Finite Group Databasebeta

← #13374522

Subgroups — #13374522

Order 1792.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#448C211yesmaximal, characteristic
2Q8×C22⋊Dic7C211yesmaximal, characteristic, complemented
3C2×#89997C211yesmaximal, characteristic, complemented
4C2×SD16×Dic7C211yesmaximal, characteristic, complemented
5#11740082C211yesmaximal, characteristic
6#11729804C211yesmaximal, characteristic, complemented
7#11729802C211yesmaximal, characteristic, complemented
8#11729801C211yesmaximal, characteristic, complemented
9#11729436C211yesmaximal, characteristic
10#11728007C211yesmaximal, characteristic, complemented
11#11727990C211yesmaximal, characteristic, complemented
12#11727977C211yesmaximal, characteristic, complemented
13#11727974C211yesmaximal, characteristic, complemented
14#11727703C211yesmaximal, characteristic, complemented
15#11727683C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C22×C7×SD16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C2×C7×#121C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C2×Q8×Dic7C2211yescharacteristic
22C2×D4×Dic7C2211yescharacteristic
23C2×#6489C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25C7×#448C418yescomplemented
26C2×C7×#103C2211yescharacteristic
27C2×C7×#103C2211yescharacteristic
28C2×C7×C22⋊C8C2211yescharacteristic
29#90002—21no—
30#90002—21no—
31#90002C2211yescharacteristic
32#90002C2211yescharacteristic
33#89997—24no—
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38#89993—21no—
39#89993C2211yescharacteristic
40#89992—21no—
41C2×#6406C2211yescharacteristic
42C2×#6406C2211yescharacteristic
43#89984—21no—
44#89984C2211yescharacteristic
45C4×C22⋊Dic7—21no—
46C4×C22⋊Dic7C2211yescharacteristic
47SD16×Dic7—24no—
48C2×#6392C2211yescharacteristic
49C2×#6391C2211yescharacteristic
50C2×#6389C2211yescharacteristic
51C2×C8×Dic7C2211yescharacteristic
52#89757C2211yescharacteristic
53C4⋊C4×Dic7C2211yescharacteristic
54#89723—21no—
55C22⋊C4×Dic7—21no—
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22885—71nomaximal, Sylow
63C22×C7×Q8—21no—
64C22×C7×Q8—22no—
65C22×C7×Q8—22no—
66C22×C7×Q8—22no—
67C22×C7×Q8—41no—
68C22×C7×Q8—41no—
69C22×C7×Q8C2×C414yescomplemented
70C22×C7×Q8C2311yescharacteristic
71C22×C7×Q8C2311yescharacteristic
72C22×C7×D4—21no—
73C22×C7×D4C2311yescharacteristic
74C23×C4×C7—21no—
75C23×C4×C7C2311yescharacteristic
76C23×Dic7—21no—
77C2×C7×SD16—22no—
78C2×C7×SD16—22no—
79C2×C7×SD16—41no—
80C2×C7×SD16—41no—
81C2×C7×SD16C2×C414yes—
82C2×C7×SD16C2×C414yes—
83C22×C7×C8C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C7×#121—22no—
86C7×#121C2×C414yes—
87C2×C7×C4⋊C4C2311yescharacteristic
88C2×C7×C22⋊C4—21no—
89C2×C22⋊Dic7—21no—
90C2×C22⋊Dic7—21no—
91C2×C22⋊Dic7—21no—
92C2×C22⋊Dic7—21no—
93C2×C22⋊Dic7—21no—
94C2×C22⋊Dic7D411yescharacteristic
95C2×C22⋊Dic7D411yescharacteristic
96Q8×Dic7—22no—
97Q8×Dic7—22no—
98Q8×Dic7—41no—
99Q8×Dic7—41no—
100D4×Dic7—22no—
101D4×Dic7—41no—
102#6489—22no—
103#6489—41no—
104C2×C4⋊Dic7—21no—
105C2×C4⋊Dic7—21no—
106C2×C4⋊Dic7—21no—
107C2×C4⋊Dic7C2311yescharacteristic
108C2×C4⋊Dic7C2311yescharacteristic
109C2×C4⋊Dic7C2311yescharacteristic
110C2×C4⋊Dic7C2311yescharacteristic
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×C4×Dic7—21no—
114C2×C4×Dic7—21no—
115C2×C4×Dic7C2311yescharacteristic
116C2×C4×Dic7C2311yescharacteristic
117C2×#1136—22no—
118C2×#1136—22no—
119C2×#1136—41no—
120C22×C7⋊C8C2311yescharacteristic
121C22×C7⋊C8C2311yescharacteristic
122C7×#103C2×C414yescomplemented
123C7×#103C2×C414yescomplemented
