Finite Group Databasebeta

← #13285086

Subgroups — #13285086

Order 1792.

2734 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic7C211yesmaximal, characteristic
2C22×#6441C211yesmaximal, characteristic
3C2×#89714C211yesmaximal, characteristic
4C2×#89418C212yesmaximal, complemented
5C7×C22⋊#95C211yesmaximal, characteristic
6#11729881C211yesmaximal, characteristic
7#11729298C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11727161C212yesmaximal, complemented
10#11727160C212yesmaximal, complemented
11Dic7⋊#95C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C24×Dic7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C23×Dic14C2211yescharacteristic
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2212yes—
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×C4×Dic7—24no—
25C22×C4×Dic7—28no—
26C22×C4×Dic7C2212yes—
27C22×C4×Dic7C2212yes—
28C2×#6441—24no—
29C2×#6441—24no—
30C2×#6441C418yescomplemented
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40#89714—24no—
41#89418—28no—
42#14702—71nomaximal, Sylow
43C25×C7C2311yescharacteristic
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—24no—
47C23×C4×C7—24no—
48C23×C4×C7Q814yescomplemented
49C23×C4×C7C2312yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2312yes—
53C23×Dic7—22no—
54C23×Dic7—22no—
55C23×Dic7—24no—
56C23×Dic7—24no—
57C23×Dic7—24no—
58C23×Dic7—24no—
59C23×Dic7C2×C414yes—
60C23×Dic7D414yes—
61C23×Dic7D414yes—
62C23×Dic7Q814yescomplemented
63C23×Dic7C2312yes—
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2312yes—
68C23×Dic7C2311yescharacteristic
69C22×Dic14—22no—
70C22×Dic14—22no—
71C22×Dic14—24no—
72C22×Dic14—24no—
73C22×Dic14C2×C414yescomplemented
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4C2×C414yes—
80C2×C22⋊Dic7—22no—
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7C2×C414yes—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7C2×C414yescomplemented
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—24no—
94C2×Dic7⋊C4—24no—
95C2×Dic7⋊C4—24no—
96C2×Dic7⋊C4C2×C414yescomplemented
97C2×Dic7⋊C4C2×C414yescomplemented
98C2×C4×Dic7—232no—
99C2×C4×Dic7—24no—
100C2×C4×Dic7—24no—
101C2×C4×Dic7—24no—
102C2×C4×Dic7—24no—
103C2×C4×Dic7—24no—
104C2×C4×Dic7D418yes—
105#6441—232no—
106C7×#95—24no—
107C7×#95—24no—
108C7⋊#95—24no—
109C7⋊#95—24no—
110C7⋊#95—24no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C22×C22⋊Q8—71no—
116C23×C42—71no—
117C2×#391—72no—
118C2×#380—71no—
119#1436—72no—
120#1436—72no—
121C4⋊#95—72no—
122C22⋊#95—71no—
123C22⋊#95—71no—
124C22⋊#95—71no—
125C22⋊#95D711yescharacteristic
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7C22×C412yes—
131C24×C7C2×D412yes—
132C24×C7C2×D412yes—
133C24×C7C2×Q812yes—
134C24×C7C2×Q812yes—
135C24×C7#4112yes—
136C24×C7#4112yes—
137C24×C7C2411yescharacteristic
138C22×C4×C7—28no—
139C22×C4×C7—216no—
140C22×C4×C7—28no—
141C22×C4×C7—28no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—216no—
147C22×C4×C7—22no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7C22×C412yes—
163C22×C4×C7C22×C412yes—
164C22×C4×C7C2×D414yes—
165C22×C4×C7C2×Q814yes—
166C22×C4×C7#4114yes—
167C22×Dic7—28no—
168C22×Dic7—216no—
169C22×Dic7—28no—
170C22×Dic7—28no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—216no—
178C22×Dic7—28no—
179C22×Dic7—216no—
180C22×Dic7—216no—
181C22×Dic7—28no—
182C22×Dic7—22no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7C22⋊C4116yes—
