Finite Group Databasebeta

← #13277182

Subgroups — #13277182

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic14C211yesmaximal, characteristic
2C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
3C2×#89701C211yesmaximal, characteristic
4C2×#89701C211yesmaximal, characteristic
5C2×#89700C211yesmaximal, characteristic
6#11729322C212yesmaximal
7#11729318C212yesmaximal
8#11729289C211yesmaximal, characteristic
9#11729289C211yesmaximal, characteristic
10#11727168C212yesmaximal
11#11727160C212yesmaximal
12C23×Dic14C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2212yes—
22C22×Dic7⋊C4C2212yes—
23C22×C4×Dic7C2212yes—
24C2×C4×Dic14—24no—
25C2×C4×Dic14—24no—
26C2×C4×Dic14—24no—
27C4×C7×C4⋊C4—24no—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39#89701—24no—
40#89701C418yescomplemented
41#89700—24no—
42#14017—71nomaximal, Sylow
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×Dic7C2312yes—
51C23×Dic7C2312yes—
52C23×Dic7C2312yes—
53C23×Dic7C2312yes—
54C22×Dic14—22no—
55C22×Dic14—22no—
56C22×Dic14—22no—
57C22×Dic14—22no—
58C22×Dic14C2×C414yes—
59C22×Dic14D414yes—
60C22×Dic14Q814yes—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4Q814yescomplemented
67C2×C42×C7—22no—
68C2×C42×C7—22no—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×C42×C7—22no—
73C2×C42×C7—22no—
74C2×C42×C7C2×C414yes—
75C2×C42×C7D414yes—
76C2×C4⋊Dic7—22no—
77C2×C4⋊Dic7—22no—
78C2×C4⋊Dic7—22no—
79C2×C4⋊Dic7—22no—
80C2×C4⋊Dic7—22no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7C2×C414yes—
84C2×C4⋊Dic7D414yes—
85C2×Dic7⋊C4—24no—
86C2×Dic7⋊C4—24no—
87C2×Dic7⋊C4—24no—
88C2×Dic7⋊C4—24no—
89C2×Dic7⋊C4—24no—
90C2×Dic7⋊C4—42no—
91C2×C4×Dic7—24no—
92C2×C4×Dic7—24no—
93C2×C4×Dic7—24no—
94C4×Dic14—232no—
95C7×#95—22no—
96C7×#95—22no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—24no—
102C7⋊#95—42no—
103C7⋊#95—42no—
104C7⋊#95C2×C418yes—
105C7⋊#95C2×C418yes—
106C22×C4×Q8—71no—
107C2×#391—71no—
108C2×#391—71no—
109C2×#389—71no—
110C2×C4×C4⋊C4D711yescharacteristic
111#1444—72no—
112#1442—72no—
113#1436—72no—
114#1436—72no—
115C4⋊#95—71no—
116C4⋊#95—71no—
117C24×C7C2411yescharacteristic
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
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—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7C22×C412yes—
151C22×C4×C7C22×C412yes—
152C22×C4×C7C22×C412yes—
153C22×C4×C7C2×D412yes—
154C22×C4×C7C2×D412yes—
155C22×C4×C7C2×D412yes—
156C22×C4×C7C2×D412yes—
157C22×C4×C7C2×D412yes—
158C22×C4×C7C2×Q812yes—
159C22×C4×C7C2×Q812yes—
160C22×C4×C7C2×Q812yes—
161C22×C4×C7C2×Q812yes—
162C22×C4×C7#4112yes—
163C22×C4×C7#4112yes—
164C22×C4×C7#4112yes—
165C22×C4×C7#4112yes—
166C22×C4×C7#4112yes—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
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×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7C22×C414yes—
191C22×Dic7C22×C414yes—
192C22×Dic7C2×D414yes—
193C22×Dic7C2×D414yes—
194C22×Dic7C2×Q814yes—
195C2×Dic14—28no—
196C2×Dic14—28no—
197C2×Dic14—28no—
198C2×Dic14—28no—
199C2×Dic14—28no—
200C2×Dic14—28no—
201C2×Dic14C4⋊C4116yescomplemented
202C7×C4⋊C4—28no—
203C7×C4⋊C4—28no—
204C42×C7—28no—
205C42×C7—28no—
206C42×C7—44no—
207C4⋊Dic7—28no—
208C4⋊Dic7—28no—
209C4⋊Dic7—44no—
210Dic7⋊C4—216no—
211Dic7⋊C4—48no—
212C4×Dic7—216no—