124C7×C22⋊C8C2×C414yescomplemented
125#6409—22no—
126#6409—22no—
127#6409—22no—
128#6409D414yescomplemented
129#6406—22no—
130#6406—41no—
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—41no—
141#6391—22no—
142#6389—41no—
143C8×Dic7—22no—
144C2×#448D711yescharacteristic
145C2×C4×SD16—71no—
146C2×#419—71no—
147#2363—71no—
148Q8×C22⋊C4—71no—
149#1973—71no—
150#1933—71no—
151#1927—71no—
152#1895—71no—
153#1880—71no—
154#1877—71no—
155#1863—71no—
156#1854—71no—
157#1763—71no—
158#1753—71no—
159C24×C7—21no—
160C24×C7C2×D411yescharacteristic
161C2×C7×Q8—24no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—28no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—42no—
172C2×C7×Q8—42no—
173C2×C7×Q8—44no—
174C2×C7×Q8—44no—
175C2×C7×Q8—44no—
176C2×C7×Q8C22×C412yes—
177C2×C7×Q8C22×C412yes—
178C2×C7×Q8C2×D412yes—
179C2×C7×Q8#4112yes—
180C2×C7×D4—24no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—81no—
187C2×C7×D4—81no—
188C2×C7×D4C22×C412yes—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—24no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—42no—
198C22×C4×C7—42no—
199C22×C4×C7C22×C412yes—
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7#4112yes—
202C22×C4×C7C2411yescharacteristic
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—42no—
208C22×Dic7—42no—
209C22×Dic7—81no—
210C22×Dic7C2×D411yescharacteristic
211C22×Dic7C2×D411yescharacteristic
212C22×Dic7C2×D411yescharacteristic
213C22×Dic7C2×D411yescharacteristic
214C7×SD16—28no—
215C7×SD16—44no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8C22×C412yes—
221C2×C7×C8C22×C412yes—
222C7×C4⋊C4—21no—
223C7×C4⋊C4C22×C412yes—
224C7×C22⋊C4—24no—
225C22⋊Dic7—22no—
226C22⋊Dic7—41no—
227C22⋊Dic7—42no—
228C22⋊Dic7—42no—
229C22⋊Dic7—42no—
230C22⋊Dic7—42no—
231C22⋊Dic7—81no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7—21no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7—42no—
240C4⋊Dic7—42no—
241C4⋊Dic7—81no—
242C4⋊Dic7C2×D412yes—
243C4×Dic7—21no—
244C4×Dic7—21no—
245C4×Dic7—21no—
246C4×Dic7—21no—
247C4×Dic7—42no—
248C4×Dic7—42no—
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—
258C23×Q8C2×D711yescharacteristic
259C22×SD16C2×D711yescharacteristic
260C22×SD16C2×D711yescharacteristic
261C22×M16—71no—
262C2×#121C2×D711yescharacteristic
263C2×C4×Q8—71no—
264C2×C4×Q8—71no—
265C2×C4×D4—71no—
266C2×#117—71no—
267#448Dic718yescomplemented
268C4×SD16—144no—
269C2×#107—71no—
270C2×#106—71no—
271#419—144no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×#103C2×D711yescharacteristic
277C2×#103C2×D711yescharacteristic
278C2×#102—71no—
279C2×#102—71no—
280C2×C22⋊C8C2×D711yescharacteristic
281C2×#97—71no—
282C2×C4×C8—71no—
283#391—71no—
284#391—71no—
285#391—141no—
286#391—141no—
287#390—71no—
288#390—141no—
289#389—71no—
290#388—141no—
291#386—141no—
292#380—71no—
293#380—141no—
294C4×C4⋊C4—71no—
295C4×C22⋊C4—71no—
296C4×C22⋊C4—141no—
297C4×C22⋊C4—141no—
298#340—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#336—71no—
303#336—71no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—22no—
311C23×C7—41no—
312C23×C7—41no—
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—22no—
324C7×Q8—48no—
325C7×Q8—41no—
326C7×Q8—41no—
327C7×Q8C4×D414yes—
328C7×D4—22no—
329C7×D4—22no—
330C7×D4—41no—
331C7×D4—41no—
332C7×D4—84no—
333C2×C4×C7—22no—
334C2×C4×C7—21no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—21no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—48no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7C4×D412yes—
350C2×C4×C7C23×C411yescharacteristic