198C22×Dic7C22×C412yes—
199C22×Dic7C22×C412yes—
200C22×Dic7C22×C412yes—
201C22×Dic7C22×C412yes—
202C22×Dic7C2×D412yes—
203C22×Dic7C2×D412yes—
204C22×Dic7C2×D414yes—
205C22×Dic7C2×D412yes—
206C22×Dic7C2×D412yes—
207C22×Dic7C2×D414yes—
208C22×Dic7C2×Q814yes—
209C22×Dic7#4114yes—
210C22×Dic7#4114yes—
211C2×Dic14—28no—
212C2×Dic14—216no—
213C2×Dic14—44no—
214C2×Dic14—48no—
215C2×Dic14—44no—
216C7×C22⋊C4—28no—
217C7×C22⋊C4—44no—
218C22⋊Dic7—28no—
219C22⋊Dic7—44no—
220C4⋊Dic7—28no—
221Dic7⋊C4—28no—
222Dic7⋊C4—28no—
223Dic7⋊C4—48no—
224C4×Dic7—216no—
225C4×Dic7—216no—
226C23×Q8—71no—
227C24×C4—71no—
228C24×C4—71no—
229C24×C4C2×D711yescharacteristic
230C2×C22⋊Q8—78no—
231C2×C22⋊Q8—144no—
232C2×C22⋊Q8—144no—
233C22×C4⋊C4—71no—
234C22×C4⋊C4—71no—
235C22×C4⋊C4—71no—
236C22×C4⋊C4—72no—
237C22×C22⋊C4—71no—
238C22×C22⋊C4—71no—
239C22×C22⋊C4C2×D711yescharacteristic
240C22×C22⋊C4C2×D711yescharacteristic
241C22×C42—72no—
242C22×C42—72no—
243C22×C42—148no—
244C22×C42—144no—
245#391—148no—
246#380—144no—
247C2×#95—72no—
248C2×#95—72no—
249C2×#95—72no—
250C2×#95—72no—
251C2×#95—72no—
252C2×#95—72no—
253C2×#95—72no—
254C2×#95C2×D712yes—
255C2×#95C2×D712yes—
256C23×C7—24no—
257C23×C7—24no—
258C23×C7—22no—
259C23×C7—24no—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—24no—
265C23×C7—22no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—24no—
271C23×C7—24no—
272C23×C7C2×C22⋊C414yes—
273C23×C7C4×Q814yes—
274C23×C7C4×Q814yes—
275C23×C7C22⋊Q814yes—
276C23×C7C22⋊Q814yes—
277C23×C7#12414yes—
278C23×C7C4⋊Q814yes—
279C23×C7C23×C411yescharacteristic
280C23×C7C22×D411yescharacteristic
281C23×C7C22×D411yescharacteristic
282C23×C7C22×D412yes—
283C23×C7C22×Q811yescharacteristic
284C23×C7C22×Q811yescharacteristic
285C23×C7C2×#4111yescharacteristic
286C23×C7C2×#4111yescharacteristic
287C23×C7C2×#4112yes—
288C23×C7C2×#4112yes—
289C23×C7C2×#4112yes—
290C2×C4×C7—232no—
291C2×C4×C7—24no—
292C2×C4×C7—24no—
293C2×C4×C7—24no—
294C2×C4×C7—24no—
295C2×C4×C7—24no—
296C2×C4×C7—24no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—41no—
302C2×C4×C7—42no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7C22⋊Q818yescomplemented
315C2×Dic7—232no—
316C2×Dic7—24no—
317C2×Dic7—24no—
318C2×Dic7—22no—
319C2×Dic7—24no—
320C2×Dic7—24no—
321C2×Dic7—24no—
322C2×Dic7—22no—
323C2×Dic7—24no—
324C2×Dic7—24no—
325C2×Dic7—24no—
326C2×Dic7—232no—
327C2×Dic7—22no—
328C2×Dic7—22no—
329C2×Dic7—24no—
330C2×Dic7—24no—
331C2×Dic7—41no—
332C2×Dic7—42no—
333C2×Dic7—41no—
334C2×Dic7—41no—
335C2×Dic7—41no—
336C2×Dic7—42no—
337C2×Dic7—42no—
338C2×Dic7—42no—
339C2×Dic7—42no—
340C2×Dic7—42no—
341C2×Dic7—42no—
342C2×Dic7—42no—
343C2×Dic7—42no—
344C2×Dic7C2×C22⋊C414yes—
345C2×Dic7C2×C22⋊C414yes—
346C2×Dic7C4×D418yes—
347C2×Dic7#12014yes—
348C2×Dic7#12118yes—
349C2×Dic7C22⋊Q818yescomplemented
350C2×Dic7#12314yes—
351Dic14—416no—
352C25C22×D711yescharacteristic
353C22×Q8—74no—
354C22×Q8—142no—
355C22×Q8—142no—
356C22×Q8—144no—
357C22×Q8—144no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—71no—
363C23×C4—74no—
364C23×C4—74no—
365C23×C4—74no—
366C23×C4—71no—
367C23×C4—72no—
368C23×C4—74no—
369C23×C4—71no—
370C23×C4—71no—
371C23×C4—72no—
372C23×C4—144no—
373C23×C4—144no—
374C23×C4—144no—
375C23×C4—144no—
376C23×C4—142no—
377C23×C4—142no—
378C23×C4Dic1414yescomplemented
379C23×C4C22×D712yes—
