Finite Group Databasebeta

← #13353309

Subgroups — #13353309

Order 1792.

1386 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90263C211yesmaximal, characteristic
2C2×#89611C211yesmaximal, characteristic
3C2×#89574C211yesmaximal, characteristic
4C2×D7×#103C211yesmaximal, characteristic
5#11731804C211yesmaximal, characteristic
6C7×#1803C211yesmaximal, characteristic, complemented
7#11729381C211yesmaximal, characteristic, complemented
8#11728240C211yesmaximal, characteristic, complemented
9#11727976C211yesmaximal, characteristic, complemented
10#11727975C211yesmaximal, characteristic, complemented
11#11727342C211yesmaximal, characteristic, complemented
12#11726659C211yesmaximal, characteristic, complemented
13#11726658C211yesmaximal, characteristic, complemented
14#11726621C211yesmaximal, characteristic
15#11726620C211yesmaximal, characteristic
16C22×Q8×D7C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×Q8×Dic7C2211yescharacteristic
19C22×#1131C2211yescharacteristic
20C22×C8×D7C2211yescharacteristic
21#90263—24no—
22#90263C418yescomplemented
23C2×#6455—21no—
24C2×#6455C2211yescharacteristic
25C2×#6455C2211yescharacteristic
26C2×D7×C4⋊C4C2211yescharacteristic
27C2×#6450—21no—
28C2×#6450C2211yescharacteristic
29C2×#6435—21no—
30C2×#6435C2211yescharacteristic
31C2×C4×Dic14—21no—
32C2×C4×Dic14C2211yescharacteristic
33C2×C7×C4⋊C8C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C2×C7×#103C2211yescharacteristic
36C7×#384C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6409C2211yescharacteristic
39C2×#6390C2211yescharacteristic
40C2×#6390C2211yescharacteristic
41C2×Dic7⋊C8C2211yescharacteristic
42C2×Dic7⋊C8C2211yescharacteristic
43#89761—21no—
44#89761—21no—
45#89749C2211yescharacteristic
46#89748C2211yescharacteristic
47#89744—21no—
48#89744—21no—
49C2×#6384C2211yescharacteristic
50C2×#6384C2211yescharacteristic
51#89708C2211yescharacteristic
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53#89611—24no—
54#89574—24no—
55D7×#103—24no—
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89324C2211yescharacteristic
63#89324C2211yescharacteristic
64#20651—71nomaximal, Sylow
65C22×C7×Q8C2311yescharacteristic
66C2×Q8×D7—22no—
67C2×Q8×D7—22no—
68C2×Q8×D7—22no—
69C2×Q8×D7C2×C414yes—
70C2×Q8×D7D414yes—
71C2×Q8×D7Q814yes—
72C22×C4×D7—21no—
73C22×C4×D7—21no—
74C22×C4×D7C2311yescharacteristic
75C22×Dic14—21no—
76C22×Dic14C2311yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C22×C7×C8C2311yescharacteristic
79C4×C7×Q8—22no—
80C4×C7×Q8C2×C414yescomplemented
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C4⋊C4C2311yescharacteristic
87C2×C42×C7—21no—
88C2×C42×C7C2311yescharacteristic
89Q8×Dic7—22no—
90Q8×Dic7C2×C414yescomplemented
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4D411yescharacteristic
94C2×(C2×D7)⋊C4D411yescharacteristic
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2311yescharacteristic
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—21no—
102C2×Dic7⋊C4—21no—
103C2×Dic7⋊C4—21no—
