Finite Group Databasebeta

← #13276935

Subgroups — #13276935

Order 1792.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6458C211yesmaximal, characteristic
2C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#89759C211yesmaximal, characteristic, complemented
4C2×#89760C211yesmaximal, characteristic, complemented
5C2×#89757C211yesmaximal, characteristic, complemented
6C2×#89711C211yesmaximal, characteristic, complemented
7C2×#89711C212yesmaximal, complemented
8C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
9#11729291C212yesmaximal, complemented
10#11727181C212yesmaximal, complemented
11#11727180C212yesmaximal, complemented
12C23×D28C2211yescharacteristic
13C23×D28C2212yes—
14C23×C4×D7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C42×C7C2212yes—
18C22×C42×C7C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2212yes—
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2212yes—
23C22×(C2×D7)⋊C4C2212yes—
24C22×(C2×D7)⋊C4C2212yes—
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2212yes—
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2212yes—
29C22×C4×Dic7C2211yescharacteristic
30C2×#6458—24no—
31C2×#6458—24no—
32C2×#6458C418yescomplemented
33C4×C7×C4⋊C4—24no—
34C2×C7×#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2211yescharacteristic
39#89760—24no—
40#89759—24no—
41#89757—24no—
42#89711—24no—
43#89711—28no—
44C4×(C2×D7)⋊C4—24no—
45#13998—71nomaximal, Sylow
46C24×D7C2312yes—
47C24×D7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×Dic7C2312yes—
54C23×Dic7C2311yescharacteristic
55C23×Dic7C2311yescharacteristic
56C23×Dic7C2311yescharacteristic
57C22×D28—24no—
58C22×D28—24no—
59C22×D28—24no—
60C22×D28—24no—
61C22×D28—22no—
62C22×D28—22no—
63C22×D28—22no—
64C22×D28—22no—
65C22×D28—22no—
66C22×D28—22no—
67C22×D28—42no—
68C22×D28—42no—
69C22×D28C2×C414yes—
70C22×D28C2×C418yes—
71C22×C4×D7—22no—
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7C2×C414yes—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4C2×C414yes—
81C2×C7×C4⋊C4D414yes—
82C2×C7×C4⋊C4D414yes—
83C2×C7×C4⋊C4D414yescomplemented
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—24no—
87C2×C42×C7—24no—
88C2×C42×C7—42no—
89C2×C42×C7D414yescomplemented
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—24no—
92C2×(C2×D7)⋊C4—24no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—24no—
98C2×(C2×D7)⋊C4—24no—
99C2×(C2×D7)⋊C4—24no—
100C2×(C2×D7)⋊C4—24no—
101C2×(C2×D7)⋊C4—24no—
102C2×(C2×D7)⋊C4—24no—
103C2×(C2×D7)⋊C4—24no—
104C2×(C2×D7)⋊C4—24no—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—42no—
108C2×(C2×D7)⋊C4—42no—
109C2×(C2×D7)⋊C4—42no—
110C2×(C2×D7)⋊C4—42no—
111C2×(C2×D7)⋊C4—42no—
112C2×(C2×D7)⋊C4C2×C418yes—
113C2×(C2×D7)⋊C4D414yescomplemented
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—24no—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7—22no—
118C2×C4⋊Dic7—24no—
119C2×C4⋊Dic7—42no—
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123#6458—232no—
124C7×#95—24no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—24no—
128C7⋊#95—24no—
129C22×#121—71no—
130C2×#390—72no—
131C2×#390—71no—
132C2×#390—71no—
133C2×#389—71no—
134C2×#380—71no—
