Finite Group Databasebeta

← #13276208

Subgroups — #13276208

Order 1792.

1854 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic14C211yesmaximal, characteristic
2C2×#89748C211yesmaximal, characteristic
3C2×C4⋊C4×Dic7C211yesmaximal, characteristic
4C2×#89418C212yesmaximal
5C7×C4⋊#95C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7#11729317C211yesmaximal, characteristic
8#11729289C211yesmaximal, characteristic
9#11727165C212yesmaximal
10#11727163C212yesmaximal
11Dic7⋊#95C212yesmaximal
12C23×Dic14C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4⋊Dic7C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×Dic7⋊C4C2212yes—
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2212yes—
23C22×C4×Dic7C2212yes—
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C2×C4×Dic14—24no—
27C2×C4×Dic14—24no—
28C2×C4×Dic14C418yescomplemented
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89748—24no—
39C4⋊C4×Dic7—24no—
40#89418—28no—
41#13926—71nomaximal, Sylow
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2312yes—
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C22×Dic14—22no—
54C22×Dic14—22no—
55C22×Dic14—22no—
56C22×Dic14—22no—
57C22×Dic14C2×C414yes—
58C22×Dic14D414yes—
59C22×Dic14Q814yes—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4Q814yescomplemented
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7C2×C414yes—
69C2×C4⋊Dic7—22no—
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7—22no—
72C2×C4⋊Dic7—22no—
73C2×C4⋊Dic7—22no—
74C2×C4⋊Dic7—22no—
75C2×C4⋊Dic7—22no—
76C2×C4⋊Dic7C2×C414yes—
77C2×C4⋊Dic7Q814yescomplemented
78C2×Dic7⋊C4—22no—
79C2×Dic7⋊C4—22no—
80C2×Dic7⋊C4—22no—
81C2×Dic7⋊C4—22no—
82C2×Dic7⋊C4—24no—
83C2×Dic7⋊C4—24no—
84C2×Dic7⋊C4—24no—
85C2×Dic7⋊C4—24no—
86C2×Dic7⋊C4—42no—
87C2×Dic7⋊C4—42no—
88C2×Dic7⋊C4C2×C414yes—
89C2×Dic7⋊C4C2×C414yes—
90C2×C4×Dic7—22no—
91C2×C4×Dic7—22no—
92C2×C4×Dic7—24no—
93C2×C4×Dic7—24no—
94C2×C4×Dic7—24no—
95C2×C4×Dic7C2×C414yes—
96C2×C4×Dic7C2×C414yes—
97C2×C4×Dic7D414yes—
98C2×C4×Dic7D414yes—
99C4×Dic14—232no—
100C7×#95—24no—
101C7×#95—42no—
102C7⋊#95—24no—
103C7⋊#95—24no—
104C7⋊#95—24no—
105C7⋊#95—24no—
106C7⋊#95—42no—
107C7⋊#95—42no—
108C7⋊#95—42no—
109C22×C4×Q8—71no—
110C2×#391—72no—
111C2×#384—71no—
112C2×C4×C4⋊C4—71no—
113#1441—72no—
114#1441—72no—
115C4⋊#95—71no—
116C4⋊#95—72no—
117C4⋊#95—71no—
118C4⋊#95—71no—
119C4⋊#95D711yescharacteristic
120C24×C7C2411yescharacteristic
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—21no—
132C22×C4×C7—22no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
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×C7C22×C412yes—
145C22×C4×C7C22×C412yes—
146C22×C4×C7C22×C412yes—
147C22×C4×C7C2×D412yes—
148C22×C4×C7C2×D412yes—
149C22×C4×C7C2×D412yes—
150C22×C4×C7C2×Q814yes—
151C22×C4×C7C2×Q812yes—
152C22×C4×C7C2×Q812yes—
153C22×C4×C7C2×Q812yes—
154C22×C4×C7#4112yes—
