Finite Group Databasebeta

← #13353906

Subgroups — #13353906

Order 1792.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#520C211yesmaximal, characteristic
2#11739676C211yesmaximal, characteristic, complemented
3C2×#89772C211yesmaximal, characteristic, complemented
4#11729889C211yesmaximal, characteristic
5#11729889C211yesmaximal, characteristic
6#11729385C211yesmaximal, characteristic, complemented
7C4×#6409C211yesmaximal, characteristic, complemented
8#11729381C211yesmaximal, characteristic, complemented
9#11729380C211yesmaximal, characteristic, complemented
10#11729363C211yesmaximal, characteristic, complemented
11C4×#6406C211yesmaximal, characteristic, complemented
12#11729359C211yesmaximal, characteristic, complemented
13#11729358C211yesmaximal, characteristic, complemented
14#11729308C211yesmaximal, characteristic, complemented
15#11729307C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C7×#520—24no—
18C7×#520C418yescomplemented
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4—21no—
22C2×C4×C7×D4—21no—
23C2×C4×C7×D4C2211yescharacteristic
24C2×C4×C7×D4C2211yescharacteristic
25C2×C7×#117—21no—
26C2×C7×#117C2211yescharacteristic
27C22×C7×C4⋊C4—21no—
28C22×C7×C4⋊C4C2211yescharacteristic
29C2×#6409C2211yescharacteristic
30C2×#6409C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37#89984C2211yescharacteristic
38#89984C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41#89772—24no—
42#89753—21no—
43#89753—21no—
44#89723—21no—
45#89723—21no—
46#89708C2211yescharacteristic
47#89707C2211yescharacteristic
48C4×C4⋊Dic7C2211yescharacteristic
49C4×C4⋊Dic7C2211yescharacteristic
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#20746—71nomaximal, Sylow
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41C2×C414yes—
69C22×C7×Q8C2311yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7—21no—
76C23×C4×C7C2311yescharacteristic
77C4×C7×Q8—22no—
78C4×C7×Q8—22no—
79C4×C7×Q8C2×C414yes—
80C4×C7×Q8C2×C414yes—
81C4×C7×D4—28no—
82C4×C7×D4—28no—
83C4×C7×D4—22no—
84C4×C7×D4—22no—
85C4×C7×D4C2×C414yes—
86C4×C7×D4C2×C414yes—
87C7×#117—28no—
88C7×#117C2×C414yes—
89C7×#117D414yes—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—28no—
95C2×C7×C4⋊C4C2×C414yes—
96C2×C7×C4⋊C4D411yescharacteristic
97C2×C7×C4⋊C4D411yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C7×C22⋊C4D411yescharacteristic
104C2×C42×C7—21no—
105C2×C42×C7—21no—
106C2×C42×C7C2311yescharacteristic
107C2×C42×C7C2311yescharacteristic
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—21no—
112C2×C4⋊Dic7C2311yescharacteristic
113C2×C4⋊Dic7C2311yescharacteristic
114C2×C4⋊Dic7C2311yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4×Dic7—21no—
117C2×C4×Dic7—21no—
118C22×C7⋊C8C2311yescharacteristic
119C22×C7⋊C8C2311yescharacteristic
120C22×C7⋊C8C2311yescharacteristic
121C22×C7⋊C8C2311yescharacteristic
122#6409—22no—
123#6409—22no—
124#6409—22no—
125#6409—22no—
126#6406—22no—
127#6406—22no—
128#6406—22no—
129#6406—22no—
130C7⋊#95—21no—
131C7⋊#95—21no—
132C7⋊#95—21no—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C22⋊(C7⋊C8)—22no—
137C22⋊(C7⋊C8)—22no—
138C4⋊(C7⋊C8)—22no—
139C4⋊(C7⋊C8)—22no—
140#6377—22no—
141C4×C7⋊C8—22no—
142C2×#520D711yescharacteristic
143C2×#433—71no—
144#2314—71no—
145#1824—71no—
146#1823—71no—
147#1805—71no—
148#1804—71no—
149#1803—71no—
150#1802—71no—
151#1788—71no—
152#1788—71no—
