Finite Group Databasebeta

← #13277185

Subgroups — #13277185

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×Q8×Dic7C211yesmaximal, characteristic
2C2×C7×#391C211yesmaximal, characteristic
3C2×#90002C211yesmaximal, characteristic
4C2×#89700C211yesmaximal, characteristic
5C2×C4×Dic7⋊C4C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7#11729317C211yesmaximal, characteristic
8#11727174C212yesmaximal
9#11727169C212yesmaximal
10#11727160C212yesmaximal
11#11727160C212yesmaximal
12C23×C7×Q8C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C2×Q8×Dic7—24no—
16C2×Q8×Dic7—24no—
17C2×Q8×Dic7—24no—
18C22×C4⋊Dic7C2212yes—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2212yes—
23C22×Dic7⋊C4C2211yescharacteristic
24C22×C4×Dic7C2212yes—
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C7×#391—24no—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30#90002C418yescomplemented
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C4×Dic7⋊C4—24no—
41#89700—24no—
42#14017—71nomaximal, Sylow
43C22×C7×Q8—22no—
44C22×C7×Q8—22no—
45C22×C7×Q8—22no—
46C22×C7×Q8—22no—
47C22×C7×Q8C2×C414yes—
48C22×C7×Q8D414yes—
49C22×C7×Q8Q814yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×Dic7C2311yescharacteristic
56C23×Dic7C2312yes—
57C23×Dic7C2312yes—
58C23×Dic7C2311yescharacteristic
59C23×Dic7C2311yescharacteristic
60C23×Dic7C2311yescharacteristic
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C42×C7—22no—
65C2×C42×C7—22no—
66C2×C42×C7—22no—
67Q8×Dic7—232no—
68C2×C4⋊Dic7—22no—
69C2×C4⋊Dic7—24no—
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7—22no—
72C2×C4⋊Dic7—22no—
73C2×C4⋊Dic7—24no—
74C2×C4⋊Dic7—24no—
75C2×C4⋊Dic7C2×C414yes—
76C2×C4⋊Dic7D414yes—
77C2×Dic7⋊C4—22no—
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—42no—
85C2×Dic7⋊C4Q814yescomplemented
86C2×C4×Dic7—22no—
87C2×C4×Dic7—24no—
88C2×C4×Dic7—22no—
89C2×C4×Dic7—22no—
90C2×C4×Dic7—22no—
91C2×C4×Dic7—24no—
92C2×C4×Dic7—24no—
93C2×C4×Dic7C2×C414yes—
94C2×C4×Dic7D414yes—
95C7×#95—24no—
96C7×#95—24no—
97C7⋊#95—24no—
98C7⋊#95—22no—
99C7⋊#95—22no—
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×#391D711yescharacteristic
109C2×#389—71no—
110C2×C4×C4⋊C4—71no—
111#1444—72no—
112#1442—72no—
113#1436—72no—
114#1436—72no—
115C4⋊#95—71no—
116C4⋊#95—71no—
117C24×C7C2411yescharacteristic
118C2×C7×Q8—28no—
119C2×C7×Q8—28no—
120C2×C7×Q8—28no—
121C2×C7×Q8—28no—
122C2×C7×Q8—28no—
123C2×C7×Q8—28no—
124C2×C7×Q8C4⋊C4116yescomplemented
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
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—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7C22×C414yes—
149C22×C4×C7C22×C412yes—
150C22×C4×C7C2×D414yes—
151C22×C4×C7C2×D412yes—
152C22×C4×C7C2×D412yes—
153C22×C4×C7C2×D412yes—
154C22×C4×C7C2×Q812yes—
155C22×C4×C7C2×Q814yes—
156C22×C4×C7C2×Q812yes—
157C22×C4×C7#4112yes—
158C22×C4×C7#4112yes—
159C22×C4×C7#4112yes—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—22no—
