Finite Group Databasebeta

← #13374177

Subgroups — #13374177

Order 1792.

1134 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
1C2×C7×#452C211yesmaximal, characteristic
2#11741533C211yesmaximal, characteristic
3C2×#90004C211yesmaximal, characteristic
4C2×#89936C211yesmaximal, characteristic, complemented
5#11740192C211yesmaximal, characteristic, complemented
6#11729820C211yesmaximal, characteristic, complemented
7#11729819C211yesmaximal, characteristic, complemented
8#11729801C211yesmaximal, characteristic, complemented
9#11729451C211yesmaximal, characteristic, complemented
10#11728009C211yesmaximal, characteristic, complemented
11#11727978C211yesmaximal, characteristic, complemented
12#11727922C211yesmaximal, characteristic, complemented
13Dic7×#102C211yesmaximal, characteristic, complemented
14#11727703C211yesmaximal, characteristic, complemented
15#11727681C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C2×D4×Dic7C2211yescharacteristic
22C2×D4×Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25C7×#452C418yescomplemented
26C2×C7×#103C2211yescharacteristic
27C2×C7×#102C2211yescharacteristic
28C2×C7×C22⋊C8C2211yescharacteristic
29#90004—24no—
30#90002C2211yescharacteristic
31#90002C2211yescharacteristic
32#90002C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37#89992—21no—
38#89992—21no—
39C2×#6406C2211yescharacteristic
40C2×#6406C2211yescharacteristic
41#89984C2211yescharacteristic
42#89983—21no—
43C4×C22⋊Dic7C2211yescharacteristic
44C2×C7⋊#95—21no—
45#89936—24no—
46C2×#6392C2211yescharacteristic
47C2×#6392C2211yescharacteristic
48C2×#6389C2211yescharacteristic
49C2×C8×Dic7C2211yescharacteristic
50#89757—21no—
51#89757C2211yescharacteristic
52#89753—21no—
53C4⋊C4×Dic7C2211yescharacteristic
54#89722—21no—
55C22⋊C4×Dic7—21no—
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22862—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×Q8C2311yescharacteristic
71C22×C7×D4—21no—
72C22×C7×D4C2311yescharacteristic
73C23×C4×C7—21no—
74C23×C4×C7C2311yescharacteristic
75C23×Dic7—21no—
76C23×Dic7—21no—
77C23×Dic7—21no—
78C2×C7×Q16—41no—
79C2×C7×Q16—41no—
80C2×C7×Q16C2×C414yescomplemented
81C2×C7×SD16—22no—
82C2×C7×SD16—22no—
83C2×C7×SD16C2×C414yescomplemented
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C7×C22⋊Q8—22no—
87C7×C22⋊Q8C2×C414yescomplemented
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C22⋊C4—21no—
91C2×C22⋊Dic7—21no—
92C2×C22⋊Dic7—21no—
93C2×C22⋊Dic7—21no—
94C2×C22⋊Dic7D411yescharacteristic
95C2×C22⋊Dic7D411yescharacteristic
96Q8×Dic7—22no—
97Q8×Dic7—41no—
98D4×Dic7—22no—
99D4×Dic7—22no—
100D4×Dic7—41no—
101D4×Dic7—41no—
102C2×C4⋊Dic7—22no—
103C2×C4⋊Dic7—21no—
104C2×C4⋊Dic7—21no—
105C2×C4⋊Dic7—21no—
106C2×C4⋊Dic7—41no—
107C2×C4⋊Dic7C2311yescharacteristic
108C2×C4⋊Dic7C2311yescharacteristic
109C2×C4⋊Dic7C2311yescharacteristic
110C2×C4⋊Dic7C2311yescharacteristic
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×C4×Dic7C2311yescharacteristic
114C2×C4×Dic7C2311yescharacteristic
115C2×#1136—22no—
116C2×#1136—22no—
117C2×#1136—41no—
118C22×C7⋊C8C2311yescharacteristic
119C22×C7⋊C8C2311yescharacteristic
120C7×#103C2×C414yescomplemented
121C7×#102C2×C414yescomplemented
122C7×C22⋊C8C2×C414yescomplemented
123#6409—22no—
124#6409—22no—
125#6409—22no—
126#6409—41no—
127#6406—22no—
128#6406D414yes—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C7⋊#95—21no—
132C7⋊#95—21no—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C7⋊#95D411yescharacteristic
139C7⋊#95D411yescharacteristic
140#6392—22no—
141#6392—41no—
142#6389—22no—
143C8×Dic7—41no—
144C2×#452D711yescharacteristic
