Finite Group Databasebeta

← #13276939

Subgroups — #13276939

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×#6501C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic, complemented
3C2×#89993C211yesmaximal, characteristic, complemented
4C2×#89759C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
6C2×#89729C212yesmaximal, complemented
7C2×#89700C211yesmaximal, characteristic, complemented
8C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
9#11729304C212yesmaximal, complemented
10#11729301C212yesmaximal, complemented
11#11729299C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C23×C22⋊D7C2212yes—
14C23×C4×D7C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C22⋊C4C2212yes—
17C22×C7×C22⋊C4C2212yes—
18C22×C42×C7C2211yescharacteristic
19C22×C22⋊Dic7C2212yes—
20C22×C22⋊Dic7C2212yes—
21C22×C22⋊Dic7C2212yes—
22C2×#6501—24no—
23C2×#6501—24no—
24C2×#6501C418yescomplemented
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2212yes—
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2212yes—
31C22×C4×Dic7C2212yes—
32C22×C4×Dic7C2211yescharacteristic
33C7×#390—24no—
34#89993—24no—
35C2×C7⋊#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40#89759—24no—
41C4⋊C4×Dic7—24no—
42#89729—28no—
43C4×(C2×D7)⋊C4—24no—
44#89700—24no—
45#13998—71nomaximal, Sylow
46C25×C7C2312yes—
47C24×D7C2311yescharacteristic
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—22no—
52C22×C7×D4—22no—
53C22×C7×D4—22no—
54C22×C7×D4C2×C414yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
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×Dic7C2312yes—
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2312yes—
70C23×Dic7C2311yescharacteristic
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⋊C4D414yescomplemented
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4—42no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×C22⋊Dic7—24no—
91C2×C22⋊Dic7—24no—
92C2×C22⋊Dic7—24no—
93C2×C22⋊Dic7—24no—
94C2×C22⋊Dic7—24no—
95C2×C22⋊Dic7—24no—
96C2×C22⋊Dic7—42no—
97C2×C22⋊Dic7—42no—
98C2×C22⋊Dic7C2×C418yes—
99#6501—232no—
100C2×(C2×D7)⋊C4—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—22no—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—42no—
108C2×(C2×D7)⋊C4D414yescomplemented
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7C2×C414yes—
113C2×C4⋊Dic7D414yes—
114C2×C4⋊Dic7D414yes—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—42no—
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—24no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—24no—
129C22×#121—71no—
130C2×#390—71no—
131C2×#390—72no—
132C2×#390D711yescharacteristic, complemented
133C2×#389—71no—
134C2×#380—71no—
135C2×C4×C4⋊C4—71no—
136C2×C4×C22⋊C4—71no—
137#1439—72no—
138#1438—72no—
139#1437—72no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7—22no—
143C24×C7—22no—
144C24×C7—22no—
145C24×C7—22no—
146C24×C7—22no—
147C24×C7—22no—
148C24×C7—22no—
149C24×C7—22no—
150C24×C7—22no—
151C24×C7—22no—
152C24×C7—22no—
153C24×C7—22no—
154C24×C7C22×C414yes—
155C24×C7C2411yescharacteristic
156C23×D7—21no—
157C23×D7—21no—
158C23×D7—21no—
159C23×D7—21no—
160C23×D7—21no—
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
168C23×D7C22×C412yes—
169C23×D7C2×D412yes—
170C23×D7#4112yes—
171C2×C7×D4—28no—
172C2×C7×D4—28no—
173C2×C7×D4—28no—
174C2×C7×D4—44no—
175C2×C7×D4—44no—
176C2×C7×D4—44no—
177C2×C7×D4—44no—
178C22×C4×C7—21no—
179C22×C4×C7—22no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—22no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—21no—