153#1763—71no—
154#1762—71no—
155C4×#103—71no—
156C4×#102—71no—
157C24×C7—21no—
158C24×C7C2×D411yescharacteristic
159C7×#41—28no—
160C7×#41—28no—
161C7×#41—28no—
162C7×#41—28no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8C22×C412yes—
167C2×C7×Q8#4112yes—
168C2×C7×Q8#4112yes—
169C2×C7×D4—24no—
170C2×C7×D4—24no—
171C2×C7×D4—24no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4C22×C412yes—
176C2×C7×D4#4112yes—
177C2×C7×D4#4112yes—
178C22×C4×C7—24no—
179C22×C4×C7—24no—
180C22×C4×C7—21no—
181C22×C4×C7—24no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—24no—
189C22×C4×C7—24no—
190C22×C4×C7—24no—
191C22×C4×C7—81no—
192C22×C4×C7—81no—
193C22×C4×C7—81no—
194C22×C4×C7—81no—
195C22×C4×C7—81no—
196C22×C4×C7—81no—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2411yescharacteristic
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C7×C4⋊C4—24no—
210C7×C4⋊C4—24no—
211C7×C4⋊C4—24no—
212C7×C4⋊C4—21no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4C22⋊C414yes—
215C7×C4⋊C4C22⋊C414yes—
216C7×C4⋊C4C22×C412yes—
217C7×C4⋊C4C22×C412yes—
218C7×C22⋊C4—24no—
219C7×C22⋊C4—24no—
220C7×C22⋊C4C22⋊C414yes—
221C7×C22⋊C4C22⋊C414yes—
222C42×C7—24no—
223C42×C7—24no—
224C42×C7C22×C412yes—
225C42×C7C22×C412yes—
226C42×C7C2×D412yes—
227C42×C7C2×D412yes—
228C22⋊Dic7—81no—
229C22⋊Dic7—81no—
230C4⋊Dic7—21no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7—21no—
237C4⋊Dic7—21no—
238C4⋊Dic7—81no—
239C4⋊Dic7—81no—
240C4×Dic7—81no—
241C4×Dic7—81no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C22×#41C2×D711yescharacteristic
255#520—24no—
256#520Dic718yescomplemented
257C2×C4×Q8C2×D711yescharacteristic
258C2×C4×Q8C2×D711yescharacteristic
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4C2×D711yescharacteristic
262C2×C4×D4C2×D711yescharacteristic
263C2×#117—21no—
264C2×#117C2×D711yescharacteristic
265C22×C4⋊C4—21no—
266C22×C4⋊C4C2×D711yescharacteristic
267#433—144no—
268C2×C4⋊C8—71no—
269C2×C4⋊C8—71no—
270C2×#103—71no—
271C2×#103—71no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#102—71no—
275C2×#102—71no—
276C2×#102—71no—
277C2×#102—71no—
278C2×C22⋊C8—71no—
279C2×C22⋊C8—71no—
280C2×#97—71no—
281C2×C4×C8—71no—
282#388—141no—
283#388—141no—
284#387—141no—
285#387—141no—
286#384—71no—
287#382—71no—
288#380—71no—
289#380—71no—
290C4×C4⋊C4—71no—
291C4×C4⋊C4—71no—
292#340—71no—
293#340—71no—
294#340—71no—
295#340—71no—
296#340—71no—
297#340—71no—
298#340—71no—
299#340—71no—
300C23×C7—22no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7C2×C22⋊C412yes—
314C23×C7C22×D411yescharacteristic
315C7×Q8—22no—
316C7×Q8—22no—
317C7×Q8—22no—
318C7×Q8#11714yes—
319C7×D4—216no—
320C7×D4—22no—
321C7×D4—22no—
322C7×D4—22no—
323C7×D4#11714yes—
324C2×C4×C7—216no—
325C2×C4×C7—22no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
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—21no—
337C2×C4×C7—21no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—84no—
349C2×C4×C7—84no—
350C2×C4×C7—84no—
351C2×C4×C7C2×C22⋊C412yes—
352C2×C4×C7C2×C22⋊C412yes—
353C2×C4×C7C2×C22⋊C412yes—
354C2×C4×C7C2×C22⋊C412yes—
355C2×C4×C7C2×C22⋊C412yes—
356C2×C4×C7C23×C411yescharacteristic
357C2×C4×C7C22×D411yescharacteristic
358C2×C4×C7C2×#4111yescharacteristic
359C2×C4×C7C2×#4111yescharacteristic
360C2×C4×C7C2×#4111yescharacteristic
361C2×C4×C7C2×#4111yescharacteristic
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C7⋊C8—41no—
