Finite Group Databasebeta

← #13276932

Subgroups — #13276932

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic
2C2×#90002C211yesmaximal, characteristic, complemented
3C2×#90002C211yesmaximal, characteristic, complemented
4C2×#89984C211yesmaximal, characteristic
5C2×C4×C22⋊Dic7C211yesmaximal, characteristic
6C2×#89757C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
8#11729323C212yesmaximal, complemented
9#11729317C212yesmaximal, complemented
10#11729300C212yesmaximal
11#11729299C212yesmaximal
12C23×C7×Q8C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C2×C7×C22⋊Q8—24no—
15C2×C7×C22⋊Q8—24no—
16C2×C7×C22⋊Q8C418yescomplemented
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2212yes—
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2212yes—
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2212yes—
28C22×C4×Dic7C2211yescharacteristic
29#90002—24no—
30#90002—24no—
31#89984—24no—
32C4×C22⋊Dic7—24no—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42#89757—24no—
43C4⋊C4×Dic7—24no—
44#13997—71nomaximal, Sylow
45C25×C7C2311yescharacteristic
46C22×C7×Q8—22no—
47C22×C7×Q8—22no—
48C22×C7×Q8—22no—
49C22×C7×Q8—22no—
50C22×C7×Q8—22no—
51C22×C7×Q8—22no—
52C22×C7×Q8C2×C414yes—
53C23×C4×C7—22no—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7C2×C414yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2312yes—
63C23×C4×C7C2311yescharacteristic
64C23×Dic7C2312yes—
65C23×Dic7C2312yes—
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C7×C22⋊Q8—232no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4C2×C418yes—
74C2×C7×C4⋊C4C2×C414yes—
75C2×C7×C4⋊C4D414yes—
76C2×C7×C4⋊C4D414yes—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4C2×C418yes—
80C2×C22⋊Dic7—22no—
81C2×C22⋊Dic7—22no—
82C2×C22⋊Dic7—22no—
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7—24no—
86C2×C22⋊Dic7—24no—
87C2×C22⋊Dic7—42no—
88C2×C22⋊Dic7Q814yescomplemented
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×C4⋊Dic7—24no—
94C2×C4⋊Dic7—22no—
95C2×C4⋊Dic7—24no—
96C2×C4⋊Dic7—42no—
97C2×C4⋊Dic7D414yes—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—22no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—24no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—24no—
105C2×C4×Dic7—42no—
106C2×C4×Dic7D414yes—
107C7⋊#95—24no—
108C7⋊#95—24no—
109C7⋊#95—22no—
110C7⋊#95—22no—
111C7⋊#95—24no—
112C7⋊#95—24no—
113C7⋊#95—24no—
114C7⋊#95—24no—
115C7⋊#95—24no—
116C22×C22⋊Q8D711yescharacteristic
117C2×#391—71no—
118C2×#391—71no—
119C2×#389—71no—
120C2×#380—71no—
121C2×C4×C4⋊C4—71no—
122C2×C4×C22⋊C4—71no—
123#1445—72no—
124#1439—72no—
125#1437—72no—
126C4⋊#95—72no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—21no—
131C24×C7—21no—
132C24×C7—21no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7C22×C412yes—
140C24×C7C2×Q812yes—
141C24×C7#4112yes—
142C24×C7C2411yescharacteristic
143C2×C7×Q8—28no—
144C2×C7×Q8—28no—
145C2×C7×Q8—28no—
146C2×C7×Q8—44no—
147C2×C7×Q8—44no—
148C2×C7×Q8—44no—
149C2×C7×Q8—44no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—28no—
167C22×C4×C7—28no—
168C22×C4×C7—28no—
169C22×C4×C7—44no—
170C22×C4×C7—44no—
171C22×C4×C7—44no—
172C22×C4×C7—44no—
173C22×C4×C7C22×C414yes—
174C22×C4×C7C22×C412yes—
175C22×C4×C7C22×C414yes—
176C22×C4×C7C22×C412yes—
177C22×C4×C7C2×D414yes—
178C22×C4×C7C2×D414yes—
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×D412yes—
182C22×C4×C7C2×D412yes—
183C22×C4×C7#4112yes—
184C22×C4×C7#4112yes—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—22no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—22no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7C2×D412yes—
221C22×Dic7C2×D414yes—
222C22×Dic7C2×D412yes—