135C2×C4×C4⋊C4D711yescharacteristic, complemented
136C2×C4×C22⋊C4—71no—
137#1439—72no—
138#1438—72no—
139#1437—72no—
140C24×C7C2411yescharacteristic
141C23×D7—21no—
142C23×D7—21no—
143C23×D7—21no—
144C23×D7—21no—
145C23×D7—21no—
146C23×D7—21no—
147C23×D7—21no—
148C23×D7—21no—
149C23×D7—21no—
150C23×D7—21no—
151C23×D7—21no—
152C23×D7—21no—
153C23×D7—22no—
154C23×D7—22no—
155C23×D7—22no—
156C23×D7—22no—
157C23×D7—22no—
158C23×D7—22no—
159C23×D7—22no—
160C23×D7—22no—
161C23×D7—22no—
162C23×D7—22no—
163C23×D7—22no—
164C23×D7—22no—
165C23×D7—22no—
166C23×D7—22no—
167C23×D7C22×C414yes—
168C23×D7C22×C412yes—
169C23×D7C2×D412yes—
170C23×D7#4112yes—
171C22×C4×C7—22no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—22no—
185C22×C4×C7—21no—
186C22×C4×C7—22no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7C22×C414yes—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2×D414yes—
195C22×C4×C7C2×D414yes—
196C22×C4×C7C2×D414yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D412yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7#4112yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7C22×C412yes—
232C22×Dic7C2×D412yes—
233C22×Dic7#4112yes—
234C2×D28—216no—
235C2×D28—216no—
236C2×D28—28no—
237C2×D28—28no—
238C2×D28—28no—
239C2×D28—48no—
240C2×D28—48no—
241C2×D28—48no—
242C2×D28—48no—
243C2×D28—48no—
244C2×D28—44no—
245C2×D28—44no—
246C2×D28—44no—
247C2×D28—44no—
248C2×C4×D7—28no—
249C2×C4×D7—28no—
250C2×C4×D7—28no—
251C2×C4×D7—44no—
252C2×C4×D7—44no—
253C2×C4×D7—44no—
254C2×C4×D7—44no—
255C7×C4⋊C4—28no—
256C7×C4⋊C4C22⋊C4116yescomplemented
257C42×C7—28no—
258C42×C7—48no—
259(C2×D7)⋊C4—28no—
260(C2×D7)⋊C4—216no—
261(C2×D7)⋊C4—28no—
262(C2×D7)⋊C4—48no—
263(C2×D7)⋊C4—48no—
264(C2×D7)⋊C4—48no—
265(C2×D7)⋊C4—48no—
266(C2×D7)⋊C4—48no—
267C4⋊Dic7—48no—
268C4⋊Dic7—44no—
269C4×Dic7—44no—
270C23×D4—71no—
271C23×D4—72no—
272C24×C4—71no—
273C2×#121—78no—
274C2×#121—144no—
275C2×#121—144no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—72no—
278C22×C4⋊C4C2×D711yescharacteristic
279C22×C4⋊C4C2×D711yescharacteristic
280C22×C22⋊C4—72no—
281C22×C22⋊C4—71no—
282C22×C22⋊C4—72no—
283C22×C22⋊C4—71no—
284C22×C22⋊C4—72no—
285C22×C22⋊C4—72no—
286C22×C22⋊C4—72no—
287C22×C22⋊C4—72no—
288C22×C42—71no—
289C22×C42C2×D712yes—
290C22×C42C2×D711yescharacteristic
291#390—148no—
292#390—144no—
293#390—144no—
294#389—144no—
295#380—144no—
296C4×C4⋊C4—24no—
297C4×C22⋊C4—144no—
298C2×#95—71no—
299C2×#95—72no—
300C2×#95—72no—
301C2×#95—71no—
302C2×#95C2×D712yes—
303C23×C7C23×C411yescharacteristic
304C23×C7C22×D411yescharacteristic
305C23×C7C22×D411yescharacteristic
306C23×C7C22×D411yescharacteristic
307C23×C7C22×D411yescharacteristic
308C23×C7C22×D411yescharacteristic
309C23×C7C2×#4111yescharacteristic
310C23×C7C2×#4111yescharacteristic
311C23×C7C2×#4111yescharacteristic
312C23×C7C2×#4111yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7H(5,𝔽2)11yescharacteristic
315C23×C7H(5,𝔽2)11yescharacteristic
316C23×C7H(5,𝔽2)11yescharacteristic
317C23×C72−1+411yescharacteristic
318C22×D7—22no—
319C22×D7—22no—
320C22×D7—22no—
321C22×D7—22no—
322C22×D7—22no—
323C22×D7—22no—
324C22×D7—22no—
325C22×D7—22no—
326C22×D7—22no—
327C22×D7—22no—
328C22×D7—22no—
