Finite Group Databasebeta

← #13363770

Subgroups — #13363770

Order 1792.

1078 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic
2#11739676C211yesmaximal, characteristic, complemented
3C2×#89771C211yesmaximal, characteristic, complemented
4#11729534C211yesmaximal, characteristic, complemented
5#11729533C211yesmaximal, characteristic, complemented
6#11729475C211yesmaximal, characteristic, complemented
7#11729475C211yesmaximal, characteristic, complemented
8#11729451C211yesmaximal, characteristic, complemented
9#11729450C211yesmaximal, characteristic, complemented
10#11729436C211yesmaximal, characteristic
11#11729435C211yesmaximal, characteristic
12#11729381C211yesmaximal, characteristic, complemented
13#11729380C211yesmaximal, characteristic, complemented
14#11729359C211yesmaximal, characteristic, complemented
15#11729358C211yesmaximal, characteristic, complemented
16C7×#542—24no—
17C7×#542C418yescomplemented
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C7×#126—21no—
20C2×C7×#124—21no—
21C2×C7×#124C2211yescharacteristic
22C2×C7×#123—21no—
23C2×C7×C22⋊Q8—21no—
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×#121C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C22×#1136C2211yescharacteristic
30C23×C7⋊C8C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39#89984C2211yescharacteristic
40#89984C2211yescharacteristic
41#89771—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×C4⋊(C7⋊C8)C2211yescharacteristic
53C2×C4⋊(C7⋊C8)C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#21896—71nomaximal, Sylow
63C22×C7×Q8—21no—
64C22×C7×Q8C2311yescharacteristic
65C22×C7×D4—21no—
66C22×C7×D4C2311yescharacteristic
67C23×C4×C7—21no—
68C23×C4×C7C2311yescharacteristic
69C7×C4⋊Q8—22no—
70C7×C4⋊Q8C2×C414yes—
71C7×#126—28no—
72C7×#124—28no—
73C7×#124—22no—
74C7×#124C2×C414yes—
75C7×#123—28no—
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8—28no—
78C7×C22⋊Q8C2×C414yes—
79C7×#121—22no—
80C7×#121C2×C414yes—
81C4×C7×Q8—22no—
82C4×C7×Q8C2×C414yes—
83C4×C7×D4—22no—
84C4×C7×D4C2×C414yes—
85C7×#117C2×C414yes—
86C7×#117D414yes—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4D411yescharacteristic
91C2×C7×C4⋊C4D411yescharacteristic
92C2×C7×C4⋊C4C2311yescharacteristic
93C2×C7×C4⋊C4C2311yescharacteristic
94C2×C7×C22⋊C4—21no—
95C2×C7×C22⋊C4—21no—
96C2×C7×C22⋊C4—21no—
97C2×C7×C22⋊C4—21no—
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4D411yescharacteristic
100C2×C7×C22⋊C4D411yescharacteristic
101C2×C42×C7—21no—
102C2×C42×C7C2311yescharacteristic
103C2×C42×C7C2311yescharacteristic
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C4⋊Dic7—21no—
107C2×C4⋊Dic7—21no—
108C2×C4⋊Dic7C2311yescharacteristic
109C2×C4⋊Dic7C2311yescharacteristic
110C2×C4⋊Dic7C2311yescharacteristic
111C2×C4⋊Dic7C2311yescharacteristic
112C2×C4×Dic7—21no—
113C2×C4×Dic7—21no—
114C2×#1136—22no—
115C2×#1136—41no—
116C2×#1136—41no—
117C22×C7⋊C8—22no—
118C22×C7⋊C8—41no—
119C22×C7⋊C8—41no—
120C22×C7⋊C8C2311yescharacteristic
121C22×C7⋊C8C2311yescharacteristic
122C22×C7⋊C8C2311yescharacteristic
123C22×C7⋊C8C2311yescharacteristic
124#6409—41no—
125#6409—41no—
126#6409—41no—
127#6409—41no—
128#6406—41no—
129#6406—41no—
130#6406—41no—
131#6406—41no—
132C7⋊#95—21no—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C4⋊(C7⋊C8)—22no—
139C4⋊(C7⋊C8)—22no—
140C4⋊(C7⋊C8)—22no—
