Finite Group Databasebeta

← #13276937

Subgroups — #13276937

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×#6493C211yesmaximal, characteristic
2C2×C7×#380C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
4C2×#89760C211yesmaximal, characteristic, complemented
5C2×#89760C211yesmaximal, characteristic, complemented
6C2×#89745C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
8C2×#89729C212yesmaximal, complemented
9#11729304C212yesmaximal, complemented
10#11727182C212yesmaximal, complemented
11#11727162C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2212yes—
14C23×D28C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2212yes—
18C22×C22⋊Dic7C2211yescharacteristic
19C22×C22⋊Dic7C2211yescharacteristic
20C2×#6493—24no—
21C2×#6493—24no—
22C2×#6493C418yescomplemented
23C22×(C2×D7)⋊C4C2212yes—
24C22×(C2×D7)⋊C4C2212yes—
25C22×(C2×D7)⋊C4C2212yes—
26C22×(C2×D7)⋊C4C2212yes—
27C22×(C2×D7)⋊C4C2212yes—
28C22×C4⋊Dic7C2211yescharacteristic
29C22×Dic7⋊C4C2212yes—
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2212yes—
32C22×C4×Dic7C2211yescharacteristic
33C7×#380—24no—
34C2×C7×#95C2212yes—
35C4×C22⋊Dic7—24no—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40#89760—24no—
41#89760—24no—
42C4⋊C4×Dic7—24no—
43#89745—24no—
44#89729—28no—
45#13998—71nomaximal, Sylow
46C25×C7C2311yescharacteristic
47C24×D7C2312yes—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7—22no—
53C23×C4×C7—22no—
54C23×C4×C7C2×C414yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2312yes—
58C23×C4×C7C2311yescharacteristic
59C22×C22⋊D7—24no—
60C22×C22⋊D7—24no—
61C22×C22⋊D7—24no—
62C22×C22⋊D7—24no—
63C22×C22⋊D7—42no—
64C22×C22⋊D7—42no—
65C22×C22⋊D7C2×C418yes—
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2312yes—
70C23×Dic7C2311yescharacteristic
71C22×D28—22no—
72C22×D28—22no—
73C22×D28—22no—
74C22×D28—22no—
75C22×D28—22no—
76C22×D28—22no—
77C22×D28C2×C414yes—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4D414yescomplemented
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—42no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—22no—
90C2×C22⋊Dic7—22no—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7D414yescomplemented
93#6493—232no—
94C2×(C2×D7)⋊C4—24no—
95C2×(C2×D7)⋊C4—24no—
96C2×(C2×D7)⋊C4—24no—
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—42no—
105C2×(C2×D7)⋊C4—42no—
106C2×(C2×D7)⋊C4—42no—
107C2×(C2×D7)⋊C4—42no—
108C2×(C2×D7)⋊C4C2×C418yes—
109C2×C4⋊Dic7C2×C414yes—
110C2×C4⋊Dic7D414yes—
111C2×C4⋊Dic7D414yes—
112C2×Dic7⋊C4—24no—
113C2×Dic7⋊C4—24no—
114C2×Dic7⋊C4—42no—
115C2×C4×Dic7—22no—
116C2×C4×Dic7—22no—
117C2×C4×Dic7—22no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—24no—
121C2×C4×Dic7—24no—
122C2×C4×Dic7—42no—
123C2×C4×Dic7D414yescomplemented
124C7×#95—24no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—24no—
128C7⋊#95—24no—
129C22×#121—71no—
130C2×#390—71no—
131C2×#390—71no—
132C2×#390—72no—
133C2×#389—71no—
134C2×#380D711yescharacteristic, complemented
135C2×C4×C4⋊C4—71no—
136C2×C4×C22⋊C4—71no—
137#1439—72no—
138#1438—72no—
139#1437—72no—
