Finite Group Databasebeta

← #13276071

Subgroups — #13276071

Order 1792.

1774 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic
3C2×#89745C211yesmaximal, characteristic
4C2×#89748C212yesmaximal
5C2×#89748C211yesmaximal, characteristic
6C2×C4⋊C4×Dic7C211yesmaximal, characteristic
7C2×#89700C211yesmaximal, characteristic
8C2×C4×Dic7⋊C4C211yesmaximal, characteristic
9#11729322C212yesmaximal
10#11727174C212yesmaximal
11Dic7⋊#95C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4⋊Dic7C2212yes—
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2212yes—
20C22×Dic7⋊C4C2212yes—
21C22×Dic7⋊C4C2212yes—
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2212yes—
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2212yes—
27C22×C4×Dic7C2211yescharacteristic
28C7×#389—24no—
29C2×C7×#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36#89757—24no—
37#89748—28no—
38#89748—24no—
39C4⋊C4×Dic7C418yescomplemented
40#89745—24no—
41C4×Dic7⋊C4—24no—
42#89700—24no—
43#13910—71nomaximal, Sylow
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2312yes—
48C23×C4×C7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2312yes—
53C23×Dic7C2311yescharacteristic
54C23×Dic7C2311yescharacteristic
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—24no—
57C2×C7×C4⋊C4—22no—
58C2×C7×C4⋊C4—24no—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—42no—
61C2×C7×C4⋊C4C2×C414yes—
62C2×C7×C4⋊C4D414yes—
63C2×C7×C4⋊C4Q814yes—
64C2×C42×C7—22no—
65C2×C42×C7—22no—
66C2×C42×C7—22no—
67C2×C4⋊Dic7—22no—
68C2×C4⋊Dic7—22no—
69C2×C4⋊Dic7—24no—
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7—24no—
72C2×C4⋊Dic7—42no—
73C2×C4⋊Dic7C2×C414yes—
74C2×C4⋊Dic7D414yes—
75C2×C4⋊Dic7Q814yes—
76C2×Dic7⋊C4—22no—
77C2×Dic7⋊C4—22no—
78C2×Dic7⋊C4—22no—
79C2×Dic7⋊C4—22no—
80C2×Dic7⋊C4—24no—
81C2×Dic7⋊C4—24no—
82C2×Dic7⋊C4—24no—
83C2×Dic7⋊C4—24no—
84C2×Dic7⋊C4—24no—
85C2×Dic7⋊C4—24no—
86C2×Dic7⋊C4—24no—
87C2×Dic7⋊C4—24no—
88C2×Dic7⋊C4—42no—
89C2×Dic7⋊C4—42no—
90C2×Dic7⋊C4—42no—
91C2×Dic7⋊C4—42no—
92C2×Dic7⋊C4D414yes—
93C2×Dic7⋊C4Q814yes—
94C2×C4×Dic7—24no—
95C2×C4×Dic7—24no—
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7C2×C418yes—
100C2×C4×Dic7C2×C414yes—
101C2×C4×Dic7D414yes—
102C2×C4×Dic7Q814yes—
103C7×#95—24no—
104C7⋊#95—24no—
105C7⋊#95—24no—
106C7⋊#95—22no—
107C7⋊#95—22no—
108C7⋊#95—24no—
109C7⋊#95C2×C418yes—
110C2×#389—71no—
111C2×#389—71no—
112C2×#389—71no—
113C2×#389D711yescharacteristic
114C2×#384—72no—
115C2×#384—71no—
116C2×C4×C4⋊C4—71no—
117C2×C4×C4⋊C4—71no—
118#1444—72no—
119#1444—72no—
120C4⋊#95—72no—
121C24×C7C2411yescharacteristic
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7C22×C414yes—
146C22×C4×C7C22×C412yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7C2×D414yes—
149C22×C4×C7C2×D412yes—
150C22×C4×C7C2×D412yes—
151C22×C4×C7C2×D412yes—