141C4⋊(C7⋊C8)—22no—
142C2×#542D711yescharacteristic
143C2×#424—71no—
144#2314—71no—
145#1988—71no—
146#1987—71no—
147#1983—71no—
148#1983—71no—
149#1895—71no—
150#1894—71no—
151#1893—71no—
152#1892—71no—
153#1805—71no—
154#1804—71no—
155#1803—71no—
156#1802—71no—
157C24×C7—21no—
158C24×C7C2×D411yescharacteristic
159C2×C7×Q8—24no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—81no—
166C2×C7×Q8—81no—
167C2×C7×Q8C22×C412yes—
168C2×C7×D4—24no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—81no—
175C2×C7×D4—81no—
176C2×C7×D4C22×C412yes—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—24no—
185C22×C4×C7—81no—
186C22×C4×C7—81no—
187C22×C4×C7C22×C412yes—
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2411yescharacteristic
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—21no—
199C7×C4⋊C4—24no—
200C7×C4⋊C4—24no—
201C7×C4⋊C4—24no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4C22⋊C414yes—
205C7×C4⋊C4C22⋊C414yes—
206C7×C4⋊C4C22×C412yes—
207C7×C4⋊C4C22×C412yes—
208C7×C22⋊C4—24no—
209C7×C22⋊C4—24no—
210C7×C22⋊C4—24no—
211C7×C22⋊C4—24no—
212C7×C22⋊C4—24no—
213C7×C22⋊C4C22⋊C414yes—
214C7×C22⋊C4C22⋊C414yes—
215C42×C7—24no—
216C42×C7C22×C412yes—
217C42×C7C22×C412yes—
218C42×C7C2×D412yes—
219C42×C7C2×D412yes—
220C22⋊Dic7—81no—
221C22⋊Dic7—81no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7—21no—
225C4⋊Dic7—21no—
226C4⋊Dic7—21no—
227C4⋊Dic7—21no—
228C4⋊Dic7—21no—
229C4⋊Dic7—21no—
230C4⋊Dic7—81no—
231C4⋊Dic7—81no—
232C4×Dic7—81no—
233C4×Dic7—81no—
234#1136—44no—
235C2×C7⋊C8—21no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8—21no—
238C2×C7⋊C8—21no—
239C2×C7⋊C8—21no—
240C2×C7⋊C8—21no—
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⋊C8—44no—
248C22×M16—71no—
249C23×C8—71no—
250#542—24no—
251#542Dic718yescomplemented
252C2×C4⋊Q8C2×D711yescharacteristic
253C2×#126—21no—
254C2×#124—21no—
255C2×#124C2×D711yescharacteristic
256C2×#123—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C2×D711yescharacteristic
259C2×#121C2×D711yescharacteristic
260C2×C4×Q8C2×D711yescharacteristic
261C2×C4×D4C2×D711yescharacteristic
262C2×#117C2×D711yescharacteristic
263#424—144no—
264C2×C4⋊C8—71no—
265C2×C4⋊C8—71no—
266C2×C4⋊C8—71no—
267C2×C4⋊C8—71no—
268C2×#103—71no—
269C2×#103—71no—
270C2×#103—71no—
271C2×#103—71no—
272C2×#102—71no—
273C2×#102—71no—
274C2×#102—71no—
275C2×#102—71no—
276#388—141no—
277#388—141no—
278#387—141no—
279#387—141no—
280#384—71no—
281#382—71no—
282#380—71no—
283#380—71no—
284C4×C4⋊C4—71no—
285C4×C4⋊C4—71no—
286#340—71no—
287#340—71no—
288#340—71no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340—71no—
294C23×C7—21no—
295C23×C7—21no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—22no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7C2×C22⋊C412yes—
308C23×C7C22×D411yescharacteristic
309C7×Q8—22no—
310C7×Q8—22no—
311C7×Q8—41no—
312C7×Q8—41no—
313C7×Q8—84no—
314C7×D4—22no—
315C7×D4—22no—
316C7×D4—41no—
317C7×D4—41no—
318C7×D4—84no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—21no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—21no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—84no—
343C2×C4×C7C2×C22⋊C412yes—
344C2×C4×C7C2×C22⋊C412yes—
345C2×C4×C7C2×C22⋊C412yes—
346C2×C4×C7C2×C22⋊C412yes—
347C2×C4×C7C2×C22⋊C412yes—
348C2×C4×C7C23×C411yescharacteristic
349C2×C4×C7C22×D411yescharacteristic