192C22×C4×C7—22no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7C22×C412yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7C2×D414yes—
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—
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—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7C22×C412yes—
241C22×Dic7C22×C414yes—
242C22×Dic7C2×D412yes—
243C22×Dic7C2×D414yes—
244C22×Dic7C2×D414yes—
245C22×Dic7C2×D412yes—
246C22×Dic7C2×D412yes—
247C22×Dic7#4112yes—
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×C22⋊C4—48no—
257C7×C22⋊C4—48no—
258C42×C7—44no—
259C22⋊Dic7—216no—
260C22⋊Dic7—48no—
261C22⋊Dic7—48no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—28no—
264(C2×D7)⋊C4—48no—
265C4⋊Dic7—44no—
266C4⋊Dic7C22⋊C4116yescomplemented
267Dic7⋊C4—48no—
268C4×Dic7—28no—
269C4×Dic7—48no—
270C23×D4—72no—
271C23×D4C2×D711yescharacteristic
272C24×C4—71no—
273C2×#121—78no—
274C2×#121—144no—
275C2×#121—144no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—72no—
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⋊C4C2×D712yes—
287C22×C22⋊C4C2×D712yes—
288C22×C42—71no—
289C22×C42—72no—
290C22×C42C2×D711yescharacteristic
291#390—24no—
292#390—144no—
293#390—148no—
294#389—144no—
295#380—144no—
296C4×C4⋊C4—144no—
297C4×C22⋊C4—144no—
298C2×#95—71no—
299C2×#95—72no—
300C2×#95—72no—
301C2×#95—72no—
302C2×#95—71no—
303C23×C7—24no—
304C23×C7—24no—
305C23×C7—24no—
306C23×C7—24no—
307C23×C7—24no—
308C23×C7—24no—
309C23×C7—24no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7—42no—
313C23×C7—42no—
314C23×C7—42no—
315C23×C7—42no—
316C23×C7—42no—
317C23×C7—42no—
318C23×C7—42no—
319C23×C7—42no—
320C23×C7—42no—
321C23×C7—42no—
322C23×C7—42no—
323C23×C7—42no—
324C23×C7—42no—
325C23×C7—42no—
326C23×C7—42no—
327C23×C7—42no—
328C23×C7—42no—
329C23×C7—42no—
330C23×C7—42no—
331C23×C7—42no—
332C23×C7—42no—
333C23×C7—42no—
334C23×C7—42no—
335C23×C7—42no—
336C23×C7—42no—
337C23×C7—42no—
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—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7C4×D414yes—
388C7×D4—416no—
389C2×C4×C7—22no—
390C2×C4×C7—24no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—24no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—24no—
397C2×C4×C7—22no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—42no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—42no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
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—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—
451C2×Dic7C2×C22⋊C418yes—
452C2×Dic7#12114yescomplemented
453C4×D7—416no—
454C25—71no—
455C25C22×D712yes—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—78no—
463C22×D4—144no—
464C22×D4—144no—
465C22×D4—144no—
466C22×D4—144no—
467C22×D4—282no—
468C22×D4—282no—
469C22×D4C4×D714yes—
470C23×C4—71no—
471C23×C4—72no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—74no—
475C23×C4—72no—
476C23×C4—142no—
477C23×C4—142no—
478C23×C4—142no—
479C23×C4—142no—
480C23×C4—142no—
481C23×C4—142no—
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D712yes—
485C23×C4C22×D711yescharacteristic
486#121—1432no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—74no—
492C2×C4⋊C4—144no—
493C2×C4⋊C4—144no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4—142no—
496C2×C4⋊C4—142no—
497C2×C4⋊C4—282no—
498C2×C4⋊C4C22⋊D714yescomplemented
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—78no—
506C2×C22⋊C4—74no—
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—142no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—144no—
516C2×C22⋊C4—144no—
