Finite Group Databasebeta

← #13371056

Subgroups — #13371056

Order 1792.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2347C211yesmaximal, characteristic, complemented
2C2×#89773C211yesmaximal, characteristic
3C22⋊C4×D28C211yesmaximal, characteristic
4#11729329C211yesmaximal, characteristic, complemented
5#11727380C211yesmaximal, characteristic, complemented
6#11727379C211yesmaximal, characteristic, complemented
7#11727371C211yesmaximal, characteristic, complemented
8#11727369C211yesmaximal, characteristic, complemented
9#11727275C211yesmaximal, characteristic
10#11727267C211yesmaximal, characteristic, complemented
11#11727228C211yesmaximal, characteristic, complemented
12C4×#6383C211yesmaximal, characteristic, complemented
13#11727217C211yesmaximal, characteristic, complemented
14#11727216C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C23×D28C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C22×#1136C2211yescharacteristic
19C2×D7×C22⋊C4—21no—
20C2×C4×D28C2211yescharacteristic
21C2×C4×D28C2211yescharacteristic
22C7×#389C2211yescharacteristic, complemented
23C7×#389C2211yescharacteristic, complemented
24C7×#388—21no—
25C7×#388—21no—
26C7×#383—21no—
27C7×#380C2211yescharacteristic
28C4×C7×C4⋊C4—21no—
29C4×C7×C4⋊C4C2211yescharacteristic, complemented
30C4×C7×C4⋊C4C2211yescharacteristic, complemented
31C4×C7×C22⋊C4C2211yescharacteristic
32#89984C2211yescharacteristic
33C2×C22⋊(C7⋊C8)C2211yescharacteristic
34#89773C418yescomplemented
35C2×#6383C2211yescharacteristic
36C2×#6383C2211yescharacteristic
37C2×#6383C2211yescharacteristic
38C2×#6383C2211yescharacteristic
39C2×#6383C2211yescharacteristic
40C2×#6383C2211yescharacteristic
41C2×#6383C2211yescharacteristic
42C2×#6383C2211yescharacteristic
43C2×#6382C2211yescharacteristic, complemented
44C2×#6381C2211yescharacteristic, complemented
45#89727—21no—
46#89711C2211yescharacteristic
47#89711C2211yescharacteristic
48C2×#6377C2211yescharacteristic, complemented
49C2×C4×C7⋊C8C2211yescharacteristic, complemented
50#89437—21no—
51#89437—21no—
52#89324C2211yescharacteristic, complemented
53#89324C2211yescharacteristic, complemented
54#89324C2211yescharacteristic, complemented
55#89324C2211yescharacteristic, complemented
56#89324C2211yescharacteristic, complemented
57#89324C2211yescharacteristic, complemented
58#89319C2211yescharacteristic, complemented
59#89319C2211yescharacteristic, complemented
60#22580—71nomaximal, Sylow
61C24×D7—21no—
62C23×C4×C7C2311yescharacteristic
63C22×D28—22no—
64C22×D28—22no—
65C22×D28—21no—
66C22×D28—22no—
67C22×D28—41no—
68C22×D28—41no—
69C22×D28C2×C414yes—
70C22×D28C2311yescharacteristic
71C22×D28C2311yescharacteristic
72C22×C4×D7—21no—
73C22×C4×D7—21no—
74C7×#117—22no—
75C7×#117C2×C414yescomplemented
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4D411yescharacteristic
85C2×C7×C22⋊C4D411yescharacteristic
86C2×C42×C7—21no—
87C2×C42×C7—21no—
88C2×C42×C7—21no—
89C2×C42×C7C2311yescharacteristic
90C2×C42×C7C2311yescharacteristic
91C2×C22⋊Dic7—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×(C2×D7)⋊C4—21no—