140C24×C7—21no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—21no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7C22×C412yes—
153C24×C7C2×D412yes—
154C24×C7#4112yes—
155C24×C7C2411yescharacteristic
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×D7—22no—
168C23×D7—22no—
169C23×D7—22no—
170C23×D7C22×C414yes—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—28no—
184C22×C4×C7—28no—
185C22×C4×C7—28no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—44no—
194C22×C4×C7—44no—
195C22×C4×C7—44no—
196C22×C4×C7—44no—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C22×C412yes—
199C22×C4×C7C2×D414yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7#4112yes—
205C22×C4×C7#4112yes—
206C2×C22⋊D7—216no—
207C2×C22⋊D7—216no—
208C2×C22⋊D7—48no—
209C2×C22⋊D7—48no—
210C2×C22⋊D7—48no—
211C2×C22⋊D7—48no—
212C2×C22⋊D7—48no—
213C22×Dic7—21no—
214C22×Dic7—22no—
215C22×Dic7—21no—
216C22×Dic7—22no—
217C22×Dic7—21no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7C22×C414yes—
240C22×Dic7C2×D412yes—
241C22×Dic7C2×D412yes—
242C22×Dic7C2×D414yes—
243C22×Dic7C2×D414yes—
244C22×Dic7C2×D412yes—
245C22×Dic7C2×D412yes—
246C22×Dic7#4112yes—
247C22×Dic7#4112yes—
248C2×D28—28no—
249C2×D28—28no—
250C2×D28—28no—
251C2×D28—44no—
252C2×D28—44no—
253C2×D28—44no—
254C2×D28—44no—
255C7×C4⋊C4—28no—
256C7×C4⋊C4—44no—
257C7×C22⋊C4—48no—
258C22⋊Dic7—28no—
259C22⋊Dic7—28no—
260(C2×D7)⋊C4—216no—
261(C2×D7)⋊C4—48no—
262(C2×D7)⋊C4—48no—
263(C2×D7)⋊C4—48no—
264(C2×D7)⋊C4—48no—
265C4⋊Dic7C22⋊C4116yescomplemented
266Dic7⋊C4—48no—
267C4×Dic7—28no—
268C4×Dic7—48no—
269C4×Dic7—44no—
270C23×D4—72no—
271C23×D4—71no—
272C24×C4C2×D711yescharacteristic
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—71no—
281C22×C22⋊C4—72no—
282C22×C22⋊C4—71no—
283C22×C22⋊C4—72no—
284C22×C22⋊C4—72no—
285C22×C22⋊C4—72no—
286C22×C22⋊C4—72no—
287C22×C22⋊C4C2×D712yes—
288C22×C42—71no—
289C22×C42—71no—
290C22×C42—72no—
291#390—144no—
292#390—148no—
293#390—144no—
294#389—144no—
295#380—24no—
296C4×C4⋊C4—144no—
297C4×C22⋊C4—144no—
298C2×#95—71no—
299C2×#95—72no—
300C2×#95—72no—
301C2×#95—71no—
302C2×#95C2×D712yes—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7C4×D414yes—
338C23×C7C23×C411yescharacteristic
339C23×C7C22×D411yescharacteristic
340C23×C7C22×D411yescharacteristic
341C23×C7C22×D411yescharacteristic
342C23×C7C22×D411yescharacteristic
343C23×C7C22×D411yescharacteristic
344C23×C7C2×#4111yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C7H(5,𝔽2)11yescharacteristic
352C23×C72−1+411yescharacteristic
353C22×D7—24no—
354C22×D7—24no—
355C22×D7—24no—
356C22×D7—24no—
357C22×D7—24no—
358C22×D7—24no—
359C22×D7—24no—
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×D7—42no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—24no—
392C2×C4×C7—24no—
393C2×C4×C7—24no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—42no—
399C2×C4×C7—42no—
400C2×C4×C7—42no—
401C2×C4×C7—42no—
402C2×C4×C7—416no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
407C2×C4×C7—42no—
408C2×C4×C7—42no—
409C2×C4×C7—42no—
410C2×C4×C7C2×C22⋊C414yes—
411C2×C4×C7C4×D414yes—
412C2×C4×C7C4×D414yes—
413C2×C4×C7#12114yes—