104C2×Dic7⋊C4D411yescharacteristic
105C2×Dic7⋊C4D411yescharacteristic
106C2×C4×Dic7—21no—
107C2×C4×Dic7—21no—
108C2×C4×Dic7—21no—
109C2×C4×Dic7—21no—
110C2×C4×Dic7—21no—
111C2×C4×Dic7C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113C22×C7⋊C8C2311yescharacteristic
114C2×#1131—22no—
115C2×#1131—22no—
116C2×#1131—22no—
117C2×C8×D7—22no—
118C2×C8×D7—22no—
119C2×C8×D7—22no—
120#6455—22no—
121#6455—28no—
122#6455—22no—
123#6455—22no—
124#6455C2×C414yes—
125D7×C4⋊C4—22no—
126D7×C4⋊C4—22no—
127#6450—28no—
128#6450—22no—
129#6450C2×C414yescomplemented
130#6435—28no—
131#6435C2×C414yes—
132#6435D414yes—
133C4×Dic14—22no—
134C4×Dic14—28no—
135C4×Dic14C2×C414yescomplemented
136C7×C4⋊C8—22no—
137C7×#103—22no—
138C7×#103—22no—
139#6409—22no—
140#6409—22no—
141C7⋊#95—21no—
142C7⋊#95—21no—
143C7⋊#95—21no—
144C7⋊#95—21no—
145#6390—22no—
146#6390—22no—
147Dic7⋊C8—22no—
148Dic7⋊C8—22no—
149#6384—22no—
150#6384—22no—
151C4⋊(C7⋊C8)—22no—
152C2×#519—71no—
153C2×#424—71no—
154C2×#419—71no—
155C22×#103—71no—
156#2317—71no—
157#1805—71no—
158#1805—71no—
159#1805—71no—
160#1805—71no—
161#1803—71no—
162#1803—71no—
163#1803—71no—
164#1803D711yescharacteristic, complemented
165#1736—71no—
166#1735—71no—
167C23×D7C2×D411yescharacteristic
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8C22×C412yes—
172C2×C7×Q8C2×D412yes—
173C2×C7×Q8C2×Q812yes—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2411yescharacteristic
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7C2×D411yescharacteristic
186C22×Dic7C2×D411yescharacteristic
187C22×Dic7C2×D411yescharacteristic
188Q8×D7—28no—
189Q8×D7—28no—
190Q8×D7—28no—
191Q8×D7C4⋊C4116yescomplemented
192C2×C4×D7—24no—
193C2×C4×D7—24no—
194C2×C4×D7—24no—
195C2×C4×D7—42no—
196C2×C4×D7—81no—
197C2×C4×D7—81no—
198C2×C4×D7C22×C412yes—
199C2×C4×D7C2×D412yes—
200C2×C4×D7C2×D412yes—
201C2×C4×D7C2×Q812yes—
202C2×C4×D7#4112yes—
203C2×C4×D7#4112yes—
204C2×Dic14—21no—
205C2×Dic14—21no—
206C2×Dic14—21no—
207C2×Dic14—24no—
208C2×Dic14—24no—
209C2×Dic14—24no—
210C2×Dic14C22×C412yes—
211C2×Dic14C2×D412yes—
212C2×Dic14C2×Q812yes—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C7×C4⋊C4—24no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—81no—
226C7×C4⋊C4—81no—
227C7×C4⋊C4C22×C412yes—
228C42×C7—24no—
229C42×C7C22×C412yes—
230C42×C7C2×D412yes—
231(C2×D7)⋊C4—24no—
232(C2×D7)⋊C4—42no—
233(C2×D7)⋊C4C22⋊C414yes—
234(C2×D7)⋊C4C22⋊C414yes—
235C4⋊Dic7—21no—
236C4⋊Dic7—24no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7—21no—
241C4⋊Dic7C22×C412yes—
242Dic7⋊C4—24no—
243Dic7⋊C4—24no—
244Dic7⋊C4—42no—
245Dic7⋊C4—81no—
246Dic7⋊C4—81no—
247Dic7⋊C4C22⋊C414yes—
248Dic7⋊C4C22⋊C414yes—
249C4×Dic7—24no—
250C4×Dic7—24no—
251C4×Dic7—24no—
252C4×Dic7—24no—
253C4×Dic7—42no—
254C4×Dic7C22×C412yes—
255C4×Dic7C2×D412yes—
256C2×C7⋊C8—21no—
257C2×C7⋊C8—21no—
258C2×C7⋊C8—21no—
259C2×C7⋊C8—21no—
260C2×C7⋊C8—21no—
261C2×C7⋊C8—21no—
262#1131—44no—
263C8×D7—44no—
264C23×Q8—71no—
265C22×M16—71no—
266C23×C8—71no—
267#519—78no—