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100C2×#1136—41no—
101C2×#1136—41no—
102C2×#1136C2×C414yescomplemented
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107D7×C22⋊C4—44no—
108C4×D28—22no—
109C4×D28—22no—
110C4×D28—41no—
111C4×D28—41no—
112C7×#95—21no—
113C7×#95—21no—
114C7×#95—21no—
115C7×#95—21no—
116C7×#95—21no—
117C7×#95D411yescharacteristic
118C7×#95D411yescharacteristic
119C7⋊#95—21no—
120C22⋊(C7⋊C8)—22no—
121#6383—22no—
122#6383—22no—
123#6383—41no—
124#6383—41no—
125#6383C2×C414yes—
126#6383C2×C414yes—
127#6383C2×C414yescomplemented
128#6383C2×C414yescomplemented
129#6382—41no—
130#6381—41no—
131#6377—41no—
132C4×C7⋊C8—41no—
133C2×#418—71no—
134#2347D711yescharacteristic, complemented
135D4×C22⋊C4—71no—
136#1936—71no—
137#1934—71no—
138#1926—71no—
139#1925—71no—
140#1864—71no—
141#1862—71no—
142#1825—71no—
143#1809—71no—
144#1786—71no—
145#1762—71no—
146C4×#102—71no—
147#1753—71no—
148C24×C7C2×D411yescharacteristic
149C23×D7—21no—
150C23×D7—21no—
151C23×D7—24no—
152C23×D7—42no—
153C23×D7—42no—
154C23×D7—42no—
155C23×D7—42no—
156C23×D7—81no—
157C23×D7—81no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7C22×C412yes—
167C22×C4×C7C2×D411yescharacteristic
168C22×C4×C7C2×D411yescharacteristic
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2×D411yescharacteristic
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7#4112yes—
173C22×C4×C7C2411yescharacteristic
174C22×Dic7—21no—
175C22×Dic7—21no—
176C2×D28—21no—
177C2×D28—21no—
178C2×D28—21no—
179C2×D28—21no—
180C2×D28—21no—
181C2×D28—21no—
182C2×D28—21no—
183C2×D28—28no—
184C2×D28—24no—
185C2×D28—21no—
186C2×D28—44no—
187C2×D28—44no—
188C2×D28—44no—
189C2×D28—42no—
190C2×D28—42no—
191C2×D28C22×C412yes—
192C2×D28C22×C412yes—
193C2×D28#4112yes—
194C2×D28#4112yes—
195C2×C4×D7—42no—
196C2×C4×D7—42no—
197C2×C4×D7—42no—
198C2×C4×D7—42no—
199C2×C4×D7—81no—
200C2×C4×D7—81no—
201C7×C4⋊C4—21no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4—21no—
206C7×C4⋊C4—21no—
207C7×C4⋊C4—42no—
208C7×C4⋊C4—42no—
209C7×C4⋊C4C22×C412yes—
210C7×C4⋊C4C22×C412yes—
211C7×C22⋊C4—24no—
212C7×C22⋊C4—22no—
213C7×C22⋊C4—41no—
214C7×C22⋊C4—81no—
215C42×C7—24no—
216C42×C7—21no—
217C42×C7—21no—
218C42×C7—21no—
219C42×C7—21no—
220C42×C7—81no—
221C42×C7—81no—
222C22⋊Dic7—42no—
223(C2×D7)⋊C4—42no—
224(C2×D7)⋊C4—42no—
225(C2×D7)⋊C4—42no—
226(C2×D7)⋊C4—42no—
227(C2×D7)⋊C4—81no—
228(C2×D7)⋊C4—81no—
229C4⋊Dic7—21no—
230C4⋊Dic7—21no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233#1136—44no—
234C2×C7⋊C8—21no—
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⋊C8C22×C412yes—
245C2×C7⋊C8C22×C412yes—
246C23×D4—71no—
247C22×M16—71no—
248C2×C4×D4—71no—
249C2×C4×D4—71no—
250C2×#117C2×D711yescharacteristic
251C22×C22⋊C4—141no—
252C2×#107—71no—
253C2×#106—71no—
254#418—78no—
255C2×#102—71no—
256C2×#102—71no—
257C2×#102—71no—
258C2×#102—71no—
259C2×#102—71no—
260C2×#102—71no—
261C2×#102—71no—
262C2×#102—71no—
263C2×C22⋊C8—71no—
264C2×#97—71no—
265C2×C4×C8—71no—
266#390—71no—
267#390—71no—
268#389C2×D711yescharacteristic, complemented
269#389C2×D711yescharacteristic, complemented