213C23×Q8—71no—
214C2×C4×Q8—144no—
215C2×C4×Q8—144no—
216C2×C4×Q8—144no—
217C22×C4⋊C4—71no—
218C22×C4⋊C4—71no—
219C22×C4⋊C4—72no—
220C22×C4⋊C4—71no—
221C22×C4⋊C4—72no—
222C22×C4⋊C4C2×D711yescharacteristic
223C22×C4⋊C4C2×D711yescharacteristic
224C22×C42—72no—
225C22×C42C2×D711yescharacteristic
226C22×C42C2×D711yescharacteristic
227C22×C42C2×D711yescharacteristic
228#391—78no—
229#391—144no—
230#389—144no—
231C4×C4⋊C4—24no—
232C2×#95—72no—
233C2×#95—72no—
234C2×#95—72no—
235C2×#95—72no—
236C2×#95—72no—
237C2×#95—72no—
238C2×#95—72no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95C2×D711yescharacteristic
242C2×#95C2×D711yescharacteristic
243C23×C7C23×C411yescharacteristic
244C23×C7C22×D411yescharacteristic
245C23×C7C22×D411yescharacteristic
246C23×C7C22×D411yescharacteristic
247C23×C7C22×Q811yescharacteristic
248C23×C7C22×Q811yescharacteristic
249C23×C7C2×#4111yescharacteristic
250C23×C7C2×#4111yescharacteristic
251C23×C7C2×#4111yescharacteristic
252C23×C7C2×#4111yescharacteristic
253C23×C7C2×#4111yescharacteristic
254C23×C7H(5,𝔽2)11yescharacteristic
255C23×C72−1+411yescharacteristic
256C23×C72−1+411yescharacteristic
257C23×C72−1+411yescharacteristic
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
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—22no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—22no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—41no—
298C2×C4×C7C2×C4⋊C414yes—
299C2×C4×C7C4×D414yes—
300C2×C4×C7C4×D414yes—
301C2×C4×C7C4×Q814yescomplemented
302C2×C4×C7#12014yes—
303C2×C4×C7C22⋊Q814yes—
304C2×C4×C7C22⋊Q814yes—
305C2×C4×C7C22⋊Q814yes—
306C2×C4×C7#12314yes—
307C2×Dic7—24no—
308C2×Dic7—24no—
309C2×Dic7—24no—
310C2×Dic7—24no—
311C2×Dic7—24no—
312C2×Dic7—24no—
313C2×Dic7—24no—
314C2×Dic7—24no—
315C2×Dic7—24no—
316C2×Dic7—24no—
317C2×Dic7—24no—
318C2×Dic7—24no—
319C2×Dic7—42no—
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×Dic7—42no—
331C2×Dic7—42no—
332C2×Dic7—42no—
333C2×Dic7—42no—
334C2×Dic7C2×C4⋊C418yes—
335Dic14—232no—
336C22×Q8—74no—
337C22×Q8—74no—
338C22×Q8—74no—
339C22×Q8—142no—
340C22×Q8—142no—
341C22×Q8—142no—
342C22×Q8—142no—
343C23×C4—72no—
344C23×C4—72no—
345C23×C4—72no—
346C23×C4—72no—
347C23×C4C22×D711yescharacteristic
348C23×C4C22×D711yescharacteristic
349C23×C4C22×D711yescharacteristic
350C23×C4C22×D711yescharacteristic
351C23×C4C22×D711yescharacteristic
352C23×C4C22×D711yescharacteristic
353C23×C4C22×D711yescharacteristic
354C4×Q8—1432no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—74no—
361C2×C4⋊C4—74no—
362C2×C4⋊C4—144no—
363C2×C4⋊C4—144no—
364C2×C4⋊C4—142no—
365C2×C4⋊C4—142no—
366C2×C4⋊C4—142no—
367C2×C4⋊C4—144no—
368C2×C4⋊C4—142no—
369C2×C4⋊C4—144no—
370C2×C4⋊C4—144no—
371C2×C4⋊C4—142no—
372C2×C4⋊C4—142no—
373C2×C4⋊C4—142no—
374C2×C4⋊C4—282no—
375C2×C4⋊C4Dic1414yescomplemented
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—144no—
384C2×C42—144no—
385C2×C42—144no—
386C2×C42C4×D714yes—
387C2×C42C22⋊D714yes—
388#95—22no—
389#95—22no—
390#95—78no—
391#95—78no—
392#95—144no—
393#95—144no—
394#95—144no—
395#95—144no—
396#95—144no—
397#95—282no—
398#95—282no—
399C22×C7C22×C4⋊C411yescharacteristic
400C22×C7C2×C4×D411yescharacteristic
401C22×C7C2×C4×D411yescharacteristic
402C22×C7C2×C4×Q811yescharacteristic
