Finite Group Databasebeta

← #13276299

Subgroups — #13276299

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×#6450C211yesmaximal, characteristic
2C2×C7×#389C211yesmaximal, characteristic
3C2×#89746C211yesmaximal, characteristic
4C2×#89757C211yesmaximal, characteristic
5C2×#89701C211yesmaximal, characteristic
6#11729320C212yesmaximal
7#11729317C212yesmaximal
8#11729317C211yesmaximal, characteristic
9C4×C7⋊#95C211yesmaximal, characteristic
10#11727164C212yesmaximal
11#11727156C212yesmaximal
12C23×Dic14C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C4⋊Dic7C2211yescharacteristic
18C22×C4⋊Dic7C2212yes—
19C22×Dic7⋊C4C2212yes—
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2212yes—
22C22×C4×Dic7C2211yescharacteristic
23C2×#6450—24no—
24C2×#6450—24no—
25C2×#6450C418yescomplemented
26C7×#389—24no—
27C2×C7×#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2211yescharacteristic
39#89757—24no—
40#89746—24no—
41#89701—24no—
42#13935—71nomaximal, Sylow
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2312yes—
47C23×C4×C7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2312yes—
53C23×Dic7C2311yescharacteristic
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—24no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—42no—
67C2×C7×C4⋊C4C2×C414yes—
68C2×C7×C4⋊C4D414yes—
69C2×C7×C4⋊C4D414yes—
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×C42×C7—22no—
73C2×C4⋊Dic7—22no—
74C2×C4⋊Dic7—24no—
75C2×C4⋊Dic7—22no—
76C2×C4⋊Dic7—22no—
77C2×C4⋊Dic7—24no—
78C2×C4⋊Dic7—42no—
79C2×Dic7⋊C4—24no—
80C2×Dic7⋊C4—24no—
81C2×Dic7⋊C4C2×C418yes—
82C2×C4×Dic7—24no—
83C2×C4×Dic7—22no—
84C2×C4×Dic7—24no—
85C2×C4×Dic7—22no—
86C2×C4×Dic7—22no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—22no—
89C2×C4×Dic7C2×C414yes—
90C2×C4×Dic7C2×C418yes—
91#6450—232no—
92C7×#95—24no—
93C7⋊#95—24no—
94C7⋊#95—22no—
95C7⋊#95—24no—
96C7⋊#95—24no—
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×#391—71no—
107C2×#389—71no—
108C2×#389D711yescharacteristic
109#1441—72no—
110#1441—72no—
111C4⋊#95—71no—
112C4⋊#95—72no—
113#1434—72no—
114C4×#95—71no—
115C24×C7C2411yescharacteristic
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
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—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7C22×C414yes—
140C22×C4×C7C22×C412yes—
141C22×C4×C7C2×D414yes—
142C22×C4×C7C2×D414yes—
143C22×C4×C7C2×D412yes—
144C22×C4×C7C2×D412yes—
145C22×C4×C7C2×D412yes—
146C22×C4×C7C2×Q812yes—
147C22×C4×C7C2×Q812yes—
148C22×C4×C7#4112yes—
149C22×C4×C7#4112yes—
150C22×C4×C7#4112yes—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—22no—
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
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—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×D414yes—
188C22×Dic7C2×Q812yes—
189C22×Dic7C2×Q814yes—
190C22×Dic7C2×Q812yes—
191C22×Dic7#4112yes—
192C22×Dic7#4112yes—
193C2×Dic14—28no—
194C2×Dic14—28no—
195C2×Dic14—28no—
196C2×Dic14—28no—
197C2×Dic14—28no—
198C2×Dic14—28no—
199C2×Dic14C4⋊C4116yescomplemented
200C7×C4⋊C4—48no—
201C7×C4⋊C4—44no—
202C7×C4⋊C4C22⋊C4116yes—
203C42×C7—44no—
204C4⋊Dic7—48no—
205C4⋊Dic7—44no—
206Dic7⋊C4—216no—
207C4×Dic7—216no—
208C4×Dic7—28no—
