Finite Group Databasebeta

← #13370080

Subgroups — #13370080

Order 1792.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90204C211yesmaximal, characteristic
2C2×#89883C211yesmaximal, characteristic
3C4⋊C4×C22⋊D7C211yesmaximal, characteristic
4C2×C7×#340C211yesmaximal, characteristic, complemented
5#11729726C211yesmaximal, characteristic, complemented
6#11729313C211yesmaximal, characteristic, complemented
7#11729307C211yesmaximal, characteristic, complemented
8#11726658C211yesmaximal, characteristic, complemented
9#11726638C211yesmaximal, characteristic, complemented
10#11726632C211yesmaximal, characteristic, complemented
11#11726621C211yesmaximal, characteristic, complemented
12#11726567C211yesmaximal, characteristic, complemented
13#11726559C211yesmaximal, characteristic, complemented
14#11726555C211yesmaximal, characteristic, complemented
15#11726537C211yesmaximal, characteristic, complemented
16C23×C7×C8C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C2×#6492—21no—
20C2×C4×C22⋊D7—21no—
21C2×C4×C22⋊D7C2211yescharacteristic
22C2×#6489—21no—
23C2×#6487C2211yescharacteristic
24C22×#1131C2211yescharacteristic
25#90204—24no—
26#90204C418yescomplemented
27C2×#6461—21no—
28C2×#6460C2211yescharacteristic
29C2×#6455C2211yescharacteristic
30C2×D7×C4⋊C4C2211yescharacteristic
31C2×#6453C2211yescharacteristic
32C2×#6452—21no—
33C2×#6450C2211yescharacteristic
34#89984C2211yescharacteristic
35#89982—21no—
36C2×C22⋊(C7⋊C8)C2211yescharacteristic
37#89883—24no—
38C2×(C2×D7)⋊C8C2211yescharacteristic
39C2×#6390C2211yescharacteristic
40C2×#6390C2211yescharacteristic
41C2×#6389C2211yescharacteristic
42C2×Dic7⋊C8C2211yescharacteristic
43#89761—21no—
44#89759C2211yescharacteristic
45#89748C2211yescharacteristic
46C4⋊C4×Dic7C2211yescharacteristic
47#89744—21no—
48C2×#6384C2211yescharacteristic
49C2×#6384C2211yescharacteristic
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52C7×#340C2211yescharacteristic
53C7×#340C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22491—71nomaximal, Sylow
63C23×C4×C7—21no—
64C23×C4×C7—21no—
65C23×C4×C7C2311yescharacteristic
66C22×C22⋊D7D411yescharacteristic
67C22×C4×D7—21no—
68C22×C4×D7C2311yescharacteristic
69C22×Dic14C2311yescharacteristic
70C22×C7×C8—22no—
71C22×C7×C8—22no—
72C22×C7×C8—41no—
73C22×C7×C8C2311yescharacteristic
74C22×C7×C8C2311yescharacteristic
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—41no—
80C2×C7×C4⋊C4C2×C414yescomplemented
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C22⋊Dic7—21no—
86C2×C22⋊Dic7—21no—
87C2×C22⋊Dic7D411yescharacteristic
88#6492—28no—
89C4×C22⋊D7—44no—
90C4×C22⋊D7C2×C414yes—
91C4×C22⋊D7D414yes—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4D411yescharacteristic
96#6489—28no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7C2311yescharacteristic
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102#6487—22no—
103#6487C2×C414yescomplemented
