Finite Group Databasebeta

← #13277231

Subgroups — #13277231

Order 1792.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#89760C211yesmaximal, characteristic
3C2×#89760C211yesmaximal, characteristic
4C2×#89711C211yesmaximal, characteristic
5C2×#89712C212yesmaximal, complemented
6C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729291C212yesmaximal, complemented
10#11727183C212yesmaximal, complemented
11#11727182C212yesmaximal, complemented
12C23×D28C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2212yes—
16C22×C42×C7C2211yescharacteristic
17C22×(C2×D7)⋊C4C2212yes—
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2212yes—
23C22×C4⋊Dic7C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C4×C7×C4⋊C4—24no—
29C2×C7×#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89760—24no—
37#89760C418yescomplemented
38#89712—28no—
39#89711—24no—
40C4×Dic7⋊C4—24no—
41#14022—71nomaximal, Sylow
42C24×D7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C22×D28—22no—
54C22×D28—22no—
55C22×D28—22no—
56C22×D28—22no—
57C22×D28—22no—
58C22×D28—22no—
59C22×D28C2×C414yes—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4C2×C414yes—
65C2×C7×C4⋊C4D414yes—
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7—24no—
69C2×C42×C7—24no—
70C2×C42×C7—42no—
71C2×C42×C7D414yes—
72C2×(C2×D7)⋊C4—24no—
73C2×(C2×D7)⋊C4—24no—
74C2×(C2×D7)⋊C4—24no—
75C2×(C2×D7)⋊C4—24no—
76C2×(C2×D7)⋊C4—24no—
77C2×(C2×D7)⋊C4—24no—
78C2×(C2×D7)⋊C4—24no—
79C2×(C2×D7)⋊C4—24no—
80C2×(C2×D7)⋊C4—24no—
81C2×(C2×D7)⋊C4—24no—
82C2×(C2×D7)⋊C4—42no—
83C2×(C2×D7)⋊C4—42no—
84C2×(C2×D7)⋊C4—42no—
85C2×(C2×D7)⋊C4—42no—
86C2×(C2×D7)⋊C4—42no—
87C2×(C2×D7)⋊C4—42no—
88C2×(C2×D7)⋊C4C2×C418yes—
89C2×(C2×D7)⋊C4C2×C418yes—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—22no—
92C2×C4⋊Dic7—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4D414yescomplemented
99C2×C4×Dic7—22no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7C2×C414yes—
105C7×#95—24no—
106C7⋊#95—22no—
107C7⋊#95—22no—
108C7⋊#95—24no—
109C7⋊#95—24no—
110C7⋊#95—42no—
111C7⋊#95—42no—
112C2×#390—71no—
113C2×#390—71no—
114C2×#390—71no—
115C2×#388—72no—
116C2×C4×C4⋊C4—71no—
117C2×C4×C4⋊C4D711yescharacteristic, complemented
118#1440—72no—
119#1439—72no—
120#1437—72no—
121C4⋊#95—71no—
122C4⋊#95—71no—
123C24×C7C2411yescharacteristic
124C23×D7—22no—
125C23×D7—22no—
126C23×D7—22no—
127C23×D7—22no—
128C23×D7—22no—
129C23×D7—22no—
130C23×D7—22no—
131C23×D7—22no—
132C23×D7—22no—
133C23×D7—22no—
134C23×D7—22no—
135C23×D7—22no—
136C23×D7—22no—
137C23×D7—22no—
138C23×D7C22×C414yes—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—22no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7C22×C414yes—
162C22×C4×C7C22×C412yes—
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D414yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2×D412yes—
169C22×C4×C7#4112yes—
170C22×C4×C7#4112yes—