152C22×C4×C7C2×Q812yes—
153C22×C4×C7C2×Q814yes—
154C22×C4×C7C2×Q812yes—
155C22×C4×C7C2×Q812yes—
156C22×C4×C7C2×Q812yes—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—22no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—22no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7C22×C412yes—
185C22×Dic7C22×C414yes—
186C22×Dic7C22×C412yes—
187C22×Dic7C2×D412yes—
188C22×Dic7C2×D412yes—
189C22×Dic7C2×D414yes—
190C22×Dic7C2×D412yes—
191C22×Dic7C2×D412yes—
192C22×Dic7C2×Q812yes—
193C22×Dic7C2×Q812yes—
194C22×Dic7C2×Q814yes—
195C22×Dic7C2×Q812yes—
196C22×Dic7C2×Q812yes—
197C22×Dic7#4112yes—
198C22×Dic7#4112yes—
199C7×C4⋊C4—48no—
200C7×C4⋊C4—44no—
201C7×C4⋊C4C4⋊C4116yescomplemented
202C42×C7—44no—
203C4⋊Dic7—48no—
204C4⋊Dic7—44no—
205C4⋊Dic7C4⋊C4116yescomplemented
206Dic7⋊C4—28no—
207Dic7⋊C4—28no—
208Dic7⋊C4—48no—
209Dic7⋊C4—48no—
210Dic7⋊C4—48no—
211Dic7⋊C4—48no—
212C4×Dic7—216no—
213C4×Dic7—44no—
214C4×Dic7C4⋊C4116yescomplemented
215C22×C4⋊C4—71no—
216C22×C4⋊C4—71no—
217C22×C4⋊C4—71no—
218C22×C4⋊C4—72no—
219C22×C4⋊C4—71no—
220C22×C4⋊C4—72no—
221C22×C4⋊C4—72no—
222C22×C4⋊C4—72no—
223C22×C4⋊C4—72no—
224C22×C4⋊C4C2×D711yescharacteristic
225C22×C4⋊C4C2×D712yes—
226C22×C4⋊C4C2×D711yescharacteristic
227C22×C42—71no—
228C22×C42—72no—
229C22×C42—71no—
230C22×C42C2×D711yescharacteristic
231#389—24no—
232#389—144no—
233#389—144no—
234#389—144no—
235#384—144no—
236#384—148no—
237C4×C4⋊C4—78no—
238C4×C4⋊C4—144no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—71no—
244C2×#95—71no—
245C2×#95C2×D712yes—
246C23×C7C23×C411yescharacteristic
247C23×C7C22×D411yescharacteristic
248C23×C7C22×D411yescharacteristic
249C23×C7C22×D411yescharacteristic
250C23×C7C22×D411yescharacteristic
251C23×C7C22×Q811yescharacteristic
252C23×C7C22×Q811yescharacteristic
253C23×C7C22×Q811yescharacteristic
254C23×C7C22×Q811yescharacteristic
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4111yescharacteristic
257C23×C7H(5,𝔽2)11yescharacteristic
258C23×C7H(5,𝔽2)11yescharacteristic
259C23×C72−1+411yescharacteristic
260C23×C72−1+411yescharacteristic
261C2×C4×C7—24no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—42no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
288C2×C4×C7C2×C4⋊C414yes—
289C2×C4×C7C2×C4⋊C414yes—
290C2×C4×C7C2×C4⋊C418yes—
291C2×C4×C7C2×C4⋊C414yes—
292C2×C4×C7#12714yes—
293C2×C4×C7C4⋊Q814yes—
294C2×C4×C7C4⋊Q814yes—
295C2×C4×C7C4⋊Q814yes—
296C2×Dic7—24no—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—24no—
300C2×Dic7—22no—
301C2×Dic7—22no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—24no—
305C2×Dic7—24no—
306C2×Dic7—24no—
307C2×Dic7—24no—
308C2×Dic7—22no—
309C2×Dic7—22no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—22no—
313C2×Dic7—22no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—42no—
323C2×Dic7—42no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C2×Dic7—42no—
