Finite Group Databasebeta

← #13277516

Subgroups — #13277516

Order 1792.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic
3C2×#89757C211yesmaximal, characteristic
4C2×#89700C211yesmaximal, characteristic
5C2×C4×Dic7⋊C4C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7#11729317C211yesmaximal, characteristic
8#11729290C212yesmaximal
9#11729289C212yesmaximal
10#11727174C212yesmaximal
11#11727165C212yesmaximal
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2212yes—
15C22×C42×C7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×C4⋊Dic7C2212yes—
18C22×C4⋊Dic7C2211yescharacteristic
19C22×C4⋊Dic7C2212yes—
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2212yes—
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C4×C7×C4⋊C4—24no—
26C2×C7×#95C2212yes—
27C2×C7⋊#95C2211yescharacteristic
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89757—24no—
37#89757C418yescomplemented
38C4×Dic7⋊C4—24no—
39#89700—24no—
40#14045—71nomaximal, Sylow
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2312yes—
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4C2×C414yes—
55C2×C7×C4⋊C4D414yes—
56C2×C7×C4⋊C4Q814yes—
57C2×C7×C4⋊C4Q814yes—
58C2×C42×C7—22no—
59C2×C42×C7—22no—
60C2×C42×C7—24no—
61C2×C42×C7—24no—
62C2×C42×C7—42no—
63C2×C42×C7D414yes—
64C2×C4⋊Dic7—22no—
65C2×C4⋊Dic7—22no—
66C2×C4⋊Dic7—22no—
67C2×C4⋊Dic7—24no—
68C2×C4⋊Dic7—22no—
69C2×C4⋊Dic7—22no—
70C2×C4⋊Dic7—24no—
71C2×C4⋊Dic7—42no—
72C2×C4⋊Dic7—42no—
73C2×C4⋊Dic7—42no—
74C2×C4⋊Dic7C2×C414yes—
75C2×C4⋊Dic7C2×C418yes—
76C2×Dic7⋊C4—22no—
77C2×Dic7⋊C4—22no—
78C2×Dic7⋊C4—22no—
79C2×Dic7⋊C4—22no—
80C2×Dic7⋊C4—22no—
81C2×Dic7⋊C4—24no—
82C2×Dic7⋊C4—42no—
83C2×Dic7⋊C4—42no—
84C2×Dic7⋊C4Q814yes—
85C2×C4×Dic7—22no—
86C2×C4×Dic7—22no—
87C2×C4×Dic7—22no—
88C2×C4×Dic7—22no—
89C2×C4×Dic7—22no—
90C2×C4×Dic7C2×C414yes—
91C7×#95—24no—
92C7⋊#95—24no—
93C7⋊#95—22no—
94C7⋊#95—22no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—42no—
98C7⋊#95—42no—
99C7⋊#95—42no—
100C7⋊#95C2×C418yes—
101C2×#389—71no—
102C2×#389—71no—
103C2×#389—71no—
104C2×C4×C4⋊C4—71no—
105C2×C4×C4⋊C4D711yescharacteristic
106#1444—72no—
107#1441—72no—
108#1436—72no—
109C4⋊#95—72no—
110C4⋊#95—71no—
111C4⋊#95—71no—
112C24×C7C2411yescharacteristic
113C22×C4×C7—21no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—21no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—21no—
132C22×C4×C7—21no—
133C22×C4×C7C22×C414yes—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C2×D412yes—
136C22×C4×C7C2×D414yes—
137C22×C4×C7C2×D412yes—
138C22×C4×C7C2×D412yes—
139C22×C4×C7C2×D412yes—
140C22×C4×C7C2×Q814yes—
141C22×C4×C7C2×Q814yes—
142C22×C4×C7C2×Q812yes—
143C22×C4×C7C2×Q812yes—
144C22×C4×C7C2×Q812yes—
145C22×C4×C7#4112yes—
146C22×C4×C7#4112yes—
147C22×C4×C7#4112yes—
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—22no—
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—21no—
171C22×Dic7—21no—
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—22no—
175C22×Dic7—21no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—22no—
179C22×Dic7—22no—
180C22×Dic7—22no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7C22×C414yes—
184C22×Dic7C22×C412yes—
185C22×Dic7C22×C412yes—
186C22×Dic7C2×Q812yes—
187C22×Dic7C2×Q812yes—
188C22×Dic7#4112yes—
189C22×Dic7#4112yes—
190C7×C4⋊C4—28no—
191C7×C4⋊C4C4⋊C4116yescomplemented
192C42×C7—28no—
193C42×C7—48no—
194C4⋊Dic7—28no—
195C4⋊Dic7—48no—
196C4⋊Dic7—48no—