145C2×#440—71no—
146C2×#417—71no—
147#2360—71no—
148#2339—71no—
149#1969—71no—
150#1935—71no—
151#1928—71no—
152#1894—71no—
153#1878—71no—
154#1877—71no—
155#1862—71no—
156#1852—71no—
157C4×#102—71no—
158#1753—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×Q8—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8C22×C412yes—
176C2×C7×Q8C22×C412yes—
177C2×C7×D4—24no—
178C2×C7×D4—21no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4—42no—
182C2×C7×D4—42no—
183C2×C7×D4C22×C412yes—
184C2×C7×D4C2×D412yes—
185C2×C7×D4#4112yes—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—24no—
194C22×C4×C7—42no—
195C22×C4×C7—42no—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7#4112yes—
199C22×C4×C7C2411yescharacteristic
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—42no—
205C22×Dic7—42no—
206C22×Dic7—42no—
207C22×Dic7—42no—
208C22×Dic7—42no—
209C22×Dic7—42no—
210C22×Dic7—81no—
211C22×Dic7—81no—
212C22×Dic7—81no—
213C22×Dic7C2×D411yescharacteristic
214C22×Dic7C2×D411yescharacteristic
215C22×Dic7C2×D411yescharacteristic
216C22×Dic7C2×D411yescharacteristic
217C7×Q16—44no—
218C7×SD16—28no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8C22×C412yes—
224C2×C7×C8C22×C412yes—
225C7×C4⋊C4—24no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4C22×C412yes—
228C7×C22⋊C4—24no—
229C22⋊Dic7—22no—
230C22⋊Dic7—41no—
231C22⋊Dic7—42no—
232C22⋊Dic7—42no—
233C22⋊Dic7—81no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7—21no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7—21no—
241C4⋊Dic7—42no—
242C4⋊Dic7—42no—
243C4⋊Dic7—81no—
244C4⋊Dic7C2×D412yes—
245C4×Dic7—21no—
246C4×Dic7—21no—
247C4×Dic7—21no—
248C4×Dic7—21no—
249C4×Dic7—42no—
250C4×Dic7—81no—
251#1136—44no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8—21no—
256C2×C7⋊C8—21no—
257C2×C7⋊C8C2×D412yes—
258C22×#41C2×D711yescharacteristic
259C22×Q16C2×D711yescharacteristic
260C22×SD16C2×D711yescharacteristic
261C22×M16—71no—
262C2×C22⋊Q8C2×D711yescharacteristic
263C2×C4×Q8—71no—
264C2×C4×D4—71no—
265C2×C4×D4—71no—
266C22×C4⋊C4—71no—
267#452Dic718yescomplemented
268#440—144no—
269C2×#107—71no—
270C2×#107—71no—
271#417—144no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×#103C2×D711yescharacteristic
277C2×#102—71no—
278C2×#102—71no—
279C2×#102C2×D711yescharacteristic
280C2×C22⋊C8C2×D711yescharacteristic
281C2×#97—71no—
282C2×C4×C8—71no—
283#391—71no—
284#391—71no—
285#391—71no—
286#389—71no—
287#389—141no—
288#387—141no—
289#386—141no—
290#386—141no—
291#385—141no—
292#381—141no—
293#380—71no—
294C4×C4⋊C4—71no—
295C4×C22⋊C4—71no—
296C4×C22⋊C4—141no—
297C2×#95—141no—
298#340—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#336—71no—
303#336—71no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—21no—
307C23×C7—22no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7C4×D412yes—
318C23×C7C22×D411yescharacteristic
319C7×Q8—22no—
320C7×Q8—22no—
321C7×Q8—22no—
322C7×Q8—22no—
323C7×Q8—41no—
324C7×Q8—41no—
325C7×Q8—41no—
326C7×Q8—41no—
327C7×D4—22no—
328C7×D4—22no—
329C7×D4—22no—
330C7×D4—48no—
331C7×D4C4×D414yes—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—48no—
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×C7C23×C411yescharacteristic
350C2×C4×C7C22×D411yescharacteristic
351C2×C4×C7C2×#4111yescharacteristic
352C2×C4×C7C2×#4111yescharacteristic
353C2×C4×C7H(5,𝔽2)11yescharacteristic
354C2×C4×C7H(5,𝔽2)11yescharacteristic
355C2×Dic7—21no—
356C2×Dic7—21no—
357C2×Dic7—21no—
358C2×Dic7—21no—
359C2×Dic7—22no—
360C2×Dic7—21no—
361C2×Dic7—21no—
362C2×Dic7—21no—
363C2×Dic7—21no—
364C2×Dic7—21no—
365C2×Dic7—21no—