327C2×Dic7—42no—
328C2×Dic7—42no—
329C2×Dic7C2×C4⋊C414yes—
330C2×Dic7C2×C4⋊C418yes—
331C2×Dic7C2×C4⋊C414yes—
332C2×Dic7C4×D414yes—
333C2×Dic7C4×Q814yes—
334C2×Dic7#12114yes—
335C2×Dic7C22⋊Q814yes—
336C2×Dic7#12514yes—
337C2×Dic7C4⋊Q814yes—
338C23×C4—71no—
339C23×C4—72no—
340C23×C4—71no—
341C23×C4—71no—
342C23×C4—71no—
343C23×C4—72no—
344C23×C4C22×D712yes—
345C23×C4C22×D711yescharacteristic
346C23×C4C22×D711yescharacteristic
347C23×C4C22×D712yes—
348C23×C4C22×D711yescharacteristic
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—74no—
356C2×C4⋊C4—74no—
357C2×C4⋊C4—74no—
358C2×C4⋊C4—74no—
359C2×C4⋊C4—74no—
360C2×C4⋊C4—142no—
361C2×C4⋊C4—142no—
362C2×C4⋊C4—142no—
363C2×C4⋊C4—142no—
364C2×C4⋊C4—144no—
365C2×C4⋊C4—144no—
366C2×C4⋊C4—144no—
367C2×C4⋊C4—144no—
368C2×C4⋊C4—144no—
369C2×C4⋊C4—144no—
370C2×C4⋊C4—144no—
371C2×C4⋊C4—144no—
372C2×C4⋊C4—144no—
373C2×C4⋊C4—142no—
374C2×C4⋊C4—142no—
375C2×C4⋊C4—144no—
376C2×C4⋊C4—142no—
377C2×C4⋊C4—282no—
378C2×C4⋊C4—282no—
379C2×C4⋊C4—282no—
380C2×C4⋊C4—282no—
381C2×C4⋊C4—282no—
382C2×C4⋊C4Dic1414yes—
383C2×C4⋊C4C4×D714yes—
384C2×C4⋊C4C22⋊D714yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—74no—
389C2×C42—74no—
390C2×C42—74no—
391C2×C42—78no—
392C2×C42—144no—
393C2×C42—144no—
394C2×C42—142no—
395C2×C42—142no—
396C2×C42—142no—
397#95—24no—
398#95—78no—
399#95—142no—
400#95—142no—
401#95—144no—
402#95—144no—
403#95—144no—
404C22×C7C22×C4⋊C411yescharacteristic
405C22×C7C22×C4⋊C411yescharacteristic
406C22×C7C22×C4⋊C411yescharacteristic
407C22×C7C2×C4×D411yescharacteristic
408C22×C7C2×C4×Q811yescharacteristic
409C22×C7#52011yescharacteristic
410C22×C7#52011yescharacteristic
411C22×C7C2×#12111yescharacteristic
412C22×C7C2×C22⋊Q811yescharacteristic
413C22×C7C2×#12511yescharacteristic
414C22×C7C2×#12711yescharacteristic
415C22×C7C2×C4⋊Q811yescharacteristic
416C22×C7C2×C4⋊Q811yescharacteristic
417C22×C7C2×C4⋊Q811yescharacteristic
418C22×C7C2×C4⋊Q811yescharacteristic
419C22×C7#53511yescharacteristic
420C22×C7#53611yescharacteristic
421C22×C7#54411yescharacteristic
422C22×C7#54411yescharacteristic
423C22×C7D4211yescharacteristic
424C22×C7D4211yescharacteristic
425C22×C7#54711yescharacteristic
426C22×C7#54711yescharacteristic
427C22×C7D4×Q811yescharacteristic
428C22×C7D4×Q811yescharacteristic
429C22×C7D4×Q811yescharacteristic
430C22×C7D4×Q811yescharacteristic
431C22×C7#55011yescharacteristic
432C22×C7#55011yescharacteristic
433C22×C7#55411yescharacteristic
434C22×C7#55411yescharacteristic
435C22×C7#55711yescharacteristic
436C22×C7#55711yescharacteristic
437C22×C7Q8211yescharacteristic
438C22×C7Q8211yescharacteristic
439C4×C7—28no—
440C4×C7—42no—
441C4×C7—42no—
442C4×C7—82no—
443C4×C7#38418yescomplemented
444Dic7—24no—
445Dic7—28no—
446Dic7—42no—
447Dic7—42no—
448Dic7—82no—
449Dic7#38918yescomplemented