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×Dic7⋊C4—21no—
110C2×Dic7⋊C4D411yescharacteristic
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×C4×Dic7—21no—
114C2×C4×Dic7C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C22×C7⋊C8C2311yescharacteristic
117C2×#1131—22no—
118C2×#1131—22no—
119C2×#1131—41no—
120#6461—28no—
121#6460—22no—
122#6460C2×C414yescomplemented
123#6455—22no—
124#6455C2×C414yescomplemented
125D7×C4⋊C4—22no—
126D7×C4⋊C4—41no—
127#6453—22no—
128#6453C2×C414yescomplemented
129#6452—28no—
130#6450—22no—
131#6450C2×C414yescomplemented
132C7⋊#95—21no—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C22⋊(C7⋊C8)—22no—
136(C2×D7)⋊C8—22no—
137#6390—22no—
138#6390—41no—
139#6389—22no—
140Dic7⋊C8—22no—
141#6384—22no—
142#6384—41no—
143C2×#552—71no—
144C2×#435—71no—
145D4×C4⋊C4—71no—
146#1992—71no—
147#1989—71no—
148#1894—71no—
149#1892—71no—
150#1872—71no—
151#1872—71no—
152#1825—71no—
153#1823—71no—
154#1803—71no—
155#1763—71no—
156#1736—71no—
157C2×#340D711yescharacteristic, complemented
158C24×C7C2×D411yescharacteristic
159C23×D7C2×D411yescharacteristic
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—24no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—42no—
170C22×C4×C7—42no—
171C22×C4×C7—42no—
172C22×C4×C7—42no—
173C22×C4×C7—81no—
174C22×C4×C7C22×C412yes—
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D412yes—
177C22×C4×C7C2411yescharacteristic
178C2×C22⋊D7—22no—
179C2×C22⋊D7—22no—
180C2×C22⋊D7C22⋊C414yes—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7C2×D411yescharacteristic
186C22×Dic7C2×D411yescharacteristic
187C22×Dic7C2×D411yescharacteristic
188C2×C4×D7—21no—
189C2×C4×D7—21no—
190C2×C4×D7—21no—
191C2×C4×D7—21no—
192C2×C4×D7—42no—
193C2×C4×D7—42no—
194C2×C4×D7—81no—
195C2×C4×D7C22×C412yes—
196C2×C4×D7C2×D412yes—
197C2×Dic14—21no—
198C2×Dic14—21no—
199C2×Dic14—21no—
200C2×Dic14—21no—
201C2×Dic14—21no—
202C2×Dic14C22×C412yes—
203C2×C7×C8—21no—
204C2×C7×C8—21no—
205C2×C7×C8—21no—
206C2×C7×C8—21no—
207C2×C7×C8—21no—
208C2×C7×C8—44no—
209C2×C7×C8#4112yes—
210C7×C4⋊C4—24no—
211C7×C4⋊C4—21no—
212C7×C4⋊C4—21no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—42no—
217C7×C4⋊C4C22×C412yes—
218C7×C4⋊C4C22×C412yes—
219C7×C4⋊C4#4112yes—
220C22⋊Dic7—24no—
221C22⋊Dic7—42no—
222C22⋊Dic7C22⋊C414yes—
223(C2×D7)⋊C4—24no—
224(C2×D7)⋊C4—24no—
225(C2×D7)⋊C4—42no—
226(C2×D7)⋊C4C22⋊C414yes—
227C4⋊Dic7—21no—
228C4⋊Dic7—24no—
229C4⋊Dic7—24no—
230C4⋊Dic7—21no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7C22×C412yes—
235Dic7⋊C4—24no—
236Dic7⋊C4—24no—
237Dic7⋊C4—24no—
238Dic7⋊C4—42no—
239Dic7⋊C4—42no—
240Dic7⋊C4—81no—
241Dic7⋊C4C22⋊C414yes—
242C4×Dic7—24no—
243C4×Dic7—24no—
244C4×Dic7—42no—
245C4×Dic7C22×C412yes—
246C4×Dic7C2×D412yes—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253#1131—44no—
254C22×M16—71no—
255C23×C8C2×D711yescharacteristic
256#552—78no—
257#552—144no—