517C2×C22⋊C4—144no—
518C2×C22⋊C4—144no—
519C2×C22⋊C4—144no—
520C2×C22⋊C4—282no—
521C2×C22⋊C4—282no—
522C2×C22⋊C4—282no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—74no—
527C2×C42—142no—
528C2×C42—142no—
529C2×C42—144no—
530C2×C42—144no—
531C2×C42—282no—
532#95—142no—
533#95—142no—
534#95—144no—
535#95—144no—
536#95—144no—
537C22×C7—44no—
538C22×C7—44no—
539C22×C7—44no—
540C22×C7—44no—
541C22×C7—44no—
542C22×C7—44no—
543C22×C7—44no—
544C22×C7—82no—
545C22×C7—82no—
546C22×C7—82no—
547C22×C7—82no—
548C22×C7—82no—
549C22×C7—82no—
550C22×C7—82no—
551C22×C7—82no—
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—24no—
588C2×D7—24no—
589C2×D7—24no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—42no—
594C2×D7—42no—
595C2×D7—42no—
596C2×D7—42no—
597C2×D7—42no—
598C2×D7—42no—
599C2×D7—42no—
600C2×D7—42no—
601C2×D7—42no—
602C4×C7—44no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7#39018yescomplemented
606Dic7—28no—
607Dic7—24no—
608Dic7—42no—
609Dic7—42no—
610Dic7—82no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—72no—
626C24—72no—
627C24—72no—
628C24—141no—
629C24—141no—
630C24—141no—
631C24—141no—
632C24—141no—
633C24—141no—
634C24—141no—
635C24—141no—
636C24—141no—
637C24—141no—
638C24—141no—
639C24—141no—
640C24C2×C4×D714yes—
641C24C23×D711yescharacteristic
642C2×D4—28no—
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—1416no—
650C2×D4—1416no—
651C2×D4—288no—
652C2×D4—288no—
653C2×D4—288no—
654C2×D4—288no—
655C2×D4—288no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—74no—
675C22×C4—72no—
676C22×C4—74no—
677C22×C4—74no—
678C22×C4—72no—
679C22×C4—72no—
680C22×C4—72no—
681C22×C4—72no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—142no—
685C22×C4—141no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
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—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—148no—
703C22×C4—148no—
704C22×C4—148no—
705C22×C4—142no—
706C22×C4—142no—
707C22×C4—142no—
708C22×C4—142no—
709C22×C4—142no—
710C22×C4—142no—
711C22×C4—142no—
712C22×C4—284no—
713C22×C4—284no—
714C22×C4—284no—
715C22×C4—284no—
716C22×C4C2×C4×D712yes—
717C22×C4#115712yes—
718C22×C4D4×D712yes—
719C22×C4D4×D712yes—
720C22×C4D4×D712yes—
721C22×C4D4×D712yes—
722C22×C4#115912yes—
723C22×C4#115912yes—
724C22×C4C2×C22⋊D714yes—
725C22×C4C2×C22⋊D712yes—
726C4⋊C4—28no—
727C4⋊C4—716no—
728C4⋊C4—288no—
729C4⋊C4—284no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—148no—
733C22⋊C4—148no—
734C22⋊C4—1416no—
735C22⋊C4—288no—
736C22⋊C4—288no—
737C22⋊C4—288no—
738C42—44no—
739C42—148no—
740C42—288no—
741C2×C7—84no—
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—44no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—74no—
794C23—142no—
795C23—142no—
796C23—142no—
797C23—142no—
798C23—142no—
799C23—142no—
800C23—142no—
801C23—142no—
802C23—142no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—142no—
812C23—281no—
813C23—281no—
814C23—281no—
815C23—281no—
816C23—281no—
817C23—281no—
818C23—281no—
819C23—281no—
820C23—281no—
821C23—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23—281no—
827C23—281no—
828C23C22×C4×D711yescharacteristic
829C23C2×#115711yescharacteristic
830C23C2×D4×D711yescharacteristic
831C23C2×D4×D711yescharacteristic
832C23C2×D4×D711yescharacteristic
833C23C2×D4×D711yescharacteristic
834C23C2×#115911yescharacteristic
835C23C2×#115911yescharacteristic
836C23#654811yescharacteristic
837C23#654811yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23#655311yescharacteristic
841C23#655411yescharacteristic
