Finite Group Databasebeta

← #13360180

Subgroups — #13360180

Order 1792.

1120 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2275C211yesmaximal, characteristic, complemented
2C2×#89787C211yesmaximal, characteristic
3C2×#89786C211yesmaximal, characteristic, complemented
4C2×C4×#1141C211yesmaximal, characteristic, complemented
5#11730834C211yesmaximal, characteristic, complemented
6#11729367C211yesmaximal, characteristic, complemented
7#11729367C211yesmaximal, characteristic, complemented
8#11729359C211yesmaximal, characteristic, complemented
9#11727241C211yesmaximal, characteristic, complemented
10#11727228C211yesmaximal, characteristic, complemented
11C4×#6383C211yesmaximal, characteristic, complemented
12#11727222C211yesmaximal, characteristic, complemented
13#11727217C211yesmaximal, characteristic, complemented
14#11727216C211yesmaximal, characteristic, complemented
15#11727190C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×#1141C2211yescharacteristic
20C22×#1141C2211yescharacteristic
21C2×#6437C2211yescharacteristic
22C2×C4×D28C2211yescharacteristic
23C2×C4×D28C2211yescharacteristic
24C4×C7×C4⋊C4C2211yescharacteristic
25C4×C7×C4⋊C4C2211yescharacteristic
26C4×C7×C4⋊C4C2211yescharacteristic
27C4×C7×C22⋊C4—21no—
28C4×C7×C22⋊C4—21no—
29C4×C7×C22⋊C4—21no—
30C7×#376C2211yescharacteristic
31C2×C7×#95—21no—
32C2×#6406C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34#89787C418yescomplemented
35#89786—24no—
36C4×#1141—24no—
37C2×#6383C2211yescharacteristic
38C2×#6383C2211yescharacteristic
39C2×#6383C2211yescharacteristic
40C2×#6383C2211yescharacteristic
41C2×#6383C2211yescharacteristic
42C2×#6383C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C2×#6381C2211yescharacteristic
45#89711C2211yescharacteristic
46#89711C2211yescharacteristic
47#89708C2211yescharacteristic
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50C2×#6377C2211yescharacteristic
51C2×C4×C7⋊C8C2211yescharacteristic
52#89437—21no—
53#89437—21no—
54#89437—21no—
55#89437—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#21513—71nomaximal, Sylow
63C22×C7×D4C2311yescharacteristic
64C23×C4×C7—21no—
65C23×C4×C7—21no—
66C23×C4×C7—21no—
67C22×D28—21no—
68C22×D28—21no—
69C22×D28C2311yescharacteristic
70C22×D28C2311yescharacteristic
71C22×C4×D7—21no—
72C22×C4×D7—21no—
73C4×C7×D4—22no—
74C4×C7×D4—22no—
75C4×C7×D4—22no—
76C4×C7×D4—22no—
77C4×C7×D4C2×C414yescomplemented
78C4×C7×D4D414yescomplemented
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⋊C4—21no—
85C2×C42×C7—21no—
86C2×C42×C7—21no—
87C2×C42×C7—21no—
88C2×C42×C7C2311yescharacteristic
89C2×C42×C7C2311yescharacteristic
90C2×C42×C7C2311yescharacteristic
91C2×#1141—22no—
92C2×#1141—22no—
93C2×#1141—22no—
94C2×#1141—22no—
95C2×#1141C2×C414yescomplemented
96C2×#1141C2×C414yescomplemented
97C2×(C2×D7)⋊C4—21no—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×(C2×D7)⋊C4—21no—
101C2×(C2×D7)⋊C4—21no—
102C2×(C2×D7)⋊C4—21no—