209C4×Dic7—44no—
210C23×Q8—71no—
211C2×C4×Q8—78no—
212C2×C4×Q8—144no—
213C2×C4×Q8—144no—
214C22×C4⋊C4—72no—
215C22×C4⋊C4—71no—
216C22×C4⋊C4—72no—
217C22×C4⋊C4C2×D711yescharacteristic
218C22×C4⋊C4C2×D712yes—
219C22×C4⋊C4C2×D711yescharacteristic
220C22×C42—71no—
221C22×C42—72no—
222C22×C42—71no—
223C22×C42C2×D711yescharacteristic
224#391—144no—
225#391—144no—
226#389—24no—
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×#95—72no—
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
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
259C2×C4×C7—24no—
260C2×C4×C7—24no—
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—41no—
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—42no—
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×C7C2×C22⋊C418yes—
283C2×C4×C7C2×C22⋊C414yes—
284C2×C4×C7C2×C4⋊C414yes—
285C2×C4×C7#11714yes—
286C2×C4×C7#12114yes—
287C2×C4×C7#12114yes—
288C2×C4×C7C22⋊Q814yes—
289C2×C4×C7C22⋊Q814yes—
290C2×Dic7—22no—
291C2×Dic7—24no—
292C2×Dic7—24no—
293C2×Dic7—22no—
294C2×Dic7—24no—
295C2×Dic7—24no—
296C2×Dic7—24no—
297C2×Dic7—24no—
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—41no—
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—42no—
324C2×Dic7—42no—
325C2×Dic7—42no—
326C2×Dic7—42no—
327C2×Dic7—42no—
328C2×Dic7—42no—
329C2×Dic7—42no—
330C2×Dic7C2×C4⋊C418yes—
331C2×Dic7C4×Q814yes—
332Dic14—232no—
333C22×Q8—74no—
334C22×Q8—74no—
335C22×Q8—74no—
336C22×Q8—142no—
337C22×Q8—142no—
338C22×Q8—142no—
339C22×Q8—142no—
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—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—78no—
359C2×C4⋊C4—144no—
360C2×C4⋊C4—144no—
361C2×C4⋊C4—144no—
362C2×C4⋊C4—144no—
363C2×C4⋊C4—142no—
364C2×C4⋊C4—142no—
365C2×C4⋊C4—142no—
366C2×C4⋊C4—282no—
367C2×C4⋊C4C4×D714yes—
368C2×C4⋊C4D2814yes—
369C2×C4⋊C4C22⋊D714yes—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—78no—
374C2×C42—74no—
375C2×C42—144no—
376C2×C42—142no—
377C2×C42—144no—
378C2×C42—142no—
379C2×C42—142no—
380C2×C42—142no—
381C2×C42—142no—
382#95—24no—
383#95—74no—
384#95—142no—
385#95—142no—
386#95—144no—
387#95—144no—
388#95—144no—
389#95—144no—
390#95—144no—
391#95—144no—
392#95—142no—
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—24no—
435Dic7—28no—
436Dic7—42no—
437Dic7—42no—
438Dic7—42no—
439Dic7—82no—
440C24C23×D711yescharacteristic
441C2×Q8—716no—
442C2×Q8—148no—
443C2×Q8—148no—
444C2×Q8—148no—
445C2×Q8—148no—
446C2×Q8—148no—
447C2×Q8—148no—
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—72no—
475C22×C4—74no—
476C22×C4—72no—
477C22×C4—72no—
478C22×C4—72no—
479C22×C4—72no—
480C22×C4—141no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—141no—
485C22×C4—141no—
486C22×C4—141no—
487C22×C4—142no—
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×C4×D714yes—
514C22×C4C2×C4×D712yes—
515C22×C4C2×D2814yes—
516C22×C4C2×D2812yes—
517C22×C4D4×D712yes—
518C22×C4#115912yes—
519C22×C4#115912yes—
520C22×C4Q8×D712yes—
521C22×C4Q8×D712yes—
522C22×C4#116112yes—
523C22×C4C2×C22⋊D714yes—
524C22×C4C2×C22⋊D712yes—
525C4⋊C4—48no—
526C4⋊C4—44no—
527C4⋊C4—1416no—
528C4⋊C4—288no—
529C4⋊C4—284no—
530C4⋊C4(C2×D7)⋊C4116yes—
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×C4×D711yescharacteristic
