Finite Group Databasebeta

← #13277237

Subgroups — #13277237

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×#89762C212yesmaximal, complemented
3C2×#89711C211yesmaximal, characteristic
4C2×#89711C211yesmaximal, characteristic
5C2×#89711C211yesmaximal, characteristic
6C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
7#11729324C212yesmaximal, complemented
8#11729289C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727183C212yesmaximal, complemented
11#11727162C212yesmaximal, complemented
12C23×D28C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C42×C7C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×(C2×D7)⋊C4C2212yes—
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2212yes—
23C22×(C2×D7)⋊C4C2212yes—
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4×Dic7C2212yes—
28C4×C7×C4⋊C4—24no—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36#89762—28no—
37#89711—24no—
38#89711—24no—
39#89711C418yescomplemented
40C4×C4⋊Dic7—24no—
41#14022—71nomaximal, Sylow
42C24×D7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×Dic7C2312yes—
51C23×Dic7C2312yes—
52C23×Dic7C2312yes—
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⋊C4—22no—
65C2×C7×C4⋊C4D414yescomplemented
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C42×C7—22no—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×C42×C7—22no—
72C2×C42×C7—22no—
73C2×C42×C7C2×C414yes—
74C2×C42×C7D414yes—
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—24no—
83C2×(C2×D7)⋊C4—24no—
84C2×(C2×D7)⋊C4—24no—
85C2×(C2×D7)⋊C4—42no—
86C2×(C2×D7)⋊C4—42no—
87C2×(C2×D7)⋊C4—42no—
88C2×(C2×D7)⋊C4—42no—
89C2×(C2×D7)⋊C4—42no—
90C2×(C2×D7)⋊C4—42no—
91C2×(C2×D7)⋊C4C2×C418yes—
92C2×(C2×D7)⋊C4C2×C418yes—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7—22no—
95C2×C4⋊Dic7—22no—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7—22no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7C2×C414yes—
101C2×C4⋊Dic7D414yes—
102C2×C4×Dic7—24no—
103C2×C4×Dic7—24no—
104C2×C4×Dic7—42no—
105C7×#95—22no—
106C7×#95—22no—
107C7⋊#95—24no—
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—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7C22×C412yes—
172C22×C4×C7C22×C412yes—
173C22×C4×C7C22×C412yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7C2×D412yes—
176C22×C4×C7C2×D412yes—
177C22×C4×C7C2×D412yes—
178C22×C4×C7C2×D412yes—
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7#4112yes—
182C22×C4×C7#4112yes—
183C22×C4×C7#4112yes—
184C22×C4×C7#4112yes—
185C22×C4×C7#4112yes—
186C22×C4×C7#4112yes—
187C22×C4×C7#4112yes—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7C22×C414yes—
208C22×Dic7C2×D414yes—
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—28no—
220C42×C7—44no—
221(C2×D7)⋊C4—216no—
222(C2×D7)⋊C4—48no—
223(C2×D7)⋊C4—48no—
224(C2×D7)⋊C4—48no—
225(C2×D7)⋊C4—48no—
226(C2×D7)⋊C4—48no—
227C4⋊Dic7—28no—
228C4⋊Dic7—28no—
229C4⋊Dic7—44no—
230C4×Dic7—48no—
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—72no—
244C22×C42C2×D711yescharacteristic
245C22×C42C2×D711yescharacteristic
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—72no—
256C2×#95—72no—
257C2×#95—72no—
258C2×#95C2×D711yescharacteristic
259C2×#95C2×D711yescharacteristic
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—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7#11714yes—
351C2×C4×C7C4×D414yes—
352C2×C4×C7C4×D414yes—
353C2×C4×C7C4×D414yes—
354C2×C4×C7#12114yes—
355C2×C4×C7#12114yes—
356C2×C4×C7#12314yes—
357C2×C4×C7#12414yes—
358C2×C4×C7#12614yes—
359C2×Dic7—24no—
360C2×Dic7—24no—
361C2×Dic7—24no—
362C2×Dic7—24no—
363C2×Dic7—24no—
364C2×Dic7—24no—
365C2×Dic7—42no—
366C2×Dic7—42no—
367C2×Dic7—42no—
368C2×Dic7—42no—
369C2×Dic7—42no—
370C2×Dic7—42no—
371C2×Dic7—42no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C2×Dic7—42no—
376C2×Dic7—42no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7—42no—
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—72no—
390C23×C4—72no—
391C23×C4—72no—
392C23×C4C22×D711yescharacteristic
393C23×C4C22×D711yescharacteristic
394C23×C4C22×D711yescharacteristic
395C23×C4C22×D711yescharacteristic
396C23×C4C22×D711yescharacteristic
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—22no—
404C2×C4⋊C4—74no—
405C2×C4⋊C4—74no—
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⋊C4—142no—
413C2×C4⋊C4D2814yescomplemented