350C2×C4×C7H(5,𝔽2)11yescharacteristic
351C2×C4×C7H(5,𝔽2)11yescharacteristic
352C2×C4×C72−1+411yescharacteristic
353C2×C4×C72−1+411yescharacteristic
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C7⋊C8—41no—
367C7⋊C8—41no—
368C7⋊C8—41no—
369C7⋊C8—41no—
370C22×Q8—21no—
371C22×Q8C22×D711yescharacteristic
372C22×D4—21no—
373C22×D4C22×D711yescharacteristic
374C23×C4—21no—
375C23×C4C22×D711yescharacteristic
376C2×M16—142no—
377C2×M16—281no—
378C2×M16—281no—
379C22×C8—71no—
380C22×C8—71no—
381C22×C8—71no—
382C22×C8—71no—
383C22×C8—142no—
384C22×C8—281no—
385C22×C8—281no—
386C4⋊Q8—22no—
387C4⋊Q8C2×Dic714yes—
388#126—28no—
389#124—28no—
390#124—22no—
391#124C2×Dic714yes—
392#123—28no—
393C22⋊Q8—22no—
394C22⋊Q8—28no—
395C22⋊Q8C2×Dic714yes—
396#121—22no—
397#121C2×Dic714yes—
398C4×Q8—22no—
399C4×Q8C2×Dic714yes—
400C4×D4—22no—
401C4×D4C2×Dic714yes—
402#117C2×Dic714yes—
403#117C22⋊D714yes—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—71no—
408C2×C4⋊C4—71no—
409C2×C4⋊C4—71no—
410C2×C4⋊C4—71no—
411C2×C4⋊C4—141no—
412C2×C4⋊C4—141no—
413C2×C4⋊C4C22⋊D711yescharacteristic
414C2×C4⋊C4C22⋊D711yescharacteristic
415C2×C4⋊C4C22×D711yescharacteristic
416C2×C4⋊C4C22×D711yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—141no—
423C2×C22⋊C4—141no—
424C2×C22⋊C4C22⋊D711yescharacteristic
425C2×C22⋊C4C22⋊D711yescharacteristic
426C2×C42—21no—
427C2×C42—141no—
428C2×C42—141no—
429C2×C42C22×D711yescharacteristic
430C2×C42C22×D711yescharacteristic
431C4⋊C8—142no—
432C4⋊C8—142no—
433C4⋊C8—142no—
434C4⋊C8—142no—
435#103—281no—
436#103—281no—
437#103—281no—
438#103—281no—
439#102—281no—
440#102—281no—
441#102—281no—
442#102—281no—
443#95—141no—
444#95—141no—
445#95—141no—
446#95—141no—
447#95—141no—
448#95—141no—
449C22×C7—22no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—41no—
453C22×C7—41no—
454C22×C7—41no—
455C22×C7—41no—
456C22×C7—42no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—81no—
460C22×C7—81no—
461C22×C7—81no—
462C22×C7—81no—
463C22×C7C22×C22⋊C411yescharacteristic
464C22×C7#53711yescharacteristic
465C22×C7#53711yescharacteristic
466C22×C7#57611yescharacteristic
467C22×C7#57711yescharacteristic
468C22×C7#57711yescharacteristic
469C22×C7#57811yescharacteristic
470C4×C7—22no—
471C4×C7—22no—
472C4×C7—22no—
473C4×C7—22no—
474C4×C7—22no—
475C4×C7—42no—
476C4×C7—42no—
477C4×C7—42no—
478C4×C7#52011yescharacteristic
479C4×C7#52011yescharacteristic
480C4×C7#53511yescharacteristic
481C4×C7#53611yescharacteristic
482Dic7—81no—
483Dic7—81no—
484Dic7—81no—
485Dic7—81no—
486C24—21no—
487C24C2×C22⋊D711yescharacteristic
488C2×Q8—24no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—81no—
495C2×Q8—81no—
496C2×Q8C22×Dic712yes—
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4C22×Dic712yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—141no—
517C22×C4—141no—
518C22×C4—141no—
519C22×C4—141no—
520C22×C4C22×Dic712yes—
521C22×C4C2×C22⋊D711yescharacteristic
522C22×C4C2×C22⋊D711yescharacteristic
523C22×C4C2×C22⋊D711yescharacteristic
524C22×C4C2×C22⋊D711yescharacteristic
525C22×C4C2×C22⋊D711yescharacteristic
526C22×C4C2×C22⋊D712yes—
527C22×C4C23×D711yescharacteristic
528M16—284no—
529C2×C8—141no—
530C2×C8—141no—
531C2×C8—141no—
532C2×C8—141no—
533C2×C8—141no—
534C2×C8—141no—
535C2×C8—141no—
536C2×C8—141no—
537C2×C8—141no—
538C2×C8—141no—
