Finite Group Databasebeta

← #13276298

Subgroups — #13276298

Order 1792.

1794 conjugacy classes of subgroups.

The subgroup lattice has 706 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×#89745C211yesmaximal, characteristic
5C2×#89700C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7C4×C7⋊#95C211yesmaximal, characteristic
8#11727165C212yesmaximal
9#11727165C212yesmaximal
10Dic7⋊#95C212yesmaximal
11#11727157C212yesmaximal
12C23×C7×Q8C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C2×Q8×Dic7—24no—
16C2×Q8×Dic7—24no—
17C2×Q8×Dic7C418yescomplemented
18C22×C4⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2212yes—
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4C2212yes—
22C22×Dic7⋊C4C2212yes—
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2212yes—
25C22×C4×Dic7C2211yescharacteristic
26C7×#391—24no—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29#90002—24no—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2211yescharacteristic
40#89745—24no—
41#89700—24no—
42#13935—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×Dic7C2312yes—
56C23×Dic7C2311yescharacteristic
57C23×Dic7C2311yescharacteristic
58C23×Dic7C2311yescharacteristic
59C23×Dic7C2312yes—
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—24no—
69C2×C4⋊Dic7—24no—
70C2×C4⋊Dic7—22no—
71C2×C4⋊Dic7—22no—
72C2×C4⋊Dic7—22no—
73C2×C4⋊Dic7C2×C418yes—
74C2×C4⋊Dic7C2×C414yes—
75C2×C4⋊Dic7D414yes—
76C2×C4⋊Dic7D414yes—
77C2×Dic7⋊C4—24no—
78C2×Dic7⋊C4—24no—
79C2×Dic7⋊C4—24no—
80C2×Dic7⋊C4—24no—
81C2×Dic7⋊C4—42no—
82C2×Dic7⋊C4—42no—
83C2×C4×Dic7—22no—
84C2×C4×Dic7—22no—
85C2×C4×Dic7—24no—
86C2×C4×Dic7—24no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—22no—
89C2×C4×Dic7—22no—
90C2×C4×Dic7C2×C414yes—
91C2×C4×Dic7C2×C418yes—
92C7×#95—24no—
93C7×#95—24no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—22no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—22no—
100C7⋊#95—22no—
101C7⋊#95—24no—
102C7⋊#95—42no—
103C7⋊#95Q814yescomplemented
104C22×C4×Q8—71no—
105C2×#391—71no—
106C2×#391D711yescharacteristic
107C2×#389—71no—
108C2×#389—71no—
109#1441—72no—
110#1441—72no—
111C4⋊#95—72no—
112C4⋊#95—71no—
113#1434—72no—
114C4×#95—71no—
115C24×C7C2411yescharacteristic
116C2×C7×Q8—28no—
117C2×C7×Q8—28no—
118C2×C7×Q8—28no—
119C2×C7×Q8—28no—
120C2×C7×Q8—28no—
121C2×C7×Q8—28no—
122C2×C7×Q8C4⋊C4116yescomplemented
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
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—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7C22×C414yes—
147C22×C4×C7C22×C412yes—
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×C7#4112yes—
156C22×C4×C7#4112yes—
157C22×C4×C7#4112yes—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—22no—
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—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7C22×C412yes—
192C22×Dic7C22×C414yes—
193C22×Dic7C22×C412yes—
194C22×Dic7C2×D414yes—
195C22×Dic7C2×D414yes—
196C22×Dic7C2×Q812yes—
197C22×Dic7C2×Q812yes—
198C22×Dic7#4112yes—
199C22×Dic7#4112yes—
200C7×C4⋊C4—44no—
201C42×C7—44no—
202C4⋊Dic7—216no—
203C4⋊Dic7—44no—
204C4⋊Dic7C22⋊C4116yes—
205Dic7⋊C4—48no—
206Dic7⋊C4—48no—
207C4×Dic7—28no—
208C4×Dic7—216no—
209C4×Dic7—44no—
210C23×Q8C2×D711yescharacteristic