171C22×C4×C7#4112yes—
172C22×C4×C7#4112yes—
173C22×C4×C7#4112yes—
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—21no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7C22×C412yes—
204C22×Dic7C22×C412yes—
205C22×Dic7C2×D412yes—
206C22×Dic7C2×D412yes—
207C22×Dic7#4112yes—
208C22×Dic7#4112yes—
209C2×D28—28no—
210C2×D28—28no—
211C2×D28—28no—
212C2×D28—44no—
213C2×D28—44no—
214C2×D28—44no—
215C2×D28—44no—
216C7×C4⋊C4—28no—
217C7×C4⋊C4—28no—
218C42×C7—28no—
219C42×C7—48no—
220(C2×D7)⋊C4—216no—
221(C2×D7)⋊C4—48no—
222(C2×D7)⋊C4—48no—
223(C2×D7)⋊C4—48no—
224(C2×D7)⋊C4—48no—
225(C2×D7)⋊C4—48no—
226C4⋊Dic7—44no—
227Dic7⋊C4—28no—
228Dic7⋊C4—28no—
229C4×Dic7—28no—
230C4×Dic7—44no—
231C23×D4—71no—
232C22×C4⋊C4—71no—
233C22×C4⋊C4—71no—
234C22×C4⋊C4—71no—
235C22×C4⋊C4C2×D711yescharacteristic
236C22×C4⋊C4C2×D711yescharacteristic
237C22×C22⋊C4—72no—
238C22×C22⋊C4—72no—
239C22×C22⋊C4—72no—
240C22×C22⋊C4—72no—
241C22×C22⋊C4—72no—
242C22×C22⋊C4—72no—
243C22×C42—71no—
244C22×C42—71no—
245C22×C42C2×D712yes—
246C22×C42C2×D711yescharacteristic
247#390—78no—
248#390—144no—
249#390—144no—
250#388—148no—
251C4×C4⋊C4—24no—
252C4×C4⋊C4—144no—
253C2×#95—72no—
254C2×#95—72no—
255C2×#95—71no—
256C2×#95—71no—
257C2×#95—72no—
258C2×#95—72no—
259C2×#95C2×D712yes—
260C23×C7C23×C411yescharacteristic
261C23×C7C22×D411yescharacteristic
262C23×C7C22×D411yescharacteristic
263C23×C7C22×D411yescharacteristic
264C23×C7C2×#4111yescharacteristic
265C23×C7C2×#4111yescharacteristic
266C23×C7C2×#4111yescharacteristic
267C23×C7C2×#4111yescharacteristic
268C23×C7C2×#4111yescharacteristic
269C23×C7C2×#4111yescharacteristic
270C23×C7C2×#4111yescharacteristic
271C23×C7H(5,𝔽2)11yescharacteristic
272C23×C7H(5,𝔽2)11yescharacteristic
273C23×C7H(5,𝔽2)11yescharacteristic
274C23×C72−1+411yescharacteristic
275C22×D7—24no—
276C22×D7—24no—
277C22×D7—24no—
278C22×D7—24no—
279C22×D7—24no—
280C22×D7—24no—
281C22×D7—24no—
282C22×D7—42no—
283C22×D7—42no—
284C22×D7—42no—
285C22×D7—42no—
286C22×D7—42no—
287C22×D7—42no—
288C22×D7—42no—
289C22×D7—42no—
290C22×D7—42no—
291C22×D7—42no—
292C22×D7—42no—
293C22×D7—42no—
294C22×D7—42no—
295C22×D7—42no—
296C22×D7—42no—
297C22×D7—42no—
298C22×D7—42no—
299C22×D7—42no—
300C22×D7—42no—
301C22×D7—42no—
302C22×D7—42no—
303C22×D7—42no—
304C22×D7—42no—
305C22×D7—42no—
306C22×D7—42no—
307C22×D7—42no—
308C22×D7—42no—
309C22×D7—42no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—24no—
317C2×C4×C7—24no—
318C2×C4×C7—24no—
319C2×C4×C7—22no—
320C2×C4×C7—24no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—41no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7#11714yes—
338C2×C4×C7C4×D414yes—
339C2×C4×C7C4×D414yes—
340C2×C4×C7#12114yes—
341C2×C4×C7#12114yes—
342C2×C4×C7#12314yes—
343C2×C4×C7#12414yes—
344C2×C4×C7#12614yes—
345C2×Dic7—22no—
346C2×Dic7—22no—
347C2×Dic7—22no—
348C2×Dic7—22no—
349C2×Dic7—22no—