450C24C23×D711yescharacteristic
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—72no—
475C22×C4—72no—
476C22×C4—72no—
477C22×C4—72no—
478C22×C4—72no—
479C22×C4—72no—
480C22×C4—72no—
481C22×C4—72no—
482C22×C4—74no—
483C22×C4—72no—
484C22×C4—74no—
485C22×C4—72no—
486C22×C4—74no—
487C22×C4—72no—
488C22×C4—72no—
489C22×C4—142no—
490C22×C4—141no—
491C22×C4—142no—
492C22×C4—141no—
493C22×C4—142no—
494C22×C4—141no—
495C22×C4—142no—
496C22×C4—141no—
497C22×C4—141no—
498C22×C4—141no—
499C22×C4—141no—
500C22×C4—141no—
501C22×C4—141no—
502C22×C4—141no—
503C22×C4—141no—
504C22×C4—141no—
505C22×C4—141no—
506C22×C4—141no—
507C22×C4—141no—
508C22×C4—141no—
509C22×C4—142no—
510C22×C4—142no—
511C22×C4—142no—
512C22×C4—142no—
513C22×C4—142no—
514C22×C4—142no—
515C22×C4—142no—
516C22×C4C2×Dic1414yes—
517C22×C4C2×Dic1412yes—
518C22×C4C2×C4×D714yes—
519C22×C4C2×C4×D712yes—
520C22×C4D4×D712yes—
521C22×C4D4×D712yes—
522C22×C4D4×D712yes—
523C22×C4Q8×D712yes—
524C22×C4Q8×D712yes—
525C22×C4Q8×D712yes—
526C22×C4C2×C22⋊D714yes—
527C22×C4C2×C22⋊D712yes—
528C4⋊C4—48no—
529C4⋊C4—44no—
530C4⋊C4—716no—
531C4⋊C4—148no—
532C4⋊C4—148no—
533C4⋊C4—288no—
534C4⋊C4—288no—
535C4⋊C4—288no—
536C4⋊C4—288no—
537C4⋊C4—288no—
538C4⋊C4—284no—
539C4⋊C4Dic7⋊C4116yescomplemented
540C42—44no—
541C42—716no—
542C42—1416no—
543C42—284no—
544C2×C7C2×#38411yescharacteristic
545C2×C7C2×#38911yescharacteristic
546C2×C7#231711yescharacteristic
547C2×C7D4×C4⋊C411yescharacteristic
548C2×C7D4×C4⋊C411yescharacteristic
549C2×C7Q8×C4⋊C411yescharacteristic
550C2×C7Q8×C4⋊C411yescharacteristic
551C2×C7#254111yescharacteristic
552C2×C7#254211yescharacteristic
553C2×C7#254611yescharacteristic
554C2×C7#255111yescharacteristic
555C2×C7#255111yescharacteristic
556C2×C7#255211yescharacteristic
557C2×C7#255211yescharacteristic
558C2×C7#256711yescharacteristic
559C23C22×Dic1411yescharacteristic
560C23C22×C4×D711yescharacteristic
561C23C2×D4×D711yescharacteristic
562C23C2×D4×D711yescharacteristic
563C23C2×D4×D711yescharacteristic
564C23#654811yescharacteristic
565C23C2×Q8×D711yescharacteristic
566C23C2×Q8×D711yescharacteristic
567C23C2×Q8×D711yescharacteristic
568C23#655111yescharacteristic
569C23D7×#4111yescharacteristic
570C23D7×#4111yescharacteristic
571C23#655311yescharacteristic
572C23#655411yescharacteristic
573C23C22×C22⋊D711yescharacteristic
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—74no—
602C2×C4—74no—
603C2×C4—74no—
604C2×C4—74no—
605C2×C4—74no—
606C2×C4—74no—
607C2×C4—74no—
608C2×C4—74no—
609C2×C4—78no—
610C2×C4—142no—
611C2×C4—144no—
612C2×C4—144no—
613C2×C4—142no—
614C2×C4—144no—
615C2×C4—142no—
616C2×C4—144no—
617C2×C4—142no—
618C2×C4—142no—
619C2×C4—144no—
620C2×C4—142no—
621C2×C4—144no—
622C2×C4—142no—
623C2×C4—142no—
624C2×C4—142no—
625C2×C4—142no—
626C2×C4—142no—
627C2×C4—142no—
