Finite Group Databasebeta

← #13374079

Subgroups — #13374079

Order 1792.

1118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2339C211yesmaximal, characteristic
2C2×#90011C211yesmaximal, characteristic
3C2×#90005C211yesmaximal, characteristic
4C2×#89790C211yesmaximal, characteristic, complemented
5#11730913C211yesmaximal, characteristic, complemented
6#11729366C211yesmaximal, characteristic, complemented
7#11729363C211yesmaximal, characteristic, complemented
8#11729361C211yesmaximal, characteristic, complemented
9#11727444C211yesmaximal, characteristic, complemented
10#11727432C211yesmaximal, characteristic, complemented
11#11727429C211yesmaximal, characteristic, complemented
12#11727421C211yesmaximal, characteristic, complemented
13#11727268C211yesmaximal, characteristic, complemented
14#11727260C211yesmaximal, characteristic, complemented
15#11727201C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C22×#1142C2211yescharacteristic
21C2×#6489C2211yescharacteristic
22C2×#6487C2211yescharacteristic
23C23×C7⋊C8C2211yescharacteristic
24C2×C4×Dic14C2211yescharacteristic
25C7×#391C2211yescharacteristic
26C7×#391C2211yescharacteristic
27C7×#386—21no—
28C7×#386—21no—
29C7×#381—21no—
30C7×#380C2211yescharacteristic
31C4×C7×C22⋊C4C2211yescharacteristic
32C2×C7×#95—21no—
33#90011C418yescomplemented
34#90005—24no—
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39C2×#6406C2211yescharacteristic
40C2×#6406C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89790—24no—
43C2×#6384C2211yescharacteristic
44C2×#6384C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47#89717—21no—
48#89716—21no—
49C4×C4⋊Dic7C2211yescharacteristic
50#89701C2211yescharacteristic
51#89700C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53C2×#6377C2211yescharacteristic
54#89424—21no—
55#89421—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#22856—71nomaximal, Sylow
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C2×C7×#41C2×C414yes—
69C22×C7×Q8C2311yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7C2311yescharacteristic
76C22×Dic14C2311yescharacteristic
77C4×C7×D4—22no—
78C4×C7×D4—22no—
79C4×C7×D4—41no—
80C4×C7×D4—41no—
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4D411yescharacteristic
87C2×C7×C22⋊C4D411yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×C42×C7C2311yescharacteristic
90C2×C22⋊Dic7—21no—
91C2×C22⋊Dic7—21no—
92C2×#1144—41no—
93C2×#1144—41no—
94C2×#1144C2×C414yescomplemented
95C2×#1142—22no—
96C2×#1142—22no—
97C2×#1142C2×C414yes—
98#6489—22no—
99#6489—41no—
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4⋊Dic7C2311yescharacteristic
103#6487—22no—
104#6487C2×C414yescomplemented
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×C4×Dic7—21no—
109C2×C4×Dic7—21no—
110C2×C4×Dic7—21no—
111C22×C7⋊C8—22no—
112C22×C7⋊C8—22no—
113C22×C7⋊C8—41no—
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C4×Dic14—22no—
119C4×Dic14—41no—
120C7×#95—21no—
121C7×#95—21no—
122C7×#95—21no—
123C7×#95—21no—
124C7×#95—21no—
125C7×#95D411yescharacteristic
126C7×#95D411yescharacteristic
127#6409—22no—
128#6409—22no—
129#6409C2×C414yescomplemented
130#6406—22no—
131#6406C2×C414yes—
132#6406D414yes—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C22⋊(C7⋊C8)C2×C414yescomplemented
138#6384—22no—
139#6384—41no—
