Finite Group Databasebeta

← #13285215

Subgroups — #13285215

Order 1792.

2494 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
1C23×C4⋊Dic7C211yesmaximal, characteristic
2C22×#6441C211yesmaximal, characteristic
3C2×#89722C211yesmaximal, characteristic
4C2×#89718C211yesmaximal, characteristic
5C2×#89428C212yesmaximal, complemented
6C7×C22⋊#95C211yesmaximal, characteristic
7#11729881C211yesmaximal, characteristic
8#11729298C211yesmaximal, characteristic
9#11727174C212yesmaximal, complemented
10#11727173C212yesmaximal, complemented
11#11727165C212yesmaximal, 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⋊Dic7—24no—
21C22×C4⋊Dic7—28no—
22C22×C4⋊Dic7C2212yes—
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2212yes—
25C22×C4⋊Dic7C2212yes—
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2212yes—
29C2×#6441—24no—
30C2×#6441—24no—
31C2×#6441—24no—
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#89722—24no—
41#89718—24no—
42#89428—28no—
43#14720—71nomaximal, Sylow
44C25×C7C2311yescharacteristic
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—24no—
48C23×C4×C7—24no—
49C23×C4×C7Q814yescomplemented
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2312yes—
53C23×C4×C7C2312yes—
54C23×Dic7—22no—
55C23×Dic7—22no—
56C23×Dic7—22no—
57C23×Dic7—24no—
58C23×Dic7—24no—
59C23×Dic7—22no—
60C23×Dic7—22no—
61C23×Dic7—42no—
62C23×Dic7—42no—
63C23×Dic7D414yes—
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2312yes—
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2312yes—
69C23×Dic7C2311yescharacteristic
70C22×Dic14—22no—
71C22×Dic14—22no—
72C22×Dic14—22no—
73C22×Dic14—24no—
74C22×Dic14—42no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4D414yes—
80C2×C7×C22⋊C4Q814yescomplemented
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7D414yes—
86C2×C22⋊Dic7Q814yescomplemented
87C2×C4⋊Dic7—232no—
88C2×C4⋊Dic7—22no—
89C2×C4⋊Dic7—24no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—24no—
93C2×C4⋊Dic7—24no—
94C2×C4⋊Dic7—24no—
95C2×C4⋊Dic7—24no—
96C2×C4⋊Dic7—24no—
97C2×C4⋊Dic7—24no—
98C2×C4⋊Dic7—42no—
99C2×C4⋊Dic7D418yes—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—24no—
107C2×Dic7⋊C4—24no—
108C2×Dic7⋊C4—42no—
109#6441—232no—
110C7×#95—24no—
111C7×#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C7⋊#95—24no—
117C7⋊#95—42no—
118C22×C22⋊Q8—71no—
119C23×C4⋊C4—71no—
120C2×#395—72no—
121C2×#385—71no—
122C2×#385—71no—
123#1444—72no—
124#1444—72no—
125#1441—72no—
126C22⋊#95—71no—
127C22⋊#95—71no—
128C22⋊#95D711yescharacteristic
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7C2×D412yes—
134C24×C7C2×D412yes—
135C24×C7C2×D412yes—
136C24×C7C2×Q812yes—
137C24×C7C2×Q812yes—
138C24×C7C2×Q812yes—
139C24×C7#4112yes—
140C24×C7C2411yescharacteristic
141C22×C4×C7—28no—
142C22×C4×C7—216no—
143C22×C4×C7—28no—
144C22×C4×C7—28no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—216no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7C2×D412yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D414yes—
167C22×C4×C7C2×Q814yes—
168C22×C4×C7C2×Q814yes—
169C22×C4×C7#4114yes—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—22no—
173C22×Dic7—28no—
174C22×Dic7—28no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—21no—
188C22×Dic7—21no—
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×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—28no—
200C22×Dic7—44no—