366C2×Dic7—21no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—84no—
379C2×Dic7—84no—
380C2×Dic7—84no—
381C2×Dic7#13712yes—
382C7×C8—22no—
383C7×C8—22no—
384C7⋊C8—22no—
385C7⋊C8—41no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—41no—
390C2×#41—41no—
391C2×#41C2×Dic714yes—
392C22×Q8C22×D711yescharacteristic
393C22×Q8C22×D711yescharacteristic
394C22×D4—21no—
395C22×D4C22×D711yescharacteristic
396C23×C4—21no—
397C23×C4—141no—
398C23×C4—141no—
399C23×C4—141no—
400C23×C4C22×D711yescharacteristic
401C2×Q16—41no—
402C2×Q16—41no—
403C2×Q16C2×Dic714yescomplemented
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16C2×Dic714yescomplemented
407C2×M16—142no—
408C2×M16—142no—
409C2×M16—281no—
410C22×C8—71no—
411C22×C8—71no—
412C22×C8C22×D711yescharacteristic
413C22×C8C22×D711yescharacteristic
414C22⋊Q8—22no—
415C22⋊Q8C2×Dic714yescomplemented
416C4×Q8—142no—
417C4×Q8—281no—
418C4×D4—142no—
419C4×D4—142no—
420C4×D4—281no—
421C4×D4—281no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—71no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—71no—
426C2×C4⋊C4—71no—
427C2×C4⋊C4—142no—
428C2×C4⋊C4—141no—
429C2×C4⋊C4—141no—
430C2×C4⋊C4—141no—
431C2×C4⋊C4—281no—
432C2×C4⋊C4C22×D711yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—71no—
435C2×C22⋊C4—71no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4—141no—
438C2×C22⋊C4—141no—
439C2×C42—71no—
440C2×C42—71no—
441C2×C42—141no—
442C2×C42—141no—
443#107—142no—
444#107—281no—
445#103—142no—
446#103—142no—
447#103—142no—
448#103—281no—
449#103C2×Dic714yescomplemented
450#102—74no—
451#102—142no—
452#102C2×Dic714yescomplemented
453C22⋊C8C2×Dic714yescomplemented
454#97—142no—
455C4×C8—281no—
456#95—71no—
457#95—71no—
458#95—141no—
459#95—141no—
460#95—141no—
461#95—141no—
462#95—141no—
463#95—141no—
464#95—141no—
465#95—141no—
466#95—141no—
467C22×C7—22no—
468C22×C7—24no—
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—41no—
474C22×C7—42no—
475C22×C7—41no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—42no—
481C22×C7C2×C4×D411yescharacteristic
482C22×C7D4211yescharacteristic
483C22×C7#54611yescharacteristic
484C22×C7C2×#13711yescharacteristic
485C22×C7#57511yescharacteristic
486C22×C7#57611yescharacteristic
487C22×C7#57811yescharacteristic
488C4×C7—22no—
489C4×C7—42no—
490C4×C7—42no—
491C4×C7—42no—
492C4×C7C2×C4×D411yescharacteristic
493C4×C7#51811yescharacteristic
494C4×C7#54611yescharacteristic
495C4×C7#55111yescharacteristic
496Dic7—22no—
497Dic7—41no—
498Dic7—42no—
499Dic7—41no—
500Dic7—41no—
501Dic7—81no—
502Dic7—81no—
503Dic7—81no—
504C24—21no—
505C24D4×D711yescharacteristic
506#41—28no—
507#41—44no—
508#41—44no—
509#41—44no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8C22×Dic712yes—
521C2×Q8C22×Dic712yes—
522C2×D4—24no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4D4×D712yes—
529C2×D4#115912yes—
530C2×D4C22×Dic712yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—71no—
542C22×C4—71no—
543C22×C4—71no—
544C22×C4—71no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—282no—
550C22×C4—282no—
551C22×C4—282no—
552C22×C4—282no—
553C22×C4—282no—
554C22×C4—282no—
555C22×C4—561no—
556C22×C4—561no—
557C22×C4—561no—
558C22×C4D4×D711yescharacteristic
559C22×C4#115912yes—
560C22×C4C22×Dic712yes—
561C22×C4C23×D711yescharacteristic
562Q16—44no—
563SD16—28no—
564M16—284no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—72no—
570C2×C8—141no—
571C2×C8—141no—
572C2×C8—141no—
573C2×C8—141no—
574C2×C8—141no—
575C2×C8C22×Dic712yes—
576C2×C8C22×Dic712yes—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—72no—