103C2×C4⋊Dic7C2311yescharacteristic
104C2×C4⋊Dic7C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2311yescharacteristic
107C22×C7⋊C8C2311yescharacteristic
108C22×C7⋊C8C2311yescharacteristic
109#6437—22no—
110#6437C2×C414yescomplemented
111C4×D28—22no—
112C4×D28—22no—
113C4×D28—22no—
114C4×D28—22no—
115C7×#95—21no—
116C7×#95—21no—
117C7×#95—21no—
118C7×#95D411yescharacteristic
119C7×#95D411yescharacteristic
120C7×#95D411yescharacteristic
121C7×#95D411yescharacteristic
122#6406—22no—
123#6406—22no—
124C7⋊#95—21no—
125C7⋊#95—21no—
126#6383—22no—
127#6383—22no—
128#6383—22no—
129#6383—22no—
130#6383C2×C414yescomplemented
131#6383C2×C414yescomplemented
132#6382—22no—
133#6381—22no—
134C4⋊(C7⋊C8)—22no—
135C4⋊(C7⋊C8)C2×C414yescomplemented
136#6377—22no—
137C4×C7⋊C8—22no—
138C2×#459—71no—
139C2×#442—71no—
140C2×C4×D8—71no—
141#2328—71no—
142#2275D711yescharacteristic, complemented
143#1982—71no—
144#1949—71no—
145#1926—71no—
146#1925—71no—
147#1879—71no—
148#1879—71no—
149#1804—71no—
150#1768—71no—
151#1762—71no—
152C4×#102—71no—
153C24×C7—21no—
154C23×D7—21no—
155C23×D7—21no—
156C2×C7×D4—21no—
157C2×C7×D4—21no—
158C2×C7×D4—21no—
159C2×C7×D4C22×C412yes—
160C2×C7×D4C2×D412yes—
161C2×C7×D4#4112yes—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—24no—
166C22×C4×C7—24no—
167C22×C4×C7—24no—
168C22×C4×C7—81no—
169C22×C4×C7—81no—
170C22×C4×C7—81no—
171C22×C4×C7—81no—
172C22×C4×C7—81no—
173C22×C4×C7—81no—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2411yescharacteristic
181C22×Dic7—21no—
182C22×Dic7—21no—
183C2×D28—21no—
184C2×D28—21no—
185C2×D28—21no—
186C2×D28—21no—
187C2×D28—21no—
188C2×D28—21no—
189C2×D28—21no—
190C2×D28—21no—
191C2×D28—21no—
192C2×D28—21no—
193C2×D28—24no—
194C2×D28—24no—
195C2×D28—81no—
196C2×D28—81no—
197C2×D28—81no—
198C2×D28—81no—
199C2×D28C22×C412yes—
200C2×D28C22×C412yes—
201C2×C4×D7—42no—
202C2×C4×D7—42no—
203C2×C4×D7—81no—
204C2×C4×D7—81no—
205C2×C4×D7—81no—
206C2×C4×D7—81no—
207C7×C4⋊C4—21no—
208C7×C4⋊C4—21no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4C22×C412yes—
211C7×C4⋊C4C2×D412yes—
212C7×C4⋊C4#4112yes—
213C7×C22⋊C4—24no—
214C7×C22⋊C4—24no—
215C7×C22⋊C4—24no—
216C42×C7—21no—
217C42×C7—21no—
218C42×C7—81no—
219C42×C7—81no—
220C42×C7—81no—
221C42×C7C22×C412yes—
222C42×C7C2×D412yes—
223C42×C7#4112yes—
224C42×C7#4112yes—
225#1141—28no—
226#1141—28no—
227(C2×D7)⋊C4—42no—
228(C2×D7)⋊C4—42no—
229(C2×D7)⋊C4—81no—
230(C2×D7)⋊C4—81no—
231(C2×D7)⋊C4—81no—
232(C2×D7)⋊C4—81no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7—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⋊C8C22×C412yes—
248C2×C7⋊C8C22×C412yes—
249C22×D8—71no—
250C22×D8—71no—
251C2×#127—71no—
252C2×C4×D4—71no—
253C2×C4×D4—71no—
254C2×C4×D4C2×D711yescharacteristic
255C2×C4×D4C2×D711yescharacteristic
256C2×C4×D4C2×D711yescharacteristic
257#459—78no—
258#442—144no—
259C4×D8—144no—
260C2×#107—71no—
261C2×#106—71no—
262C2×C4⋊C8—71no—
263C2×C4⋊C8—71no—
264C2×#102—71no—
265C2×#102—71no—