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—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—144no—
440C2×C42—144no—
441C2×C42—282no—
442C2×C42C4×D714yes—
443C2×C42C22⋊D714yes—
444#95—22no—
445#95—22no—
446#95—144no—
447#95—144no—
448#95—144no—
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—24no—
503C4×C7—42no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7#38818yescomplemented
508Dic7—44no—
509Dic7—44no—
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—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—74no—
567C22×C4—74no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4C2×C4×D712yes—
588C22×C4C2×C4×D712yes—
589C22×C4C2×C4×D712yes—
590C22×C4C2×D2812yes—
591C22×C4C2×D2812yes—
592C22×C4C2×D2812yes—
593C22×C4#115712yes—
594C22×C4#115712yes—
595C22×C4#115712yes—
596C22×C4#115712yes—
597C22×C4D4×D712yes—
598C22×C4#115912yes—
599C22×C4#116112yes—
600C22×C4#116112yes—
601C22×C4C2×C22⋊D712yes—
602C22×C4C2×C22⋊D712yes—
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—28no—
617C42—44no—
618C42—288no—
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
677C23C2×#115911yescharacteristic
678C23C2×#116111yescharacteristic
679C23C2×#116111yescharacteristic
680C23#655311yescharacteristic
681C23#655311yescharacteristic
682C23#655311yescharacteristic
683C23#655411yescharacteristic
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—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—144no—
727C2×C4—144no—
728C2×C4—144no—
729C2×C4—144no—
730C2×C4—144no—
731C2×C4—144no—
732C2×C4—282no—
733C2×C4—282no—
734C2×C4—282no—
735C2×C4—282no—
736C2×C4—282no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—282no—
741C2×C4—282no—
742C2×C4—282no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4C4×D2814yes—
748C2×C4#645514yes—
749C2×C4#645614yes—
750C2×C4#645714yes—
751C2×C4#646114yes—
752C2×C4C4×C22⋊D714yes—
753C2×C4#649314yes—
754C2×C4#650214yes—
755C2×C4#651014yes—
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×C4×D2811yescharacteristic
773C22C4×#115711yescharacteristic
774C22#9016811yescharacteristic
775C22#9017011yescharacteristic
776C22C2×#645511yescharacteristic
777C22C2×#645611yescharacteristic
778C22C2×#645711yescharacteristic
779C22C2×#646111yescharacteristic
780C22#9021211yescharacteristic
781C22#9021411yescharacteristic
782C22#9022511yescharacteristic
783C22#9022611yescharacteristic
784C22D4×D2811yescharacteristic
785C22#9024111yescharacteristic
786C22#9024311yescharacteristic
787C22#9024411yescharacteristic
788C22#9024611yescharacteristic
789C22#9025411yescharacteristic
790C22#9025611yescharacteristic
791C22#9025611yescharacteristic
792C22#9026811yescharacteristic
793C22#9026811yescharacteristic
794C22#9027511yescharacteristic
795C22#9027511yescharacteristic
796C22#9027611yescharacteristic
797C22#9027611yescharacteristic
798C22#9027611yescharacteristic
799C22#9027611yescharacteristic
800C22C2×C4×C22⋊D711yescharacteristic
801C22C2×#649311yescharacteristic
802C22#9048211yescharacteristic
803C22C2×#650211yescharacteristic
804C22C2×#651011yescharacteristic
805C22#9052111yescharacteristic
806C22#9052411yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—284no—
814C4—284no—
815C4—562no—
816C4#8976218yescomplemented
817C2—564no—
818C2#1173108311yescharacteristic
819C2#1173109011yescharacteristic
820C2#1173109811yescharacteristic
821C2#1173110011yescharacteristic
822C2#1173111811yescharacteristic
823C2#1173113711yescharacteristic
824C2#1173113911yescharacteristic
825C2#1173122511yescharacteristic
826C2C4×#649311yescharacteristic
827C2C2×#8976211yescharacteristic
828C2#1173968111yescharacteristic
829C2#1173979511yescharacteristic
830C2#1173979711yescharacteristic
831C2#1173992111yescharacteristic
832C2#1173992911yescharacteristic
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
2. C2×#89762C2semidirect
6. C2×C4×C4⋊Dic7C2semidirect
7. #11729324C2semidirect
8. #11729289C2semidirect
9. #11729289C2semidirect
10. #11727183C2semidirect
11. #11727162C2semidirect
39. #89711C4semidirect
65. C2×C7×C4⋊C4D4semidirect
117. C2×C4×C4⋊C4D7semidirect
413. C2×C4⋊C4D28semidirect
507. C4×C7#388semidirect
756. C7#14022semidirect
816. C4#89762semidirect

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×#897622
C2×#897112
C2×C4×C4⋊Dic72
#117293242
#117292892
#117271832
#117271622
#140227