201C22×Dic7—48no—
202C22×Dic7—48no—
203C22×Dic7—48no—
204C22×Dic7—48no—
205C22×Dic7—44no—
206C22×Dic7—44no—
207C22×Dic7C2×D412yes—
208C22×Dic7C2×D412yes—
209C22×Dic7C2×D414yes—
210C22×Dic7C2×D412yes—
211C22×Dic7C2×D414yes—
212C22×Dic7C2×D412yes—
213C22×Dic7C2×Q814yes—
214C2×Dic14—28no—
215C2×Dic14—48no—
216C2×Dic14—48no—
217C2×Dic14—44no—
218C2×Dic14—44no—
219C7×C22⋊C4—28no—
220C7×C22⋊C4—28no—
221C22⋊Dic7—28no—
222C22⋊Dic7—28no—
223C4⋊Dic7—28no—
224C4⋊Dic7—216no—
225C4⋊Dic7—216no—
226C4⋊Dic7—48no—
227Dic7⋊C4—28no—
228Dic7⋊C4—28no—
229Dic7⋊C4—48no—
230C23×Q8—71no—
231C24×C4—71no—
232C24×C4—71no—
233C24×C4C2×D711yescharacteristic
234C2×C22⋊Q8—144no—
235C2×C22⋊Q8—144no—
236C2×C22⋊Q8—144no—
237C22×C4⋊C4—72no—
238C22×C4⋊C4—72no—
239C22×C4⋊C4—71no—
240C22×C4⋊C4—71no—
241C22×C4⋊C4—71no—
242C22×C4⋊C4—72no—
243C22×C4⋊C4—72no—
244C22×C4⋊C4—148no—
245C22×C4⋊C4—144no—
246C22×C22⋊C4—71no—
247C22×C22⋊C4—71no—
248C22×C22⋊C4C2×D711yescharacteristic
249C22×C22⋊C4C2×D711yescharacteristic
250#395—148no—
251#385—144no—
252#385—144no—
253C2×#95—72no—
254C2×#95—72no—
255C2×#95—72no—
256C2×#95—72no—
257C2×#95—72no—
258C2×#95—72no—
259C2×#95C2×D712yes—
260C2×#95C2×D712yes—
261C23×C7—22no—
262C23×C7—24no—
263C23×C7—22no—
264C23×C7—24no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—24no—
271C23×C7—24no—
272C23×C7—24no—
273C23×C7—24no—
274C23×C7—24no—
275C23×C7—24no—
276C23×C7—24no—
277C23×C7#12014yes—
278C23×C7C22⋊Q814yes—
279C23×C7C22⋊Q814yes—
280C23×C7C22⋊Q814yes—
281C23×C7C4⋊Q814yes—
282C23×C7C4⋊Q814yes—
283C23×C7C4⋊Q814yes—
284C23×C7C22×D411yescharacteristic
285C23×C7C22×D411yescharacteristic
286C23×C7C22×D412yes—
287C23×C7C22×D411yescharacteristic
288C23×C7C22×Q811yescharacteristic
289C23×C7C22×Q811yescharacteristic
290C23×C7C22×Q811yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4112yes—
293C23×C7H(5,𝔽2)12yes—
294C23×C72−1+412yes—
295C2×C4×C7—232no—
296C2×C4×C7—24no—
297C2×C4×C7—24no—
298C2×C4×C7—24no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—24no—
305C2×C4×C7—24no—
306C2×C4×C7—24no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—42no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7C22⋊Q818yescomplemented
320C2×Dic7—22no—
321C2×Dic7—22no—
322C2×Dic7—24no—
323C2×Dic7—24no—
324C2×Dic7—22no—
325C2×Dic7—22no—
326C2×Dic7—22no—
327C2×Dic7—24no—
328C2×Dic7—22no—
329C2×Dic7—24no—
330C2×Dic7—22no—
331C2×Dic7—24no—
332C2×Dic7—24no—
333C2×Dic7—24no—
334C2×Dic7—24no—
335C2×Dic7—24no—
336C2×Dic7—24no—
337C2×Dic7—416no—
338C2×Dic7—416no—
339C2×Dic7—41no—
340C2×Dic7—42no—
341C2×Dic7—41no—
342C2×Dic7—42no—
343C2×Dic7—41no—
344C2×Dic7—42no—
345C2×Dic7—41no—
346C2×Dic7—42no—
347C2×Dic7—42no—
348C2×Dic7—42no—
349C2×Dic7—42no—
350C2×Dic7—42no—
351C2×Dic7—42no—
352C2×Dic7—42no—
353C2×Dic7—42no—
354C2×Dic7—42no—
355C2×Dic7#12014yes—
356Dic14—416no—
357C25C22×D711yescharacteristic
358C22×Q8—142no—
359C22×Q8—142no—
360C22×Q8—144no—
361C22×Q8—142no—
362C22×Q8—282no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—71no—
368C23×C4—71no—
369C23×C4—71no—
370C23×C4—72no—
371C23×C4—72no—
372C23×C4—71no—
373C23×C4—74no—
374C23×C4—144no—
375C23×C4—144no—
376C23×C4—142no—
377C23×C4—142no—
378C23×C4—142no—
379C23×C4—142no—
380C23×C4—142no—
381C23×C4—282no—
382C23×C4—282no—
383C23×C4Dic1414yescomplemented
384C23×C4C22×D712yes—
385C23×C4C22×D711yescharacteristic
386C23×C4C22×D711yescharacteristic