350C2×Dic7—22no—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7C4×D414yes—
380D28—416no—
381C25—72no—
382C22×D4—74no—
383C22×D4—142no—
384C22×D4—142no—
385C22×D4—142no—
386C22×D4—142no—
387C22×D4—142no—
388C22×D4—142no—
389C23×C4—71no—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—72no—
394C23×C4C22×D712yes—
395C23×C4C22×D711yescharacteristic
396C23×C4C22×D712yes—
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—74no—
404C2×C4⋊C4—142no—
405C2×C4⋊C4—142no—
406C2×C4⋊C4—142no—
407C2×C4⋊C4—142no—
408C2×C4⋊C4—142no—
409C2×C4⋊C4—142no—
410C2×C4⋊C4—142no—
411C2×C4⋊C4—142no—
412C2×C4⋊C4C4×D714yes—
413C2×C4⋊C4C22⋊D714yes—
414C2×C22⋊C4—78no—
415C2×C22⋊C4—78no—
416C2×C22⋊C4—144no—
417C2×C22⋊C4—144no—
418C2×C22⋊C4—144no—
419C2×C22⋊C4—144no—
420C2×C22⋊C4—144no—
421C2×C22⋊C4—144no—
422C2×C22⋊C4—144no—
423C2×C22⋊C4—144no—
424C2×C22⋊C4—144no—
425C2×C22⋊C4—144no—
426C2×C22⋊C4—282no—
427C2×C22⋊C4—282no—
428C2×C22⋊C4—282no—
429C2×C22⋊C4—282no—
430C2×C22⋊C4—282no—
431C2×C22⋊C4—282no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—24no—
435C2×C42—24no—
436C2×C42—42no—
437C2×C42—74no—
438C2×C42—142no—
439C2×C42—142no—
440C2×C42—142no—
441C2×C42—142no—
442C2×C42—142no—
443C2×C42D2814yes—
444#95—24no—
445#95—144no—
446#95—144no—
447#95—142no—
448#95—142no—
449#95—282no—
450#95—282no—
451C22×C7C2×#11711yescharacteristic
452C22×C7C2×C4×D411yescharacteristic
453C22×C7C2×C4×D411yescharacteristic
454C22×C7C2×C4×D411yescharacteristic
455C22×C7C4×#4111yescharacteristic
456C22×C7#51811yescharacteristic
457C22×C7#52011yescharacteristic
458C22×C7C2×#12111yescharacteristic
459C22×C7C2×#12111yescharacteristic
460C22×C7C2×#12311yescharacteristic
461C22×C7#52511yescharacteristic
462C22×C7C2×#12411yescharacteristic
463C22×C7C2×#12611yescharacteristic
464C22×C7#52911yescharacteristic
465C22×C7#53211yescharacteristic
466C22×C7#53511yescharacteristic
467C22×C7#53711yescharacteristic
468C22×C7#54011yescharacteristic
469C22×C7#54211yescharacteristic
470C22×C7D4211yescharacteristic
471C22×C7#54611yescharacteristic
472C22×C7#54711yescharacteristic
473C22×C7#54811yescharacteristic
474C22×C7#55011yescharacteristic
475C22×C7#55011yescharacteristic
476C22×C7#55011yescharacteristic
477C22×C7#55311yescharacteristic
478C22×C7#55311yescharacteristic
479C22×C7#55511yescharacteristic
480C22×C7#55611yescharacteristic
481C22×C7#55611yescharacteristic
482C22×C7#55911yescharacteristic
483C22×C7#55911yescharacteristic
484C22×C7#55911yescharacteristic
485C22×C7#55911yescharacteristic
486C2×D7—44no—
487C2×D7—44no—
488C2×D7—44no—
489C2×D7—44no—
490C2×D7—44no—
491C2×D7—44no—
492C2×D7—44no—
493C2×D7—82no—
494C2×D7—82no—
495C2×D7—82no—
496C2×D7—82no—
497C2×D7—82no—
498C2×D7—82no—
499C2×D7—82no—
500C2×D7—82no—
501C4×C7—24no—
502C4×C7—44no—
503C4×C7—42no—
504C4×C7—44no—
505C4×C7#38818yescomplemented
506Dic7—24no—
507Dic7—42no—
508Dic7—42no—
509Dic7—42no—
510Dic7—82no—
