic
552C22×C4C23×D711yescharacteristic
553D8—148no—
554M16—148no—
555M16—148no—
556C2×C8—72no—
557C2×C8—72no—
558C2×C8—72no—
559C2×C8—72no—
560C2×C8—72no—
561C2×C8—72no—
562C2×C8—141no—
563C2×C8—141no—
564C2×C8—141no—
565C2×C8—141no—
566C2×C8—141no—
567C2×C8—141no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—72no—
575C4⋊C4—141no—
576C4⋊C4—141no—
577C4⋊C4—141no—
578C4⋊C4—141no—
579C4⋊C4—141no—
580C4⋊C4—282no—
581C4⋊C4C2×C4×D712yes—
582C22⋊C4—24no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—144no—
588C22⋊C4—282no—
589C22⋊C4—282no—
590C22⋊C4—282no—
591C22⋊C4—282no—
592C42—22no—
593C42—22no—
594C42—21no—
595C42—21no—
596C42—42no—
597C42—282no—
598C42D4×D712yes—
599C42#115912yes—
600C2×C7—42no—
601C2×C7—82no—
602C2×C7C4×#12111yescharacteristic
603C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
604C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
605C2×C7#305511yescharacteristic
606C2×C7#305511yescharacteristic
607C2×C7#318311yescharacteristic
608C2×C7#318411yescharacteristic
609D7—82no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—142no—
624C23—281no—
625C23—281no—
626C23—281no—
627C23—281no—
628C23—281no—
629C23—281no—
630C23C4×C22⋊D712yes—
631C23C22×C22⋊D711yescharacteristic
632D4—22no—
633D4—22no—
634D4—48no—
635D4—41no—
636D4—41no—
637D4—142no—
638D4—142no—
639D4—288no—
640D4—281no—
641D4—281no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—142no—
669C2×C4—281no—
670C2×C4—281no—
671C2×C4—281no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4—281no—
677C2×C4—564no—
678C2×C4C4×C22⋊D712yes—
679C2×C4#649512yes—
680C2×C4#650212yes—
681C2×C4#650212yes—
682C2×C4#651212yes—
683C2×C4C22×C4×D711yescharacteristic
684C2×C4C2×#115711yescharacteristic
685C2×C4C2×D4×D711yescharacteristic
686C2×C4C2×#115911yescharacteristic
687C2×C4D7×#4111yescharacteristic
688C2×C4D7×#4111yescharacteristic
689C8—74no—
690C8—142no—
691C8—142no—
692C8—142no—
693C7#2153811yescharacteristic, complemented, Sylow
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—282no—
709C22—282no—
710C22—282no—
711C22—561no—
712C22—561no—
713C22—561no—
714C22—561no—
715C22C2×C4×C22⋊D711yescharacteristic
716C22C2×#649511yescharacteristic
717C22C2×#650211yescharacteristic
718C22C2×#651211yescharacteristic
719C22#9051311yescharacteristic
720C22#9051311yescharacteristic
721C22#9052311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—81no—
729C4—81no—
730C4—282no—
731C4—561no—
732C4—561no—
733C4C4×#115911yescharacteristic
734C4#9022911yescharacteristic
735C4C4×D4×D711yescharacteristic
736C4#9023811yescharacteristic
737C2—42no—
738C2—82no—
739C2—562no—
740C2C4×#649511yescharacteristic
741C2C4×#650211yescharacteristic
742C2C4×#651211yescharacteristic
743C2#1174006611yescharacteristic
744C2#1174036911yescharacteristic
745C2#1174058411yescharacteristic
746C2#1174074011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×#121C2
socleC23×C7C22×D4
prime radicalC2×#89811C2
cosocleC22×C4×C7C24
hypercenterC4×#121D7
hypocenterC7#21538
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C4×C7×#121C2semidirect
3. C2×#89786C2semidirect
4. C4×#6493C2semidirect
5. C2×C4×#1136C2semidirect
6. #11729436C2semidirect
7. #11729363C2semidirect
8. #11727401C2semidirect
9. #11727398C2semidirect
10. #11727372C2semidirect
11. #11727369C2semidirect
12. #11727271C2semidirect
13. #11727267C2semidirect
14. #11727235C2semidirect
15. #11727228C2semidirect
38. #89811C4semidirect
73. C7×#121C2×C4semidirect
96. C2×#1141C2×C4semidirect
98. #6493C2×C4semidirect
114. C2×#1136C2×C4semidirect
126. #6406C2×C4semidirect
132. #6383C2×C4semidirect
134. #6382C2×C4semidirect
137. #6377D4semidirect
144. C4×#121D7semidirect
381. C7⋊C8C4×D4semidirect
407. #121C4×D7semidirect
693. C7#21538semidirect

Maximal subgroups

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

subgroupindex
C4×C7×#1212
C2×#898112
C2×#897862
C4×#64932
C2×C4×#11362
#117294362
#117293632
#117274012
#117273982
#117273722
#117273692
#117272712
#117272672
#117272352
#117272282
#215387