387C23×C4C22×D712yes—
388C22⋊Q8—1432no—
389C2×C4⋊C4—78no—
390C2×C4⋊C4—144no—
391C2×C4⋊C4—144no—
392C2×C4⋊C4—144no—
393C2×C4⋊C4—144no—
394C2×C4⋊C4—142no—
395C2×C4⋊C4—142no—
396C2×C4⋊C4—142no—
397C2×C4⋊C4—142no—
398C2×C4⋊C4—142no—
399C2×C4⋊C4—142no—
400C2×C4⋊C4—1432no—
401C2×C4⋊C4—142no—
402C2×C4⋊C4—142no—
403C2×C4⋊C4—142no—
404C2×C4⋊C4—144no—
405C2×C4⋊C4—144no—
406C2×C4⋊C4—144no—
407C2×C4⋊C4—144no—
408C2×C4⋊C4—144no—
409C2×C4⋊C4—282no—
410C2×C4⋊C4—282no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—74no—
416C2×C22⋊C4—74no—
417C2×C22⋊C4—142no—
418C2×C22⋊C4—142no—
419C2×C22⋊C4—142no—
420C2×C22⋊C4—142no—
421C2×C22⋊C4Dic1414yescomplemented
422C2×C22⋊C4D2814yes—
423#95—24no—
424#95—24no—
425#95—144no—
426#95—144no—
427#95—144no—
428#95—144no—
429#95—144no—
430#95—282no—
431C22×C7—24no—
432C22×C7—24no—
433C22×C7—24no—
434C22×C7—24no—
435C22×C7—24no—
436C22×C7—24no—
437C22×C7—28no—
438C22×C7—28no—
439C22×C7—28no—
440C22×C7—28no—
441C22×C7#39518yescomplemented
442C22×C7C2×#12011yescharacteristic
443C22×C7C2×#12011yescharacteristic
444C22×C7C2×C22⋊Q811yescharacteristic
445C22×C7C2×C22⋊Q812yes—
446C22×C7C2×C22⋊Q811yescharacteristic
447C22×C7C2×C22⋊Q811yescharacteristic
448C22×C7#52511yescharacteristic
449C22×C7#52512yes—
450C22×C7C2×C4⋊Q811yescharacteristic
451C22×C7C2×C4⋊Q811yescharacteristic
452C22×C7C2×C4⋊Q811yescharacteristic
453C22×C7#53411yescharacteristic
454C22×C7#53611yescharacteristic
455C22×C7#53912yes—
456C22×C7#54412yes—
457C22×C7D4212yes—
458C22×C7D4212yes—
459C22×C7#54712yes—
460C22×C7#54712yes—
461C22×C7D4×Q812yes—
462C22×C7D4×Q812yes—
463C22×C7#55412yes—
464C22×C7#55412yes—
465C4×C7—28no—
466C4×C7—42no—
467C4×C7—42no—
468C4×C7—44no—
469Dic7—24no—
470Dic7—42no—
471Dic7—42no—
472Dic7—44no—
473Dic7—42no—
474Dic7—44no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24C2×Dic1412yes—
480C24C2×Dic1412yes—
481C24C2×D2812yes—
482C24D4×D712yes—
483C24D4×D712yes—
484C24#115912yes—
485C24Q8×D712yes—
486C24C23×D711yescharacteristic
487C2×Q8—148no—
488C2×Q8—288no—
489C2×Q8—284no—
490C2×Q8—288no—
491C2×Q8—284no—
492C22×C4—28no—
493C22×C4—216no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—216no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—74no—
516C22×C4—72no—
517C22×C4—72no—
518C22×C4—72no—
519C22×C4—74no—
520C22×C4—72no—
521C22×C4—74no—
522C22×C4—148no—
523C22×C4—141no—
524C22×C4—141no—
525C22×C4—142no—
526C22×C4—148no—
527C22×C4—148no—
528C22×C4—142no—
529C22×C4—142no—
530C22×C4—141no—
531C22×C4—141no—
532C22×C4—141no—
533C22×C4—142no—
534C22×C4—142no—
535C22×C4—142no—
536C22×C4—141no—
537C22×C4—141no—
538C22×C4—141no—
539C22×C4—142no—
540C22×C4—142no—
541C22×C4—142no—
542C22×C4—142no—
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—284no—
553C22×C4—288no—
554C22×C4—288no—
555C22×C4—288no—
556C22×C4—288no—
557C22×C4—284no—
558C22×C4—284no—
559C22×C4C2×Dic1414yes—
560C22×C4C2×Dic1414yes—
561C22×C4C2×D2812yes—
562C22×C4C2×D2812yes—
563C22×C4D4×D714yes—
564C22×C4#115914yes—
565C4⋊C4—1416no—
566C4⋊C4—148no—
567C4⋊C4—148no—
568C4⋊C4—1416no—
569C4⋊C4—148no—
570C4⋊C4—288no—
571C4⋊C4—288no—
572C22⋊C4—28no—
573C22⋊C4—28no—
574C22⋊C4—148no—
575C22⋊C4—148no—
576C2×C7—28no—
577C2×C7C2×#39511yescharacteristic
578C2×C7#240311yescharacteristic
579C2×C7#240611yescharacteristic
580C2×C7#243411yescharacteristic
581C2×C7#244012yes—
582C2×C7#244012yes—
583C2×C7#244912yes—
584C2×C7#244912yes—