414C2×C4×C7#12114yes—
415C2×C4×C7#12414yes—
416C2×C4×C7#12714yes—
417C22⋊D7—432no—
418C2×Dic7—24no—
419C2×Dic7—24no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—24no—
424C2×Dic7—24no—
425C2×Dic7—24no—
426C2×Dic7—24no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—41no—
440C2×Dic7—41no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—41no—
445C2×Dic7—41no—
446C2×Dic7—41no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—41no—
450C2×Dic7—41no—
451C2×Dic7C2×C22⋊C418yes—
452C2×Dic7#12114yescomplemented
453D28—416no—
454C25—72no—
455C25C22×D711yescharacteristic
456C22×D4—78no—
457C22×D4—74no—
458C22×D4—144no—
459C22×D4—144no—
460C22×D4—144no—
461C22×D4—144no—
462C22×D4—142no—
463C22×D4—142no—
464C22×D4—142no—
465C22×D4—142no—
466C22×D4—142no—
467C22×D4—142no—
468C22×D4—282no—
469C22×D4—282no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—71no—
477C23×C4—72no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4C4×D714yes—
482C23×C4C22×D712yes—
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D712yes—
485C23×C4C22×D711yescharacteristic
486#121—1432no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—74no—
493C2×C4⋊C4—74no—
494C2×C4⋊C4—74no—
495C2×C4⋊C4—144no—
496C2×C4⋊C4—144no—
497C2×C4⋊C4—282no—
498C2×C4⋊C4C22⋊D714yescomplemented
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—78no—
504C2×C22⋊C4—144no—
505C2×C22⋊C4—144no—
506C2×C22⋊C4—142no—
507C2×C22⋊C4—142no—
508C2×C22⋊C4—142no—
509C2×C22⋊C4—142no—
510C2×C22⋊C4—142no—
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—144no—
519C2×C22⋊C4—282no—
520C2×C22⋊C4—282no—
521C2×C22⋊C4—282no—
522C2×C22⋊C4—282no—
523C2×C42—74no—
524C2×C42—142no—
525C2×C42—142no—
526C2×C42—144no—
527C2×C42—144no—
528C2×C42—142no—
529C2×C42—142no—
530C2×C42—142no—
531C2×C42—282no—
532#95—24no—
533#95—142no—
534#95—142no—
535#95—144no—
536#95—144no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7C22×C22⋊C411yescharacteristic
553C22×C7C2×C4×D411yescharacteristic
554C22×C7C2×C4×D411yescharacteristic
555C22×C7C2×C4×D411yescharacteristic
556C22×C7C4×#4111yescharacteristic
557C22×C7#51811yescharacteristic
558C22×C7#52011yescharacteristic
559C22×C7C2×#12111yescharacteristic
560C22×C7C2×#12111yescharacteristic
561C22×C7C2×#12111yescharacteristic
562C22×C7#52511yescharacteristic
563C22×C7C2×#12411yescharacteristic
564C22×C7#52911yescharacteristic
565C22×C7C2×#12711yescharacteristic
566C22×C7#53211yescharacteristic
567C22×C7#53511yescharacteristic
568C22×C7#53711yescharacteristic
569C22×C7#54011yescharacteristic
570C22×C7#54211yescharacteristic
571C22×C7D4211yescharacteristic
572C22×C7D4211yescharacteristic
573C22×C7D4211yescharacteristic
574C22×C7#54611yescharacteristic
575C22×C7#54611yescharacteristic
576C22×C7#54611yescharacteristic
577C22×C7#54711yescharacteristic
578C22×C7#54811yescharacteristic
579C22×C7#54811yescharacteristic
580C22×C7#54811yescharacteristic
581C22×C7#55011yescharacteristic
582C22×C7#55011yescharacteristic
583C22×C7#55011yescharacteristic
584C22×C7#55311yescharacteristic
585C22×C7#55311yescharacteristic
586C22×C7#55511yescharacteristic