266C2×#102—71no—
267C2×#102—71no—
268C2×#102—71no—
269C2×#102—71no—
270C2×#102—71no—
271C2×#102—71no—
272C2×#97—71no—
273C2×C4×C8—71no—
274#390—71no—
275#390—71no—
276#386—141no—
277#386—141no—
278#386—141no—
279#386—141no—
280#382—71no—
281C4×C4⋊C4C2×D711yescharacteristic
282C4×C4⋊C4C2×D711yescharacteristic
283C4×C4⋊C4C2×D711yescharacteristic
284C4×C22⋊C4—21no—
285C4×C22⋊C4—21no—
286C4×C22⋊C4—21no—
287#376C2×D711yescharacteristic
288C2×#95—21no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#336—71no—
294#336—71no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7C22×D411yescharacteristic
303C22×D7—22no—
304C22×D7—22no—
305C22×D7—41no—
306C22×D7—41no—
307C22×D7—41no—
308C22×D7—41no—
309C22×D7—41no—
310C22×D7—41no—
311C22×D7—41no—
312C22×D7—41no—
313C22×D7—41no—
314C22×D7—41no—
315C22×D7—41no—
316C22×D7—41no—
317C7×D4—22no—
318C7×D4—22no—
319C7×D4—22no—
320C7×D4C4×D414yes—
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—21no—
332C2×C4×C7—21no—
333C2×C4×C7—22no—
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—84no—
345C2×C4×C7—84no—
346C2×C4×C7—84no—
347C2×C4×C7C4×D412yes—
348C2×C4×C7C4×D412yes—
349C2×C4×C7#12112yes—
350C2×C4×C7#12112yes—
351C2×C4×C7C23×C411yescharacteristic
352C2×C4×C7C22×D411yescharacteristic
353C2×C4×C7C2×#4111yescharacteristic
354C2×C4×C7C2×#4111yescharacteristic
355C2×C4×C7C2×#4111yescharacteristic
356C2×C4×C7C2×#4111yescharacteristic
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363D28—22no—
364D28—22no—
365D28—22no—
366D28—22no—
367D28—41no—
368D28—41no—
369D28—41no—
370D28—41no—
371D28—84no—
372D28—84no—
373C4×D7—84no—
374C4×D7—84no—
375C7⋊C8—22no—
376C7⋊C8—22no—
377C7⋊C8—41no—
378C7⋊C8—41no—
379C22×D4—71no—
380C22×D4—71no—
381C22×D4—141no—
382C22×D4—141no—
383C22×D4C22×D711yescharacteristic
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—141no—
388C23×C4—141no—
389C2×D8—74no—
390C2×D8—74no—
391C2×D8—142no—
392C2×D8—142no—
393C2×D8—142no—
394C2×D8—142no—
395C22×C8—71no—
396C22×C8—71no—
397C22×C8—71no—
398C22×C8—71no—
399#127—74no—
400#127—142no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—142no—
406C4×D4—142no—
407C4×D4—142no—
408C4×D4—142no—
409C4×D4C4×D714yescomplemented
410C4×D4D2814yescomplemented
411C2×C4⋊C4—71no—
412C2×C4⋊C4—71no—
413C2×C4⋊C4C22×D711yescharacteristic
414C2×C4⋊C4C22×D711yescharacteristic
415C2×C4⋊C4C22×D711yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—141no—
420C2×C22⋊C4—141no—
421C2×C22⋊C4—141no—
422C2×C22⋊C4—141no—
423C2×C22⋊C4—141no—
424C2×C22⋊C4—141no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42C22×D711yescharacteristic
429C2×C42C22×D711yescharacteristic
430C2×C42C22×D711yescharacteristic
431#107—142no—
432#106—142no—
433C4⋊C8—74no—
434C4⋊C8—142no—
435#102—74no—
436#102—74no—
437#102—142no—
438#102—142no—
439#102—142no—
440#102—142no—
441#102—142no—
442#102—142no—
443#97—142no—
444C4×C8—142no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—141no—
449#95—141no—