380C23×C4C22×D711yescharacteristic
381C23×C4C22×D711yescharacteristic
382C23×C4C22×D712yes—
383C22⋊Q8—1432no—
384C2×C4⋊C4—74no—
385C2×C4⋊C4—74no—
386C2×C4⋊C4—74no—
387C2×C4⋊C4—142no—
388C2×C4⋊C4—142no—
389C2×C4⋊C4—142no—
390C2×C4⋊C4—142no—
391C2×C4⋊C4—142no—
392C2×C4⋊C4—142no—
393C2×C4⋊C4—144no—
394C2×C4⋊C4—144no—
395C2×C4⋊C4—144no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—74no—
402C2×C22⋊C4—142no—
403C2×C22⋊C4—142no—
404C2×C22⋊C4—142no—
405C2×C22⋊C4—142no—
406C2×C22⋊C4—142no—
407C2×C22⋊C4C4×D714yes—
408C2×C42—78no—
409C2×C42—144no—
410C2×C42—144no—
411C2×C42—144no—
412C2×C42—144no—
413C2×C42—1432no—
414C2×C42—144no—
415#95—24no—
416#95—24no—
417#95—144no—
418#95—144no—
419#95—144no—
420#95—144no—
421#95—144no—
422#95—144no—
423#95—144no—
424C22×C7—24no—
425C22×C7—24no—
426C22×C7—28no—
427C22×C7—24no—
428C22×C7—24no—
429C22×C7—28no—
430C22×C7—24no—
431C22×C7—24no—
432C22×C7—28no—
433C22×C7—28no—
434C22×C7#39118yescomplemented
435C22×C7C22×C22⋊C411yescharacteristic
436C22×C7C2×C4×D412yes—
437C22×C7C2×C4×Q811yescharacteristic
438C22×C7C2×C4×Q811yescharacteristic
439C22×C7C4×#4112yes—
440C22×C7C2×#12011yescharacteristic
441C22×C7C2×#12112yes—
442C22×C7C2×C22⋊Q811yescharacteristic
443C22×C7C2×C22⋊Q812yes—
444C22×C7C2×C22⋊Q811yescharacteristic
445C22×C7C2×C22⋊Q812yes—
446C22×C7C2×#12311yescharacteristic
447C22×C7#52512yes—
448C22×C7#52512yes—
449C22×C7#52511yescharacteristic
450C22×C7#52511yescharacteristic
451C22×C7C2×#12411yescharacteristic
452C22×C7#52912yes—
453C22×C7#52912yes—
454C22×C7C2×C4⋊Q811yescharacteristic
455C22×C7#53212yes—
456C22×C7#53312yes—
457C22×C7#53312yes—
458C4×C7—28no—
459C4×C7—42no—
460C4×C7—42no—
461C4×C7—82no—
462Dic7—28no—
463Dic7—24no—
464Dic7—42no—
465Dic7—42no—
466Dic7—82no—
467Dic7#38618yes—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24C2×Dic1412yes—
473C24C2×C4×D712yes—
474C24#115712yes—
475C24D4×D712yes—
476C24D4×D712yes—
477C24#115912yes—
478C24Q8×D712yes—
479C24C23×D711yescharacteristic
480C2×Q8—148no—
481C2×Q8—1416no—
482C2×Q8—284no—
483C2×Q8—288no—
484C2×Q8—284no—
485C22×C4—28no—
486C22×C4—216no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—216no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—72no—
510C22×C4—74no—
511C22×C4—72no—
512C22×C4—72no—
513C22×C4—74no—
514C22×C4—716no—
515C22×C4—72no—
516C22×C4—74no—
517C22×C4—72no—
518C22×C4—72no—
519C22×C4—74no—
520C22×C4—74no—
521C22×C4—72no—
522C22×C4—72no—
523C22×C4—148no—
524C22×C4—1416no—
525C22×C4—1416no—
526C22×C4—148no—
527C22×C4—1416no—
528C22×C4—148no—
529C22×C4—1416no—
530C22×C4—148no—
531C22×C4—148no—
532C22×C4—142no—
533C22×C4—142no—
534C22×C4—142no—
535C22×C4—142no—
536C22×C4—142no—
537C22×C4—142no—
538C22×C4—142no—
539C22×C4—141no—
540C22×C4—141no—
541C22×C4—141no—
542C22×C4—141no—
543C22×C4—142no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4C2×Dic1414yes—
554C22×C4C2×C4×D712yes—
555C22×C4C2×C4×D712yes—
556C22×C4D4×D714yes—
557C22×C4#115914yes—
558C4⋊C4—148no—
559C4⋊C4—148no—
560C4⋊C4—148no—
561C4⋊C4—288no—
562C22⋊C4—28no—
563C22⋊C4—44no—
564C22⋊C4—148no—
565C22⋊C4—284no—
566C42—1416no—
567C42—1416no—
568C2×C7—28no—
569C2×C7C2×#38611yescharacteristic
570C2×C7C2×#39111yescharacteristic
571C2×C7#229711yescharacteristic
572C2×C7C4×C22⋊Q812yes—
573C2×C7C4×C22⋊Q812yes—
574C2×C7#284811yescharacteristic
575C2×C7#284811yescharacteristic
576C2×C7#285012yes—