351C2×C4×C7C22×D411yescharacteristic
352C2×C4×C7C2×#4111yescharacteristic
353C2×C4×C7C2×#4111yescharacteristic
354C2×C4×C7H(5,𝔽2)11yescharacteristic
355C2×C4×C7H(5,𝔽2)11yescharacteristic
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—21no—
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—41no—
379C2×Dic7—84no—
380C2×Dic7#13712yes—
381C7×C8—22no—
382C7×C8—22no—
383C7⋊C8—22no—
384C7⋊C8—41no—
385C22×Q8—21no—
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—41no—
390C22×Q8—41no—
391C22×Q8C2×Dic714yescomplemented
392C22×Q8C22×D711yescharacteristic
393C22×Q8C22×D711yescharacteristic
394C22×D4—21no—
395C22×D4C22×D711yescharacteristic
396C23×C4—21no—
397C23×C4—141no—
398C23×C4C22×D711yescharacteristic
399C2×SD16—22no—
400C2×SD16—22no—
401C2×SD16—41no—
402C2×SD16—41no—
403C2×SD16C2×Dic714yes—
404C2×SD16C2×Dic714yes—
405C2×M16—142no—
406C2×M16—142no—
407C2×M16—281no—
408C22×C8—71no—
409C22×C8—71no—
410C22×C8C22×D711yescharacteristic
411C22×C8C22×D711yescharacteristic
412#121—22no—
413#121C2×Dic714yes—
414C4×Q8—142no—
415C4×Q8—142no—
416C4×Q8—281no—
417C4×Q8—281no—
418C4×D4—142no—
419C4×D4—281no—
420#117—142no—
421#117—281no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—71no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—71no—
426C2×C4⋊C4—141no—
427C2×C4⋊C4—141no—
428C2×C4⋊C4—141no—
429C2×C4⋊C4C22×D711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—71no—
432C2×C22⋊C4—71no—
433C2×C22⋊C4—141no—
434C2×C22⋊C4—141no—
435C2×C22⋊C4—141no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4—141no—
438C2×C42—71no—
439C2×C42—71no—
440C2×C42—141no—
441C2×C42—141no—
442C2×C42—141no—
443C2×C42—141no—
444#107—281no—
445#106—142no—
446#103—74no—
447#103—142no—
448#103—142no—
449#103—142no—
450#103C2×Dic714yescomplemented
451#103C2×Dic714yescomplemented
452#102—142no—
453#102—281no—
454C22⋊C8C2×Dic714yescomplemented
455#97—281no—
456C4×C8—142no—
457#95—71no—
458#95—71no—
459#95—141no—
460#95—141no—
461#95—141no—
462#95—141no—
463#95—141no—
464#95—141no—
465#95—141no—
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—22no—
469C22×C7—41no—
470C22×C7—41no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—81no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—81no—
480C22×C7C2×C4×D411yescharacteristic
481C22×C7D4211yescharacteristic
482C22×C7#54611yescharacteristic
483C22×C7C2×#13711yescharacteristic
484C22×C7#57511yescharacteristic
485C22×C7#57711yescharacteristic
486C22×C7#57711yescharacteristic
487C4×C7—22no—
488C4×C7—24no—
489C4×C7—42no—
490C4×C7—42no—
491C4×C7C2×C4×D411yescharacteristic
492C4×C7#51811yescharacteristic
493C4×C7#54611yescharacteristic
494C4×C7#55111yescharacteristic
495Dic7—22no—
496Dic7—41no—
497Dic7—42no—
498Dic7—41no—
499Dic7—41no—
500Dic7—81no—
501Dic7—81no—
502Dic7—81no—
503C24—21no—
504C24D4×D711yescharacteristic
505C2×Q8—24no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—28no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8D4×D712yes—
521C2×Q8#115912yes—
522C2×Q8C22×Dic712yes—
523C2×Q8C22×Dic712yes—
524C2×D4—24no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4C22×Dic712yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—71no—
544C22×C4—71no—
545C22×C4—71no—
546C22×C4—71no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—141no—
550C22×C4—141no—
551C22×C4—282no—
552C22×C4—282no—
553C22×C4—561no—
554C22×C4D4×D711yescharacteristic
555C22×C4#115912yes—
556C22×C4C22×Dic712yes—
557C22×C4C23×D711yescharacteristic
558SD16—28no—
559SD16—44no—