450#95C22⋊D711yescharacteristic
451#95C22⋊D711yescharacteristic
452#95C22⋊D711yescharacteristic
453#95C22⋊D711yescharacteristic
454C22×C7—24no—
455C22×C7—42no—
456C22×C7—42no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—42no—
461C22×C7C2×C4×D411yescharacteristic
462C22×C7C2×#12111yescharacteristic
463C22×C7#52511yescharacteristic
464C22×C7#57611yescharacteristic
465C22×C7#57611yescharacteristic
466C22×C7#57611yescharacteristic
467C22×C7#57711yescharacteristic
468C2×D7—42no—
469C2×D7—42no—
470C2×D7—42no—
471C2×D7—42no—
472C2×D7—42no—
473C2×D7—42no—
474C2×D7—81no—
475C2×D7—81no—
476C2×D7—81no—
477C2×D7—81no—
478C2×D7—81no—
479C2×D7—81no—
480C2×D7—81no—
481C2×D7—81no—
482C4×C7—22no—
483C4×C7—22no—
484C4×C7—22no—
485C4×C7—22no—
486C4×C7—41no—
487C4×C7—41no—
488C4×C7—42no—
489C4×C7—42no—
490C4×C7—42no—
491C4×C7C2×C4×D411yescharacteristic
492C4×C7C4×#4111yescharacteristic
493C4×C7#52911yescharacteristic
494C4×C7#53211yescharacteristic
495Dic7—81no—
496Dic7—81no—
497C24—21no—
498C24—141no—
499C24—141no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—72no—
504C2×D4—72no—
505C2×D4—144no—
506C2×D4—144no—
507C2×D4—141no—
508C2×D4—141no—
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—561no—
518C2×D4—561no—
519C2×D4—561no—
520C2×D4—561no—
521C2×D4C2×C4×D712yes—
522C2×D4C2×D2812yes—
523C2×D4#115712yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—141no—
537C22×C4—141no—
538C22×C4—282no—
539C22×C4—282no—
540C22×C4—561no—
541C22×C4—561no—
542C22×C4—561no—
543C22×C4—561no—
544C22×C4C2×C22⋊D711yescharacteristic
545C22×C4C2×C22⋊D711yescharacteristic
546C22×C4C2×C22⋊D711yescharacteristic
547C22×C4C2×C22⋊D711yescharacteristic
548C22×C4C2×C22⋊D711yescharacteristic
549C22×C4C2×C22⋊D711yescharacteristic
550C22×C4C23×D711yescharacteristic
551D8—148no—
552D8—148no—
553C2×C8—72no—
554C2×C8—72no—
555C2×C8—141no—
556C2×C8—141no—
557C2×C8—141no—
558C2×C8—141no—
559C2×C8—141no—
560C2×C8—141no—
561C2×C8—141no—
562C2×C8—141no—
563C2×C8—141no—
564C2×C8—141no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—141no—
569C4⋊C4—141no—
570C4⋊C4—141no—
571C4⋊C4—141no—
572C4⋊C4C2×C4×D712yes—
573C4⋊C4C2×D2812yes—
574C4⋊C4#115712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—282no—
579C22⋊C4—282no—
580C22⋊C4—561no—
581C22⋊C4—561no—
582C22⋊C4—561no—
583C22⋊C4—561no—
584C42—21no—
585C42—21no—
586C42—81no—
587C42—81no—
588C42—81no—
589C42C2×C4×D712yes—
590C42C2×D2812yes—
591C42#115712yes—
592C42#115712yes—
593C2×C7—44no—
594C2×C7C4×#12111yescharacteristic
595C2×C7#294611yescharacteristic
596C2×C7#294811yescharacteristic
597C2×C7#304111yescharacteristic
598C2×C7#304511yescharacteristic
599C2×C7#311911yescharacteristic
600C2×C7#312211yescharacteristic
601D7—82no—
602D7—82no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—142no—
611C23—142no—
612C23—281no—
613C23—281no—
614C23—281no—
615C23—281no—
616C23—281no—
617C23—281no—
618C23—281no—
619C23—281no—
620C23—281no—
621C23—281no—
622C23—281no—