375C7⋊C8—41no—
376C7⋊C8—41no—
377C7⋊C8—41no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41C2×Dic714yes—
384C22×Q8C22×D711yescharacteristic
385C22×D4—21no—
386C22×D4C22×D711yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—21no—
391C23×C4C22×D711yescharacteristic
392C22×C8—71no—
393C22×C8—71no—
394C22×C8—71no—
395C22×C8—71no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8C2×Dic714yes—
399C4×Q8C2×Dic714yes—
400C4×D4—28no—
401C4×D4—28no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4C2×Dic714yes—
405C4×D4C2×Dic714yes—
406#117—28no—
407#117C2×Dic714yes—
408#117C22⋊D714yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—28no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—141no—
419C2×C4⋊C4—141no—
420C2×C4⋊C4C2×Dic714yes—
421C2×C4⋊C4C22⋊D711yescharacteristic
422C2×C4⋊C4C22⋊D711yescharacteristic
423C2×C4⋊C4C22×D711yescharacteristic
424C2×C4⋊C4C22×D711yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—141no—
428C2×C22⋊C4—141no—
429C2×C22⋊C4C22⋊D711yescharacteristic
430C2×C22⋊C4C22⋊D711yescharacteristic
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—141no—
434C2×C42—141no—
435C2×C42C22×D711yescharacteristic
436C2×C42C22×D711yescharacteristic
437C4⋊C8—142no—
438C4⋊C8—142no—
439#103—142no—
440#103—142no—
441#103—142no—
442#103—142no—
443#102—142no—
444#102—142no—
445#102—142no—
446#102—142no—
447C22⋊C8—142no—
448C22⋊C8—142no—
449#97—142no—
450C4×C8—142no—
451#95—141no—
452#95—141no—
453#95—141no—
454#95—141no—
455#95—141no—
456#95—141no—
457C22×C7—22no—
458C22×C7—22no—
459C22×C7—22no—
460C22×C7—24no—
461C22×C7—41no—
462C22×C7—42no—
463C22×C7—41no—
464C22×C7—42no—
465C22×C7—41no—
466C22×C7—42no—
467C22×C7—41no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7C22×C22⋊C411yescharacteristic
472C22×C7#52511yescharacteristic
473C22×C7#52511yescharacteristic
474C22×C7#57611yescharacteristic
475C22×C7#57711yescharacteristic
476C22×C7#57711yescharacteristic
477C22×C7#57811yescharacteristic
478C4×C7—22no—
479C4×C7—22no—
480C4×C7—22no—
481C4×C7—22no—
482C4×C7—22no—
483C4×C7—24no—
484C4×C7—42no—
485C4×C7—42no—
486C4×C7C2×#11711yescharacteristic
487C4×C7C2×#11711yescharacteristic
488C4×C7#52511yescharacteristic
489C4×C7#52511yescharacteristic
490Dic7—81no—
491Dic7—81no—
492Dic7—81no—
493Dic7—81no—
494C24—21no—
495C24C2×C22⋊D711yescharacteristic
496#41—28no—
497#41—28no—
498#41—28no—
499#41—28no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8#115712yes—
504C2×Q8#115712yes—
505C2×Q8C22×Dic712yes—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4#115712yes—
513C2×D4#115712yes—
514C2×D4C22×Dic712yes—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—141no—
535C22×C4—141no—
536C22×C4—141no—
537C22×C4—141no—
538C22×C4C22×Dic712yes—
539C22×C4C2×C22⋊D711yescharacteristic
540C22×C4C2×C22⋊D711yescharacteristic
541C22×C4C2×C22⋊D711yescharacteristic
542C22×C4C2×C22⋊D711yescharacteristic
543C22×C4C2×C22⋊D711yescharacteristic
544C22×C4C2×C22⋊D712yes—
545C22×C4C23×D711yescharacteristic
546C2×C8—141no—
547C2×C8—141no—
548C2×C8—141no—
549C2×C8—141no—
550C2×C8—141no—
551C2×C8—141no—
552C2×C8—141no—
553C2×C8—141no—
554C2×C8—141no—
555C2×C8—141no—
556C2×C8—141no—
557C2×C8—141no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—141no—
564C4⋊C4—141no—
565C4⋊C4—141no—
566C4⋊C4—141no—
567C4⋊C4—141no—
568C4⋊C4—141no—
569C4⋊C4—141no—