258C2×#126—141no—
259C2×#125—71no—
260C2×#125—141no—
261C2×#123—141no—
262C2×C22⋊Q8—71no—
263C2×C22⋊Q8—71no—
264C2×C4×Q8—71no—
265C2×C4×D4—71no—
266C2×C4×D4—141no—
267C2×#117—71no—
268C2×#117—141no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4C2×D711yescharacteristic
271C22×C4⋊C4C2×D711yescharacteristic
272#435—144no—
273C2×C4⋊C8—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×#103—71no—
277C2×#103—71no—
278C2×C22⋊C8—71no—
279C2×C22⋊C8—71no—
280C2×#97—71no—
281#389—141no—
282#385—141no—
283#385—141no—
284#384—71no—
285#380—71no—
286#380—71no—
287C4×C4⋊C4—71no—
288#340—71no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340—71no—
294#340—71no—
295#340—71no—
296#340C2×D711yescharacteristic
297#340C2×D711yescharacteristic
298#340C2×D711yescharacteristic
299#340C2×D711yescharacteristic
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7C2×C22⋊C412yes—
305C23×C7AGL(1,ℤ/8)12yes—
306C23×C7#13712yes—
307C23×C7C22×D411yescharacteristic
308C22×D7—21no—
309C22×D7—21no—
310C22×D7—21no—
311C22×D7—21no—
312C22×D7—21no—
313C22×D7—21no—
314C22×D7C2×C22⋊C412yes—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—48no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—84no—
335C2×C4×C7C2×C22⋊C412yes—
336C2×C4×C7C23×C411yescharacteristic
337C2×C4×C7C22×D411yescharacteristic
338C2×C4×C7C2×#4111yescharacteristic
339C2×C4×C7C2×#4111yescharacteristic
340C2×C4×C7H(5,𝔽2)11yescharacteristic
341C2×C4×C72−1+411yescharacteristic
342C22⋊D7—28no—
343C2×Dic7—21no—
344C2×Dic7—21no—
345C2×Dic7—21no—
346C2×Dic7—21no—
347C2×Dic7—21no—
348C2×Dic7—21no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7C2×C22⋊C412yes—
362C2×Dic7C2×C22⋊C412yes—
363C2×Dic7C2×C22⋊C412yes—
364C4×D7—22no—
365C4×D7—22no—
366C4×D7—22no—
367C4×D7—22no—
368C4×D7—84no—
369Dic14—22no—
370Dic14—22no—
371Dic14—41no—
372Dic14—41no—
373C7×C8—22no—
374C7×C8—41no—
375C7⋊C8—41no—
376C7⋊C8—41no—
377C22×Q8—71no—
378C22×D4—71no—
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—71no—
382C23×C4—141no—
383C23×C4C22×D711yescharacteristic
384C2×M16—142no—
385C2×M16—142no—
386C2×M16—281no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—41no—
390C22×C8—71no—
391C22×C8—71no—
392C22×C8C22×D711yescharacteristic
393C22×C8C22×D711yescharacteristic
394#126—148no—
395#125—74no—
396#125—142no—
397#125—148no—
398#123—148no—
399C22⋊Q8—74no—
400C22⋊Q8—74no—
401C22⋊Q8—142no—
402C22⋊Q8—142no—
403C4×Q8—74no—
404C4×Q8—142no—
405C4×D4—74no—
406C4×D4—74no—
407C4×D4—284no—
408#117—74no—
409#117—148no—
410#117—142no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—71no—
419C2×C4⋊C4—71no—
420C2×C4⋊C4—141no—
421C2×C4⋊C4—141no—
422C2×C4⋊C4—141no—
423C2×C4⋊C4—141no—
424C2×C4⋊C4—141no—
425C2×C4⋊C4—142no—
426C2×C4⋊C4—141no—
427C2×C4⋊C4—141no—
428C2×C4⋊C4—141no—
429C2×C4⋊C4—281no—
430C2×C4⋊C4C4×D714yescomplemented
431C2×C4⋊C4C22×D711yescharacteristic
432C2×C4⋊C4C22×D711yescharacteristic