628C2×C4—281no—
629C2×C4—281no—
630C2×C4—281no—
631C2×C4—281no—
632C2×C4—281no—
633C2×C4—281no—
634C2×C4—281no—
635C2×C4—281no—
636C2×C4—282no—
637C2×C4—282no—
638C2×C4—282no—
639C2×C4—282no—
640C2×C4—282no—
641C2×C4—282no—
642C2×C4—282no—
643C2×C4#645114yes—
644C2×C4#645114yes—
645C2×C4D7×C4⋊C414yes—
646C2×C4D7×C4⋊C414yes—
647C2×C4C2×Dic7⋊C418yes—
648C2×C4C2×Dic7⋊C414yes—
649C2×C4#650314yes—
650C2×C4#650714yes—
651C7#1391011yescharacteristic, complemented, Sylow
652C22C2×#645111yescharacteristic
653C22C2×#645111yescharacteristic
654C22C2×D7×C4⋊C411yescharacteristic
655C22C2×D7×C4⋊C411yescharacteristic
656C22D4×Dic1411yescharacteristic
657C22#9023011yescharacteristic
658C22C4×D4×D711yescharacteristic
659C22#9023711yescharacteristic
660C22Q8×Dic1411yescharacteristic
661C22#9026011yescharacteristic
662C22C4×Q8×D711yescharacteristic
663C22#9026511yescharacteristic
664C22#9029011yescharacteristic
665C22D7×#12111yescharacteristic
666C22#9029811yescharacteristic
667C22#9030011yescharacteristic
668C22D7×C22⋊Q811yescharacteristic
669C22#9031911yescharacteristic
670C22#9032211yescharacteristic
671C22#9032311yescharacteristic
672C22#9037611yescharacteristic
673C22D7×#12511yescharacteristic
674C22#9038011yescharacteristic
675C22#9038111yescharacteristic
676C22#9041311yescharacteristic
677C22D7×C4⋊Q811yescharacteristic
678C22#9041811yescharacteristic
679C22#9042011yescharacteristic
680C22C22×Dic7⋊C411yescharacteristic
681C22D4×C22⋊D711yescharacteristic
682C22C2×#650311yescharacteristic
683C22C2×#650711yescharacteristic
684C22Q8×C22⋊D711yescharacteristic
685C22#9051511yescharacteristic
686C22#9052511yescharacteristic
687C4—28no—
688C4—42no—
689C4—42no—
690C4—78no—
691C4—82no—
692C4—148no—
693C4—144no—
694C4—282no—
695C4—282no—
696C4—562no—
697C4#8974818yescomplemented
698C2#1173341311yescharacteristic
699C2#1173342611yescharacteristic
700C2#1173350511yescharacteristic
701C2#1173350911yescharacteristic
702C2#1173351011yescharacteristic
703C2#1173351611yescharacteristic
704C2D7×#38911yescharacteristic
705C2#1173364711yescharacteristic
706C2C2×#8974811yescharacteristic
707C2D4×Dic7⋊C411yescharacteristic
708C2Q8×Dic7⋊C411yescharacteristic
709C2#1174011411yescharacteristic
710C2#1174022511yescharacteristic
711C2#1174048211yescharacteristic
712C2#1174068711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#389D7
hypocenterC7#13910
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
39. C4⋊C4×Dic7C4semidirect
201. C7×C4⋊C4C4⋊C4semidirect
205. C4⋊Dic7C4⋊C4semidirect
214. C4×Dic7C4⋊C4semidirect
443. C4×C7#384semidirect
449. Dic7#389semidirect
539. C4⋊C4Dic7⋊C4semidirect
651. C7#13910semidirect
697. C4#89748semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×#897572
C2×#897452
C2×#897482
C2×C4⋊C4×Dic72
C2×#897002
C2×C4×Dic7⋊C42
#117293222
#117271742
Dic7⋊#952
#139107