270#388—21no—
271#388—21no—
272#386—141no—
273#386—141no—
274#383—21no—
275#380—71no—
276#380C2×D711yescharacteristic
277#379—141no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4C2×D711yescharacteristic, complemented
280C4×C4⋊C4C2×D711yescharacteristic, complemented
281C4×C22⋊C4C2×D711yescharacteristic
282#340—71no—
283#340—71no—
284#340—71no—
285#340—71no—
286#340—71no—
287#340—71no—
288#336—71no—
289#336—71no—
290C23×C7—21no—
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—21no—
296C23×C7C4×D412yes—
297C23×C7C22×D411yescharacteristic
298C22×D7—22no—
299C22×D7—22no—
300C22×D7—22no—
301C22×D7—22no—
302C22×D7—48no—
303C22×D7—41no—
304C22×D7—41no—
305C22×D7—41no—
306C22×D7—41no—
307C22×D7—48no—
308C22×D7—41no—
309C22×D7—41no—
310C22×D7—41no—
311C22×D7—41no—
312C22×D7—41no—
313C22×D7—41no—
314C22×D7—84no—
315C22×D7—84no—
316C22×D7—84no—
317C22×D7—84no—
318C22×D7—84no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
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—21no—
337C2×C4×C7—21no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7C4×D412yes—
349C2×C4×C7AGL(1,ℤ/8)12yes—
350C2×C4×C7C23×C411yescharacteristic
351C2×C4×C7C2×#4111yescharacteristic
352C2×C4×C7C2×#4111yescharacteristic
353C2×C4×C7C2×#4111yescharacteristic
354C2×C4×C7H(5,𝔽2)11yescharacteristic
355C2×C4×C7H(5,𝔽2)11yescharacteristic
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362D28—22no—
363D28—22no—
364D28—22no—
365D28—22no—
366D28—22no—
367D28—48no—
368D28—41no—
369D28—41no—
370D28#11714yes—
371C4×D7—84no—
372C4×D7—84no—
373C7⋊C8—22no—
374C7⋊C8—22no—
375C7⋊C8—41no—
376C7⋊C8—41no—
377C25—141no—
378C22×D4—74no—
379C22×D4—71no—
380C22×D4—71no—
381C22×D4—142no—
382C22×D4—142no—
383C22×D4—142no—
384C22×D4—141no—
385C22×D4—281no—
386C22×D4—281no—
387C23×C4—141no—
388C23×C4—141no—
389C23×C4C22×D711yescharacteristic
390C2×M16—74no—
391C2×M16—281no—
392C2×M16—281no—
393C22×C8—71no—
394C22×C8—71no—
395C22×C8—71no—
396C22×C8—71no—
397C4×D4—142no—
398C4×D4—142no—
399C4×D4—281no—
400C4×D4—281no—
401#117—22no—
402#117C4×D714yescomplemented
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—71no—
406C2×C4⋊C4—71no—
407C2×C4⋊C4C22×D711yescharacteristic
408C2×C4⋊C4C22×D711yescharacteristic
409C2×C4⋊C4C22×D711yescharacteristic
410C2×C4⋊C4C22×D711yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—141no—
414C2×C22⋊C4—141no—
415C2×C22⋊C4—141no—
416C2×C22⋊C4—141no—
417C2×C22⋊C4—141no—
418C2×C22⋊C4—141no—
419C2×C22⋊C4—141no—
420C2×C22⋊C4—284no—
421C2×C22⋊C4C22⋊D711yescharacteristic
422C2×C22⋊C4C22⋊D711yescharacteristic
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42C22×D711yescharacteristic
427C2×C42C22×D711yescharacteristic
428#107—281no—
429#106—281no—
430#102—74no—
431#102—74no—
432#102—74no—
433#102—74no—
434#102—142no—
435#102—142no—
436#102—281no—
437#102—281no—
438C22⋊C8—142no—
439#97—281no—
440C4×C8—281no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—141no—
447#95C22⋊D711yescharacteristic
448#95C22⋊D711yescharacteristic
449C22×C7—22no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—41no—