170C22×Dic7—22no—
171C22×Dic7—21no—
172C22×Dic7—22no—
173C22×Dic7—21no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—21no—
177C22×Dic7—22no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—22no—
190C22×Dic7—21no—
191C22×Dic7—22no—
192C22×Dic7C22×C412yes—
193C22×Dic7C22×C414yes—
194C22×Dic7C22×C412yes—
195C22×Dic7C2×D414yes—
196C22×Dic7C2×D412yes—
197C22×Dic7C2×D412yes—
198C22×Dic7C2×Q812yes—
199C22×Dic7C2×Q812yes—
200C22×Dic7#4112yes—
201C22×Dic7#4112yes—
202C7×C4⋊C4—44no—
203C42×C7—44no—
204C4⋊Dic7—216no—
205C4⋊Dic7—28no—
206C4⋊Dic7—28no—
207Dic7⋊C4—28no—
208Dic7⋊C4—28no—
209Dic7⋊C4—48no—
210C4×Dic7—216no—
211C4×Dic7—28no—
212C4×Dic7—28no—
213C23×Q8C2×D711yescharacteristic
214C2×C4×Q8—144no—
215C2×C4×Q8—144no—
216C2×C4×Q8—144no—
217C22×C4⋊C4—71no—
218C22×C4⋊C4—71no—
219C22×C4⋊C4—71no—
220C22×C4⋊C4—72no—
221C22×C4⋊C4—71no—
222C22×C4⋊C4—72no—
223C22×C4⋊C4C2×D711yescharacteristic
224C22×C42—71no—
225C22×C42—71no—
226C22×C42—72no—
227C22×C42C2×D711yescharacteristic
228#391—24no—
229#391—78no—
230#389—144no—
231C4×C4⋊C4—144no—
232C2×#95—72no—
233C2×#95—72no—
234C2×#95—72no—
235C2×#95—72no—
236C2×#95—71no—
237C2×#95—72no—
238C2×#95—71no—
239C2×#95—72no—
240C2×#95—72no—
241C2×#95C2×D712yes—
242C2×#95C2×D712yes—
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
258C7×Q8—232no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—24no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
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—41no—
272C2×C4×C7—41no—
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—42no—
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×C7C2×C4⋊C418yes—
287C2×C4×C7C2×C4⋊C414yes—
288C2×C4×C7C4×D414yes—
289C2×C4×C7C4×D414yes—
290C2×C4×C7#12014yes—
291C2×C4×C7C22⋊Q814yes—
292C2×C4×C7C22⋊Q814yes—
293C2×C4×C7#12314yes—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—22no—
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—24no—
308C2×Dic7—24no—
309C2×Dic7—22no—
310C2×Dic7—22no—
311C2×Dic7—24no—
312C2×Dic7—24no—
313C2×Dic7—22no—
314C2×Dic7—22no—
315C2×Dic7—22no—
316C2×Dic7—24no—
317C2×Dic7—24no—
318C2×Dic7—42no—
319C2×Dic7—41no—
320C2×Dic7—41no—
321C2×Dic7—42no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—42no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328C2×Dic7—42no—
329C2×Dic7—42no—
330C2×Dic7—42no—
331C2×Dic7—41no—
332C2×Dic7—42no—
333C2×Dic7—42no—
334C2×Dic7C4×Q814yescomplemented
335C2×Dic7C22⋊Q814yes—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8Dic1414yes—
341C22×Q8C4×D714yes—
342C22×Q8C22⋊D714yes—
343C23×C4—71no—
344C23×C4—71no—
345C23×C4—71no—
346C23×C4—72no—
347C23×C4—72no—
348C23×C4—71no—
349C23×C4C22×D712yes—
350C23×C4C22×D711yescharacteristic
351C23×C4C22×D711yescharacteristic
352C23×C4C22×D712yes—
353C23×C4C22×D711yescharacteristic
354C4×Q8—1432no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—74no—
359C2×C4⋊C4—74no—
360C2×C4⋊C4—74no—
361C2×C4⋊C4—144no—
362C2×C4⋊C4—144no—