197C4⋊Dic7—44no—
198Dic7⋊C4—28no—
199Dic7⋊C4—28no—
200Dic7⋊C4—48no—
201C4×Dic7—28no—
202C4×Dic7—44no—
203C22×C4⋊C4—71no—
204C22×C4⋊C4—71no—
205C22×C4⋊C4—72no—
206C22×C4⋊C4—71no—
207C22×C4⋊C4—71no—
208C22×C4⋊C4—72no—
209C22×C4⋊C4—72no—
210C22×C4⋊C4C2×D711yescharacteristic
211C22×C4⋊C4C2×D711yescharacteristic
212C22×C42—71no—
213C22×C42—71no—
214C22×C42C2×D712yes—
215C22×C42C2×D711yescharacteristic
216#389—78no—
217#389—144no—
218#389—144no—
219C4×C4⋊C4—24no—
220C4×C4⋊C4—144no—
221C2×#95—72no—
222C2×#95—71no—
223C2×#95—72no—
224C2×#95—72no—
225C2×#95—72no—
226C2×#95—71no—
227C2×#95—72no—
228C2×#95—72no—
229C2×#95—72no—
230C2×#95C2×D712yes—
231C23×C7C23×C411yescharacteristic
232C23×C7C22×D411yescharacteristic
233C23×C7C22×D411yescharacteristic
234C23×C7C22×Q811yescharacteristic
235C23×C7C22×Q811yescharacteristic
236C23×C7C22×Q811yescharacteristic
237C23×C7C2×#4111yescharacteristic
238C23×C7C2×#4111yescharacteristic
239C23×C7C2×#4111yescharacteristic
240C23×C7C2×#4111yescharacteristic
241C23×C7C2×#4111yescharacteristic
242C23×C7H(5,𝔽2)11yescharacteristic
243C23×C7H(5,𝔽2)11yescharacteristic
244C23×C7H(5,𝔽2)11yescharacteristic
245C23×C72−1+411yescharacteristic
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—24no—
251C2×C4×C7—22no—
252C2×C4×C7—24no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—22no—
259C2×C4×C7—24no—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—41no—
268C2×C4×C7—41no—
269C2×C4×C7—42no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7C2×C4⋊C418yes—
273C2×C4×C7C2×C4⋊C414yes—
274C2×C4×C7C4×D414yes—
275C2×C4×C7C4×Q814yes—
276C2×C4×C7#12114yes—
277C2×C4×C7C22⋊Q814yes—
278C2×C4×C7C22⋊Q814yes—
279C2×C4×C7#12514yes—
280C2×C4×C7C4⋊Q814yes—
281C2×Dic7—22no—
282C2×Dic7—22no—
283C2×Dic7—22no—
284C2×Dic7—22no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—22no—
288C2×Dic7—24no—
289C2×Dic7—22no—
290C2×Dic7—24no—
291C2×Dic7—22no—
292C2×Dic7—24no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—42no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—42no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—42no—
309C2×Dic7—41no—
310C2×Dic7—42no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—42no—
318C2×Dic7—42no—
319C2×Dic7—42no—
320C2×Dic7—42no—
321C2×Dic7—42no—
322C2×Dic7C4×Q814yes—
323C23×C4—71no—
324C23×C4—72no—
325C23×C4—71no—
326C23×C4—71no—
327C23×C4—71no—
328C23×C4—72no—
329C23×C4C22×D712yes—
330C23×C4C22×D711yescharacteristic
331C23×C4C22×D712yes—
332C23×C4C22×D711yescharacteristic
333C23×C4C22×D711yescharacteristic
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—74no—
337C2×C4⋊C4—74no—
338C2×C4⋊C4—78no—
339C2×C4⋊C4—142no—
340C2×C4⋊C4—142no—
341C2×C4⋊C4—142no—
342C2×C4⋊C4—142no—
343C2×C4⋊C4—142no—
344C2×C4⋊C4—142no—
345C2×C4⋊C4—142no—
346C2×C4⋊C4—144no—
347C2×C4⋊C4—144no—
348C2×C4⋊C4—142no—
349C2×C4⋊C4—142no—
350C2×C4⋊C4—144no—
351C2×C4⋊C4—142no—
352C2×C4⋊C4—282no—
353C2×C4⋊C4—282no—
354C2×C4⋊C4—282no—
355C2×C4⋊C4—282no—
356C2×C4⋊C4—282no—
357C2×C4⋊C4Dic1414yes—
358C2×C4⋊C4Dic1414yes—
359C2×C4⋊C4C4×D714yes—
360C2×C4⋊C4C22⋊D714yes—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—42no—
366C2×C42—74no—
367C2×C42—142no—
368C2×C42—142no—
369C2×C42—142no—
370C2×C42—142no—
371C2×C42—142no—
372C2×C42D2814yes—
373#95—24no—
374#95—78no—
375#95—144no—
376#95—142no—
377#95—142no—
378#95—144no—
379#95—144no—
380#95—282no—
381#95—282no—
382#95—282no—
383C22×C7C22×C4⋊C411yescharacteristic