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—44no—
603C4×C7—42no—
604C4×C7—82no—
605C4×C7#39018yescomplemented
606Dic7—28no—
607Dic7—24no—
608Dic7—42no—
609Dic7—42no—
610Dic7—42no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—74no—
624C24—142no—
625C24—142no—
626C24—142no—
627C24—142no—
628C24—142no—
629C24—142no—
630C24—142no—
631C24—142no—
632C24—142no—
633C24—142no—
634C24—142no—
635C24—142no—
636C24—142no—
637C24—142no—
638C24C2×C4×D712yes—
639C24D4×D712yes—
640C24#116112yes—
641C24C23×D711yescharacteristic
642C2×D4—1416no—
643C2×D4—1416no—
644C2×D4—148no—
645C2×D4—148no—
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—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—74no—
683C22×C4—72no—
684C22×C4—74no—
685C22×C4—74no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—72no—
689C22×C4—72no—
690C22×C4—72no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—142no—
694C22×C4—142no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—142no—
698C22×C4—142no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4C2×C4×D712yes—
718C22×C4C2×C4×D712yes—
719C22×C4#115712yes—
720C22×C4D4×D712yes—
721C22×C4D4×D712yes—
722C22×C4D4×D712yes—
723C22×C4#115912yes—
724C22×C4C2×C22⋊D714yes—
725C22×C4C2×C22⋊D712yes—
726C4⋊C4—28no—
727C4⋊C4—44no—
728C4⋊C4—716no—
729C4⋊C4—288no—
730C22⋊C4—48no—
731C22⋊C4—1416no—
732C22⋊C4—148no—
733C22⋊C4—148no—
734C22⋊C4—288no—
735C22⋊C4—288no—
736C22⋊C4—288no—
737C22⋊C4—288no—
738C42—148no—
739C42—288no—
740C42—284no—
741C2×C7—44no—
742C2×C7C2×#39011yescharacteristic
743C2×C7C4×#12111yescharacteristic
744C2×C7#232411yescharacteristic
745C2×C7D4×C22⋊C411yescharacteristic
746C2×C7#234111yescharacteristic
747C2×C7#236111yescharacteristic
748C2×C7#236311yescharacteristic
749C2×C7#241411yescharacteristic
750C2×C7#241611yescharacteristic
751C2×C7#242611yescharacteristic
752C2×C7#242811yescharacteristic
753C2×C7#249011yescharacteristic
754C2×C7#249111yescharacteristic
755C2×C7#254011yescharacteristic
756C2×C7#254111yescharacteristic
757D7—84no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—144no—
793C23—144no—
794C23—144no—
795C23—144no—
796C23—144no—
797C23—144no—
798C23—144no—
799C23—282no—
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#645614yes—
828C23C22×C4×D711yescharacteristic
829C23C2×#115711yescharacteristic
830C23C2×D4×D711yescharacteristic
831C23C2×D4×D711yescharacteristic
832C23C2×D4×D711yescharacteristic
833C23C2×D4×D711yescharacteristic
834C23C2×#115911yescharacteristic
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—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—416no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—78no—
868C2×C4—74no—
869C2×C4—142no—
870C2×C4—144no—
871C2×C4—142no—
872C2×C4—144no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—144no—
876C2×C4—144no—
877C2×C4—142no—
878C2×C4—144no—
879C2×C4—144no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—142no—
889C2×C4—142no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—281no—
893C2×C4—281no—
894C2×C4—281no—
895C2×C4—281no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4D7×C22⋊C414yes—