433C2×C4⋊C4C22×D711yescharacteristic
434C2×C4⋊C4C22×D711yescharacteristic
435C2×C22⋊C4—71no—
436C2×C22⋊C4—71no—
437C2×C22⋊C4—141no—
438C2×C22⋊C4—141no—
439C2×C22⋊C4—141no—
440C2×C22⋊C4—141no—
441C2×C22⋊C4—141no—
442C2×C42—71no—
443C2×C42—141no—
444C2×C42—141no—
445C2×C42—141no—
446C4⋊C8—142no—
447#103—142no—
448#103—142no—
449#103—281no—
450#103—281no—
451C22⋊C8—142no—
452C22⋊C8—142no—
453#97—142no—
454#95—141no—
455#95—141no—
456#95—141no—
457C22×C7—22no—
458C22×C7—22no—
459C22×C7—22no—
460C22×C7—22no—
461C22×C7—22no—
462C22×C7—22no—
463C22×C7#41714yes—
464C22×C7C22×C22⋊C411yescharacteristic
465C22×C7#54611yescharacteristic
466C22×C7#54711yescharacteristic
467C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C7C2×#13711yescharacteristic
469C22×C7#57711yescharacteristic
470C22×C7#57811yescharacteristic
471C2×D7—22no—
472C2×D7—22no—
473C2×D7—22no—
474C2×D7—41no—
475C2×D7—41no—
476C2×D7—41no—
477C2×D7—41no—
478C4×C7—22no—
479C4×C7—42no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—81no—
483C4×C7C4×#4111yescharacteristic
484C4×C7#52011yescharacteristic
485C4×C7#54611yescharacteristic
486C4×C7#54711yescharacteristic
487Dic7—22no—
488Dic7—22no—
489Dic7—22no—
490Dic7—42no—
491Dic7—42no—
492Dic7—81no—
493Dic7—81no—
494C24—71no—
495C24D4×D711yescharacteristic
496C2×Q8—72no—
497C2×Q8—141no—
498C2×Q8—141no—
499C2×Q8—141no—
500C2×Q8—141no—
501C2×Q8—141no—
502C2×D4—74no—
503C2×D4—142no—
504C2×D4—142no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—71no—
519C22×C4—71no—
520C22×C4—71no—
521C22×C4—72no—
522C22×C4—72no—
523C22×C4—81no—
524C22×C4—141no—
525C22×C4—141no—
526C22×C4—141no—
527C22×C4—141no—
528C22×C4—141no—
529C22×C4—141no—
530C22×C4—141no—
531C22×C4—141no—
532C22×C4—282no—
533C22×C4—282no—
534C22×C4—561no—
535C22×C4C2×C4×D712yes—
536C22×C4D4×D711yescharacteristic
537C22×C4D4×D712yes—
538C22×C4C23×D711yescharacteristic
539M16—284no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—44no—
546C2×C8—141no—
547C2×C8—141no—
548C2×C8—141no—
549C2×C8—141no—
550C2×C8—141no—
551C2×C8—141no—
552C2×C8#115712yes—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—74no—
561C4⋊C4—72no—
562C4⋊C4—144no—
563C4⋊C4—144no—
564C4⋊C4—144no—
565C4⋊C4—144no—
566C4⋊C4—144no—
567C4⋊C4—141no—
568C4⋊C4—141no—
569C4⋊C4—141no—
570C4⋊C4—141no—
571C4⋊C4—141no—
572C4⋊C4—282no—
573C4⋊C4—282no—
574C4⋊C4—561no—
575C4⋊C4C2×C4×D712yes—
576C4⋊C4C2×C4×D712yes—
577C4⋊C4#115712yes—
578C22⋊C4—74no—
579C22⋊C4—74no—
580C22⋊C4—144no—
581C22⋊C4—144no—
582C22⋊C4—144no—
583C22⋊C4—282no—
584C22⋊C4—282no—
585C42—72no—
586C42—72no—
587C42—144no—
588C42—144no—
589C42—282no—
590C2×C7—24no—
591C2×C7#233911yescharacteristic
592C2×C7C2×#41711yescharacteristic
593C2×C7#289811yescharacteristic
594C2×C7#331011yescharacteristic
595C2×C7#331211yescharacteristic
596C2×C7#334311yescharacteristic
597C2×C7#334411yescharacteristic
598D7—42no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—72no—