453C22×C7—41no—
454C22×C7—41no—
455C22×C7—41no—
456C22×C7C2×C4×D411yescharacteristic
457C22×C7#54611yescharacteristic
458C22×C7#54611yescharacteristic
459C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
460C22×C7#57511yescharacteristic
461C22×C7#57611yescharacteristic
462C22×C7#57711yescharacteristic
463C2×D7—24no—
464C2×D7—42no—
465C2×D7—42no—
466C2×D7—42no—
467C2×D7—42no—
468C2×D7—42no—
469C2×D7—42no—
470C2×D7—42no—
471C2×D7—42no—
472C2×D7—42no—
473C2×D7—816no—
474C2×D7—81no—
475C2×D7—81no—
476C2×D7—81no—
477C2×D7—81no—
478C4×C7—22no—
479C4×C7—22no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—41no—
483C4×C7—41no—
484C4×C7—41no—
485C4×C7—81no—
486C4×C7—81no—
487C4×C7C2×#11711yescharacteristic
488C4×C7#51811yescharacteristic
489C4×C7#55111yescharacteristic
490C4×C7#55111yescharacteristic
491Dic7—81no—
492Dic7—81no—
493C24—141no—
494C24—141no—
495C24—144no—
496C24—282no—
497C24—282no—
498C24—282no—
499C24—282no—
500C24—561no—
501C24—561no—
502C24C2×C22⋊D711yescharacteristic
503C2×D4—72no—
504C2×D4—72no—
505C2×D4—72no—
506C2×D4—72no—
507C2×D4—148no—
508C2×D4—144no—
509C2×D4—141no—
510C2×D4—141no—
511C2×D4—141no—
512C2×D4—141no—
513C2×D4—141no—
514C2×D4—141no—
515C2×D4—141no—
516C2×D4—141no—
517C2×D4—284no—
518C2×D4—284no—
519C2×D4—284no—
520C2×D4—282no—
521C2×D4—282no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—141no—
531C22×C4—141no—
532C22×C4—282no—
533C22×C4—282no—
534C22×C4—282no—
535C22×C4—282no—
536C22×C4—561no—
537C22×C4—561no—
538C22×C4C2×C4×D712yes—
539C22×C4#115712yes—
540C22×C4C2×C22⋊D711yescharacteristic
541C22×C4C2×C22⋊D711yescharacteristic
542C22×C4C2×C22⋊D711yescharacteristic
543C22×C4C2×C22⋊D711yescharacteristic
544C22×C4C2×C22⋊D711yescharacteristic
545C22×C4C23×D711yescharacteristic
546M16—284no—
547C2×C8—72no—
548C2×C8—72no—
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—
558C2×C8—141no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—141no—
568C4⋊C4—141no—
569C4⋊C4—141no—
570C4⋊C4—141no—
571C4⋊C4C2×C4×D712yes—
572C4⋊C4C2×C4×D712yes—
573C22⋊C4—24no—
574C22⋊C4—22no—
575C22⋊C4—41no—
576C22⋊C4—81no—
577C22⋊C4—282no—
578C22⋊C4—282no—
579C22⋊C4—282no—
580C22⋊C4—282no—
581C22⋊C4—282no—
582C22⋊C4—561no—
583C22⋊C4—561no—
584C42—24no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—81no—
590C42—81no—
591C2×C7—42no—
592C2×C7#234211yescharacteristic
593C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
594C2×C7#294611yescharacteristic
595C2×C7#331111yescharacteristic
596C2×C7#331811yescharacteristic
597C2×C7#332211yescharacteristic
598C2×C7#332411yescharacteristic
599D7—44no—
600D7—82no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—142no—
608C23—142no—
609C23—142no—
610C23—142no—
611C23—288no—
612C23—288no—
613C23—281no—
614C23—281no—
615C23—281no—
616C23—281no—
617C23—281no—
618C23—281no—
619C23—281no—
620C23—281no—
621C23—281no—
622C23—281no—
623C23—564no—
624C23—564no—
625C23—564no—
626C23—564no—
627C23—564no—
628C23C4×C22⋊D712yes—
629C23C22×C22⋊D711yescharacteristic
630D4—74no—
631D4—142no—
632D4—142no—
633D4—142no—
634D4—142no—
635D4—142no—
636D4—288no—