577C2×C7#285511yescharacteristic
578C2×C7#285511yescharacteristic
579C2×C7#285712yes—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—22no—
587C23—24no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23C4×Dic1414yes—
597C23#644114yes—
598C23D7×C22⋊C414yes—
599C23#644814yes—
600C23#645014yes—
601C23#645114yes—
602C23#645914yes—
603C23C22×Dic1411yescharacteristic
604C23C22×C4×D711yescharacteristic
605C23C2×#115711yescharacteristic
606C23C2×D4×D711yescharacteristic
607C23C2×D4×D712yes—
608C23C2×D4×D711yescharacteristic
609C23C2×#115911yescharacteristic
610C23C2×#115912yes—
611C23C2×Q8×D711yescharacteristic
612C23D7×#4112yes—
613C23D7×#4112yes—
614Q8—2816no—
615C2×C4—232no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—74no—
640C2×C4—78no—
641C2×C4—74no—
642C2×C4—78no—
643C2×C4—74no—
644C2×C4—74no—
645C2×C4—78no—
646C2×C4—1432no—
647C2×C4—1432no—
648C2×C4—144no—
649C2×C4—144no—
650C2×C4—144no—
651C2×C4—144no—
652C2×C4—142no—
653C2×C4—144no—
654C2×C4—144no—
655C2×C4—144no—
656C2×C4—142no—
657C2×C4—144no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—144no—
661C2×C4—144no—
662C2×C4—281no—
663C2×C4—281no—
664C2×C4—282no—
665C2×C4—282no—
666C2×C4—281no—
667C2×C4—281no—
668C2×C4—282no—
669C2×C4—282no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—282no—
674C2×C4—282no—
675C2×C4#644118yescomplemented
676C7#1470211yescharacteristic, complemented, Sylow
677C22—24no—
678C22—28no—
679C22—24no—
680C22—24no—
681C22—24no—
682C22—28no—
683C22—24no—
684C22—24no—
685C22—28no—
686C22—28no—
687C22#8941818yescomplemented
688C22C2×C4×Dic1411yescharacteristic
689C22C2×#644111yescharacteristic
690C22C2×#644112yes—
691C22C2×D7×C22⋊C411yescharacteristic
692C22C2×#644811yescharacteristic
693C22C2×#645011yescharacteristic
694C22C2×#645111yescharacteristic
695C22C2×#645911yescharacteristic
696C22#9020812yes—
697C22C4×#115912yes—
698C22#9022912yes—
699C22C4×D4×D712yes—
700C22#9023812yes—
701C22#9027711yescharacteristic
702C22#9027712yes—
703C22D7×#12011yescharacteristic
704C22#9028712yes—
705C22D7×#12112yes—
706C22#9031312yes—
707C22D7×C22⋊Q812yes—
708C22#9034012yes—
709C22D7×#12311yescharacteristic
710C22#9034711yescharacteristic
711C4—28no—
712C4—42no—
713C4—42no—
714C4—78no—
715C4—82no—
716C4—144no—
717C4—148no—
718C4—282no—
719C4—282no—
720C4—562no—
721C2—28no—
722C2C2×#8941811yescharacteristic
723C2C4×#644112yes—
724C2#1173129111yescharacteristic
725C2#1173144612yes—
726C2#1173156211yescharacteristic
727C2#1173182612yes—
728C2#1173203411yescharacteristic
729C2#1173210011yescharacteristic
730C2#1173210311yescharacteristic
731C2#1173231412yes—
732C2D7×#38611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#14702
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#89418C2semidirect
9. #11727161C2semidirect
10. #11727160C2semidirect
11. Dic7⋊#95C2semidirect
30. C2×#6441C4semidirect
48. C23×C4×C7Q8semidirect
62. C23×Dic7Q8semidirect
73. C22×Dic14C2×C4semidirect
88. C2×C4⋊Dic7C2×C4semidirect
96. C2×Dic7⋊C4C2×C4semidirect
97. C2×Dic7⋊C4C2×C4semidirect
314. C2×C4×C7C22⋊Q8semidirect
349. C2×Dic7C22⋊Q8semidirect
378. C23×C4Dic14semidirect
434. C22×C7#391semidirect
675. C2×C4#6441semidirect
676. C7#14702semidirect
687. C22#89418semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic72
C22×#64412
C2×#897142
C2×#894182
C7×C22⋊#952
#117298812
#117292982
#117271612
#117271602
Dic7⋊#952
#147027