329C22×D7—22no—
330C22×D7—22no—
331C22×D7—22no—
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—24no—
337C22×D7—24no—
338C22×D7—24no—
339C22×D7—24no—
340C22×D7—24no—
341C22×D7—24no—
342C22×D7—24no—
343C22×D7—41no—
344C22×D7—41no—
345C22×D7—41no—
346C22×D7—41no—
347C22×D7—41no—
348C22×D7—41no—
349C22×D7—41no—
350C22×D7—41no—
351C22×D7—41no—
352C22×D7—41no—
353C22×D7—41no—
354C22×D7—41no—
355C22×D7—41no—
356C22×D7—41no—
357C22×D7—41no—
358C22×D7—41no—
359C22×D7—42no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C22×D7—42no—
371C22×D7—42no—
372C22×D7—42no—
373C22×D7—42no—
374C22×D7—42no—
375C22×D7—42no—
376C22×D7—42no—
377C22×D7—42no—
378C22×D7—42no—
379C22×D7—42no—
380C22×D7—42no—
381C22×D7—42no—
382C22×D7—42no—
383C22×D7—42no—
384C22×D7—42no—
385C22×D7—42no—
386C22×D7—42no—
387C22×D7C4×D414yes—
388C2×C4×C7—24no—
389C2×C4×C7—24no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—24no—
393C2×C4×C7—22no—
394C2×C4×C7—24no—
395C2×C4×C7—24no—
396C2×C4×C7—24no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—24no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—24no—
405C2×C4×C7—24no—
406C2×C4×C7—42no—
407C2×C4×C7—42no—
408C2×C4×C7—42no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—42no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7C2×C22⋊C418yes—
415C2×C4×C7C2×C22⋊C414yes—
416C2×C4×C7C4×D414yes—
417C2×C4×C7C4×D414yes—
418C2×C4×C7#12114yes—
419C2×C4×C7#12114yes—
420C2×C4×C7#12114yescomplemented
421C2×C4×C7#12414yes—
422C2×C4×C7#12714yes—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—41no—
440C2×Dic7—41no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—42no—
445C2×Dic7—42no—
446C2×Dic7—42no—
447C2×Dic7—42no—
448C2×Dic7—42no—
449C2×Dic7—42no—
450C2×Dic7—42no—
451D28—432no—
452D28—416no—
453C4×D7—416no—
454C25—71no—
455C25—72no—
456C22×D4—74no—
457C22×D4—78no—
458C22×D4—144no—
459C22×D4—144no—
460C22×D4—144no—
461C22×D4—142no—
462C22×D4—142no—
463C22×D4—142no—
464C22×D4—142no—
465C22×D4—142no—
466C22×D4—144no—
467C22×D4—142no—
468C22×D4—282no—
469C22×D4—282no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—74no—
474C23×C4—72no—
475C23×C4—142no—
476C23×C4—142no—
477C23×C4—142no—
478C23×C4—142no—
479C23×C4—142no—
480C23×C4—142no—
481C23×C4C22×D712yes—
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D712yes—
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#121—1432no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—142no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—142no—
493C2×C4⋊C4—142no—
494C2×C4⋊C4—282no—
495C2×C4⋊C4C4×D714yes—
496C2×C4⋊C4D2814yes—
497C2×C4⋊C4D2814yescomplemented
498C2×C4⋊C4C22⋊D714yes—
499C2×C22⋊C4—78no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—142no—
502C2×C22⋊C4—142no—
503C2×C22⋊C4—144no—
504C2×C22⋊C4—142no—
505C2×C22⋊C4—142no—
506C2×C22⋊C4—142no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—144no—
516C2×C22⋊C4—144no—
517C2×C22⋊C4—144no—
518C2×C22⋊C4—282no—
519C2×C22⋊C4—282no—
520C2×C22⋊C4—282no—
521C2×C22⋊C4—282no—
522C2×C22⋊C4—282no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—24no—
526C2×C42—24no—
527C2×C42—42no—
528C2×C42—142no—
529C2×C42—142no—
530C2×C42—142no—