223C22×Dic7C2×Q812yes—
224C22×Dic7C2×Q812yes—
225C22×Dic7#4112yes—
226C22×Dic7#4112yes—
227C7×C4⋊C4—216no—
228C7×C4⋊C4C22⋊C4116yescomplemented
229C7×C22⋊C4—216no—
230C22⋊Dic7—28no—
231C22⋊Dic7—28no—
232C22⋊Dic7—48no—
233C4⋊Dic7—28no—
234C4⋊Dic7—48no—
235C4⋊Dic7—44no—
236C4×Dic7—28no—
237C4×Dic7—48no—
238C4×Dic7—44no—
239C23×Q8C2×D711yescharacteristic
240C24×C4C2×D711yescharacteristic
241C2×C22⋊Q8—24no—
242C2×C22⋊Q8—24no—
243C2×C22⋊Q8Dic718yescomplemented
244C22×C4⋊C4—71no—
245C22×C4⋊C4—71no—
246C22×C4⋊C4—72no—
247C22×C4⋊C4C2×D712yes—
248C22×C4⋊C4C2×D711yescharacteristic
249C22×C22⋊C4—71no—
250C22×C22⋊C4—71no—
251C22×C22⋊C4—72no—
252C22×C22⋊C4C2×D712yes—
253C22×C42—71no—
254C22×C42—71no—
255C22×C42—72no—
256#391—144no—
257#391—144no—
258#389—144no—
259#380—144no—
260C4×C4⋊C4—144no—
261C4×C22⋊C4—144no—
262C2×#95—71no—
263C2×#95—72no—
264C2×#95—72no—
265C2×#95—72no—
266C2×#95—72no—
267C2×#95—72no—
268C2×#95—72no—
269C2×#95—72no—
270C2×#95—71no—
271C23×C7—22no—
272C23×C7—22no—
273C23×C7—22no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—22no—
281C23×C7—22no—
282C23×C7—22no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—41no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7C4×Q814yes—
306C23×C7C23×C411yescharacteristic
307C23×C7C22×D411yescharacteristic
308C23×C7C22×D411yescharacteristic
309C23×C7C22×D411yescharacteristic
310C23×C7C22×D411yescharacteristic
311C23×C7C22×Q811yescharacteristic
312C23×C7C2×#4111yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7H(5,𝔽2)11yescharacteristic
318C23×C72−1+411yescharacteristic
319C23×C72−1+411yescharacteristic
320C23×C72−1+411yescharacteristic
321C7×Q8—416no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—24no—
327C2×C4×C7—24no—
328C2×C4×C7—24no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—24no—
333C2×C4×C7—24no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—41no—
339C2×C4×C7—42no—
340C2×C4×C7—41no—
341C2×C4×C7—42no—
342C2×C4×C7—416no—
343C2×C4×C7C2×C22⋊C418yes—
344C2×C4×C7C2×C22⋊C414yes—
345C2×C4×C7C4×D414yes—
346C2×C4×C7C4×D414yes—
347C2×C4×C7#12114yes—
348C2×C4×C7#12114yes—
349C2×C4×C7#12414yes—
350C2×C4×C7#12714yes—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—24no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—24no—
365C2×Dic7—24no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—42no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—42no—
375C2×Dic7—42no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—42no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7C22⋊Q814yescomplemented
393C25C22×D711yescharacteristic
394C22×Q8—22no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8C2×Dic714yes—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—72no—
410C23×C4—71no—
411C23×C4—71no—
412C23×C4—72no—
413C23×C4C2×Dic714yes—
414C23×C4C22×D712yes—
415C23×C4C22×D711yescharacteristic
416C23×C4C22×D712yes—
417C23×C4C22×D711yescharacteristic
418C22⋊Q8—232no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—74no—
422C2×C4⋊C4—142no—
423C2×C4⋊C4—142no—
424C2×C4⋊C4—144no—
425C2×C4⋊C4—142no—
426C2×C4⋊C4—142no—
427C2×C4⋊C4—144no—
428C2×C4⋊C4—142no—
429C2×C4⋊C4—282no—
430C2×C4⋊C4C2×Dic718yes—
431C2×C4⋊C4C2×Dic714yes—
432C2×C4⋊C4C22⋊D714yes—
433C2×C4⋊C4C22⋊D714yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—74no—
437C2×C22⋊C4—142no—
438C2×C22⋊C4—142no—
439C2×C22⋊C4—142no—
440C2×C22⋊C4—142no—
441C2×C22⋊C4—142no—
442C2×C22⋊C4—144no—
443C2×C22⋊C4—144no—
444C2×C22⋊C4—282no—
445C2×C22⋊C4C2×Dic718yes—
446C2×C42—74no—
447C2×C42—142no—
448C2×C42—142no—
449C2×C42—144no—
450C2×C42—142no—
451C2×C42—142no—
452C2×C42—144no—
453C2×C42—142no—
454C2×C42—282no—
455#95—142no—
456#95—142no—
457#95—144no—