155C22×C4×C7#4112yes—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—22no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7C22×C412yes—
184C22×Dic7C22×C412yes—
185C22×Dic7C22×C412yes—
186C22×Dic7C22×C412yes—
187C22×Dic7C2×D412yes—
188C22×Dic7C2×D412yes—
189C22×Dic7C2×D412yes—
190C22×Dic7C2×D412yes—
191C22×Dic7C2×D412yes—
192C22×Dic7C2×D412yes—
193C22×Dic7C2×Q814yes—
194C22×Dic7C2×Q812yes—
195C22×Dic7C2×Q812yes—
196C22×Dic7#4112yes—
197C22×Dic7#4112yes—
198C2×Dic14—28no—
199C2×Dic14—28no—
200C2×Dic14—28no—
201C2×Dic14—28no—
202C2×Dic14—28no—
203C2×Dic14—28no—
204C2×Dic14C4⋊C4116yescomplemented
205C7×C4⋊C4—28no—
206C7×C4⋊C4—44no—
207C42×C7—28no—
208C4⋊Dic7—28no—
209C4⋊Dic7—28no—
210C4⋊Dic7—44no—
211Dic7⋊C4—28no—
212Dic7⋊C4—28no—
213Dic7⋊C4—48no—
214Dic7⋊C4—48no—
215C4×Dic7—28no—
216C4×Dic7—48no—
217C4×Dic7C22⋊C4116yes—
218C23×Q8—71no—
219C2×C4×Q8—78no—
220C2×C4×Q8—144no—
221C2×C4×Q8—144no—
222C22×C4⋊C4—71no—
223C22×C4⋊C4—71no—
224C22×C4⋊C4—71no—
225C22×C4⋊C4—71no—
226C22×C4⋊C4—72no—
227C22×C4⋊C4—71no—
228C22×C4⋊C4—72no—
229C22×C4⋊C4C2×D711yescharacteristic
230C22×C4⋊C4C2×D711yescharacteristic
231C22×C42—71no—
232C22×C42—71no—
233C22×C42—72no—
234C22×C42C2×D711yescharacteristic
235#391—148no—
236#384—144no—
237C4×C4⋊C4—144no—
238C2×#95—72no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95—72no—
242C2×#95—72no—
243C2×#95—72no—
244C2×#95—72no—
245C2×#95C2×D712yes—
246C2×#95C2×D712yes—
247C23×C7C23×C411yescharacteristic
248C23×C7C22×D411yescharacteristic
249C23×C7C22×D411yescharacteristic
250C23×C7C22×D411yescharacteristic
251C23×C7C22×Q811yescharacteristic
252C23×C7C22×Q811yescharacteristic
253C23×C7C22×Q811yescharacteristic
254C23×C7C2×#4111yescharacteristic
255C23×C7C2×#4111yescharacteristic
256C23×C7C2×#4111yescharacteristic
257C23×C7C2×#4111yescharacteristic
258C23×C7H(5,𝔽2)11yescharacteristic
259C23×C7H(5,𝔽2)11yescharacteristic
260C23×C72−1+411yescharacteristic
261C23×C72−1+411yescharacteristic
262C2×C4×C7—22no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—24no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—42no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—42no—
279C2×C4×C7—41no—
280C2×C4×C7—42no—
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×C7—42no—
289C2×C4×C7C2×C22⋊C414yes—
290C2×C4×C7C2×C4⋊C414yes—
291C2×C4×C7C4×Q814yes—
292C2×C4×C7C4×Q814yes—
293C2×C4×C7C22⋊Q814yes—
294C2×C4×C7C22⋊Q814yes—
295C2×C4×C7#12414yes—
296C2×C4×C7C4⋊Q814yes—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—22no—
300C2×Dic7—22no—
301C2×Dic7—22no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—22no—
305C2×Dic7—22no—
306C2×Dic7—22no—
307C2×Dic7—22no—
308C2×Dic7—22no—
309C2×Dic7—22no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—24no—
313C2×Dic7—24no—
314C2×Dic7—24no—
315C2×Dic7—42no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320C2×Dic7—42no—