842C23C22×C22⋊D711yescharacteristic
843D4—416no—
844D4—2832no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—78no—
867C2×C4—74no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—144no—
871C2×C4—142no—
872C2×C4—144no—
873C2×C4—144no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—144no—
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—281no—
887C2×C4—281no—
888C2×C4—281no—
889C2×C4—281no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—281no—
893C2×C4—281no—
894C2×C4—2816no—
895C2×C4—282no—
896C2×C4—282no—
897C2×C4—282no—
898C2×C4—282no—
899C2×C4—282no—
900C2×C4—282no—
901C2×C4—282no—
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—44no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—82no—
925C22—144no—
926C22—144no—
927C22—144no—
928C22—282no—
929C22—282no—
930C22—282no—
931C22—282no—
932C22—282no—
933C22—282no—
934C22—282no—
935C22—282no—
936C22—282no—
937C22—282no—
938C22—282no—
939C22—282no—
940C22C2×D7×C22⋊C411yescharacteristic
941C22C2×(C22⋊D7)⋊C411yescharacteristic
942C22C2×#644711yescharacteristic
943C22C2×#644811yescharacteristic
944C22C4×#115911yescharacteristic
945C22C4×D4×D711yescharacteristic
946C22#9023611yescharacteristic
947C22#9023711yescharacteristic
948C22#9024211yescharacteristic
949C22#9024911yescharacteristic
950C22#9024911yescharacteristic
951C22#9025411yescharacteristic
952C22#9028911yescharacteristic
953C22#9029011yescharacteristic
954C22D7×#12111yescharacteristic
955C22#9029711yescharacteristic
956C22#9029811yescharacteristic
957C22#9029911yescharacteristic
958C22#9030011yescharacteristic
959C22#9030311yescharacteristic
960C22#9036711yescharacteristic
961C22#9036811yescharacteristic
962C22#9037111yescharacteristic
963C22#9037311yescharacteristic
964C22#9040711yescharacteristic
965C22#9040811yescharacteristic
966C22#9040911yescharacteristic
967C22#9041011yescharacteristic
968C22C2×C4×C22⋊D711yescharacteristic
969C22D4×C22⋊D711yescharacteristic
970C22C2×#650211yescharacteristic
971C22C2×#650311yescharacteristic
972C22#9049711yescharacteristic
973C22#9052211yescharacteristic
974C22#9052511yescharacteristic
975C4—42no—
976C4—42no—
977C4—44no—
978C4—148no—
979C4—144no—
980C4—282no—
981C4—282no—
982C4—562no—
983C4#8972918yescomplemented
984C2—84no—
985C2—284no—
986C2#1173373611yescharacteristic
987C2#1173374611yescharacteristic
988C2#1173387511yescharacteristic
989C2#1173387611yescharacteristic
990C2#1173388311yescharacteristic
991C2#1173388411yescharacteristic
992C2#1173389511yescharacteristic
993C2#1173389711yescharacteristic
994C2C2×#8972911yescharacteristic
995C2#1173978611yescharacteristic
996C2#1173984411yescharacteristic
997C2#1174011311yescharacteristic
998C2#1174011411yescharacteristic
999C2#1174044011yescharacteristic
1000C2#1174063111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#390C2
socle, cosocleC24×C7C24
prime radicalC22×#6501C2
hypercenterC2×#390D7
hypocenterC7#13998
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×C7×#390C2semidirect
3. C2×#89993C2semidirect
4. C2×#89759C2semidirect
5. C2×C4⋊C4×Dic7C2semidirect
6. C2×#89729C2semidirect
7. C2×#89700C2semidirect
8. C2×C4×(C2×D7)⋊C4C2semidirect
9. #11729304C2semidirect
10. #11729301C2semidirect
11. #11729299C2semidirect
24. C2×#6501C4semidirect
80. C2×C7×C4⋊C4D4semidirect
108. C2×(C2×D7)⋊C4D4semidirect
123. C2×C4×Dic7D4semidirect
132. C2×#390D7semidirect
266. 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×#65012
C2×C7×#3902
C2×#899932
C2×#897592
C2×C4⋊C4×Dic72
C2×#897292
C2×#897002
C2×C4×(C2×D7)⋊C42
#117293042
#117293012
#117292992
#139987