Finite Group Databasebeta

← #13275779

Subgroups — #13275779

Order 1792.

2510 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic7⋊C4C211yesmaximal, characteristic
2C2×C7×#385C211yesmaximal, characteristic
3C2×#89982C211yesmaximal, characteristic
4C2×#89748C212yesmaximal, complemented
5C2×#89722C211yesmaximal, characteristic
6C2×#89718C211yesmaximal, characteristic
7C2×#89714C211yesmaximal, characteristic
8C2×C22⋊C4×Dic7C211yesmaximal, characteristic
9#11729322C212yesmaximal, complemented
10#11727174C212yesmaximal, complemented
11Dic7⋊#95C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C24×Dic7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2212yes—
21C22×Dic7⋊C4—24no—
22C22×Dic7⋊C4—28no—
23C22×Dic7⋊C4C2212yes—
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2212yes—
27C22×Dic7⋊C4C2212yes—
28C22×Dic7⋊C4C2212yes—
29C22×C4×Dic7C2212yes—
30C7×#385—24no—
31C2×C7×#95C2212yes—
32#89982—24no—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2212yes—
39#89748—28no—
40#89722—24no—
41#89718—24no—
42#89714—24no—
43C22⋊C4×Dic7C418yescomplemented
44#13880—71nomaximal, Sylow
45C25×C7C2311yescharacteristic
46C23×C4×C7—22no—
47C23×C4×C7—24no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—42no—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2312yes—
54C23×C4×C7C2312yes—
55C23×Dic7—24no—
56C23×Dic7—24no—
57C23×Dic7—22no—
58C23×Dic7—24no—
59C23×Dic7—22no—
60C23×Dic7—22no—
61C23×Dic7—42no—
62C23×Dic7C2×C414yes—
63C23×Dic7D414yes—
64C23×Dic7Q814yes—
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2312yes—
68C23×Dic7C2312yes—
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—42no—
74C2×C7×C22⋊C4—22no—
75C2×C7×C22⋊C4—22no—
76C2×C7×C22⋊C4—22no—
77C2×C7×C22⋊C4C2×C414yes—
78C2×C7×C22⋊C4D414yes—
79C2×C7×C22⋊C4Q814yes—
80C2×C22⋊Dic7—22no—
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7C2×C414yes—
84C2×C22⋊Dic7D414yes—
85C2×C22⋊Dic7Q814yes—
86C2×C4⋊Dic7—24no—
87C2×C4⋊Dic7—24no—
88C2×C4⋊Dic7—42no—
89C2×Dic7⋊C4—232no—
90C2×Dic7⋊C4—24no—
91C2×Dic7⋊C4—24no—
92C2×Dic7⋊C4—24no—
93C2×Dic7⋊C4—24no—
94C2×Dic7⋊C4—24no—
95C2×Dic7⋊C4—24no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—24no—
99C2×Dic7⋊C4—24no—
100C2×Dic7⋊C4—24no—
101C2×Dic7⋊C4—24no—
102C2×Dic7⋊C4—24no—
103C2×Dic7⋊C4—42no—
104C2×Dic7⋊C4—42no—
105C2×Dic7⋊C4D418yes—
106C2×C4×Dic7—24no—
107C2×C4×Dic7—24no—
108C2×C4×Dic7C2×C418yescomplemented
109C7×#95—24no—
110C7⋊#95—24no—
111C7⋊#95—22no—
112C7⋊#95—22no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95C2×C418yescomplemented
116C23×C4⋊C4—71no—
117C2×#385—71no—
118C2×#385—71no—
119C2×#385—71no—
120C2×#385D711yescharacteristic
121C2×#384—72no—
122C2×#380—71no—
123C2×C4×C22⋊C4—71no—
124#1444—72no—
125#1444—72no—
126C4⋊#95—72no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7C22×C412yes—