268#519—144no—
269C2×C4×Q8—71no—
270C2×C4×Q8—71no—
271C2×C4×Q8—71no—
272C2×C4×Q8—141no—
273C2×C4×Q8—141no—
274C2×C4×Q8C2×D711yescharacteristic
275C2×#117—71no—
276C2×#117—71no—
277C2×#117—71no—
278C2×#117—141no—
279C2×#117—141no—
280C22×C4⋊C4—71no—
281#424—144no—
282C2×C4⋊C8—71no—
283C2×C4⋊C8—71no—
284C2×C4⋊C8—71no—
285C2×C4⋊C8C2×D711yescharacteristic
286#419—144no—
287C2×#103—71no—
288C2×#103—71no—
289C2×#103—71no—
290C2×#103—71no—
291C2×#103—71no—
292C2×#103—71no—
293C2×#103—144no—
294C2×#103C2×D711yescharacteristic
295C2×#103C2×D711yescharacteristic
296#389—141no—
297#389—141no—
298#385—141no—
299#385—141no—
300#384—71no—
301#384C2×D711yescharacteristic
302#382—71no—
303#382—71no—
304#340—71no—
305#340—71no—
306#340—71no—
307#340—71no—
308#340—71no—
309#340—71no—
310#340C2×D711yescharacteristic
311#340C2×D711yescharacteristic
312C23×C7C22×D411yescharacteristic
313C22×D7—21no—
314C22×D7—21no—
315C22×D7—21no—
316C22×D7—21no—
317C22×D7C2×C22⋊C412yes—
318C22×D7#12112yes—
319C22×D7C22⋊Q812yes—
320C7×Q8—22no—
321C7×Q8—22no—
322C7×Q8—22no—
323C7×Q8C2×C4⋊C414yes—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—21no—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—22no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7C2×C22⋊C412yes—
341C2×C4×C7C2×C22⋊C412yes—
342C2×C4×C7C23×C411yescharacteristic
343C2×C4×C7C22×D411yescharacteristic
344C2×C4×C7C22×D411yescharacteristic
345C2×C4×C7C22×Q811yescharacteristic
346C2×C4×C7C2×#4111yescharacteristic
347C2×C4×C7C2×#4111yescharacteristic
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—21no—
352C2×Dic7—21no—
353C2×Dic7—21no—
354C2×Dic7—21no—
355C2×Dic7—22no—
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×Dic7C2×C22⋊C412yes—
365C2×Dic7C2×C22⋊C412yes—
366C2×Dic7C2×C22⋊C412yes—
367C2×Dic7#12112yes—
368C2×Dic7C22⋊Q812yes—
369C4×D7—216no—
370C4×D7—84no—
371C4×D7C2×C4⋊C414yes—
372C4×D7#11714yes—
373C4×D7#12114yes—
374C4×D7C22⋊Q814yes—
375Dic14—22no—
376Dic14—22no—
377Dic14—22no—
378Dic14—216no—
379Dic14C2×C4⋊C414yes—
380C7×C8—41no—
381C7×C8—41no—
382C7⋊C8—41no—
383C7⋊C8—41no—
384C22×Q8—74no—
385C22×Q8—74no—
386C22×Q8—74no—
387C22×Q8—71no—
388C22×Q8—141no—
389C22×Q8—142no—
390C22×Q8—142no—
391C22×Q8—142no—
392C22×Q8C22×D711yescharacteristic
393C23×C4—71no—
394C23×C4—141no—
395C23×C4—141no—
396C2×M16—142no—
397C2×M16—142no—
398C2×M16—142no—
399C22×C8—71no—
400C22×C8—71no—
401C22×C8—142no—
402C22×C8—142no—
403C22×C8—142no—
404C22×C8C22×D711yescharacteristic
405C22×C8C22×D711yescharacteristic
406C4×Q8—22no—
407C4×Q8—74no—
408C4×Q8—74no—
409C4×Q8—74no—
410C4×Q8—148no—
411C4×Q8—142no—
412C4×Q8—142no—
413C4×Q8—148no—
414C4×Q8—142no—
415C4×Q8C4×D714yescomplemented
416#117—74no—
417#117—74no—
418#117—74no—
419#117—148no—
420#117—148no—
421#117—142no—
422#117—142no—
423#117—142no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—71no—
428C2×C4⋊C4—71no—
429C2×C4⋊C4—71no—
430C2×C4⋊C4—71no—
431C2×C4⋊C4—71no—
432C2×C4⋊C4—142no—
433C2×C4⋊C4—142no—
434C2×C4⋊C4—141no—
435C2×C4⋊C4—141no—