384C22×C7C2×C4×D411yescharacteristic
385C22×C7C2×C4×Q811yescharacteristic
386C22×C7C2×C4×Q811yescharacteristic
387C22×C7C4×#4111yescharacteristic
388C22×C7#51811yescharacteristic
389C22×C7#52011yescharacteristic
390C22×C7C2×#12111yescharacteristic
391C22×C7C2×C22⋊Q811yescharacteristic
392C22×C7C2×C22⋊Q811yescharacteristic
393C22×C7#52511yescharacteristic
394C22×C7C2×#12511yescharacteristic
395C22×C7#52911yescharacteristic
396C22×C7C2×C4⋊Q811yescharacteristic
397C22×C7#53311yescharacteristic
398C22×C7#53511yescharacteristic
399C22×C7#53711yescharacteristic
400C22×C7#54011yescharacteristic
401C22×C7#54211yescharacteristic
402C22×C7#54611yescharacteristic
403C22×C7#54611yescharacteristic
404C22×C7D4×Q811yescharacteristic
405C22×C7#55011yescharacteristic
406C22×C7#55211yescharacteristic
407C22×C7#55311yescharacteristic
408C22×C7#55411yescharacteristic
409C22×C7#55411yescharacteristic
410C22×C7#55411yescharacteristic
411C22×C7#55411yescharacteristic
412C22×C7#55411yescharacteristic
413C22×C7#55511yescharacteristic
414C22×C7#55711yescharacteristic
415C22×C7#55711yescharacteristic
416C22×C7Q8211yescharacteristic
417C22×C7Q8211yescharacteristic
418C4×C7—28no—
419C4×C7—24no—
420C4×C7—42no—
421C4×C7—44no—
422C4×C7#38918yes—
423Dic7—24no—
424Dic7—42no—
425Dic7—44no—
426Dic7—42no—
427Dic7—42no—
428Dic7—82no—
429C24C23×D711yescharacteristic
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—72no—
451C22×C4—72no—
452C22×C4—72no—
453C22×C4—74no—
454C22×C4—72no—
455C22×C4—72no—
456C22×C4—72no—
457C22×C4—141no—
458C22×C4—141no—
459C22×C4—141no—
460C22×C4—141no—
461C22×C4—141no—
462C22×C4—141no—
463C22×C4—141no—
464C22×C4—142no—
465C22×C4—141no—
466C22×C4—141no—
467C22×C4—141no—
468C22×C4—142no—
469C22×C4—141no—
470C22×C4—141no—
471C22×C4—142no—
472C22×C4—141no—
473C22×C4—141no—
474C22×C4—142no—
475C22×C4—141no—
476C22×C4—141no—
477C22×C4—141no—
478C22×C4—141no—
479C22×C4—142no—
480C22×C4—141no—
481C22×C4—142no—
482C22×C4—141no—
483C22×C4—141no—
484C22×C4—141no—
485C22×C4—142no—
486C22×C4—142no—
487C22×C4—142no—
488C22×C4—142no—
489C22×C4—142no—
490C22×C4—142no—
491C22×C4—142no—
492C22×C4C2×Dic1414yes—
493C22×C4C2×Dic1414yes—
494C22×C4C2×Dic1412yes—
495C22×C4C2×Dic1412yes—
496C22×C4C2×C4×D714yes—
497C22×C4C2×C4×D712yes—
498C22×C4C2×D2812yes—
499C22×C4C2×D2812yes—
500C22×C4C2×D2812yes—
501C22×C4#115712yes—
502C22×C4#115712yes—
503C22×C4#115912yes—
504C22×C4Q8×D712yes—
505C22×C4C2×C22⋊D714yes—
506C22×C4C2×C22⋊D712yes—
507C4⋊C4—28no—
508C4⋊C4—148no—
509C4⋊C4—148no—
510C4⋊C4—148no—
511C4⋊C4—288no—
512C4⋊C4—288no—
513C4⋊C4—288no—
514C4⋊C4—284no—
515C4⋊C4Dic7⋊C4116yescomplemented
516C42—28no—
517C42—48no—
518C42—148no—
519C42—284no—
520C2×C7C2×#38911yescharacteristic
521C2×C7C4×C22⋊Q811yescharacteristic
522C2×C7#232411yescharacteristic
523C2×C7#234911yescharacteristic
524C2×C7Q8×C4⋊C411yescharacteristic
525C2×C7#236911yescharacteristic
526C2×C7#237011yescharacteristic
527C2×C7#241411yescharacteristic
528C2×C7#241711yescharacteristic
529C2×C7#245111yescharacteristic
530C2×C7#245411yescharacteristic
531C2×C7#250711yescharacteristic
532C2×C7#250811yescharacteristic
533C2×C7#256711yescharacteristic
534C2×C7#258411yescharacteristic
535C23C22×Dic1411yescharacteristic
536C23C22×Dic1411yescharacteristic
537C23C22×C4×D711yescharacteristic
538C23C22×D2811yescharacteristic
539C23C2×#115711yescharacteristic
540C23C2×#115711yescharacteristic