560M16—284no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—72no—
566C2×C8—141no—
567C2×C8—141no—
568C2×C8—141no—
569C2×C8—141no—
570C2×C8—141no—
571C2×C8C22×Dic712yes—
572C2×C8C22×Dic712yes—
573C4⋊C4—21no—
574C4⋊C4—72no—
575C4⋊C4—141no—
576C4⋊C4—141no—
577C4⋊C4—141no—
578C4⋊C4—141no—
579C4⋊C4—141no—
580C4⋊C4—141no—
581C4⋊C4—141no—
582C4⋊C4—282no—
583C4⋊C4—282no—
584C4⋊C4—561no—
585C4⋊C4C22×Dic712yes—
586C22⋊C4—24no—
587C22⋊C4—142no—
588C22⋊C4—281no—
589C22⋊C4—282no—
590C22⋊C4—282no—
591C22⋊C4—282no—
592C22⋊C4—282no—
593C22⋊C4—561no—
594C42—141no—
595C42—141no—
596C42—141no—
597C42—141no—
598C42—282no—
599C42—282no—
600C42—282no—
601C42—561no—
602C2×C7—42no—
603C2×C7—82no—
604C2×C7#235811yescharacteristic
605C2×C7C4×#13711yescharacteristic
606C2×C7#294911yescharacteristic
607C2×C7#326611yescharacteristic
608C2×C7#327111yescharacteristic
609C2×C7#332611yescharacteristic
610C2×C7#332911yescharacteristic
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23D4×Dic712yes—
625C23C2×D4×D711yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—48no—
632Q8—41no—
633Q8—41no—
634Q8D4×Dic714yes—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—84no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—48no—
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—142no—
667C2×C4—141no—
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×C4D4×Dic712yes—
682C2×C4C2×D4×D711yescharacteristic
683C2×C4C2×#115911yescharacteristic
684C2×C4C2×#115911yescharacteristic
685C2×C4#654811yescharacteristic
686C2×C4#654811yescharacteristic
687C2×C4C23×Dic711yescharacteristic
688C8—22no—
689C8—22no—
690C8—142no—
691C8—281no—
692C7#2288511yescharacteristic, complemented, Sylow
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22#9028111yescharacteristic
708C22#9028211yescharacteristic
709C22#9045311yescharacteristic
710C22#9045311yescharacteristic
711C22D7×#13711yescharacteristic
712C22#9046811yescharacteristic
713C22C2×D4×Dic711yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—142no—
719C4—281no—
720C4—281no—
721C4—282no—
722C4—281no—
723C4—561no—
724C4—561no—
725C4—561no—
726C4#9027811yescharacteristic
727C4#9028211yescharacteristic
728C4C2×D4×Dic711yescharacteristic
729C4#9048911yescharacteristic
730C2—42no—
731C2—82no—
732C2#1173750011yescharacteristic
733C2#1173750111yescharacteristic
734C2#1173750611yescharacteristic
735C2#1173751011yescharacteristic
736C2#1174002411yescharacteristic
737C2#1174128811yescharacteristic
738C2Dic7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#448C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
cosocleC22×C4×C7C24
hypercenterC2×#448D7
hypocenterC7#22885
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊Dic7C2semidirect
3. C2×#89997C2semidirect
4. C2×SD16×Dic7C2semidirect
6. #11729804C2semidirect
7. #11729802C2semidirect
8. #11729801C2semidirect
10. #11728007C2semidirect
11. #11727990C2semidirect
12. #11727977C2semidirect
13. #11727974C2semidirect
14. #11727703C2semidirect
15. #11727683C2semidirect
25. C7×#448C4semidirect
69. C22×C7×Q8C2×C4semidirect
122. C7×#103C2×C4semidirect
123. C7×#103C2×C4semidirect
124. C7×C22⋊C8C2×C4semidirect
128. #6409D4semidirect
267. #448Dic7semidirect
391. C22×Q8C2×Dic7semidirect
450. #103C2×Dic7semidirect
451. #103C2×Dic7semidirect
454. C22⋊C8C2×Dic7semidirect
692. C7#22885semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4482
Q8×C22⋊Dic72
C2×#899972
C2×SD16×Dic72
#117400822
#117298042
#117298022
#117298012
#117294362
#117280072
#117279902
#117279772
#117279742
#117277032
#117276832
#228857