140#6382—41no—
141#6381—22no—
142#6377—22no—
143#6377—41no—
144C2×#452—71no—
145C2×#440—71no—
146C2×#416—71no—
147#2362—71no—
148#2339D711yescharacteristic
149#1971—71no—
150#1935—71no—
151#1928—71no—
152#1892—71no—
153#1878—71no—
154#1877—71no—
155#1864—71no—
156#1854—71no—
157#1762—71no—
158#1752—71no—
159C24×C7—21no—
160C24×C7C2×D411yescharacteristic
161C7×#41—28no—
162C7×#41—44no—
163C7×#41—44no—
164C7×#41—44no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8C22×C412yes—
171C2×C7×D4—24no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—42no—
176C2×C7×D4—42no—
177C2×C7×D4C22×C412yes—
178C2×C7×D4C2×D412yes—
179C2×C7×D4#4112yes—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—24no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—42no—
189C22×C4×C7—42no—
190C22×C4×C7—42no—
191C22×C4×C7—42no—
192C22×C4×C7—42no—
193C22×C4×C7—42no—
194C22×C4×C7—81no—
195C22×C4×C7—81no—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7#4112yes—
203C22×C4×C7C2411yescharacteristic
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C2×Dic14—21no—
209C2×Dic14—21no—
210C2×Dic14—21no—
211C2×Dic14—21no—
212C2×Dic14—21no—
213C2×Dic14C22×C412yes—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—21no—
218C7×C22⋊C4—41no—
219C7×C22⋊C4—41no—
220C7×C22⋊C4—42no—
221C7×C22⋊C4—42no—
222C7×C22⋊C4—81no—
223C42×C7—21no—
224C42×C7—21no—
225C42×C7—21no—
226C42×C7—21no—
227C22⋊Dic7—24no—
228C22⋊Dic7—42no—
229#1144—44no—
230#1142—28no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7C22×C412yes—
236C4⋊Dic7C2×D412yes—
237Dic7⋊C4—24no—
238Dic7⋊C4—42no—
239Dic7⋊C4—42no—
240C4×Dic7—42no—
241C4×Dic7—42no—
242C4×Dic7—42no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—44no—
253C2×C7⋊C8C22×C412yes—
254C2×C7⋊C8C22×C412yes—
255C2×C7⋊C8C2×D412yes—
256C22×#41C2×D711yescharacteristic
257C22×Q16—71no—
258C22×SD16—71no—
259C23×C8—71no—
260C2×C22⋊Q8—71no—
261C2×C4×Q8—71no—
262C2×C4×D4C2×D711yescharacteristic
263C2×C4×D4C2×D711yescharacteristic
264C2×#117—71no—
265#452—78no—
266#440—144no—
267C2×#107—71no—
268C2×#106—71no—
269#416—144no—
270C2×#103—71no—
271C2×#103—71no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#102—71no—
276C2×#102—71no—
277C2×#102—71no—
278C2×C22⋊C8—71no—
279C2×#97—71no—
280C2×#97—71no—
281#391—71no—
282#391C2×D711yescharacteristic
283#391C2×D711yescharacteristic
284#389—71no—
285#388—141no—
286#388—141no—
287#387—141no—
288#386—21no—
289#386—21no—
290#381—21no—
291#380C2×D711yescharacteristic
292C4×C4⋊C4—71no—
293C4×C4⋊C4—141no—
294C4×C22⋊C4C2×D711yescharacteristic
295C2×#95—21no—
296#340—71no—
297#340—71no—
298#340—71no—
299#340—71no—
300#336—71no—
301#336—71no—
302C23×C7—22no—
303C23×C7—21no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7C4×D412yes—
316C23×C7C22×D411yescharacteristic
317C7×Q8—22no—
318C7×Q8—22no—
319C7×Q8—41no—
320C7×Q8—41no—
321C7×D4—22no—
322C7×D4—22no—
323C7×D4—22no—
324C7×D4—48no—
325C7×D4C4×D414yes—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—48no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—84no—
355C2×C4×C7—84no—
356C2×C4×C7C4×D412yes—
357C2×C4×C7C23×C411yescharacteristic
358C2×C4×C7C22×D411yescharacteristic
359C2×C4×C7C2×#4111yescharacteristic
360C2×C4×C7C2×#4111yescharacteristic
361C2×C4×C7H(5,𝔽2)11yescharacteristic
362C2×C4×C7H(5,𝔽2)11yescharacteristic