541C23C2×#115911yescharacteristic
542C23#654811yescharacteristic
543C23C2×Q8×D711yescharacteristic
544C23#655111yescharacteristic
545C23D7×#4111yescharacteristic
546C23D7×#4111yescharacteristic
547C23#655311yescharacteristic
548C23#655311yescharacteristic
549C23C22×C22⋊D711yescharacteristic
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—74no—
577C2×C4—142no—
578C2×C4—142no—
579C2×C4—142no—
580C2×C4—142no—
581C2×C4—142no—
582C2×C4—142no—
583C2×C4—142no—
584C2×C4—144no—
585C2×C4—142no—
586C2×C4—142no—
587C2×C4—142no—
588C2×C4—142no—
589C2×C4—142no—
590C2×C4—144no—
591C2×C4—142no—
592C2×C4—142no—
593C2×C4—144no—
594C2×C4—142no—
595C2×C4—281no—
596C2×C4—282no—
597C2×C4—281no—
598C2×C4—281no—
599C2×C4—282no—
600C2×C4—281no—
601C2×C4—281no—
602C2×C4—281no—
603C2×C4—281no—
604C2×C4—281no—
605C2×C4—281no—
606C2×C4—281no—
607C2×C4—282no—
608C2×C4—281no—
609C2×C4—281no—
610C2×C4—282no—
611C2×C4—282no—
612C2×C4—282no—
613C2×C4—282no—
614C2×C4—282no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4C4×Dic1414yes—
619C2×C4#643214yes—
620C2×C4#643314yes—
621C2×C4C4×D2814yes—
622C2×C4#646014yes—
623C2×C4C2×Dic7⋊C418yes—
624C2×C4C2×Dic7⋊C414yes—
625C2×C4#648714yes—
626C2×C4#649314yes—
627C7#1404511yescharacteristic, complemented, Sylow
628C22C2×C4×Dic1411yescharacteristic
629C22C2×#643211yescharacteristic
630C22C2×#643311yescharacteristic
631C22C2×C4×D2811yescharacteristic
632C22C2×#646011yescharacteristic
633C22#9020111yescharacteristic
634C22#9020211yescharacteristic
635C22#9020411yescharacteristic
636C22#9021511yescharacteristic
637C22#9021611yescharacteristic
638C22#9022111yescharacteristic
639C22#9022311yescharacteristic
640C22C4×#115911yescharacteristic
641C22#9023011yescharacteristic
642C22#9023011yescharacteristic
643C22#9023411yescharacteristic
644C22#9023411yescharacteristic
645C22#9023611yescharacteristic
646C22#9024811yescharacteristic
647C22#9025311yescharacteristic
648C22Q8×Dic1411yescharacteristic
649C22Q8×Dic1411yescharacteristic
650C22#9026011yescharacteristic
651C22#9026011yescharacteristic
652C22C4×Q8×D711yescharacteristic
653C22#9026511yescharacteristic
654C22#9026911yescharacteristic
655C22#9027311yescharacteristic
656C22C22×Dic7⋊C411yescharacteristic
657C22C2×#648711yescharacteristic
658C22C2×#649311yescharacteristic
659C22#9049711yescharacteristic
660C22Q8×C22⋊D711yescharacteristic
661C22#9052011yescharacteristic
662C22#9052511yescharacteristic
663C4—28no—
664C4—24no—
665C4—42no—
666C4—44no—
667C4—144no—
668C4—282no—
669C4—284no—
670C4—282no—
671C4—282no—
672C4—562no—
673C4#8970018yes—
674C2#1173110211yescharacteristic
675C2#1173110611yescharacteristic
676C2#1173113011yescharacteristic
677C2#1173113211yescharacteristic
678C2#1173116611yescharacteristic
679C2#1173117211yescharacteristic
680C2C4×#646011yescharacteristic
681C2#1173120811yescharacteristic
682C2C2×#8970011yescharacteristic
683C2#1173963911yescharacteristic
684C2#1173972111yescharacteristic
685C2#1173977911yescharacteristic
686C2#1173980811yescharacteristic
687C2Q8×Dic7⋊C411yescharacteristic
688C2#1173991511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#14045
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. #89757C4semidirect
191. C7×C4⋊C4C4⋊C4semidirect
515. C4⋊C4Dic7⋊C4semidirect
627. C7#14045semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
C2×#897572
C2×#897002
C2×C4×Dic7⋊C42
#117293172
#117292902
#117292892
#117271742
#117271652
#140457