132C24×C7C2×D412yes—
133C24×C7C2×D412yes—
134C24×C7C2×D412yes—
135C24×C7C2×Q812yes—
136C24×C7C2×Q812yes—
137C24×C7C2×Q812yes—
138C24×C7C2411yescharacteristic
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—28no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7—21no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—48no—
161C22×C4×C7—48no—
162C22×C4×C7—44no—
163C22×C4×C7—44no—
164C22×C4×C7C22×C414yes—
165C22×C4×C7C2×D414yes—
166C22×C4×C7C2×D414yes—
167C22×C4×C7C2×Q814yes—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—216no—
175C22×Dic7—28no—
176C22×Dic7—216no—
177C22×Dic7—28no—
178C22×Dic7—28no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—22no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—48no—
196C22×Dic7—48no—
197C22×Dic7—44no—
198C22×Dic7—44no—
199C22×Dic7C4⋊C4116yescomplemented
200C22×Dic7C22×C412yes—
201C22×Dic7C22×C414yes—
202C22×Dic7C22×C412yes—
203C22×Dic7C2×D414yes—
204C22×Dic7C2×D412yes—
205C22×Dic7C2×D414yes—
206C22×Dic7C2×D412yes—
207C22×Dic7C2×D414yes—
208C22×Dic7C2×Q812yes—
209C22×Dic7C2×Q814yes—
210C22×Dic7C2×Q812yes—
211C22×Dic7#4114yes—
212C7×C4⋊C4—48no—
213C7×C22⋊C4—44no—
214C7×C22⋊C4C4⋊C4116yescomplemented
215C22⋊Dic7—44no—
216C22⋊Dic7C4⋊C4116yescomplemented
217C4⋊Dic7—48no—
218Dic7⋊C4—216no—
219Dic7⋊C4—216no—
220Dic7⋊C4—48no—
221Dic7⋊C4—48no—
222Dic7⋊C4—44no—
223Dic7⋊C4—44no—
224C4×Dic7—216no—
225C24×C4—71no—
226C24×C4—71no—
227C24×C4C2×D711yescharacteristic
228C22×C4⋊C4—72no—
229C22×C4⋊C4—72no—
230C22×C4⋊C4—71no—
231C22×C4⋊C4—71no—
232C22×C4⋊C4—72no—
233C22×C4⋊C4—72no—
234C22×C4⋊C4—72no—
235C22×C4⋊C4—148no—
236C22×C4⋊C4—144no—
237C22×C4⋊C4C2×D712yes—
238C22×C22⋊C4—71no—
239C22×C22⋊C4—71no—
240C22×C22⋊C4C2×D711yescharacteristic
241C22×C22⋊C4C2×D711yescharacteristic
242C22×C42—72no—
243#385—24no—
244#385—144no—
245#385—144no—
246#385—144no—
247#384—148no—
248#380—144no—
249C4×C22⋊C4—78no—
250C2×#95—72no—
251C2×#95—72no—
252C2×#95—72no—
253C2×#95—72no—
254C2×#95—71no—
255C2×#95—71no—
256C2×#95C2×D712yes—
257C23×C7—24no—
258C23×C7—24no—
259C23×C7—22no—
260C23×C7—24no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—24no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—24no—
271C23×C7—24no—
272C23×C7—24no—
273C23×C7C2×C4⋊C414yes—
274C23×C7C2×C4⋊C414yes—
275C23×C7C2×C4⋊C414yes—
276C23×C7#12714yes—
277C23×C7C4⋊Q814yes—
278C23×C7C4⋊Q814yes—
279C23×C7C4⋊Q814yes—
280C23×C7C23×C411yescharacteristic
281C23×C7C22×D411yescharacteristic
282C23×C7C22×D411yescharacteristic
283C23×C7C22×D412yes—
284C23×C7C22×D411yescharacteristic
285C23×C7C22×Q811yescharacteristic
286C23×C7C22×Q811yescharacteristic
287C23×C7C22×Q811yescharacteristic
288C23×C7C2×#4112yes—
289C23×C7H(5,𝔽2)12yes—
290C23×C72−1+412yes—