623C23—281no—
624C23C22×C22⋊D711yescharacteristic
625D4—22no—
626D4—22no—
627D4—22no—
628D4—142no—
629D4—142no—
630D4—142no—
631D4—142no—
632D4—281no—
633D4—281no—
634D4—281no—
635D4—281no—
636D4—564no—
637D4—564no—
638D4C4×D2814yes—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—281no—
666C2×C4—281no—
667C2×C4—281no—
668C2×C4—281no—
669C2×C4—281no—
670C2×C4—281no—
671C2×C4—564no—
672C2×C4—564no—
673C2×C4C4×C22⋊D712yes—
674C2×C4C4×C22⋊D712yes—
675C2×C4#649312yes—
676C2×C4#649312yes—
677C2×C4C22×C4×D711yescharacteristic
678C2×C4C22×D2811yescharacteristic
679C2×C4C2×#115711yescharacteristic
680C2×C4C2×#115711yescharacteristic
681C2×C4C2×#115711yescharacteristic
682C2×C4C2×#115711yescharacteristic
683C8—142no—
684C8—142no—
685C8—281no—
686C8—281no—
687C7#2151311yescharacteristic, complemented, Sylow
688C22—24no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—282no—
696C22—282no—
697C22—282no—
698C22—282no—
699C22—282no—
700C22—282no—
701C22—561no—
702C22—561no—
703C22—561no—
704C22—561no—
705C22—561no—
706C22—561no—
707C22—561no—
708C22—561no—
709C22C2×C4×C22⋊D711yescharacteristic
710C22C2×#649311yescharacteristic
711C22#9048211yescharacteristic
712C22#9052611yescharacteristic
713C22#9052611yescharacteristic
714C22#9052611yescharacteristic
715C22#9052811yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—41no—
723C4—42no—
724C4—41no—
725C4—561no—
726C4—561no—
727C4C2×C4×D2811yescharacteristic
728C4C4×#115711yescharacteristic
729C4#9016811yescharacteristic
730C4#9017011yescharacteristic
731C2—44no—
732C2—562no—
733C2—562no—
734C2C4×#649311yescharacteristic
735C2#1173998311yescharacteristic
736C2#1173998511yescharacteristic
737C2#1173998711yescharacteristic
738C2#1174000911yescharacteristic
739C2#1174001011yescharacteristic
740C2#1174001311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2275C2
socleC23×C7C22×D4
prime radicalC2×#89787C2
cosocleC22×C4×C7C24
hypercenter#2275D7
hypocenterC7#21513
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
1. C7×#2275C2semidirect
3. C2×#89786C2semidirect
4. C2×C4×#1141C2semidirect
5. #11730834C2semidirect
6. #11729367C2semidirect
7. #11729367C2semidirect
8. #11729359C2semidirect
9. #11727241C2semidirect
10. #11727228C2semidirect
11. C4×#6383C2semidirect
12. #11727222C2semidirect
13. #11727217C2semidirect
14. #11727216C2semidirect
15. #11727190C2semidirect
34. #89787C4semidirect
77. C4×C7×D4C2×C4semidirect
78. C4×C7×D4D4semidirect
95. C2×#1141C2×C4semidirect
96. C2×#1141C2×C4semidirect
110. #6437C2×C4semidirect
130. #6383C2×C4semidirect
131. #6383C2×C4semidirect
135. C4⋊(C7⋊C8)C2×C4semidirect
142. #2275D7semidirect
409. C4×D4C4×D7semidirect
410. C4×D4D28semidirect
687. C7#21513semidirect

Maximal subgroups

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

subgroupindex
C7×#22752
C2×#897872
C2×#897862
C2×C4×#11412
#117308342
#117293672
#117293592
#117272412
#117272282
C4×#63832
#117272222
#117272172
#117272162
#117271902
#215137