580C4⋊C4—141no—
581C4⋊C4—141no—
582C4⋊C4—141no—
583C4⋊C4—141no—
584C4⋊C4—141no—
585C4⋊C4—141no—
586C4⋊C4—141no—
587C4⋊C4—282no—
588C4⋊C4—282no—
589C4⋊C4—561no—
590C4⋊C4C22×Dic712yes—
591C22⋊C4—24no—
592C22⋊C4—142no—
593C22⋊C4—281no—
594C22⋊C4—282no—
595C22⋊C4—282no—
596C22⋊C4—561no—
597C42—141no—
598C42—141no—
599C42—141no—
600C42—141no—
601C42—282no—
602C42—561no—
603C2×C7—42no—
604C2×C7—44no—
605C2×C7#235811yescharacteristic
606C2×C7C4×#13711yescharacteristic
607C2×C7#295111yescharacteristic
608C2×C7#327311yescharacteristic
609C2×C7#327611yescharacteristic
610C2×C7#331411yescharacteristic
611C2×C7#331511yescharacteristic
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—22no—
618C23—21no—
619C23—22no—
620C23—21no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23D4×Dic712yes—
626C23C2×D4×D711yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—48no—
639D4D4×Dic714yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—72no—
657C2×C4—141no—
658C2×C4—141no—
659C2×C4—141no—
660C2×C4—141no—
661C2×C4—141no—
662C2×C4—141no—
663C2×C4—141no—
664C2×C4—141no—
665C2×C4—141no—
666C2×C4—141no—
667C2×C4—142no—
668C2×C4—141no—
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×C4—281no—
678C2×C4—281no—
679C2×C4—281no—
680C2×C4—564no—
681C2×C4—564no—
682C2×C4—564no—
683C2×C4D4×Dic712yes—
684C2×C4C2×D4×D711yescharacteristic
685C2×C4C2×#115911yescharacteristic
686C2×C4C2×#115911yescharacteristic
687C2×C4#654811yescharacteristic
688C2×C4#654811yescharacteristic
689C2×C4C23×Dic711yescharacteristic
690C8—22no—
691C8—22no—
692C8—142no—
693C8—281no—
694C7#2286211yescharacteristic, complemented, Sylow
695C22—22no—
696C22—24no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22#9028111yescharacteristic
710C22#9028211yescharacteristic
711C22#9046011yescharacteristic
712C22#9046211yescharacteristic
713C22D7×#13711yescharacteristic
714C22#9046811yescharacteristic
715C22C2×D4×Dic711yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—142no—
721C4—281no—
722C4—282no—
723C4—281no—
724C4—281no—
725C4—561no—
726C4—561no—
727C4—561no—
728C4#9027811yescharacteristic
729C4#9028211yescharacteristic
730C4C2×D4×Dic711yescharacteristic
731C4#9048911yescharacteristic
732C2—42no—
733C2—44no—
734C2#1173768811yescharacteristic
735C2#1173769711yescharacteristic
736C2#1173769911yescharacteristic
737C2#1173771911yescharacteristic
738C2#1174002411yescharacteristic
739C2#1174134311yescharacteristic
740C2Dic7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#452C2
socleC23×C7C22×D4
prime radicalC22×C7×#41C22
cosocleC22×C4×C7C24
hypercenterC2×#452D7
hypocenterC7#22862
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
4. C2×#89936C2semidirect
5. #11740192C2semidirect
6. #11729820C2semidirect
7. #11729819C2semidirect
8. #11729801C2semidirect
9. #11729451C2semidirect
10. #11728009C2semidirect
11. #11727978C2semidirect
12. #11727922C2semidirect
13. Dic7×#102C2semidirect
14. #11727703C2semidirect
15. #11727681C2semidirect
25. C7×#452C4semidirect
80. C2×C7×Q16C2×C4semidirect
83. C2×C7×SD16C2×C4semidirect
87. C7×C22⋊Q8C2×C4semidirect
120. C7×#103C2×C4semidirect
121. C7×#102C2×C4semidirect
122. C7×C22⋊C8C2×C4semidirect
267. #452Dic7semidirect
403. C2×Q16C2×Dic7semidirect
406. C2×SD16C2×Dic7semidirect
415. C22⋊Q8C2×Dic7semidirect
449. #103C2×Dic7semidirect
452. #102C2×Dic7semidirect
453. C22⋊C8C2×Dic7semidirect
694. C7#22862semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4522
#117415332
C2×#900042
C2×#899362
#117401922
#117298202
#117298192
#117298012
#117294512
#117280092
#117279782
#117279222
Dic7×#1022
#117277032
#117276812
#228627