570C4⋊C4—141no—
571C4⋊C4—561no—
572C4⋊C4—561no—
573C4⋊C4C22⋊Dic714yes—
574C4⋊C4C22⋊Dic714yes—
575C4⋊C4C22×Dic712yes—
576C4⋊C4C22×Dic712yes—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—561no—
580C22⋊C4—561no—
581C22⋊C4C22⋊Dic714yes—
582C22⋊C4C22⋊Dic714yes—
583C42—24no—
584C42—24no—
585C42—561no—
586C42—561no—
587C42C22×Dic712yes—
588C42C22×Dic712yes—
589C42C2×C22⋊D712yes—
590C42C2×C22⋊D712yes—
591C2×C7—42no—
592C2×C7—44no—
593C2×C7#228011yescharacteristic
594C2×C7#289711yescharacteristic
595C2×C7#289811yescharacteristic
596C2×C7#311911yescharacteristic
597C2×C7#312011yescharacteristic
598C2×C7#312411yescharacteristic
599C2×C7#312511yescharacteristic
600C23—21no—
601C23—21no—
602C23—22no—
603C23—22no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23C2×C22⋊Dic712yes—
614C23C22×C22⋊D711yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—22no—
618Q8#648914yes—
619D4—216no—
620D4—22no—
621D4—22no—
622D4—22no—
623D4#648914yes—
624C2×C4—216no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—281no—
652C2×C4—281no—
653C2×C4—281no—
654C2×C4—281no—
655C2×C4—281no—
656C2×C4—281no—
657C2×C4—281no—
658C2×C4—281no—
659C2×C4—281no—
660C2×C4—281no—
661C2×C4—281no—
662C2×C4—281no—
663C2×C4C2×C22⋊Dic712yes—
664C2×C4C2×C22⋊Dic712yes—
665C2×C4C2×C22⋊Dic712yes—
666C2×C4C2×C22⋊Dic712yes—
667C2×C4C2×C22⋊Dic712yes—
668C2×C4C2×#115711yescharacteristic
669C2×C4C2×#115711yescharacteristic
670C2×C4C2×#115711yescharacteristic
671C2×C4C2×#115711yescharacteristic
672C2×C4C23×Dic711yescharacteristic
673C2×C4C22×C22⋊D711yescharacteristic
674C8—281no—
675C8—281no—
676C8—281no—
677C8—281no—
678C7#2074611yescharacteristic, complemented, Sylow
679C22—22no—
680C22—24no—
681C22—22no—
682C22—22no—
683C22—42no—
684C22—41no—
685C22—42no—
686C22—41no—
687C22—42no—
688C22—41no—
689C22—42no—
690C22—42no—
691C22—41no—
692C22—42no—
693C22#9048211yescharacteristic
694C22#9048211yescharacteristic
695C22#9052611yescharacteristic
696C22#9052711yescharacteristic
697C22#9052811yescharacteristic
698C22#9052911yescharacteristic
699C22C22×C22⋊Dic711yescharacteristic
700C4—22no—
701C4—24no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—561no—
709C4—561no—
710C4—561no—
711C4—561no—
712C4C2×#648911yescharacteristic
713C4C2×#648911yescharacteristic
714C4#9048211yescharacteristic
715C4#9048211yescharacteristic
716C2—42no—
717C2—44no—
718C2#1174001311yescharacteristic
719C2#1174001411yescharacteristic
720C2#1174002011yescharacteristic
721C2#1174002111yescharacteristic
722C2#1174147211yescharacteristic
723C2#1174154411yescharacteristic
724C2#1174155611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#520C2
socleC23×C7C22×D4
prime radicalC22×C7×#41C22
cosocleC22×C4×C7C24
hypercenterC2×#520D7
hypocenterC7#20746
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. #11739676C2semidirect
3. C2×#89772C2semidirect
6. #11729385C2semidirect
7. C4×#6409C2semidirect
8. #11729381C2semidirect
9. #11729380C2semidirect
10. #11729363C2semidirect
11. C4×#6406C2semidirect
12. #11729359C2semidirect
13. #11729358C2semidirect
14. #11729308C2semidirect
15. #11729307C2semidirect
18. C7×#520C4semidirect
256. #520Dic7semidirect
678. C7#20746semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5202
#117396762
C2×#897722
#117298892
#117293852
C4×#64092
#117293812
#117293802
#117293632
C4×#64062
#117293592
#117293582
#117293082
#117293072
#207467