458#95—144no—
459#95—144no—
460#95—144no—
461#95—144no—
462#95—144no—
463#95—144no—
464C22×C7—24no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—42no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7C22×C22⋊C411yescharacteristic
480C22×C7C2×C4×D411yescharacteristic
481C22×C7C2×C4×D411yescharacteristic
482C22×C7C2×C4×Q811yescharacteristic
483C22×C7C4×#4111yescharacteristic
484C22×C7#51911yescharacteristic
485C22×C7#52011yescharacteristic
486C22×C7C2×#12111yescharacteristic
487C22×C7C2×#12111yescharacteristic
488C22×C7C2×C22⋊Q811yescharacteristic
489C22×C7#52511yescharacteristic
490C22×C7C2×#12411yescharacteristic
491C22×C7#52911yescharacteristic
492C22×C7C2×#12711yescharacteristic
493C22×C7#53311yescharacteristic
494C22×C7#53611yescharacteristic
495C22×C7#53711yescharacteristic
496C22×C7#54111yescharacteristic
497C22×C7#54211yescharacteristic
498C22×C7#54611yescharacteristic
499C22×C7#54611yescharacteristic
500C22×C7#54611yescharacteristic
501C22×C7#54711yescharacteristic
502C22×C7#54711yescharacteristic
503C22×C7#54711yescharacteristic
504C22×C7#54811yescharacteristic
505C22×C7#54811yescharacteristic
506C22×C7#54811yescharacteristic
507C22×C7D4×Q811yescharacteristic
508C22×C7D4×Q811yescharacteristic
509C22×C7D4×Q811yescharacteristic
510C22×C7#55211yescharacteristic
511C22×C7#55211yescharacteristic
512C22×C7#55411yescharacteristic
513C22×C7#55611yescharacteristic
514C4×C7—28no—
515C4×C7—42no—
516C4×C7—44no—
517C4×C7#39018yes—
518Dic7—24no—
519Dic7—42no—
520Dic7—44no—
521Dic7—42no—
522Dic7—42no—
523Dic7—82no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24Q8×D712yes—
537C24#116112yes—
538C24C22×Dic712yes—
539C24C23×D711yescharacteristic
540C2×Q8—28no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—44no—
544C2×Q8—44no—
545C2×Q8—44no—
546C2×Q8—44no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—72no—
574C22×C4—74no—
575C22×C4—72no—
576C22×C4—72no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—142no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—142no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—142no—
593C22×C4—141no—
594C22×C4—142no—
595C22×C4—141no—
596C22×C4—141no—
597C22×C4—142no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—142no—
604C22×C4—141no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4D4×D712yes—
613C22×C4D4×D712yes—
614C22×C4#115912yes—
615C22×C4#115912yes—
616C22×C4C22×Dic714yes—
617C22×C4C22×Dic712yes—
618C22×C4C22×Dic714yes—
619C22×C4C22×Dic712yes—
620C22×C4C2×C22⋊D714yes—
621C22×C4C2×C22⋊D714yes—
622C22×C4C2×C22⋊D712yes—
623C22×C4C2×C22⋊D712yes—
624C4⋊C4—216no—
625C4⋊C4—148no—
626C4⋊C4—288no—
627C4⋊C4—284no—
628C4⋊C4C22⋊Dic7116yescomplemented
629C22⋊C4—216no—
630C22⋊C4—148no—
631C22⋊C4—148no—
632C22⋊C4—288no—
633C42—148no—
634C42—288no—
635C42—284no—
636C2×C7—44no—
637C2×C7C2×#39011yescharacteristic
638C2×C7C4×C22⋊Q811yescharacteristic
639C2×C7#232311yescharacteristic
640C2×C7#233911yescharacteristic
641C2×C7Q8×C22⋊C411yescharacteristic
642C2×C7#236011yescharacteristic
643C2×C7#236211yescharacteristic
644C2×C7#241511yescharacteristic
645C2×C7#241711yescharacteristic
646C2×C7#242711yescharacteristic
647C2×C7#242911yescharacteristic
648C2×C7#248911yescharacteristic
649C2×C7#249211yescharacteristic
650C2×C7#254011yescharacteristic
651C2×C7#254211yescharacteristic
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23Q8×Dic714yes—
687C23C2×D4×D711yescharacteristic
688C23C2×D4×D711yescharacteristic
689C23C2×#115911yescharacteristic
690C23C2×#115911yescharacteristic
691C23C2×Q8×D711yescharacteristic
692C23C2×#116111yescharacteristic
693C23#655111yescharacteristic
694C23#655111yescharacteristic
695C23D7×#4111yescharacteristic