531C2×C42D2814yescomplemented
532#95—24no—
533#95—142no—
534#95—142no—
535#95—144no—
536#95—144no—
537C22×C7C22×C22⋊C411yescharacteristic
538C22×C7C2×C4×D411yescharacteristic
539C22×C7C2×C4×D411yescharacteristic
540C22×C7C2×C4×D411yescharacteristic
541C22×C7C4×#4111yescharacteristic
542C22×C7#51811yescharacteristic
543C22×C7#52011yescharacteristic
544C22×C7C2×#12111yescharacteristic
545C22×C7C2×#12111yescharacteristic
546C22×C7C2×#12111yescharacteristic
547C22×C7#52511yescharacteristic
548C22×C7C2×#12411yescharacteristic
549C22×C7#52911yescharacteristic
550C22×C7C2×#12711yescharacteristic
551C22×C7#53211yescharacteristic
552C22×C7#53511yescharacteristic
553C22×C7#53711yescharacteristic
554C22×C7#54011yescharacteristic
555C22×C7#54211yescharacteristic
556C22×C7D4211yescharacteristic
557C22×C7D4211yescharacteristic
558C22×C7D4211yescharacteristic
559C22×C7#54611yescharacteristic
560C22×C7#54611yescharacteristic
561C22×C7#54611yescharacteristic
562C22×C7#54711yescharacteristic
563C22×C7#54811yescharacteristic
564C22×C7#54811yescharacteristic
565C22×C7#54811yescharacteristic
566C22×C7#55011yescharacteristic
567C22×C7#55011yescharacteristic
568C22×C7#55011yescharacteristic
569C22×C7#55311yescharacteristic
570C22×C7#55311yescharacteristic
571C22×C7#55511yescharacteristic
572C2×D7—24no—
573C2×D7—24no—
574C2×D7—24no—
575C2×D7—42no—
576C2×D7—42no—
577C2×D7—42no—
578C2×D7—42no—
579C2×D7—42no—
580C2×D7—42no—
581C2×D7—42no—
582C2×D7—42no—
583C2×D7—42no—
584C2×D7—42no—
585C2×D7—42no—
586C2×D7—42no—
587C2×D7—44no—
588C2×D7—44no—
589C2×D7—44no—
590C2×D7—44no—
591C2×D7—44no—
592C2×D7—44no—
593C2×D7—44no—
594C2×D7—82no—
595C2×D7—82no—
596C2×D7—82no—
597C2×D7—82no—
598C2×D7—82no—
599C2×D7—82no—
600C2×D7—82no—
601C2×D7—82no—
602C4×C7—28no—
603C4×C7—24no—
604C4×C7—42no—
605C4×C7—44no—
606C4×C7#39018yescomplemented
607Dic7—42no—
608Dic7—42no—
609Dic7—42no—
610Dic7—82no—
611C24—72no—
612C24—72no—
613C24—72no—
614C24—74no—
615C24—141no—
616C24—141no—
617C24—141no—
618C24—141no—
619C24—141no—
620C24—141no—
621C24—141no—
622C24—141no—
623C24—141no—
624C24—141no—
625C24—141no—
626C24—141no—
627C24—142no—
628C24—142no—
629C24—142no—
630C24—142no—
631C24—142no—
632C24—142no—
633C24—142no—
634C24—142no—
635C24—142no—
636C24—142no—
637C24—142no—
638C24—142no—
639C24—142no—
640C24—142no—
641C24C23×D711yescharacteristic
642C2×D4—1416no—
643C2×D4—148no—
644C2×D4—148no—
645C2×D4—1416no—
646C2×D4—148no—
647C2×D4—288no—
648C2×D4—288no—
649C2×D4—288no—
650C2×D4—288no—
651C2×D4—288no—
652C2×D4—284no—
653C2×D4—284no—
654C2×D4—284no—
655C2×D4—284no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—72no—
677C22×C4—72no—
678C22×C4—72no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4—141no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—141no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—148no—
698C22×C4—148no—
699C22×C4—148no—
700C22×C4—142no—
701C22×C4—142no—
702C22×C4—142no—
703C22×C4—142no—
704C22×C4—142no—
705C22×C4—142no—
706C22×C4—142no—
707C22×C4—284no—
708C22×C4—284no—
709C22×C4—284no—
710C22×C4—284no—
711C22×C4C2×C4×D714yes—
712C22×C4C2×C4×D712yes—
713C22×C4C2×D2812yes—
714C22×C4C2×D2814yes—
715C22×C4C2×D2812yes—