436C2×C4⋊C4—141no—
437C2×C4⋊C4—141no—
438C2×C4⋊C4—141no—
439C2×C4⋊C4—141no—
440C2×C4⋊C4C22×D711yescharacteristic
441C2×C4⋊C4C22×D711yescharacteristic
442C2×C4⋊C4C22×D711yescharacteristic
443C2×C22⋊C4—71no—
444C2×C22⋊C4—71no—
445C2×C22⋊C4—141no—
446C2×C22⋊C4—141no—
447C2×C42—21no—
448C2×C42—71no—
449C2×C42—141no—
450C2×C42—141no—
451C2×C42—141no—
452C2×C42—141no—
453C2×C42—141no—
454C2×C42C22×D711yescharacteristic
455C4⋊C8—22no—
456C4⋊C8—142no—
457C4⋊C8—142no—
458C4⋊C8—142no—
459#103—22no—
460#103—22no—
461#103—142no—
462#103—142no—
463#103—142no—
464#103—142no—
465#103—142no—
466#103—142no—
467#95—141no—
468#95—141no—
469#95—141no—
470#95—141no—
471C22×C7C22×C22⋊C411yescharacteristic
472C22×C7C2×#12111yescharacteristic
473C22×C7C2×C22⋊Q811yescharacteristic
474C22×C7#57711yescharacteristic
475C22×C7#57711yescharacteristic
476C22×C7#57811yescharacteristic
477C22×C7#57811yescharacteristic
478C2×D7—22no—
479C2×D7—22no—
480C2×D7—22no—
481C2×D7—22no—
482C2×D7—22no—
483C2×D7—22no—
484C2×D7#38014yes—
485C4×C7—22no—
486C4×C7—22no—
487C4×C7—24no—
488C4×C7—42no—
489C4×C7—81no—
490C4×C7—81no—
491C4×C7C22×C4⋊C411yescharacteristic
492C4×C7C2×#11711yescharacteristic
493C4×C7C2×#12111yescharacteristic
494C4×C7C2×C22⋊Q811yescharacteristic
495Dic7—22no—
496Dic7—22no—
497Dic7—24no—
498Dic7—42no—
499Dic7—81no—
500Dic7—81no—
501Dic7#38014yes—
502C24—71no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—716no—
507C2×Q8—72no—
508C2×Q8—72no—
509C2×Q8—72no—
510C2×Q8—144no—
511C2×Q8—144no—
512C2×Q8—144no—
513C2×Q8—148no—
514C2×Q8—148no—
515C2×Q8—148no—
516C2×Q8—141no—
517C2×Q8—141no—
518C2×Q8—141no—
519C2×Q8C2×C4×D712yes—
520C2×Q8D4×D712yes—
521C2×Q8Q8×D712yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—71no—
527C22×C4—72no—
528C22×C4—72no—
529C22×C4—72no—
530C22×C4—72no—
531C22×C4—72no—
532C22×C4—72no—
533C22×C4—71no—
534C22×C4—71no—
535C22×C4—144no—
536C22×C4—144no—
537C22×C4—144no—
538C22×C4—141no—
539C22×C4—141no—
540C22×C4—141no—
541C22×C4—141no—
542C22×C4—282no—
543C22×C4—561no—
544C22×C4—561no—
545C22×C4D4×D711yescharacteristic
546C22×C4D4×D711yescharacteristic
547C22×C4C23×D711yescharacteristic
548M16—284no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—141no—
556C2×C8—141no—
557C2×C8—141no—
558C2×C8—141no—
559C2×C8—141no—
560C2×C8—141no—
561C2×C8—284no—
562C4⋊C4—24no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—74no—
569C4⋊C4—74no—
570C4⋊C4—72no—
571C4⋊C4—81no—
572C4⋊C4—81no—
573C4⋊C4—144no—
574C4⋊C4—144no—
575C4⋊C4—144no—
576C4⋊C4—141no—
577C4⋊C4—141no—
578C4⋊C4—141no—
579C4⋊C4—141no—
580C4⋊C4—141no—
581C4⋊C4—282no—
582C4⋊C4—561no—
583C4⋊C4—561no—
584C4⋊C4C2×C4×D712yes—
585C22⋊C4—74no—
586C22⋊C4—74no—
587C22⋊C4—144no—
588C22⋊C4—282no—
589C42—24no—
590C42—72no—
591C42—72no—
592C42—144no—
593C42—144no—
594C42—144no—
595C42—144no—
596C42—282no—
597C42C2×C4×D712yes—
598C42D4×D712yes—
599C2×C7C2×#38011yescharacteristic
600C2×C7#289811yescharacteristic
601C2×C7#289811yescharacteristic
602C2×C7#304311yescharacteristic