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—24no—
298C2×C4×C7—24no—
299C2×C4×C7—24no—
300C2×C4×C7—416no—
301C2×C4×C7—42no—
302C2×C4×C7—42no—
303C2×C4×C7—42no—
304C2×C4×C7—42no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7C2×C4⋊C418yescomplemented
316C2×Dic7—24no—
317C2×Dic7—24no—
318C2×Dic7—24no—
319C2×Dic7—22no—
320C2×Dic7—24no—
321C2×Dic7—22no—
322C2×Dic7—24no—
323C2×Dic7—24no—
324C2×Dic7—24no—
325C2×Dic7—24no—
326C2×Dic7—232no—
327C2×Dic7—24no—
328C2×Dic7—24no—
329C2×Dic7—24no—
330C2×Dic7—416no—
331C2×Dic7—42no—
332C2×Dic7—42no—
333C2×Dic7—42no—
334C2×Dic7—42no—
335C2×Dic7—41no—
336C2×Dic7—41no—
337C2×Dic7—41no—
338C2×Dic7—41no—
339C2×Dic7—41no—
340C2×Dic7—41no—
341C2×Dic7—42no—
342C2×Dic7—42no—
343C2×Dic7—42no—
344C2×Dic7—42no—
345C2×Dic7C2×C4⋊C414yes—
346C2×Dic7C2×C4⋊C414yes—
347C2×Dic7C2×C4⋊C418yescomplemented
348C2×Dic7C4×D418yes—
349C2×Dic7#12014yes—
350C2×Dic7C22⋊Q818yes—
351C2×Dic7#12314yes—
352C25C22×D711yescharacteristic
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—42no—
358C23×C4—71no—
359C23×C4—74no—
360C23×C4—74no—
361C23×C4—74no—
362C23×C4—72no—
363C23×C4—71no—
364C23×C4—72no—
365C23×C4—71no—
366C23×C4—71no—
367C23×C4—144no—
368C23×C4—144no—
369C23×C4—144no—
370C23×C4—142no—
371C23×C4—142no—
372C23×C4—142no—
373C23×C4—282no—
374C23×C4C22×D711yescharacteristic
375C23×C4C22×D711yescharacteristic
376C23×C4C22×D712yes—
377C23×C4C22×D712yes—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—78no—
382C2×C4⋊C4—144no—
383C2×C4⋊C4—144no—
384C2×C4⋊C4—144no—
385C2×C4⋊C4—144no—
386C2×C4⋊C4—1432no—
387C2×C4⋊C4—144no—
388C2×C4⋊C4—144no—
389C2×C4⋊C4—142no—
390C2×C4⋊C4—142no—
391C2×C4⋊C4—144no—
392C2×C4⋊C4—144no—
393C2×C4⋊C4—144no—
394C2×C4⋊C4—144no—
395C2×C4⋊C4—144no—
396C2×C4⋊C4—144no—
397C2×C4⋊C4—144no—
398C2×C4⋊C4—282no—
399C2×C4⋊C4—282no—
400C2×C4⋊C4—282no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—74no—
405C2×C22⋊C4—74no—
406C2×C22⋊C4—74no—
407C2×C22⋊C4—142no—
408C2×C22⋊C4—142no—
409C2×C22⋊C4—142no—
410C2×C22⋊C4Dic1414yes—
411C2×C22⋊C4C4×D714yes—
412C2×C22⋊C4C22⋊D714yes—
413C2×C42—78no—
414C2×C42—144no—
415C2×C42—144no—
416#95—24no—
417#95—78no—
418#95—142no—
419#95—142no—
420#95—144no—
421#95—144no—
422#95—144no—
423C22×C7—24no—
424C22×C7—28no—
425C22×C7—28no—
426C22×C7—24no—
427C22×C7—24no—
428C22×C7—28no—
429C22×C7—28no—
430C22×C7—24no—
431C22×C7—24no—
432C22×C7—24no—
433C22×C7#38418yescomplemented
434C22×C7C22×C4⋊C411yescharacteristic
435C22×C7C22×C4⋊C411yescharacteristic
436C22×C7C22×C4⋊C411yescharacteristic
437C22×C7C2×C4×D412yes—
438C22×C7#52012yes—
439C22×C7C2×#12011yescharacteristic
440C22×C7C2×C22⋊Q812yes—
441C22×C7C2×#12311yescharacteristic
442C22×C7C2×#12711yescharacteristic
443C22×C7C2×C4⋊Q811yescharacteristic
444C22×C7C2×C4⋊Q811yescharacteristic