403C22×C7C4×#4111yescharacteristic
404C22×C7#51911yescharacteristic
405C22×C7#52011yescharacteristic
406C22×C7C2×#12011yescharacteristic
407C22×C7C2×C22⋊Q811yescharacteristic
408C22×C7C2×C22⋊Q811yescharacteristic
409C22×C7C2×C22⋊Q811yescharacteristic
410C22×C7C2×#12311yescharacteristic
411C22×C7#52511yescharacteristic
412C22×C7#52911yescharacteristic
413C22×C7#53311yescharacteristic
414C22×C7#53611yescharacteristic
415C22×C7#53711yescharacteristic
416C22×C7#54111yescharacteristic
417C22×C7#54211yescharacteristic
418C22×C7#54611yescharacteristic
419C22×C7#54711yescharacteristic
420C22×C7#54811yescharacteristic
421C22×C7#54811yescharacteristic
422C22×C7#54811yescharacteristic
423C22×C7D4×Q811yescharacteristic
424C22×C7D4×Q811yescharacteristic
425C22×C7#55011yescharacteristic
426C22×C7#55611yescharacteristic
427C22×C7#55611yescharacteristic
428C22×C7#55711yescharacteristic
429C22×C7#55711yescharacteristic
430C22×C7#55711yescharacteristic
431C22×C7#55711yescharacteristic
432C22×C7Q8211yescharacteristic
433C22×C7#55911yescharacteristic
434C4×C7—24no—
435C4×C7—24no—
436C4×C7—42no—
437C4×C7—42no—
438C4×C7—42no—
439C4×C7—42no—
440C4×C7#38518yes—
441Dic7—28no—
442Dic7—44no—
443Dic7—44no—
444Dic7—82no—
445C24C23×D711yescharacteristic
446C2×Q8—716no—
447C2×Q8—148no—
448C2×Q8—148no—
449C2×Q8—148no—
450C2×Q8—148no—
451C2×Q8—148no—
452C2×Q8—148no—
453C22×C4—21no—
454C22×C4—21no—
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—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—74no—
486C22×C4—74no—
487C22×C4—74no—
488C22×C4—74no—
489C22×C4—74no—
490C22×C4—142no—
491C22×C4—142no—
492C22×C4—142no—
493C22×C4—142no—
494C22×C4—142no—
495C22×C4—142no—
496C22×C4—142no—
497C22×C4—142no—
498C22×C4—142no—
499C22×C4—142no—
500C22×C4—142no—
501C22×C4—142no—
502C22×C4—142no—
503C22×C4—142no—
504C22×C4—142no—
505C22×C4—142no—
506C22×C4—142no—
507C22×C4—142no—
508C22×C4—142no—
509C22×C4—142no—
510C22×C4—142no—
511C22×C4—142no—
512C22×C4—142no—
513C22×C4C2×Dic1412yes—
514C22×C4C2×Dic1412yes—
515C22×C4C2×Dic1412yes—
516C22×C4C2×C4×D712yes—
517C22×C4C2×C4×D712yes—
518C22×C4C2×C4×D712yes—
519C22×C4#115712yes—
520C22×C4#115712yes—
521C22×C4#115712yes—
522C22×C4#115712yes—
523C22×C4D4×D712yes—
524C22×C4D4×D712yes—
525C22×C4Q8×D712yes—
526C22×C4#116112yes—
527C22×C4C2×C22⋊D712yes—
528C22×C4C2×C22⋊D712yes—
529C22×C4C2×C22⋊D712yes—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—1416no—
533C4⋊C4—148no—
534C4⋊C4—148no—
535C4⋊C4—288no—
536C4⋊C4—284no—
537C42—28no—
538C42—28no—
539C42—44no—
540C42—1416no—
541C2×C7C2×#38511yescharacteristic
542C2×C7C4×C22⋊Q811yescharacteristic
543C2×C7#232311yescharacteristic
544C2×C7Q8×C4⋊C411yescharacteristic
545C2×C7#235111yescharacteristic
546C2×C7#236511yescharacteristic
547C2×C7#236711yescharacteristic
548C2×C7#240711yescharacteristic
549C2×C7#240911yescharacteristic
550C2×C7#244611yescharacteristic
551C2×C7#244811yescharacteristic
552C2×C7#245111yescharacteristic
553C2×C7#245311yescharacteristic
554C2×C7#258111yescharacteristic
555C2×C7#258211yescharacteristic
556C23C22×Dic1411yescharacteristic
557C23C22×C4×D711yescharacteristic
558C23C2×#115711yescharacteristic
559C23C2×#115711yescharacteristic
560C23C2×#115711yescharacteristic
561C23C2×#115711yescharacteristic
562C23C2×D4×D711yescharacteristic