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375Dic14—22no—
376Dic14—22no—
377Dic14—41no—
378Dic14—41no—
379C7⋊C8—22no—
380C7⋊C8—22no—
381C7⋊C8—22no—
382C7⋊C8—41no—
383C2×#41—22no—
384C2×#41—22no—
385C2×#41—22no—
386C2×#41—41no—
387C2×#41—41no—
388C2×#41C4×D714yes—
389C22×Q8—71no—
390C22×Q8C22×D711yescharacteristic
391C22×D4—21no—
392C22×D4C22×D711yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—21no—
396C23×C4C22×D711yescharacteristic
397C2×Q16—74no—
398C2×Q16—281no—
399C2×Q16—281no—
400C2×SD16—74no—
401C2×SD16—142no—
402C2×SD16—142no—
403C22×C8—71no—
404C22×C8—71no—
405C22×C8—71no—
406C22×C8—71no—
407C22×C8—142no—
408C22×C8—142no—
409C22×C8—281no—
410C22⋊Q8—74no—
411C22⋊Q8—142no—
412C4×Q8—142no—
413C4×Q8—281no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—41no—
417C4×D4—41no—
418#117—142no—
419#117—281no—
420C2×C4⋊C4—71no—
421C2×C4⋊C4—71no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—141no—
424C2×C4⋊C4—141no—
425C2×C4⋊C4—141no—
426C2×C4⋊C4C22×D711yescharacteristic
427C2×C4⋊C4C22×D711yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—141no—
432C2×C22⋊C4—141no—
433C2×C22⋊C4C22⋊D711yescharacteristic
434C2×C22⋊C4C22⋊D711yescharacteristic
435C2×C42—141no—
436C2×C42—141no—
437C2×C42—141no—
438C2×C42C22×D711yescharacteristic
439C2×C42C22×D711yescharacteristic
440#107—142no—
441#106—281no—
442#103—74no—
443#103—142no—
444#103—142no—
445#103—142no—
446#103—281no—
447#102—74no—
448#102—74no—
449#102—142no—
450C22⋊C8—74no—
451#97—142no—
452#97—281no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—141no—
459#95—141no—
460#95—141no—
461#95—141no—
462#95C22⋊D711yescharacteristic
463#95C22⋊D711yescharacteristic
464C22×C7—22no—
465C22×C7—24no—
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—41no—
476C22×C7—41no—
477C22×C7—42no—
478C22×C7C2×C4×D411yescharacteristic
479C22×C7D4211yescharacteristic
480C22×C7#54611yescharacteristic
481C22×C7#57511yescharacteristic
482C22×C7#57511yescharacteristic
483C22×C7#57711yescharacteristic
484C22×C7#57811yescharacteristic
485C4×C7—22no—
486C4×C7—42no—
487C4×C7—41no—
488C4×C7—41no—
489C4×C7—41no—
490C4×C7—41no—
491C4×C7—81no—
492C4×C7—81no—
493C4×C7C2×C4×D411yescharacteristic
494C4×C7#51811yescharacteristic
495C4×C7#54611yescharacteristic
496C4×C7#55111yescharacteristic
497Dic7—42no—
498Dic7—42no—
499Dic7—42no—
500Dic7—81no—
501C24—21no—
502C24C2×C22⋊D711yescharacteristic
503#41—28no—
504#41—44no—
505#41—44no—
506#41—44no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—72no—
513C2×Q8—141no—
514C2×Q8—141no—
515C2×Q8—141no—
516C2×Q8—141no—
517C2×Q8—141no—
518C2×Q8C2×C4×D712yes—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4C2×C4×D712yes—
526C2×D4D4×D712yes—
527C2×D4#115912yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—141no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4C2×C4×D712yes—
549C22×C4#115712yes—
550C22×C4C2×C22⋊D711yescharacteristic
551C22×C4C2×C22⋊D711yescharacteristic
552C22×C4C2×C22⋊D711yescharacteristic
553C22×C4C2×C22⋊D711yescharacteristic
554C22×C4C2×C22⋊D711yescharacteristic
555C22×C4C23×D711yescharacteristic
556Q16—284no—
557SD16—148no—
558C2×C8—72no—
559C2×C8—72no—
560C2×C8—72no—
561C2×C8—141no—
562C2×C8—141no—
563C2×C8—141no—
564C2×C8—141no—
565C2×C8—141no—
566C2×C8—141no—
567C2×C8—141no—
568C2×C8—141no—