604C23—141no—
605C23—141no—
606C23—141no—
607C23—141no—
608C23—141no—
609C23—141no—
610C23D7×C22⋊C412yes—
611C23#647412yes—
612C23#647812yes—
613C23C2×D4×D711yescharacteristic
614Q8—142no—
615Q8—142no—
616Q8—281no—
617Q8—281no—
618D4—148no—
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—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—72no—
639C2×C4—72no—
640C2×C4—72no—
641C2×C4—84no—
642C2×C4—141no—
643C2×C4—141no—
644C2×C4—141no—
645C2×C4—141no—
646C2×C4—141no—
647C2×C4—141no—
648C2×C4—142no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—142no—
653C2×C4—142no—
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×C4—281no—
664C2×C4—564no—
665C2×C4D7×C22⋊C412yes—
666C2×C4C22×C4×D711yescharacteristic
667C2×C4C2×#115711yescharacteristic
668C2×C4C2×#115711yescharacteristic
669C2×C4C2×D4×D711yescharacteristic
670C2×C4#654811yescharacteristic
671C2×C4#655111yescharacteristic
672C8—22no—
673C8—41no—
674C8—281no—
675C8—281no—
676C7#2249111yescharacteristic, complemented, Sylow
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—142no—
684C22—142no—
685C22—142no—
686C22—281no—
687C22—281no—
688C22—281no—
689C22—281no—
690C22#8954314yes—
691C22C2×D7×C22⋊C411yescharacteristic
692C22#9018111yescharacteristic
693C22#9019811yescharacteristic
694C22C2×#647411yescharacteristic
695C22C2×#647811yescharacteristic
696C22#9045311yescharacteristic
697C22#9045711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—142no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—561no—
709C4—561no—
710C4C4×#115711yescharacteristic
711C4#9018111yescharacteristic
712C4#9019511yescharacteristic
713C4#9019811yescharacteristic
714C2—24no—
715C2—282no—
716C2#1173081311yescharacteristic
717C2C2×#8954311yescharacteristic
718C2#1173620711yescharacteristic
719C2#1173623511yescharacteristic
720C2#1173625511yescharacteristic
721C2#1173657111yescharacteristic
722C2#1173660311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#340C2
socleC23×C7C22×D4
prime radicalC22×C22⋊D7D4
cosocleC22×C4×C7C24
hypercenterC2×#340D7
hypocenterC7#22491
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×C7×#340C2semidirect
5. #11729726C2semidirect
6. #11729313C2semidirect
7. #11729307C2semidirect
8. #11726658C2semidirect
9. #11726638C2semidirect
10. #11726632C2semidirect
11. #11726621C2semidirect
12. #11726567C2semidirect
13. #11726559C2semidirect
14. #11726555C2semidirect
15. #11726537C2semidirect
26. #90204C4semidirect
80. C2×C7×C4⋊C4C2×C4semidirect
103. #6487C2×C4semidirect
122. #6460C2×C4semidirect
124. #6455C2×C4semidirect
128. #6453C2×C4semidirect
131. #6450C2×C4semidirect
157. C2×#340D7semidirect
430. C2×C4⋊C4C4×D7semidirect
676. C7#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#902042
C2×#898832
C4⋊C4×C22⋊D72
C2×C7×#3402
#117297262
#117293132
#117293072
#117266582
#117266382
#117266322
#117266212
#117265672
#117265592
#117265552
#117265372
#224917