445C22×C7C2×C4⋊Q811yescharacteristic
446C22×C7#53511yescharacteristic
447C22×C7#53611yescharacteristic
448C22×C7#54412yes—
449C22×C7D4212yes—
450C22×C7D4212yes—
451C22×C7#54712yes—
452C22×C7#54712yes—
453C22×C7D4×Q812yes—
454C22×C7D4×Q812yes—
455C22×C7#55412yes—
456C22×C7#55412yes—
457C4×C7—28no—
458C4×C7—44no—
459C4×C7—81no—
460C4×C7—81no—
461Dic7—28no—
462Dic7—24no—
463Dic7—44no—
464Dic7—81no—
465Dic7—81no—
466Dic7#38518yescomplemented
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×Dic1412yes—
472C24C2×C4×D712yes—
473C24D4×D712yes—
474C24D4×D712yes—
475C24Q8×D712yes—
476C24Q8×D712yes—
477C24C2×C22⋊D712yes—
478C24C23×D711yescharacteristic
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—72no—
505C22×C4—74no—
506C22×C4—72no—
507C22×C4—72no—
508C22×C4—74no—
509C22×C4—716no—
510C22×C4—72no—
511C22×C4—74no—
512C22×C4—74no—
513C22×C4—72no—
514C22×C4—74no—
515C22×C4—72no—
516C22×C4—74no—
517C22×C4—148no—
518C22×C4—1416no—
519C22×C4—1416no—
520C22×C4—148no—
521C22×C4—142no—
522C22×C4—142no—
523C22×C4—142no—
524C22×C4—142no—
525C22×C4—142no—
526C22×C4—142no—
527C22×C4—148no—
528C22×C4—142no—
529C22×C4—142no—
530C22×C4—142no—
531C22×C4—142no—
532C22×C4—142no—
533C22×C4—142no—
534C22×C4—141no—
535C22×C4—141no—
536C22×C4—141no—
537C22×C4—141no—
538C22×C4—142no—
539C22×C4—142no—
540C22×C4—142no—
541C22×C4—142no—
542C22×C4—141no—
543C22×C4—141no—
544C22×C4—288no—
545C22×C4—288no—
546C22×C4—284no—
547C22×C4—284no—
548C22×C4C2×Dic1414yes—
549C22×C4C2×C4×D714yes—
550C22×C4D4×D714yes—
551C22×C4C2×C22⋊D714yes—
552C4⋊C4—48no—
553C4⋊C4—1416no—
554C4⋊C4—1416no—
555C4⋊C4—288no—
556C4⋊C4—288no—
557C4⋊C4—284no—
558C4⋊C4—284no—
559C4⋊C4—288no—
560C22⋊C4—44no—
561C22⋊C4—716no—
562C22⋊C4—284no—
563C22⋊C4Dic7⋊C4116yescomplemented
564C42—1416no—
565C2×C7—28no—
566C2×C7C2×#38411yescharacteristic
567C2×C7C2×#38511yescharacteristic
568C2×C7#231711yescharacteristic
569C2×C7D4×C4⋊C412yes—
570C2×C7D4×C4⋊C412yes—
571C2×C7#243311yescharacteristic
572C2×C7#243411yescharacteristic
573C2×C7#244012yes—
574C2×C7#244012yes—
575C2×C7#250111yescharacteristic
576C2×C7#250211yescharacteristic
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—24no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23#645114yes—
594C23#645114yes—
595C23D7×C4⋊C414yes—
596C23D7×C4⋊C414yes—
597C23C2×Dic7⋊C414yes—
598C23#650314yes—
599C23#650714yes—
600C23C22×Dic1411yescharacteristic
601C23C22×C4×D711yescharacteristic
602C23C2×D4×D711yescharacteristic
603C23C2×D4×D711yescharacteristic
604C23C2×D4×D712yes—
605C23#654812yes—
606C23C2×Q8×D711yescharacteristic
607C23C2×Q8×D711yescharacteristic
608C23D7×#4112yes—
609C23#655412yes—
610C23C22×C22⋊D711yescharacteristic
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—416no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—74no—