603C2×C7#304411yescharacteristic
604C2×C7#308211yescharacteristic
605C2×C7#308211yescharacteristic
606D7—24no—
607C23—72no—
608C23—72no—
609C23—72no—
610C23—141no—
611C23—141no—
612C23—141no—
613C23—141no—
614C23C2×D4×D711yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—22no—
618Q8—74no—
619Q8—1416no—
620Q8—142no—
621Q8—142no—
622Q8—142no—
623Q8D7×C4⋊C414yes—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—72no—
641C2×C4—72no—
642C2×C4—72no—
643C2×C4—74no—
644C2×C4—74no—
645C2×C4—74no—
646C2×C4—74no—
647C2×C4—72no—
648C2×C4—72no—
649C2×C4—1416no—
650C2×C4—142no—
651C2×C4—141no—
652C2×C4—141no—
653C2×C4—141no—
654C2×C4—141no—
655C2×C4—142no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—281no—
659C2×C4—281no—
660C2×C4—281no—
661C2×C4—281no—
662C2×C4—281no—
663C2×C4—281no—
664C2×C4—281no—
665C2×C4—281no—
666C2×C4—564no—
667C2×C4D7×C22⋊C412yes—
668C2×C4D7×C22⋊C412yes—
669C2×C4C22×C4×D711yescharacteristic
670C2×C4C2×D4×D711yescharacteristic
671C2×C4C2×D4×D711yescharacteristic
672C2×C4C2×Q8×D711yescharacteristic
673C2×C4D7×#4111yescharacteristic
674C2×C4D7×#4111yescharacteristic
675C8—41no—
676C8—41no—
677C8—281no—
678C8—281no—
679C7#2065111yescharacteristic, complemented, Sylow
680C22—74no—
681C22—142no—
682C22—142no—
683C22—142no—
684C22—142no—
685C22—142no—
686C22—142no—
687C22C2×D7×C22⋊C411yescharacteristic
688C22D7×#12111yescharacteristic
689C22D7×C22⋊Q811yescharacteristic
690C22#9045311yescharacteristic
691C22#9045711yescharacteristic
692C22#9046611yescharacteristic
693C22#9047011yescharacteristic
694C4—22no—
695C4—22no—
696C4—24no—
697C4—42no—
698C4—74no—
699C4—81no—
700C4—81no—
701C4—142no—
702C4—142no—
703C4—144no—
704C4—282no—
705C4—561no—
706C4—561no—
707C4C2×D7×C4⋊C411yescharacteristic
708C4D7×#11711yescharacteristic
709C4D7×#12111yescharacteristic
710C4D7×C22⋊Q811yescharacteristic
711C2—144no—
712C2D7×#38011yescharacteristic
713C2#1173623511yescharacteristic
714C2#1173632811yescharacteristic
715C2#1173783011yescharacteristic
716C2#1173792311yescharacteristic
717C2#1173845811yescharacteristic
718C2#1173855511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1803C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
cosocleC22×C4×C7C24
hypercenter#1803D7
hypocenterC7#20651
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
6. C7×#1803C2semidirect
7. #11729381C2semidirect
8. #11728240C2semidirect
9. #11727976C2semidirect
10. #11727975C2semidirect
11. #11727342C2semidirect
12. #11726659C2semidirect
13. #11726658C2semidirect
22. #90263C4semidirect
80. C4×C7×Q8C2×C4semidirect
90. Q8×Dic7C2×C4semidirect
129. #6450C2×C4semidirect
135. C4×Dic14C2×C4semidirect
164. #1803D7semidirect
191. Q8×D7C4⋊C4semidirect
415. C4×Q8C4×D7semidirect
679. C7#20651semidirect

Maximal subgroups

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

subgroupindex
C2×#902632
C2×#896112
C2×#895742
C2×D7×#1032
#117318042
C7×#18032
#117293812
#117282402
#117279762
#117279752
#117273422
#117266592
#117266582
#117266212
#117266202
#206517