363C2×C4⋊C4—142no—
364C2×C4⋊C4—142no—
365C2×C4⋊C4—142no—
366C2×C4⋊C4—142no—
367C2×C4⋊C4—142no—
368C2×C4⋊C4—142no—
369C2×C4⋊C4—142no—
370C2×C4⋊C4—142no—
371C2×C4⋊C4—144no—
372C2×C4⋊C4—142no—
373C2×C4⋊C4—144no—
374C2×C4⋊C4—144no—
375C2×C4⋊C4—282no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—74no—
380C2×C42—74no—
381C2×C42—144no—
382C2×C42—144no—
383C2×C42—142no—
384C2×C42—142no—
385C2×C42—142no—
386C2×C42—144no—
387C2×C42—142no—
388#95—24no—
389#95—24no—
390#95—78no—
391#95—78no—
392#95—144no—
393#95—144no—
394#95—142no—
395#95—142no—
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—28no—
435C4×C7—42no—
436C4×C7—42no—
437C4×C7—82no—
438C4×C7#38518yes—
439Dic7—24no—
440Dic7—24no—
441Dic7—42no—
442Dic7—44no—
443Dic7—42no—
444Dic7—44no—
445C24C23×D711yescharacteristic
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—28no—
452C2×Q8Dic7⋊C4116yescomplemented
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
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—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—72no—
477C22×C4—72no—
478C22×C4—72no—
479C22×C4—72no—
480C22×C4—72no—
481C22×C4—72no—
482C22×C4—72no—
483C22×C4—74no—
484C22×C4—72no—
485C22×C4—74no—
486C22×C4—141no—
487C22×C4—141no—
488C22×C4—141no—
489C22×C4—141no—
490C22×C4—141no—
491C22×C4—141no—
492C22×C4—141no—
493C22×C4—141no—
494C22×C4—141no—
495C22×C4—142no—
496C22×C4—142no—
497C22×C4—141no—
498C22×C4—141no—
499C22×C4—142no—
500C22×C4—142no—
501C22×C4—141no—
502C22×C4—142no—
503C22×C4—141no—
504C22×C4—141no—
505C22×C4—142no—
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—142no—
515C22×C4—141no—
516C22×C4—142no—
517C22×C4—141no—
518C22×C4C2×Dic1414yes—
519C22×C4C2×Dic1412yes—
520C22×C4C2×C4×D714yes—
521C22×C4C2×C4×D712yes—
522C22×C4D4×D712yes—
523C22×C4D4×D712yes—
524C22×C4#115912yes—
525C22×C4#115912yes—
526C22×C4Q8×D712yes—
527C22×C4#116112yes—
528C22×C4C2×C22⋊D714yes—
529C22×C4C2×C22⋊D712yes—
530C4⋊C4—44no—
531C4⋊C4—148no—
532C4⋊C4—148no—
533C4⋊C4—1416no—
534C4⋊C4—148no—
535C4⋊C4—148no—
536C4⋊C4—288no—
537C42—44no—
538C42—1416no—
539C42—148no—
540C42—148no—
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×D4×D711yescharacteristic
559C23C2×D4×D711yescharacteristic
560C23C2×#115911yescharacteristic
561C23C2×#115911yescharacteristic
562C23C2×Q8×D711yescharacteristic
563C23C2×#116111yescharacteristic
564C23#655111yescharacteristic
565C23#655111yescharacteristic
566C23D7×#4111yescharacteristic
567C23D7×#4111yescharacteristic
568C23#655311yescharacteristic
569C23#655411yescharacteristic
570C23C22×C22⋊D711yescharacteristic
571Q8—232no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—74no—
600C2×C4—74no—
601C2×C4—142no—
602C2×C4—142no—
603C2×C4—142no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—142no—
607C2×C4—142no—
608C2×C4—142no—
609C2×C4—142no—
610C2×C4—142no—
611C2×C4—142no—
612C2×C4—142no—
613C2×C4—142no—
614C2×C4—144no—
615C2×C4—144no—
616C2×C4—142no—