696C23D7×#4111yescharacteristic
697C23#655311yescharacteristic
698C23#655411yescharacteristic
699C23C23×Dic711yescharacteristic
700C23C22×C22⋊D711yescharacteristic
701C23C22×C22⋊D711yescharacteristic
702Q8—416no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—416no—
724C2×C4—74no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—144no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—144no—
740C2×C4—144no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—281no—
744C2×C4—281no—
745C2×C4—282no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4—281no—
749C2×C4—281no—
750C2×C4—282no—
751C2×C4—282no—
752C2×C4—281no—
753C2×C4—281no—
754C2×C4—281no—
755C2×C4—281no—
756C2×C4—281no—
757C2×C4—281no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4—282no—
761C2×C4—282no—
762C2×C4—282no—
763C2×C4—282no—
764C2×C4—282no—
765C2×C4—282no—
766C2×C4D4×Dic714yes—
767C2×C4D4×Dic714yes—
768C2×C4#649914yes—
769C2×C4#650114yes—
770C2×C4#650114yes—
771C2×C4#650314yes—
772C2×C4C2×C22⋊Dic718yes—
773C2×C4C2×C22⋊Dic714yes—
774C7#1399711yescharacteristic, complemented, Sylow
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22#9031311yescharacteristic
791C22#9031511yescharacteristic
792C22#9031611yescharacteristic
793C22D7×C22⋊Q811yescharacteristic
794C22#9031811yescharacteristic
795C22#9031911yescharacteristic
796C22#9032011yescharacteristic
797C22#9032111yescharacteristic
798C22#9032211yescharacteristic
799C22#9032311yescharacteristic
800C22#9032411yescharacteristic
801C22#9032611yescharacteristic
802C22#9033011yescharacteristic
803C22#9033211yescharacteristic
804C22#9033311yescharacteristic
805C22#9033411yescharacteristic
806C22C2×D4×Dic711yescharacteristic
807C22C2×D4×Dic711yescharacteristic
808C22C2×#649911yescharacteristic
809C22C2×#650111yescharacteristic
810C22C2×#650111yescharacteristic
811C22C2×#650311yescharacteristic
812C22C2×Q8×Dic711yescharacteristic
813C22#9050311yescharacteristic
814C22Q8×C22⋊D711yescharacteristic
815C22Q8×C22⋊D711yescharacteristic
816C22#9050811yescharacteristic
817C22#9050811yescharacteristic
818C22#9051511yescharacteristic
819C22#9051511yescharacteristic
820C22#41×Dic711yescharacteristic
821C22#9051811yescharacteristic
822C22#9052011yescharacteristic
823C22#9052011yescharacteristic
824C22C22×C22⋊Dic711yescharacteristic
825C4—28no—
826C4—42no—
827C4—44no—
828C4—144no—
829C4—284no—
830C4—282no—
831C4—282no—
832C4—282no—
833C4—562no—
834C4#8999318yes—
835C2—44no—
836C2Dic7×C22⋊Q811yescharacteristic
837C2#1174018911yescharacteristic
838C2#1174019211yescharacteristic
839C2#1174019311yescharacteristic
840C2#1174019711yescharacteristic
841C2#1174020111yescharacteristic
842C2#1174020211yescharacteristic
843C2#1174021711yescharacteristic
844C2#1174021811yescharacteristic
845C2#1174022411yescharacteristic
846C2#1174022511yescharacteristic
847C2#1174025811yescharacteristic
848C2C2×#8999311yescharacteristic
849C2Q8×C22⋊Dic711yescharacteristic
850C2#1174153311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C7×C22⋊Q8C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22×C22⋊Q8D7
hypocenterC7#13997
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#90002C2semidirect
3. C2×#90002C2semidirect
6. C2×#89757C2semidirect
7. C2×C4⋊C4×Dic7C2semidirect
8. #11729323C2semidirect
9. #11729317C2semidirect
16. C2×C7×C22⋊Q8C4semidirect
88. C2×C22⋊Dic7Q8semidirect
228. C7×C4⋊C4C22⋊C4semidirect
243. C2×C22⋊Q8Dic7semidirect
392. C2×Dic7C22⋊Q8semidirect
628. C4⋊C4C22⋊Dic7semidirect
774. C7#13997semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×#900022
C2×#899842
C2×C4×C22⋊Dic72
C2×#897572
C2×C4⋊C4×Dic72
#117293232
#117293172
#117293002
#117292992
#139977