551C23C22×D2811yescharacteristic
552C23C2×D4×D711yescharacteristic
553C23C2×#115911yescharacteristic
554C23C2×#115911yescharacteristic
555C23#654811yescharacteristic
556C23C2×Q8×D711yescharacteristic
557C23C2×Q8×D711yescharacteristic
558C23C2×#116111yescharacteristic
559C23#655111yescharacteristic
560C23D7×#4111yescharacteristic
561C23D7×#4111yescharacteristic
562C23#655411yescharacteristic
563C23#655411yescharacteristic
564C23C22×C22⋊D711yescharacteristic
565Q8—1432no—
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—144no—
596C2×C4—144no—
597C2×C4—144no—
598C2×C4—142no—
599C2×C4—144no—
600C2×C4—144no—
601C2×C4—144no—
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—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×C4D7×C4⋊C414yes—
636C2×C4#645514yes—
637C2×C4#645814yes—
638C2×C4#646014yes—
639C2×C4C2×(C2×D7)⋊C418yes—
640C2×C4C2×(C2×D7)⋊C414yes—
641C2×C4#650114yes—
642C2×C4#650914yes—
643C7#1393511yescharacteristic, complemented, Sylow
644C22C2×D7×C4⋊C411yescharacteristic
645C22C2×#645511yescharacteristic
646C22C2×#645811yescharacteristic
647C22C2×#646011yescharacteristic
648C22C4×#115911yescharacteristic
649C22#9023711yescharacteristic
650C22#9024511yescharacteristic
651C22#9024611yescharacteristic
652C22C4×Q8×D711yescharacteristic
653C22#9026311yescharacteristic
654C22Q8×D2811yescharacteristic
655C22#9026711yescharacteristic
656C22#9028911yescharacteristic
657C22#9029011yescharacteristic
658C22#9029111yescharacteristic
659C22#9029411yescharacteristic
660C22#9031311yescharacteristic
661C22#9031611yescharacteristic
662C22#9032311yescharacteristic
663C22#9032411yescharacteristic
664C22#9037611yescharacteristic
665C22#9037611yescharacteristic
666C22#9038211yescharacteristic
667C22#9038811yescharacteristic
668C22#9041211yescharacteristic
669C22#9041311yescharacteristic
670C22#9041911yescharacteristic
671C22#9042411yescharacteristic
672C22C22×(C2×D7)⋊C411yescharacteristic
673C22C2×#650111yescharacteristic
674C22#9049711yescharacteristic
675C22C2×#650911yescharacteristic
676C22Q8×C22⋊D711yescharacteristic
677C22#9051511yescharacteristic
678C22#9052211yescharacteristic
679C4—28no—
680C4—42no—
681C4—42no—
682C4—82no—
683C4—144no—
684C4—148no—
685C4—282no—
686C4—282no—
687C4—282no—
688C4—562no—
689C4#8975918yes—
690C2#1173340711yescharacteristic
691C2#1173341511yescharacteristic
692C2#1173342611yescharacteristic
693C2#1173342711yescharacteristic
694C2#1173345411yescharacteristic
695C2#1173345811yescharacteristic
696C2#1173366311yescharacteristic
697C2#1173366611yescharacteristic
698C2C2×#8975911yescharacteristic
699C2#1173977511yescharacteristic
700C2Q8×(C2×D7)⋊C411yescharacteristic
701C2#1174009111yescharacteristic
702C2#1174020211yescharacteristic
703C2#1174047411yescharacteristic
704C2#1174068011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#389C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#389D7
hypocenterC7#13935
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
25. C2×#6450C4semidirect
103. C7⋊#95Q8semidirect
199. C2×Dic14C4⋊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×#64502
C2×C7×#3892
C2×#897462
C2×#897572
C2×#897012
#117293202
#117293172
C4×C7⋊#952
#117271642
#117271562
#139357