563C23C2×D4×D711yescharacteristic
564C23C2×Q8×D711yescharacteristic
565C23C2×#116111yescharacteristic
566C23#655311yescharacteristic
567C23#655411yescharacteristic
568C23#655411yescharacteristic
569C23#655411yescharacteristic
570C23C22×C22⋊D711yescharacteristic
571Q8—1432no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—78no—
613C2×C4—144no—
614C2×C4—144no—
615C2×C4—144no—
616C2×C4—144no—
617C2×C4—144no—
618C2×C4—144no—
619C2×C4—144no—
620C2×C4—144no—
621C2×C4—144no—
622C2×C4—144no—
623C2×C4—144no—
624C2×C4—144no—
625C2×C4—282no—
626C2×C4—282no—
627C2×C4—282no—
628C2×C4—282no—
629C2×C4—282no—
630C2×C4—282no—
631C2×C4—282no—
632C2×C4—282no—
633C2×C4—282no—
634C2×C4—282no—
635C2×C4—282no—
636C2×C4—282no—
637C2×C4—282no—
638C2×C4—282no—
639C2×C4—282no—
640C2×C4C4×Dic1414yescomplemented
641C2×C4D7×C4⋊C414yes—
642C2×C4#645614yes—
643C2×C4#645714yes—
644C2×C4#645914yes—
645C2×C4#648714yes—
646C2×C4C4×C22⋊D714yes—
647C2×C4#650014yes—
648C2×C4#650914yes—
649C7#1401711yescharacteristic, complemented, Sylow
650C22C2×C4×Dic1411yescharacteristic
651C22#9016111yescharacteristic
652C22C4×#115711yescharacteristic
653C22#9017011yescharacteristic
654C22C2×D7×C4⋊C411yescharacteristic
655C22C2×#645611yescharacteristic
656C22C2×#645711yescharacteristic
657C22C2×#645911yescharacteristic
658C22#9020711yescharacteristic
659C22#9020911yescharacteristic
660C22#9021411yescharacteristic
661C22#9022511yescharacteristic
662C22D4×Dic1411yescharacteristic
663C22D4×Dic1411yescharacteristic
664C22#9024111yescharacteristic
665C22#9024211yescharacteristic
666C22#9024311yescharacteristic
667C22#9024311yescharacteristic
668C22#9024311yescharacteristic
669C22#9024411yescharacteristic
670C22Q8×Dic1411yescharacteristic
671C22#9025811yescharacteristic
672C22#9025811yescharacteristic
673C22#9025811yescharacteristic
674C22#9026111yescharacteristic
675C22#9027511yescharacteristic
676C22#9027511yescharacteristic
677C22#9027611yescharacteristic
678C22C2×#648711yescharacteristic
679C22C2×C4×C22⋊D711yescharacteristic
680C22#9048211yescharacteristic
681C22C2×#650011yescharacteristic
682C22C2×#650911yescharacteristic
683C22#9051611yescharacteristic
684C22#9052411yescharacteristic
685C4—24no—
686C4—24no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—148no—
692C4—284no—
693C4—284no—
694C4—562no—
695C4#8976118yes—
696C2C4⋊C4×Dic1411yescharacteristic
697C2#1173108211yescharacteristic
698C2#1173109611yescharacteristic
699C2#1173110011yescharacteristic
700C2#1173111711yescharacteristic
701C2#1173111811yescharacteristic
702C2#1173111911yescharacteristic
703C2#1173112111yescharacteristic
704C2C4×#648711yescharacteristic
705C2C2×#8976111yescharacteristic
706C2#1173968011yescharacteristic
707C2#1173979411yescharacteristic
708C2#1173984711yescharacteristic
709C2#1173992511yescharacteristic
710C2#1173992711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#14017
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
40. #89701C4semidirect
66. C2×C7×C4⋊C4Q8semidirect
201. C2×Dic14C4⋊C4semidirect
301. C2×C4×C7C4×Q8semidirect
375. C2×C4⋊C4Dic14semidirect
640. C2×C4C4×Dic14semidirect
649. C7#14017semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic142
C2×C4×C7×C4⋊C42
C2×#897012
C2×#897002
#117293222
#117293182
#117292892
#117271682
#117271602
#140177