585C2×C7#258311yescharacteristic
586C2×C7#262711yescharacteristic
587C2×C7#284811yescharacteristic
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—24no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23#643214yes—
605C23#644114yes—
606C23#644114yes—
607C23#644514yes—
608C23#645114yes—
609C23#645114yes—
610C23#646014yes—
611C23C22×Dic1411yescharacteristic
612C23C22×Dic1411yescharacteristic
613C23C22×D2811yescharacteristic
614C23C2×D4×D711yescharacteristic
615C23C2×D4×D711yescharacteristic
616C23C2×D4×D712yes—
617C23C2×#115911yescharacteristic
618C23C2×#115912yes—
619C23C2×Q8×D711yescharacteristic
620C23#655312yes—
621C23#655412yes—
622Q8—2816no—
623C2×C4—232no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4—74no—
648C2×C4—142no—
649C2×C4—144no—
650C2×C4—144no—
651C2×C4—142no—
652C2×C4—142no—
653C2×C4—142no—
654C2×C4—142no—
655C2×C4—144no—
656C2×C4—144no—
657C2×C4—144no—
658C2×C4—142no—
659C2×C4—144no—
660C2×C4—144no—
661C2×C4—144no—
662C2×C4—144no—
663C2×C4—144no—
664C2×C4—142no—
665C2×C4—2816no—
666C2×C4—2816no—
667C2×C4—282no—
668C2×C4—282no—
669C2×C4—282no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—282no—
674C2×C4—282no—
675C2×C4—281no—
676C2×C4—281no—
677C2×C4—282no—
678C2×C4—282no—
679C2×C4—281no—
680C2×C4—282no—
681C2×C4—281no—
682C2×C4—282no—
683C2×C4#644118yescomplemented
684C7#1472011yescharacteristic, complemented, Sylow
685C22—24no—
686C22—24no—
687C22—24no—
688C22—28no—
689C22—24no—
690C22—28no—
691C22—24no—
692C22—28no—
693C22—24no—
694C22—28no—
695C22#8942818yescomplemented
696C22C2×#643211yescharacteristic
697C22C2×#644111yescharacteristic
698C22C2×#644112yes—
699C22C2×#644111yescharacteristic
700C22C2×#644511yescharacteristic
701C22C2×#645111yescharacteristic
702C22C2×#645111yescharacteristic
703C22C2×#646011yescharacteristic
704C22#9021012yes—
705C22D4×Dic1412yes—
706C22#9023412yes—
707C22D4×D2812yes—
708C22#9024612yes—
709C22#9027712yes—
710C22#9027711yescharacteristic
711C22D7×#12011yescharacteristic
712C22#9030012yes—
713C22#9030212yes—
714C22#9032312yes—
715C22#9032612yes—
716C22#9033911yescharacteristic
717C22#9034411yescharacteristic
718C22#9035612yes—
719C4—28no—
720C4—42no—
721C4—42no—
722C4—44no—
723C4—144no—
724C4—282no—
725C4—284no—
726C4—282no—
727C4—284no—
728C4—282no—
729C2—28no—
730C2C2×#8942811yescharacteristic
731C2#1173093812yes—
732C2#1173129111yescharacteristic
733C2#1173134412yes—
734C2#1173153511yescharacteristic
735C2#1173185711yescharacteristic
736C2#1173186712yes—
737C2#1173193311yescharacteristic
738C2#1173213211yescharacteristic
739C2#1173215512yes—
740C2#1173232911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutator, socle, cosocleC24×C7C24
FittingC7×C22⋊#95C2
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#14720
LCSG ▷ C24×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
5. C2×#89428C2semidirect
9. #11727174C2semidirect
10. #11727173C2semidirect
11. #11727165C2semidirect
49. C23×C4×C7Q8semidirect
80. C2×C7×C22⋊C4Q8semidirect
86. C2×C22⋊Dic7Q8semidirect
319. C2×C4×C7C22⋊Q8semidirect
383. C23×C4Dic14semidirect
421. C2×C22⋊C4Dic14semidirect
441. C22×C7#395semidirect
683. C2×C4#6441semidirect
684. C7#14720semidirect
695. C22#89428semidirect

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×#897222
C2×#897182
C2×#894282
C7×C22⋊#952
#117298812
#117292982
#117271742
#117271732
#117271652
#147207