321C2×Dic7—42no—
322C2×Dic7—42no—
323C2×Dic7—42no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C2×Dic7—42no—
327C2×Dic7—42no—
328C2×Dic7—42no—
329C2×Dic7—42no—
330C2×Dic7C2×C22⋊C414yes—
331C2×Dic7C2×C22⋊C414yes—
332C2×Dic7C2×C4⋊C414yes—
333C2×Dic7C2×C4⋊C414yes—
334C2×Dic7#11714yes—
335C2×Dic7#12114yes—
336C2×Dic7#12114yes—
337C2×Dic7C22⋊Q814yes—
338C2×Dic7C22⋊Q814yes—
339Dic14—232no—
340C22×Q8—74no—
341C22×Q8—74no—
342C22×Q8—74no—
343C22×Q8—142no—
344C22×Q8—142no—
345C22×Q8—142no—
346C22×Q8—142no—
347C23×C4—71no—
348C23×C4—71no—
349C23×C4—71no—
350C23×C4—71no—
351C23×C4—72no—
352C23×C4—72no—
353C23×C4C22×D712yes—
354C23×C4C22×D712yes—
355C23×C4C22×D711yescharacteristic
356C23×C4C22×D711yescharacteristic
357C23×C4C22×D711yescharacteristic
358C4×Q8—1432no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—74no—
365C2×C4⋊C4—74no—
366C2×C4⋊C4—74no—
367C2×C4⋊C4—74no—
368C2×C4⋊C4—142no—
369C2×C4⋊C4—142no—
370C2×C4⋊C4—142no—
371C2×C4⋊C4—142no—
372C2×C4⋊C4—142no—
373C2×C4⋊C4—142no—
374C2×C4⋊C4—142no—
375C2×C4⋊C4—142no—
376C2×C4⋊C4—144no—
377C2×C4⋊C4—144no—
378C2×C4⋊C4—144no—
379C2×C4⋊C4—144no—
380C2×C4⋊C4—142no—
381C2×C4⋊C4—142no—
382C2×C4⋊C4—142no—
383C2×C4⋊C4—282no—
384C2×C4⋊C4—282no—
385C2×C4⋊C4Dic1414yescomplemented
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—74no—
389C2×C42—74no—
390C2×C42—74no—
391C2×C42—74no—
392C2×C42—142no—
393C2×C42—142no—
394C2×C42—144no—
395C2×C42—144no—
396C2×C42—144no—
397C2×C42C4×D714yes—
398#95—24no—
399#95—42no—
400#95—144no—
401#95—144no—
402#95—144no—
403#95—144no—
404#95—282no—
405#95—282no—
406#95—282no—
407C22×C7C22×C22⋊C411yescharacteristic
408C22×C7C22×C4⋊C411yescharacteristic
409C22×C7C2×#11711yescharacteristic
410C22×C7C2×C4×Q811yescharacteristic
411C22×C7C2×C4×Q811yescharacteristic
412C22×C7#52011yescharacteristic
413C22×C7#52011yescharacteristic
414C22×C7C2×#12111yescharacteristic
415C22×C7C2×#12111yescharacteristic
416C22×C7C2×C22⋊Q811yescharacteristic
417C22×C7C2×C22⋊Q811yescharacteristic
418C22×C7C2×C22⋊Q811yescharacteristic
419C22×C7C2×C22⋊Q811yescharacteristic
420C22×C7C2×#12411yescharacteristic
421C22×C7C2×C4⋊Q811yescharacteristic
422C22×C7#53511yescharacteristic
423C22×C7#53611yescharacteristic
424C22×C7#53711yescharacteristic
425C22×C7#53711yescharacteristic
426C22×C7D4×Q811yescharacteristic
427C22×C7D4×Q811yescharacteristic
428C22×C7#55011yescharacteristic
429C22×C7#55011yescharacteristic
430C22×C7#55411yescharacteristic
431C22×C7#55411yescharacteristic
432C22×C7#55611yescharacteristic
433C22×C7#55611yescharacteristic
434C22×C7#55711yescharacteristic
435C22×C7#55711yescharacteristic
436C22×C7#55711yescharacteristic
437C22×C7#55711yescharacteristic
438C22×C7Q8211yescharacteristic
439C22×C7Q8211yescharacteristic
440C22×C7#55911yescharacteristic
441C22×C7#55911yescharacteristic
442C4×C7—24no—
443C4×C7—42no—