636C2×C4—78no—
637C2×C4—74no—
638C2×C4—78no—
639C2×C4—74no—
640C2×C4—78no—
641C2×C4—74no—
642C2×C4—1432no—
643C2×C4—144no—
644C2×C4—144no—
645C2×C4—144no—
646C2×C4—142no—
647C2×C4—144no—
648C2×C4—144no—
649C2×C4—144no—
650C2×C4—144no—
651C2×C4—142no—
652C2×C4—144no—
653C2×C4—144no—
654C2×C4—144no—
655C2×C4—144no—
656C2×C4—2816no—
657C2×C4—282no—
658C2×C4—282no—
659C2×C4—282no—
660C2×C4—282no—
661C2×C4—282no—
662C2×C4—281no—
663C2×C4—281no—
664C2×C4—282no—
665C2×C4—281no—
666C2×C4—282no—
667C2×C4—281no—
668C2×C4—281no—
669C2×C4—281no—
670C2×C4—282no—
671C2×C4C2×Dic7⋊C418yescomplemented
672C7#1388011yescharacteristic, complemented, Sylow
673C22—28no—
674C22—24no—
675C22—24no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—28no—
682C22—24no—
683C22#8974818yescomplemented
684C22C2×#645111yescharacteristic
685C22C2×#645111yescharacteristic
686C22C2×D7×C4⋊C411yescharacteristic
687C22C2×D7×C4⋊C411yescharacteristic
688C22D4×Dic1412yes—
689C22#9023012yes—
690C22C4×D4×D712yes—
691C22#9023712yes—
692C22D7×#12011yescharacteristic
693C22#9028112yes—
694C22#9028311yescharacteristic
695C22#9031412yes—
696C22D7×C22⋊Q812yes—
697C22#9032312yes—
698C22#9032712yes—
699C22#9033911yescharacteristic
700C22D7×#12311yescharacteristic
701C22#9034612yes—
702C22C22×Dic7⋊C411yescharacteristic
703C22D4×C22⋊D712yes—
704C22C2×#650311yescharacteristic
705C22C2×#650711yescharacteristic
706C22#9051512yes—
707C4—28no—
708C4—44no—
709C4—78no—
710C4—81no—
711C4—81no—
712C4—144no—
713C4—148no—
714C4—284no—
715C4—561no—
716C4—561no—
717C2—28no—
718C2#1173182711yescharacteristic
719C2#1173183812yes—
720C2#1173185711yescharacteristic
721C2#1173186112yes—
722C2#1173190511yescharacteristic
723C2D7×#38511yescharacteristic
724C2C2×#8974811yescharacteristic
725C2D4×Dic7⋊C412yes—
726C2#1174003311yescharacteristic
727C2#1174020812yes—
728C2#1174030411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#385C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7#13880
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#89748C2semidirect
9. #11729322C2semidirect
10. #11727174C2semidirect
11. Dic7⋊#95C2semidirect
43. C22⋊C4×Dic7C4semidirect
108. C2×C4×Dic7C2×C4semidirect
115. C7⋊#95C2×C4semidirect
199. C22×Dic7C4⋊C4semidirect
214. C7×C22⋊C4C4⋊C4semidirect
216. C22⋊Dic7C4⋊C4semidirect
315. C2×C4×C7C2×C4⋊C4semidirect
347. C2×Dic7C2×C4⋊C4semidirect
433. C22×C7#384semidirect
466. Dic7#385semidirect
563. C22⋊C4Dic7⋊C4semidirect
671. C2×C4C2×Dic7⋊C4semidirect
672. C7#13880semidirect
683. C22#89748semidirect

Maximal subgroups

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

subgroupindex
C23×Dic7⋊C42
C2×C7×#3852
C2×#899822
C2×#897482
C2×#897222
C2×#897182
C2×#897142
C2×C22⋊C4×Dic72
#117293222
#117271742
Dic7⋊#952
#138807