569C2×C8—141no—
570C2×C8—284no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—72no—
576C4⋊C4—72no—
577C4⋊C4—144no—
578C4⋊C4—141no—
579C4⋊C4—141no—
580C4⋊C4—141no—
581C4⋊C4—141no—
582C4⋊C4—282no—
583C4⋊C4—282no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—144no—
590C22⋊C4—282no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—282no—
596C42—282no—
597C42—282no—
598C2×C7—42no—
599C2×C7—44no—
600C2×C7#235811yescharacteristic
601C2×C7#294311yescharacteristic
602C2×C7#294711yescharacteristic
603C2×C7#326711yescharacteristic
604C2×C7#326911yescharacteristic
605C2×C7#331111yescharacteristic
606C2×C7#331511yescharacteristic
607C23—22no—
608C23—22no—
609C23—21no—
610C23—22no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23C4×C22⋊D712yes—
621C23C22×C22⋊D711yescharacteristic
622Q8—22no—
623Q8—22no—
624Q8—41no—
625Q8—41no—
626Q8—142no—
627Q8—142no—
628Q8—281no—
629Q8—281no—
630D4—22no—
631D4—22no—
632D4—22no—
633D4—48no—
634D4(C22⋊D7)⋊C414yes—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—48no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—281no—
669C2×C4—281no—
670C2×C4—281no—
671C2×C4—281no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4—281no—
677C2×C4C4×C22⋊D712yes—
678C2×C4C22×C4×D711yescharacteristic
679C2×C4C2×#115711yescharacteristic
680C2×C4C2×D4×D711yescharacteristic
681C2×C4C2×#115911yescharacteristic
682C2×C4#654811yescharacteristic
683C2×C4#654811yescharacteristic
684C8—142no—
685C8—142no—
686C8—142no—
687C8—281no—
688C7#2285611yescharacteristic, complemented, Sylow
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22C2×C4×C22⋊D711yescharacteristic
704C22D4×C22⋊D711yescharacteristic
705C22#9049711yescharacteristic
706C22#9051311yescharacteristic
707C22#9051311yescharacteristic
708C22#9052711yescharacteristic
709C22#9052911yescharacteristic
710C4—22no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—42no—
716C4—81no—
717C4—81no—
718C4—282no—
719C4—282no—
720C4—282no—
721C4—561no—
722C4C2×(C22⋊D7)⋊C411yescharacteristic
723C4#9017711yescharacteristic
724C4#9018111yescharacteristic
725C4#9018611yescharacteristic
726C2—42no—
727C2—44no—
728C2#1173954411yescharacteristic
729C2#1173995111yescharacteristic
730C2#1174001611yescharacteristic
731C2#1174094211yescharacteristic
732C2#1174094811yescharacteristic
733C2#1174095811yescharacteristic
734C2#1174097311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2339C2
socleC23×C7C22×D4
prime radicalC22×C7×#41C22
cosocleC22×C4×C7C24
hypercenter#2339D7
hypocenterC7#22856
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
4. C2×#89790C2semidirect
5. #11730913C2semidirect
6. #11729366C2semidirect
7. #11729363C2semidirect
8. #11729361C2semidirect
9. #11727444C2semidirect
10. #11727432C2semidirect
11. #11727429C2semidirect
12. #11727421C2semidirect
13. #11727268C2semidirect
14. #11727260C2semidirect
15. #11727201C2semidirect
33. #90011C4semidirect
94. C2×#1144C2×C4semidirect
104. #6487C2×C4semidirect
129. #6409C2×C4semidirect
137. C22⋊(C7⋊C8)C2×C4semidirect
688. C7#22856semidirect

Maximal subgroups

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

subgroupindex
C7×#23392
C2×#900112
C2×#900052
C2×#897902
#117309132
#117293662
#117293632
#117293612
#117274442
#117274322
#117274292
#117274212
#117272682
#117272602
#117272012
#228567