903C2×C4(C22⋊D7)⋊C414yes—
904C2×C4#644714yes—
905C2×C4#644814yes—
906C2×C4C4×C22⋊D714yes—
907C2×C4#650214yes—
908C2×C4#650314yes—
909C7#1399811yescharacteristic, complemented, Sylow
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
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×D7×C22⋊C411yescharacteristic
941C22C2×(C22⋊D7)⋊C411yescharacteristic
942C22C2×#644711yescharacteristic
943C22C2×#644811yescharacteristic
944C22C2×#645611yescharacteristic
945C22#9019511yescharacteristic
946C22#9019811yescharacteristic
947C22#9020511yescharacteristic
948C22#9021211yescharacteristic
949C22#9021311yescharacteristic
950C22#9022111yescharacteristic
951C22#9022311yescharacteristic
952C22#9028711yescharacteristic
953C22#9029011yescharacteristic
954C22#9029011yescharacteristic
955C22D7×#12111yescharacteristic
956C22#9029811yescharacteristic
957C22#9030011yescharacteristic
958C22#9030011yescharacteristic
959C22#9031011yescharacteristic
960C22#9031511yescharacteristic
961C22#9031811yescharacteristic
962C22#9032011yescharacteristic
963C22#9032111yescharacteristic
964C22#9032111yescharacteristic
965C22#9032411yescharacteristic
966C22#9032411yescharacteristic
967C22#9033411yescharacteristic
968C22C2×C4×C22⋊D711yescharacteristic
969C22D4×C22⋊D711yescharacteristic
970C22C2×#650211yescharacteristic
971C22C2×#650311yescharacteristic
972C22#9050811yescharacteristic
973C22#9052011yescharacteristic
974C22#9052511yescharacteristic
975C4—42no—
976C4—44no—
977C4—82no—
978C4—144no—
979C4—148no—
980C4—282no—
981C4—282no—
982C4—282no—
983C4#8972918yescomplemented
984C2—44no—
985C2—564no—
986C2#1173131011yescharacteristic
987C2#1173131711yescharacteristic
988C2#1173132211yescharacteristic
989C2#1173133211yescharacteristic
990C2#1173135911yescharacteristic
991C2#1173136011yescharacteristic
992C2#1173145211yescharacteristic
993C2#1173146411yescharacteristic
994C2C2×#8972911yescharacteristic
995C2#1173960811yescharacteristic
996C2#1173968911yescharacteristic
997C2#1174009411yescharacteristic
998C2#1174011411yescharacteristic
999C2#1174020011yescharacteristic
1000C2#1174022411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#380C2
socle, cosocleC24×C7C24
prime radicalC22×#6493C2
hypercenterC2×#380D7
hypocenterC7#13998
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C7×#380C2semidirect
3. C2×C4×C22⋊Dic7C2semidirect
4. C2×#89760C2semidirect
5. C2×#89760C2semidirect
6. C2×#89745C2semidirect
7. C2×C4⋊C4×Dic7C2semidirect
8. C2×#89729C2semidirect
9. #11729304C2semidirect
10. #11727182C2semidirect
11. #11727162C2semidirect
22. C2×#6493C4semidirect
83. C2×C7×C4⋊C4D4semidirect
92. C2×C22⋊Dic7D4semidirect
123. C2×C4×Dic7D4semidirect
134. C2×#380D7semidirect
265. C4⋊Dic7C22⋊C4semidirect
452. C2×Dic7#121semidirect
498. C2×C4⋊C4C22⋊D7semidirect
605. C4×C7#390semidirect
909. C7#13998semidirect
983. C4#89729semidirect

Maximal subgroups

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

subgroupindex
C22×#64932
C2×C7×#3802
C2×C4×C22⋊Dic72
C2×#897602
C2×#897452
C2×C4⋊C4×Dic72
C2×#897292
#117293042
#117271822
#117271622
#139987