211C2×C4×Q8—78no—
212C2×C4×Q8—144no—
213C2×C4×Q8—144no—
214C22×C4⋊C4—71no—
215C22×C4⋊C4—72no—
216C22×C4⋊C4—71no—
217C22×C4⋊C4—72no—
218C22×C4⋊C4—72no—
219C22×C4⋊C4C2×D711yescharacteristic
220C22×C42—71no—
221C22×C42—72no—
222C22×C42—71no—
223C22×C42C2×D711yescharacteristic
224#391—24no—
225#391—144no—
226#389—144no—
227#389—144no—
228C2×#95—71no—
229C2×#95—71no—
230C2×#95—71no—
231C2×#95—71no—
232C2×#95—72no—
233C2×#95—72no—
234C2×#95—72no—
235C2×#95—72no—
236C2×#95—72no—
237C2×#95—72no—
238C2×#95C2×D712yes—
239C2×#95C2×D712yes—
240C23×C7C23×C411yescharacteristic
241C23×C7C22×D411yescharacteristic
242C23×C7C22×D411yescharacteristic
243C23×C7C22×D411yescharacteristic
244C23×C7C22×Q811yescharacteristic
245C23×C7C22×Q811yescharacteristic
246C23×C7C2×#4111yescharacteristic
247C23×C7C2×#4111yescharacteristic
248C23×C7C2×#4111yescharacteristic
249C23×C7C2×#4111yescharacteristic
250C23×C7C2×#4111yescharacteristic
251C23×C7H(5,𝔽2)11yescharacteristic
252C23×C72−1+411yescharacteristic
253C23×C72−1+411yescharacteristic
254C23×C72−1+411yescharacteristic
255C7×Q8—232no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
261C2×C4×C7—24no—
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—41no—
269C2×C4×C7—41no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7C2×C22⋊C414yes—
284C2×C4×C7C2×C4⋊C418yes—
285C2×C4×C7C2×C4⋊C414yes—
286C2×C4×C7#11714yes—
287C2×C4×C7#12114yes—
288C2×C4×C7#12114yes—
289C2×C4×C7C22⋊Q814yes—
290C2×C4×C7C22⋊Q814yes—
291C2×Dic7—22no—
292C2×Dic7—24no—
293C2×Dic7—22no—
294C2×Dic7—24no—
295C2×Dic7—24no—
296C2×Dic7—24no—
297C2×Dic7—24no—
298C2×Dic7—24no—
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—41no—
313C2×Dic7—41no—
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—41no—
323C2×Dic7—41no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C2×Dic7—42no—
327C2×Dic7—42no—
328C2×Dic7—42no—
329C2×Dic7—42no—
330C2×Dic7—42no—
331C2×Dic7C2×C22⋊C418yes—
332C2×Dic7C4×Q814yes—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8Dic1414yes—
338C22×Q8C4×D714yes—
339C22×Q8C22⋊D714yes—
340C23×C4—72no—
341C23×C4—71no—
342C23×C4—71no—
343C23×C4—71no—
344C23×C4—71no—
345C23×C4—72no—
346C23×C4C22×D712yes—
347C23×C4C22×D711yescharacteristic
348C23×C4C22×D711yescharacteristic
349C23×C4C22×D712yes—
350C23×C4C22×D711yescharacteristic
351C4×Q8—1432no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—74no—
356C2×C4⋊C4—74no—
357C2×C4⋊C4—74no—
358C2×C4⋊C4—78no—
359C2×C4⋊C4—144no—
360C2×C4⋊C4—144no—
361C2×C4⋊C4—144no—
362C2×C4⋊C4—144no—
363C2×C4⋊C4—144no—
364C2×C4⋊C4—142no—
365C2×C4⋊C4—142no—
366C2×C4⋊C4—144no—
367C2×C4⋊C4—142no—
368C2×C4⋊C4—282no—
369C2×C4⋊C4—282no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—78no—
374C2×C42—74no—
375C2×C42—144no—
376C2×C42—144no—
377C2×C42—142no—
378C2×C42—142no—
379C2×C42—142no—
380C2×C42—142no—
381C2×C42—142no—
382#95—24no—
383#95—24no—
384#95—74no—
385#95—142no—
386#95—142no—
387#95—144no—
388#95—144no—
389#95—144no—
390#95—142no—
391#95—144no—
392#95—144no—
393#95—282no—
394C22×C7C22×C22⋊C411yescharacteristic
395C22×C7C22×C4⋊C411yescharacteristic
396C22×C7C2×#11711yescharacteristic
397C22×C7C2×C4×Q811yescharacteristic
398C22×C7C4×#4111yescharacteristic
399C22×C7#51911yescharacteristic
400C22×C7#52011yescharacteristic