511C24—74no—
512C24—142no—
513C24—142no—
514C24—142no—
515C24—142no—
516C24—142no—
517C24—142no—
518C24—142no—
519C24—142no—
520C24—142no—
521C24—142no—
522C24—142no—
523C24—142no—
524C24—142no—
525C24—142no—
526C24C23×D711yescharacteristic
527C2×D4—148no—
528C2×D4—148no—
529C2×D4—148no—
530C2×D4—284no—
531C2×D4—284no—
532C2×D4—284no—
533C2×D4—284no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—141no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4C2×C4×D714yes—
592C22×C4C2×C4×D712yes—
593C22×C4C2×D2812yes—
594C22×C4C2×D2812yes—
595C22×C4C2×D2812yes—
596C22×C4#115712yes—
597C22×C4#115712yes—
598C22×C4#115712yes—
599C22×C4#115712yes—
600C22×C4D4×D712yes—
601C22×C4#116112yes—
602C22×C4C2×C22⋊D714yes—
603C22×C4C2×C22⋊D712yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—148no—
607C4⋊C4—148no—
608C4⋊C4—284no—
609C22⋊C4—1416no—
610C22⋊C4—288no—
611C22⋊C4—288no—
612C22⋊C4—288no—
613C22⋊C4—288no—
614C22⋊C4—288no—
615C42—28no—
616C42—48no—
617C42—148no—
618C42—284no—
619C2×C7C2×#38811yescharacteristic
620C2×C7C4×#12111yescharacteristic
621C2×C7#232411yescharacteristic
622C2×C7#235411yescharacteristic
623C2×C7#235711yescharacteristic
624C2×C7#236611yescharacteristic
625C2×C7#236711yescharacteristic
626C2×C7#241411yescharacteristic
627C2×C7#241611yescharacteristic
628C2×C7#244511yescharacteristic
629C2×C7#244811yescharacteristic
630C2×C7#251211yescharacteristic
631C2×C7#251311yescharacteristic
632C2×C7#254811yescharacteristic
633C2×C7#259211yescharacteristic
634D7—84no—
635C23—144no—
636C23—144no—
637C23—144no—
638C23—144no—
639C23—144no—
640C23—144no—
641C23—144no—
642C23—282no—
643C23—282no—
644C23—282no—
645C23—282no—
646C23—282no—
647C23—282no—
648C23—282no—
649C23—282no—
650C23—282no—
651C23—282no—
652C23—282no—
653C23—282no—
654C23—282no—
655C23—282no—
656C23—282no—
657C23—282no—
658C23—282no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23—282no—
668C23—282no—
669C23—282no—
670C23C22×C4×D711yescharacteristic
671C23C22×D2811yescharacteristic
672C23C2×#115711yescharacteristic
673C23C2×#115711yescharacteristic
674C23C2×#115711yescharacteristic
675C23C2×#115711yescharacteristic
676C23C2×D4×D711yescharacteristic
677C23#654811yescharacteristic
678C23C2×#116111yescharacteristic
679C23#655111yescharacteristic
680C23D7×#4111yescharacteristic
681C23D7×#4111yescharacteristic
682C23#655311yescharacteristic
683C23#655311yescharacteristic
684C23C22×C22⋊D711yescharacteristic
685D4—2816no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—74no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—281no—
730C2×C4—281no—
731C2×C4—281no—
732C2×C4—281no—
733C2×C4—281no—
734C2×C4—281no—
735C2×C4—281no—
736C2×C4—281no—
737C2×C4—281no—
738C2×C4—281no—
739C2×C4—281no—
740C2×C4—281no—
741C2×C4—282no—
742C2×C4—282no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4—282no—
748C2×C4#643514yes—
749C2×C4C4×D2814yes—