444C4×C7—44no—
445C4×C7—82no—
446C4×C7#39118yescomplemented
447Dic7—24no—
448Dic7—24no—
449Dic7—42no—
450Dic7—44no—
451Dic7—82no—
452Dic7#38018yes—
453C24C23×D711yescharacteristic
454C2×Q8—716no—
455C2×Q8—148no—
456C2×Q8—148no—
457C2×Q8—148no—
458C2×Q8—148no—
459C2×Q8—148no—
460C2×Q8—148no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—72no—
485C22×C4—72no—
486C22×C4—72no—
487C22×C4—72no—
488C22×C4—72no—
489C22×C4—72no—
490C22×C4—72no—
491C22×C4—72no—
492C22×C4—72no—
493C22×C4—72no—
494C22×C4—72no—
495C22×C4—72no—
496C22×C4—72no—
497C22×C4—72no—
498C22×C4—74no—
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—142no—
508C22×C4—142no—
509C22×C4—142no—
510C22×C4—141no—
511C22×C4—141no—
512C22×C4—141no—
513C22×C4—142no—
514C22×C4—141no—
515C22×C4—142no—
516C22×C4—142no—
517C22×C4—141no—
518C22×C4—141no—
519C22×C4—142no—
520C22×C4—142no—
521C22×C4—142no—
522C22×C4—142no—
523C22×C4—142no—
524C22×C4—142no—
525C22×C4—142no—
526C22×C4C2×Dic1414yes—
527C22×C4C2×Dic1412yes—
528C22×C4C2×C4×D712yes—
529C22×C4C2×C4×D712yes—
530C22×C4C2×C4×D712yes—
531C22×C4#115712yes—
532C22×C4D4×D712yes—
533C22×C4D4×D712yes—
534C22×C4D4×D712yes—
535C22×C4#115912yes—
536C22×C4Q8×D712yes—
537C22×C4Q8×D712yes—
538C4⋊C4—28no—
539C4⋊C4—44no—
540C4⋊C4—148no—
541C4⋊C4—148no—
542C4⋊C4—148no—
543C4⋊C4—148no—
544C4⋊C4—288no—
545C4⋊C4—288no—
546C4⋊C4—284no—
547C42—28no—
548C42—716no—
549C42—148no—
550C42—288no—
551C2×C7C2×#38011yescharacteristic
552C2×C7C2×#39111yescharacteristic
553C2×C7#231111yescharacteristic
554C2×C7Q8×C4⋊C411yescharacteristic
555C2×C7Q8×C4⋊C411yescharacteristic
556C2×C7#235511yescharacteristic
557C2×C7#235511yescharacteristic
558C2×C7#253811yescharacteristic
559C2×C7#253811yescharacteristic
560C2×C7#254611yescharacteristic
561C2×C7#254811yescharacteristic
562C2×C7#256711yescharacteristic
563C2×C7#256811yescharacteristic
564C2×C7#258211yescharacteristic
565C2×C7#258211yescharacteristic
566C23C22×Dic1411yescharacteristic
567C23C22×C4×D711yescharacteristic
568C23C2×#115711yescharacteristic
569C23C2×D4×D711yescharacteristic
570C23C2×D4×D711yescharacteristic
571C23C2×D4×D711yescharacteristic
572C23C2×#115911yescharacteristic
573C23#654811yescharacteristic
574C23C2×Q8×D711yescharacteristic
575C23C2×Q8×D711yescharacteristic
576C23#655111yescharacteristic
577C23D7×#4111yescharacteristic
578C23D7×#4111yescharacteristic
579C23#655311yescharacteristic
580C23#655411yescharacteristic
581Q8—1432no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—74no—
610C2×C4—74no—
611C2×C4—74no—
612C2×C4—74no—
613C2×C4—74no—
614C2×C4—74no—
615C2×C4—74no—
616C2×C4—74no—
617C2×C4—74no—
618C2×C4—142no—
619C2×C4—142no—
620C2×C4—142no—
621C2×C4—142no—
622C2×C4—142no—
623C2×C4—142no—
624C2×C4—142no—
625C2×C4—142no—
626C2×C4—142no—
627C2×C4—142no—
628C2×C4—142no—
629C2×C4—142no—
630C2×C4—144no—
631C2×C4—144no—