401C22×C7C2×#12111yescharacteristic
402C22×C7C2×#12111yescharacteristic
403C22×C7C2×C22⋊Q811yescharacteristic
404C22×C7C2×C22⋊Q811yescharacteristic
405C22×C7#52911yescharacteristic
406C22×C7#52911yescharacteristic
407C22×C7#53311yescharacteristic
408C22×C7#53311yescharacteristic
409C22×C7#54111yescharacteristic
410C22×C7#54111yescharacteristic
411C22×C7#54211yescharacteristic
412C22×C7#54211yescharacteristic
413C22×C7#54611yescharacteristic
414C22×C7#54611yescharacteristic
415C22×C7#54711yescharacteristic
416C22×C7#54711yescharacteristic
417C22×C7#54811yescharacteristic
418C22×C7#54811yescharacteristic
419C22×C7#54811yescharacteristic
420C22×C7#54811yescharacteristic
421C22×C7D4×Q811yescharacteristic
422C22×C7D4×Q811yescharacteristic
423C22×C7D4×Q811yescharacteristic
424C22×C7#55011yescharacteristic
425C22×C7#55711yescharacteristic
426C22×C7#55711yescharacteristic
427C22×C7#55711yescharacteristic
428C22×C7Q8211yescharacteristic
429C4×C7—28no—
430C4×C7—42no—
431C4×C7—42no—
432C4×C7—82no—
433C4×C7#38018yes—
434Dic7—28no—
435Dic7—24no—
436Dic7—42no—
437Dic7—42no—
438Dic7—42no—
439Dic7—82no—
440C24C23×D711yescharacteristic
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8Dic7⋊C4116yescomplemented
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
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—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—72no—
472C22×C4—74no—
473C22×C4—74no—
474C22×C4—74no—
475C22×C4—72no—
476C22×C4—72no—
477C22×C4—72no—
478C22×C4—72no—
479C22×C4—72no—
480C22×C4—141no—
481C22×C4—141no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—141no—
485C22×C4—142no—
486C22×C4—142no—
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—141no—
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—142no—
507C22×C4—142no—
508C22×C4—142no—
509C22×C4—142no—
510C22×C4—142no—
511C22×C4—142no—
512C22×C4—142no—
513C22×C4C2×Dic1414yes—
514C22×C4C2×Dic1412yes—
515C22×C4C2×C4×D714yes—
516C22×C4C2×C4×D712yes—
517C22×C4D4×D712yes—
518C22×C4D4×D712yes—
519C22×C4#115912yes—
520C22×C4#115912yes—
521C22×C4Q8×D712yes—
522C22×C4#116112yes—
523C22×C4C2×C22⋊D714yes—
524C22×C4C2×C22⋊D712yes—
525C4⋊C4—44no—
526C4⋊C4—716no—
527C4⋊C4—1416no—
528C4⋊C4—288no—
529C4⋊C4—288no—
530C4⋊C4—284no—
531C42—44no—
532C42—1416no—
533C42—148no—
534C42—284no—
535C2×C7C2×#38011yescharacteristic
536C2×C7#229511yescharacteristic
537C2×C7#232011yescharacteristic
538C2×C7#233911yescharacteristic
539C2×C7Q8×C22⋊C411yescharacteristic
540C2×C7Q8×C4⋊C411yescharacteristic
541C2×C7#235111yescharacteristic
542C2×C7#242611yescharacteristic
543C2×C7#242611yescharacteristic
544C2×C7#242911yescharacteristic
545C2×C7#242911yescharacteristic
546C2×C7#245111yescharacteristic
547C2×C7#245111yescharacteristic
548C2×C7#245311yescharacteristic
549C2×C7#245311yescharacteristic
550C23C22×Dic1411yescharacteristic
551C23C22×C4×D711yescharacteristic
552C23C2×D4×D711yescharacteristic
553C23C2×D4×D711yescharacteristic
554C23C2×#115911yescharacteristic
555C23C2×#115911yescharacteristic
556C23C2×Q8×D711yescharacteristic
557C23C2×#116111yescharacteristic
558C23#655111yescharacteristic
559C23#655111yescharacteristic
560C23D7×#4111yescharacteristic
561C23D7×#4111yescharacteristic
562C23#655311yescharacteristic
563C23#655411yescharacteristic