716C22×C4C2×D2814yes—
717C22×C4C2×D2812yes—
718C22×C4C2×D2812yes—
719C22×C4C2×D2812yes—
720C22×C4#115712yes—
721C22×C4#115712yes—
722C22×C4D4×D712yes—
723C22×C4#116112yes—
724C22×C4C2×C22⋊D714yes—
725C22×C4C2×C22⋊D712yes—
726C4⋊C4—28no—
727C4⋊C4—288no—
728C4⋊C4—284no—
729C4⋊C4(C2×D7)⋊C4116yescomplemented
730C22⋊C4—148no—
731C22⋊C4—148no—
732C22⋊C4—1416no—
733C22⋊C4—288no—
734C22⋊C4—288no—
735C22⋊C4—288no—
736C22⋊C4—288no—
737C22⋊C4—288no—
738C42—28no—
739C42—48no—
740C42—284no—
741C2×C7C2×#39011yescharacteristic
742C2×C7C4×#12111yescharacteristic
743C2×C7#232411yescharacteristic
744C2×C7D4×C22⋊C411yescharacteristic
745C2×C7#234111yescharacteristic
746C2×C7#236111yescharacteristic
747C2×C7#236311yescharacteristic
748C2×C7#241411yescharacteristic
749C2×C7#241611yescharacteristic
750C2×C7#242611yescharacteristic
751C2×C7#242811yescharacteristic
752C2×C7#249011yescharacteristic
753C2×C7#249111yescharacteristic
754C2×C7#254011yescharacteristic
755C2×C7#254111yescharacteristic
756D7—44no—
757D7—84no—
758C23—74no—
759C23—142no—
760C23—142no—
761C23—142no—
762C23—142no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—142no—
773C23—142no—
774C23—142no—
775C23—142no—
776C23—142no—
777C23—144no—
778C23—144no—
779C23—144no—
780C23—144no—
781C23—144no—
782C23—144no—
783C23—144no—
784C23—281no—
785C23—281no—
786C23—281no—
787C23—281no—
788C23—281no—
789C23—281no—
790C23—281no—
791C23—281no—
792C23—281no—
793C23—281no—
794C23—281no—
795C23—281no—
796C23—281no—
797C23—281no—
798C23—281no—
799C23—281no—
800C23—282no—
801C23—282no—
802C23—282no—
803C23—282no—
804C23—282no—
805C23—282no—
806C23—282no—
807C23—282no—
808C23—282no—
809C23—282no—
810C23—282no—
811C23—282no—
812C23—282no—
813C23—282no—
814C23—282no—
815C23—282no—
816C23—282no—
817C23—282no—
818C23—282no—
819C23—282no—
820C23—282no—
821C23—282no—
822C23—282no—
823C23—282no—
824C23—282no—
825C23—282no—
826C23—282no—
827C23—282no—
828C23C22×C4×D711yescharacteristic
829C23C22×D2811yescharacteristic
830C23C22×D2811yescharacteristic
831C23C22×D2811yescharacteristic
832C23C2×#115711yescharacteristic
833C23C2×#115711yescharacteristic
834C23C2×D4×D711yescharacteristic
835C23#654811yescharacteristic
836C23C2×#116111yescharacteristic
837C23#655111yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23#655311yescharacteristic
841C23#655311yescharacteristic
842C23C22×C22⋊D711yescharacteristic
843D4—2832no—
844D4—2816no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—281no—
881C2×C4—281no—
882C2×C4—281no—
883C2×C4—281no—
884C2×C4—281no—
885C2×C4—281no—
886C2×C4—281no—
887C2×C4—281no—
888C2×C4—281no—
889C2×C4—281no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—2816no—
893C2×C4—282no—
894C2×C4—282no—
895C2×C4—282no—
896C2×C4—282no—
897C2×C4—282no—
898C2×C4—282no—
899C2×C4—282no—
900C2×C4C4×D2814yes—
901C2×C4C4×D2814yes—
902C2×C4#643714yes—
903C2×C4#643814yes—
904C2×C4#645814yescomplemented
905C2×C4C2×(C2×D7)⋊C418yes—
906C2×C4C2×(C2×D7)⋊C414yes—
907C2×C4#649314yes—
908C2×C4#649314yes—
909C7#1399811yescharacteristic, complemented, Sylow
910C22—144no—
911C22—144no—
912C22—144no—
913C22—282no—
914C22—282no—
915C22—282no—
916C22—282no—
917C22—282no—
918C22—282no—