539C2×C8—141no—
540C2×C8—141no—
541C2×C8—284no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—141no—
548C4⋊C4—141no—
549C4⋊C4—141no—
550C4⋊C4—141no—
551C4⋊C4—141no—
552C4⋊C4—141no—
553C4⋊C4—141no—
554C4⋊C4—141no—
555C4⋊C4—561no—
556C4⋊C4—561no—
557C4⋊C4C22⋊Dic714yes—
558C4⋊C4C22⋊Dic714yes—
559C4⋊C4C22×Dic712yes—
560C4⋊C4C22×Dic712yes—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—24no—
566C22⋊C4—561no—
567C22⋊C4—561no—
568C22⋊C4C22⋊Dic714yes—
569C22⋊C4C22⋊Dic714yes—
570C42—24no—
571C42—561no—
572C42—561no—
573C42C22×Dic712yes—
574C42C22×Dic712yes—
575C42C2×C22⋊D712yes—
576C42C2×C22⋊D712yes—
577C2×C7—42no—
578C2×C7—82no—
579C2×C7#231111yescharacteristic
580C2×C7#289711yescharacteristic
581C2×C7#289811yescharacteristic
582C2×C7#325711yescharacteristic
583C2×C7#325811yescharacteristic
584C2×C7#326211yescharacteristic
585C2×C7#326311yescharacteristic
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23C2×C22⋊Dic712yes—
600C23C22×C22⋊D711yescharacteristic
601Q8—22no—
602Q8—22no—
603Q8—41no—
604Q8—41no—
605Q8—84no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4—84no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—281no—
636C2×C4—281no—
637C2×C4—281no—
638C2×C4—281no—
639C2×C4—281no—
640C2×C4—281no—
641C2×C4—281no—
642C2×C4—281no—
643C2×C4—281no—
644C2×C4—281no—
645C2×C4—281no—
646C2×C4—281no—
647C2×C4C2×C22⋊Dic712yes—
648C2×C4C2×C22⋊Dic712yes—
649C2×C4C2×C22⋊Dic712yes—
650C2×C4C2×C22⋊Dic712yes—
651C2×C4C2×C22⋊Dic712yes—
652C2×C4#655311yescharacteristic
653C2×C4#655311yescharacteristic
654C2×C4#655411yescharacteristic
655C2×C4#655411yescharacteristic
656C2×C4C23×Dic711yescharacteristic
657C2×C4C22×C22⋊D711yescharacteristic
658C8—281no—
659C8—281no—
660C8—281no—
661C8—281no—
662C7#2189611yescharacteristic, complemented, Sylow
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22#9052411yescharacteristic
678C22#9052411yescharacteristic
679C22#9052611yescharacteristic
680C22#9052711yescharacteristic
681C22#9052811yescharacteristic
682C22#9052911yescharacteristic
683C22C22×C22⋊Dic711yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—561no—
693C4—561no—
694C4—561no—
695C4—561no—
696C4#9051611yescharacteristic
697C4#9051811yescharacteristic
698C4#9051811yescharacteristic
699C4#9052111yescharacteristic
700C2—42no—
701C2—82no—
702C2#1174091011yescharacteristic
703C2#1174091111yescharacteristic
704C2#1174091311yescharacteristic
705C2#1174091411yescharacteristic
706C2#1174153211yescharacteristic
707C2#1174154411yescharacteristic
708C2#1174155611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#542C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
cosocleC22×C4×C7C24
hypercenterC2×#542D7
hypocenterC7#21896
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
2. #11739676C2semidirect
3. C2×#89771C2semidirect
4. #11729534C2semidirect
5. #11729533C2semidirect
6. #11729475C2semidirect
7. #11729475C2semidirect
8. #11729451C2semidirect
9. #11729450C2semidirect
12. #11729381C2semidirect
13. #11729380C2semidirect
14. #11729359C2semidirect
15. #11729358C2semidirect
17. C7×#542C4semidirect
251. #542Dic7semidirect
662. C7#21896semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5422
#117396762
C2×#897712
#117295342
#117295332
#117294752
#117294512
#117294502
#117294362
#117294352
#117293812
#117293802
#117293592
#117293582
#218967