564C23C22×C22⋊D711yescharacteristic
565Q8—232no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—78no—
594C2×C4—74no—
595C2×C4—142no—
596C2×C4—144no—
597C2×C4—142no—
598C2×C4—142no—
599C2×C4—142no—
600C2×C4—144no—
601C2×C4—144no—
602C2×C4—144no—
603C2×C4—144no—
604C2×C4—142no—
605C2×C4—142no—
606C2×C4—144no—
607C2×C4—142no—
608C2×C4—142no—
609C2×C4—142no—
610C2×C4—142no—
611C2×C4—142no—
612C2×C4—142no—
613C2×C4—142no—
614C2×C4—142no—
615C2×C4—142no—
616C2×C4—281no—
617C2×C4—281no—
618C2×C4—281no—
619C2×C4—281no—
620C2×C4—281no—
621C2×C4—281no—
622C2×C4—281no—
623C2×C4—281no—
624C2×C4—281no—
625C2×C4—281no—
626C2×C4—281no—
627C2×C4—281no—
628C2×C4—282no—
629C2×C4—282no—
630C2×C4—282no—
631C2×C4—282no—
632C2×C4—282no—
633C2×C4—282no—
634C2×C4—282no—
635C2×C4#644014yes—
636C2×C4#644114yes—
637C2×C4#644114yes—
638C2×C4D7×C22⋊C414yes—
639C2×C4C2×Dic7⋊C418yes—
640C2×C4C2×Dic7⋊C414yes—
641C2×C4#650214yes—
642C2×C4#650214yes—
643C7#1393511yescharacteristic, complemented, Sylow
644C22C2×#644011yescharacteristic
645C22C2×#644111yescharacteristic
646C22C2×#644111yescharacteristic
647C22C2×D7×C22⋊C411yescharacteristic
648C22Q8×Dic1411yescharacteristic
649C22#9026011yescharacteristic
650C22#9026011yescharacteristic
651C22#9026111yescharacteristic
652C22C4×Q8×D711yescharacteristic
653C22#9026311yescharacteristic
654C22C4×#116111yescharacteristic
655C22#9026511yescharacteristic
656C22#9031311yescharacteristic
657C22#9031511yescharacteristic
658C22#9031611yescharacteristic
659C22#9032111yescharacteristic
660C22#9032211yescharacteristic
661C22#9032311yescharacteristic
662C22#9032411yescharacteristic
663C22#9033411yescharacteristic
664C22#9036711yescharacteristic
665C22#9036811yescharacteristic
666C22#9037111yescharacteristic
667C22#9037311yescharacteristic
668C22#9041711yescharacteristic
669C22#9041811yescharacteristic
670C22#9041911yescharacteristic
671C22#9042211yescharacteristic
672C22C22×Dic7⋊C411yescharacteristic
673C22C2×#650211yescharacteristic
674C22C2×#650211yescharacteristic
675C22Q8×C22⋊D711yescharacteristic
676C22#9050811yescharacteristic
677C22#9052211yescharacteristic
678C22#9052511yescharacteristic
679C4—28no—
680C4—42no—
681C4—42no—
682C4—82no—
683C4—148no—
684C4—144no—
685C4—282no—
686C4—282no—
687C4—282no—
688C4—562no—
689C4#8971418yes—
690C2#1173392211yescharacteristic
691C2#1173392811yescharacteristic
692C2#1173395311yescharacteristic
693C2#1173395411yescharacteristic
694C2#1173395611yescharacteristic
695C2#1173395711yescharacteristic
696C2#1173405811yescharacteristic
697C2#1173405911yescharacteristic
698C2C2×#8971411yescharacteristic
699C2Q8×Dic7⋊C411yescharacteristic
700C2#1173990611yescharacteristic
701C2#1174020011yescharacteristic
702C2#1174020311yescharacteristic
703C2#1174044011yescharacteristic
704C2#1174069911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#391C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#391D7
hypocenterC7#13935
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
17. C2×Q8×Dic7C4semidirect
103. C7⋊#95Q8semidirect
122. C2×C7×Q8C4⋊C4semidirect
447. C2×Q8Dic7⋊C4semidirect
643. C7#13935semidirect

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×#897452
C2×#897002
#117293172
C4×C7⋊#952
#117271652
Dic7⋊#952
#117271572
#139357