632C2×C4—142no—
633C2×C4—142no—
634C2×C4—144no—
635C2×C4—142no—
636C2×C4—282no—
637C2×C4—282no—
638C2×C4—282no—
639C2×C4—281no—
640C2×C4—281no—
641C2×C4—281no—
642C2×C4—282no—
643C2×C4—281no—
644C2×C4—282no—
645C2×C4—282no—
646C2×C4—282no—
647C2×C4—282no—
648C2×C4—282no—
649C2×C4—282no—
650C2×C4—282no—
651C2×C4C4×Dic1414yes—
652C2×C4#644114yes—
653C2×C4D7×C22⋊C414yes—
654C2×C4#644814yes—
655C2×C4#645014yes—
656C2×C4#645114yes—
657C2×C4D7×C4⋊C414yes—
658C2×C4#645914yes—
659C7#1392611yescharacteristic, complemented, Sylow
660C22C2×C4×Dic1411yescharacteristic
661C22C2×#644111yescharacteristic
662C22C2×D7×C22⋊C411yescharacteristic
663C22C2×#644811yescharacteristic
664C22C2×#645011yescharacteristic
665C22C2×#645111yescharacteristic
666C22C2×D7×C4⋊C411yescharacteristic
667C22#9019511yescharacteristic
668C22C2×#645911yescharacteristic
669C22D7×#11711yescharacteristic
670C22#9021411yescharacteristic
671C22D4×Dic1411yescharacteristic
672C22#9023011yescharacteristic
673C22#9024411yescharacteristic
674C22#9025011yescharacteristic
675C22Q8×Dic1411yescharacteristic
676C22#9025811yescharacteristic
677C22#9025911yescharacteristic
678C22#9026011yescharacteristic
679C22D7×#12111yescharacteristic
680C22D7×#12111yescharacteristic
681C22#9029811yescharacteristic
682C22#9029911yescharacteristic
683C22D7×C22⋊Q811yescharacteristic
684C22D7×C22⋊Q811yescharacteristic
685C22#9031911yescharacteristic
686C22#9032011yescharacteristic
687C22#9036211yescharacteristic
688C22#9037211yescharacteristic
689C22#9037611yescharacteristic
690C22#9038111yescharacteristic
691C22#9040911yescharacteristic
692C22#9041211yescharacteristic
693C22#9041311yescharacteristic
694C22#9041811yescharacteristic
695C4—24no—
696C4—44no—
697C4—42no—
698C4—78no—
699C4—82no—
700C4—144no—
701C4—144no—
702C4—284no—
703C4—282no—
704C4—562no—
705C4#8941818yescomplemented
706C2C2×#8941811yescharacteristic
707C2C4⋊C4×Dic1411yescharacteristic
708C2#1173108711yescharacteristic
709C2D7×#38011yescharacteristic
710C2#1173144811yescharacteristic
711C2#1173160311yescharacteristic
712C2#1173176811yescharacteristic
713C2#1173350411yescharacteristic
714C2#1173350511yescharacteristic
715C2#1173351611yescharacteristic
716C2#1173352211yescharacteristic
717C2#1173379111yescharacteristic
718C2#1173379811yescharacteristic
719C2#1173399011yescharacteristic
720C2#1173399311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4⋊#95D7
hypocenterC7#13926
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
28. C2×C4×Dic14C4semidirect
65. C2×C7×C4⋊C4Q8semidirect
77. C2×C4⋊Dic7Q8semidirect
204. C2×Dic14C4⋊C4semidirect
385. C2×C4⋊C4Dic14semidirect
446. C4×C7#391semidirect
659. C7#13926semidirect
705. C4#89418semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic142
C2×#897482
C2×C4⋊C4×Dic72
C2×#894182
C7×C4⋊#952
#117293172
#117292892
#117271652
#117271632
Dic7⋊#952
#139267