637D4—281no—
638D4—281no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—41no—
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—41no—
668C2×C4—281no—
669C2×C4—281no—
670C2×C4—281no—
671C2×C4—281no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—564no—
675C2×C4—564no—
676C2×C4C4×C22⋊D712yes—
677C2×C4#651212yes—
678C2×C4C22×C4×D711yescharacteristic
679C2×C4C2×#115711yescharacteristic
680C2×C4D7×#4111yescharacteristic
681C2×C4D7×#4111yescharacteristic
682C2×C4#655311yescharacteristic
683C2×C4#655311yescharacteristic
684C8—142no—
685C8—142no—
686C8—281no—
687C8—281no—
688C7#2258011yescharacteristic, complemented, Sylow
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—144no—
697C22—282no—
698C22—282no—
699C22—282no—
700C22—282no—
701C22—282no—
702C22—282no—
703C22—282no—
704C22—282no—
705C22—282no—
706C22—5616no—
707C22—561no—
708C22—561no—
709C22—561no—
710C22—561no—
711C22C2×C4×C22⋊D711yescharacteristic
712C22C2×#651211yescharacteristic
713C22#9051311yescharacteristic
714C22#9052011yescharacteristic
715C22#9052011yescharacteristic
716C22#9052611yescharacteristic
717C22#9052811yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—561no—
728C4—561no—
729C4D7×#11711yescharacteristic
730C4#9021211yescharacteristic
731C4#9021811yescharacteristic
732C4#9021811yescharacteristic
733C2—42no—
734C2—284no—
735C2—562no—
736C2#1173971611yescharacteristic
737C2C4×#651211yescharacteristic
738C2#1174000911yescharacteristic
739C2#1174106111yescharacteristic
740C2#1174106211yescharacteristic
741C2#1174111011yescharacteristic
742C2#1174111111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2347C2
socleC23×C7C22×D4
prime radicalC23×D28C22
cosocleC22×C4×C7C24
hypercenter#2347D7
hypocenterC7#22580
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
1. C7×#2347C2semidirect
4. #11729329C2semidirect
5. #11727380C2semidirect
6. #11727379C2semidirect
7. #11727371C2semidirect
8. #11727369C2semidirect
10. #11727267C2semidirect
11. #11727228C2semidirect
12. C4×#6383C2semidirect
13. #11727217C2semidirect
14. #11727216C2semidirect
15. #11727202C2semidirect
22. C7×#389C22semidirect
23. C7×#389C22semidirect
29. C4×C7×C4⋊C4C22semidirect
30. C4×C7×C4⋊C4C22semidirect
34. #89773C4semidirect
43. C2×#6382C22semidirect
44. C2×#6381C22semidirect
48. C2×#6377C22semidirect
49. C2×C4×C7⋊C8C22semidirect
52. #89324C22semidirect
53. #89324C22semidirect
54. #89324C22semidirect
55. #89324C22semidirect
56. #89324C22semidirect
57. #89324C22semidirect
58. #89319C22semidirect
59. #89319C22semidirect
75. C7×#117C2×C4semidirect
102. C2×#1136C2×C4semidirect
127. #6383C2×C4semidirect
128. #6383C2×C4semidirect
134. #2347D7semidirect
268. #389C2×D7semidirect
269. #389C2×D7semidirect
279. C4×C4⋊C4C2×D7semidirect
280. C4×C4⋊C4C2×D7semidirect
402. #117C4×D7semidirect
688. C7#22580semidirect

Maximal subgroups

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

subgroupindex
C7×#23472
C2×#897732
C22⋊C4×D282
#117293292
#117273802
#117273792
#117273712
#117273692
#117272752
#117272672
#117272282
C4×#63832
#117272172
#117272162
#117272022
#225807