919C22—282no—
920C22—282no—
921C22—282no—
922C22—282no—
923C22—282no—
924C22—282no—
925C22—284no—
926C22—284no—
927C22—284no—
928C22—284no—
929C22—284no—
930C22—284no—
931C22—284no—
932C22—562no—
933C22—562no—
934C22—562no—
935C22—562no—
936C22—562no—
937C22—562no—
938C22—562no—
939C22—562no—
940C22C2×C4×D2811yescharacteristic
941C22C2×C4×D2811yescharacteristic
942C22C2×#643711yescharacteristic
943C22C2×#643811yescharacteristic
944C22C2×#645811yescharacteristic
945C22#9019811yescharacteristic
946C22#9020111yescharacteristic
947C22#9020511yescharacteristic
948C22#9021511yescharacteristic
949C22#9021611yescharacteristic
950C22#9022111yescharacteristic
951C22#9022311yescharacteristic
952C22C4×D4×D711yescharacteristic
953C22#9023611yescharacteristic
954C22#9023911yescharacteristic
955C22D4×D2811yescharacteristic
956C22D4×D2811yescharacteristic
957C22#9024511yescharacteristic
958C22#9024511yescharacteristic
959C22#9025311yescharacteristic
960C22C4×#116111yescharacteristic
961C22#9026511yescharacteristic
962C22#9026711yescharacteristic
963C22#9026711yescharacteristic
964C22#9026811yescharacteristic
965C22#9026811yescharacteristic
966C22#9027111yescharacteristic
967C22#9027311yescharacteristic
968C22C22×(C2×D7)⋊C411yescharacteristic
969C22C2×#649311yescharacteristic
970C22C2×#649311yescharacteristic
971C22D4×C22⋊D711yescharacteristic
972C22#9050811yescharacteristic
973C22#9052011yescharacteristic
974C22#9052511yescharacteristic
975C4—28no—
976C4—24no—
977C4—42no—
978C4—44no—
979C4—282no—
980C4—282no—
981C4—282no—
982C4—562no—
983C4#8971118yescomplemented
984C2—284no—
985C2—564no—
986C2#1173109411yescharacteristic
987C2C4×#645811yescharacteristic
988C2#1173120811yescharacteristic
989C2#1173121911yescharacteristic
990C2#1173123211yescharacteristic
991C2#1173123311yescharacteristic
992C2#1173124311yescharacteristic
993C2#1173124411yescharacteristic
994C2C2×#8971111yescharacteristic
995C2#1173963811yescharacteristic
996C2#1173972111yescharacteristic
997C2D4×(C2×D7)⋊C411yescharacteristic
998C2#1173985411yescharacteristic
999C2#1173990211yescharacteristic
1000C2#1173994011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, cosocleC24×C7C24
prime radicalC22×#6458C2
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#13998
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C4⋊C4C2semidirect
3. C2×#89759C2semidirect
4. C2×#89760C2semidirect
5. C2×#89757C2semidirect
6. C2×#89711C2semidirect
7. C2×#89711C2semidirect
8. C2×C4×(C2×D7)⋊C4C2semidirect
9. #11729291C2semidirect
10. #11727181C2semidirect
11. #11727180C2semidirect
32. C2×#6458C4semidirect
83. C2×C7×C4⋊C4D4semidirect
89. C2×C42×C7D4semidirect
113. C2×(C2×D7)⋊C4D4semidirect
135. C2×C4×C4⋊C4D7semidirect
256. C7×C4⋊C4C22⋊C4semidirect
420. C2×C4×C7#121semidirect
497. C2×C4⋊C4D28semidirect
531. C2×C42D28semidirect
606. C4×C7#390semidirect
729. C4⋊C4(C2×D7)⋊C4semidirect
904. C2×C4#6458semidirect
909. C7#13998semidirect
983. C4#89711semidirect

Maximal subgroups

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

subgroupindex
C22×#64582
C2×C4×C7×C4⋊C42
C2×#897592
C2×#897602
C2×#897572
C2×#897112
C2×C4×(C2×D7)⋊C42
#117292912
#117271812
#117271802
#139987