750C2×C4#643814yes—
751C2×C4#643914yes—
752C2×C4#645814yes—
753C2×C4C4×C22⋊D714yes—
754C2×C4#649214yes—
755C2×C4#649314yes—
756C7#1402211yescharacteristic, complemented, Sylow
757C22—284no—
758C22—284no—
759C22—284no—
760C22—284no—
761C22—284no—
762C22—284no—
763C22—284no—
764C22—562no—
765C22—562no—
766C22—562no—
767C22—562no—
768C22—562no—
769C22—562no—
770C22—562no—
771C22—562no—
772C22C2×#643511yescharacteristic
773C22C2×C4×D2811yescharacteristic
774C22C2×#643811yescharacteristic
775C22C2×#643911yescharacteristic
776C22C2×#645811yescharacteristic
777C22#9019811yescharacteristic
778C22#9020111yescharacteristic
779C22#9020511yescharacteristic
780C22#9021511yescharacteristic
781C22#9021611yescharacteristic
782C22#9022111yescharacteristic
783C22#9022311yescharacteristic
784C22C4×D4×D711yescharacteristic
785C22#9023611yescharacteristic
786C22#9023911yescharacteristic
787C22#9024411yescharacteristic
788C22#9024411yescharacteristic
789C22#9025011yescharacteristic
790C22#9025011yescharacteristic
791C22#9025311yescharacteristic
792C22#9025911yescharacteristic
793C22#9025911yescharacteristic
794C22C4×#116111yescharacteristic
795C22#9026511yescharacteristic
796C22#9027111yescharacteristic
797C22#9027311yescharacteristic
798C22#9027611yescharacteristic
799C22#9027611yescharacteristic
800C22C2×C4×C22⋊D711yescharacteristic
801C22C2×#649211yescharacteristic
802C22C2×#649311yescharacteristic
803C22D4×C22⋊D711yescharacteristic
804C22#9050811yescharacteristic
805C22#9052011yescharacteristic
806C22#9052511yescharacteristic
807C4—24no—
808C4—42no—
809C4—44no—
810C4—44no—
811C4—144no—
812C4—282no—
813C4—282no—
814C4—282no—
815C4—562no—
816C4#8971218yescomplemented
817C2—564no—
818C2#1173108411yescharacteristic
819C2#1173109111yescharacteristic
820C2#1173113811yescharacteristic
821C2#1173114011yescharacteristic
822C2#1173115711yescharacteristic
823C2#1173118011yescharacteristic
824C2C4×#645811yescharacteristic
825C2#1173120811yescharacteristic
826C2C2×#8971211yescharacteristic
827C2#1173963811yescharacteristic
828C2#1173972111yescharacteristic
829C2#1173978811yescharacteristic
830C2#1173980311yescharacteristic
831C2#1173991111yescharacteristic
832C2#1173991411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, cosocleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#14022
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C4⋊C4C2semidirect
5. C2×#89712C2semidirect
6. C2×C4×Dic7⋊C4C2semidirect
7. #11729317C2semidirect
8. #11729317C2semidirect
9. #11729291C2semidirect
10. #11727183C2semidirect
11. #11727182C2semidirect
37. #89760C4semidirect
98. C2×Dic7⋊C4D4semidirect
117. C2×C4×C4⋊C4D7semidirect
505. C4×C7#388semidirect
756. C7#14022semidirect
816. C4#89712semidirect

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×#897602
C2×#897112
C2×#897122
C2×C4×Dic7⋊C42
#117293172
#117292912
#117271832
#117271822
#140227