617C2×C4—142no—
618C2×C4—144no—
619C2×C4—142no—
620C2×C4—144no—
621C2×C4—142no—
622C2×C4—142no—
623C2×C4—144no—
624C2×C4—144no—
625C2×C4—282no—
626C2×C4—281no—
627C2×C4—281no—
628C2×C4—282no—
629C2×C4—281no—
630C2×C4—282no—
631C2×C4—282no—
632C2×C4—281no—
633C2×C4—282no—
634C2×C4—281no—
635C2×C4—281no—
636C2×C4—282no—
637C2×C4—282no—
638C2×C4—281no—
639C2×C4—281no—
640C2×C4—282no—
641C2×C4#644114yes—
642C2×C4#644114yes—
643C2×C4(C22⋊D7)⋊C414yes—
644C2×C4(C22⋊D7)⋊C414yes—
645C2×C4C2×Dic7⋊C418yes—
646C2×C4C2×Dic7⋊C414yes—
647C2×C4#649814yes—
648C2×C4#650014yes—
649C7#1401711yescharacteristic, complemented, Sylow
650C22C2×#644111yescharacteristic
651C22C2×#644111yescharacteristic
652C22C2×(C22⋊D7)⋊C411yescharacteristic
653C22C2×(C22⋊D7)⋊C411yescharacteristic
654C22Q8×Dic1411yescharacteristic
655C22#9026011yescharacteristic
656C22#9026011yescharacteristic
657C22#9026111yescharacteristic
658C22C4×Q8×D711yescharacteristic
659C22#9026311yescharacteristic
660C22C4×#116111yescharacteristic
661C22#9026511yescharacteristic
662C22D7×C22⋊Q811yescharacteristic
663C22#9031811yescharacteristic
664C22#9031911yescharacteristic
665C22#9032011yescharacteristic
666C22#9032111yescharacteristic
667C22#9032211yescharacteristic
668C22#9032311yescharacteristic
669C22#9032411yescharacteristic
670C22#9036211yescharacteristic
671C22#9037111yescharacteristic
672C22#9037211yescharacteristic
673C22#9037311yescharacteristic
674C22#9041211yescharacteristic
675C22#9041911yescharacteristic
676C22#9042211yescharacteristic
677C22#9042311yescharacteristic
678C22C22×Dic7⋊C411yescharacteristic
679C22C2×#649811yescharacteristic
680C22C2×#650011yescharacteristic
681C22Q8×C22⋊D711yescharacteristic
682C22#9050811yescharacteristic
683C22#9052211yescharacteristic
684C22#9052511yescharacteristic
685C4—28no—
686C4—42no—
687C4—42no—
688C4—82no—
689C4—144no—
690C4—144no—
691C4—282no—
692C4—282no—
693C4—284no—
694C4—284no—
695C4#8971818yes—
696C2#1173392411yescharacteristic
697C2#1173393711yescharacteristic
698C2#1173393811yescharacteristic
699C2#1173395311yescharacteristic
700C2#1173395611yescharacteristic
701C2#1173399211yescharacteristic
702C2#1173399311yescharacteristic
703C2#1173405611yescharacteristic
704C2C2×#8971811yescharacteristic
705C2Q8×Dic7⋊C411yescharacteristic
706C2#1173990611yescharacteristic
707C2#1174019611yescharacteristic
708C2#1174025711yescharacteristic
709C2#1174040811yescharacteristic
710C2#1174067911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#391C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#391D7
hypocenterC7#14017
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
30. #90002C4semidirect
85. C2×Dic7⋊C4Q8semidirect
124. C2×C7×Q8C4⋊C4semidirect
334. C2×Dic7C4×Q8semidirect
452. C2×Q8Dic7⋊C4semidirect
649. C7#14017semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic72
C2×C7×#3912
C2×#900022
C2×#897002
C2×C4×Dic7⋊C42
#117293172
#117271742
#117271692
#117271602
#140177