Finite Group Databasebeta

← #13275530

Subgroups — #13275530

Order 1792.

2574 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
4C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
7C2×#89704C211yesmaximal, characteristic, complemented
8#11729304C212yesmaximal
9#11729301C212yesmaximal, complemented
10#11727182C212yesmaximal, complemented
11#11727175C212yesmaximal, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C42×C7C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×C22⋊Dic7C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20C2×C4×C22⋊D7—24no—
21C2×C4×C22⋊D7—24no—
22C2×C4×C22⋊D7C418yescomplemented
23C22×(C2×D7)⋊C4C2212yes—
24C22×(C2×D7)⋊C4C2212yes—
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2212yes—
27C22×Dic7⋊C4C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C4×C7×C22⋊C4—24no—
32C2×C7×#95C2212yes—
33C4×C22⋊Dic7—24no—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C4×(C2×D7)⋊C4—24no—
41C4×(C2×D7)⋊C4—24no—
42#89704—24no—
43C4×Dic7⋊C4—24no—
44#13847—71nomaximal, Sylow
45C25×C7C2311yescharacteristic
46C24×D7C2311yescharacteristic
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7—22no—
53C23×C4×C7C2×C414yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C22×C22⋊D7—24no—
59C22×C22⋊D7—24no—
60C22×C22⋊D7—22no—
61C22×C22⋊D7—22no—
62C22×C22⋊D7C2×C414yes—
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2312yes—
65C23×Dic7C2312yes—
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C22×C4×D7—22no—
69C22×C4×D7—22no—
70C22×C4×D7—22no—
71C22×C4×D7—22no—
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7C2×C414yes—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C42×C7—22no—
79C2×C42×C7—22no—
80C2×C42×C7—22no—
81C2×C42×C7—22no—
82C2×C42×C7—22no—
83C2×C42×C7D414yescomplemented
84C2×C22⋊Dic7—24no—
85C2×C22⋊Dic7—22no—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—24no—
88C2×C22⋊Dic7—24no—
89C2×C22⋊Dic7C2×C414yes—
90C4×C22⋊D7—232no—
91C2×(C2×D7)⋊C4—24no—
92C2×(C2×D7)⋊C4—24no—
93C2×(C2×D7)⋊C4—24no—
94C2×(C2×D7)⋊C4—24no—
95C2×(C2×D7)⋊C4—24no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—24no—
99C2×(C2×D7)⋊C4C2×C414yes—
100C2×Dic7⋊C4—24no—
101C2×Dic7⋊C4—24no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—24no—
105C2×Dic7⋊C4C2×C414yes—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7C2×C414yes—
112C2×C4×Dic7D414yes—
113C2×C4×Dic7D414yes—
114C2×C4×Dic7D414yescomplemented
115C7×#95—24no—
116C7⋊#95—24no—
117C7⋊#95—24no—
118C7⋊#95—24no—
119C7⋊#95—24no—
120C7⋊#95—24no—
121C7⋊#95—24no—
122C22×C4×D4—71no—
123C2×C4×C4⋊C4—71no—
124C2×C4×C22⋊C4—71no—
125C2×C4×C22⋊C4—71no—
126C2×C4×C22⋊C4—71no—
127C2×C4×C22⋊C4D711yescharacteristic, complemented
128C2×#376—71no—
129#1445—72no—
130#1439—72no—
131#1439—72no—
132#1438—72no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—22no—
140C24×C7—21no—
141C24×C7—21no—
142C24×C7C22×C412yes—
143C24×C7#4114yes—
144C24×C7C2411yescharacteristic
145C23×D7—21no—
146C23×D7—21no—
147C23×D7—21no—
148C23×D7—21no—
149C23×D7—22no—
150C23×D7—22no—
151C23×D7—21no—
152C23×D7—21no—
153C23×D7—22no—
154C23×D7C22×C412yes—
155C23×D7#4114yes—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—21no—
161C22×C4×C7—22no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—28no—
175C22×C4×C7—28no—
176C22×C4×C7—28no—
177C22×C4×C7—44no—
178C22×C4×C7—44no—
179C22×C4×C7—44no—
180C22×C4×C7—44no—
181C22×C4×C7C22×C412yes—
182C22×C4×C7C22×C412yes—
183C22×C4×C7C2×D414yes—
184C22×C4×C7C2×D412yes—
185C22×C4×C7C2×D412yes—
186C22×C4×C7C2×D412yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7#4114yes—
189C22×C4×C7#4112yes—
190C22×C4×C7#4112yes—
191C2×C22⋊D7—216no—
192C2×C22⋊D7—216no—
193C2×C22⋊D7—28no—
194C2×C22⋊D7—28no—
195C2×C22⋊D7—28no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7C22×C412yes—
219C22×Dic7C22×C412yes—
220C22×Dic7C22×C412yes—
221C22×Dic7C2×D414yes—
222C22×Dic7C2×D412yes—
223C22×Dic7C2×D412yes—
224C22×Dic7C2×D412yes—
225C22×Dic7C2×D412yes—
226C22×Dic7#4114yes—
227C2×C4×D7—28no—
228C2×C4×D7—28no—
229C2×C4×D7—28no—
230C2×C4×D7—44no—
231C2×C4×D7—44no—
232C2×C4×D7—44no—
233C2×C4×D7—44no—
234C7×C22⋊C4—216no—
235C42×C7—28no—
236C42×C7—44no—
237C22⋊Dic7—216no—
238C22⋊Dic7—28no—
239(C2×D7)⋊C4—216no—
240(C2×D7)⋊C4—216no—
241(C2×D7)⋊C4—28no—
242Dic7⋊C4—216no—
243Dic7⋊C4—28no—
244C4×Dic7—28no—
245C4×Dic7—44no—
246C4×Dic7C22⋊C4116yescomplemented
247C23×D4—71no—
248C24×C4—71no—
249C24×C4C2×D711yescharacteristic
250C2×C4×D4—78no—
251C2×C4×D4—144no—
252C2×C4×D4—144no—
253C22×C4⋊C4—71no—
254C22×C4⋊C4—72no—
255C22×C22⋊C4—71no—
256C22×C22⋊C4—71no—
257C22×C22⋊C4—72no—
258C22×C22⋊C4—72no—
259C22×C22⋊C4—72no—
260C22×C22⋊C4C2×D712yes—
261C22×C42—71no—
262C22×C42—71no—
263C22×C42—71no—
264C22×C42C2×D711yescharacteristic
265C22×C42C2×D711yescharacteristic
266C4×C4⋊C4—144no—
267C4×C22⋊C4—24no—
268C4×C22⋊C4—144no—
269C4×C22⋊C4—144no—
270C4×C22⋊C4—144no—
271#376—144no—
272C2×#95—72no—
273C2×#95—72no—
274C2×#95—72no—
275C2×#95—72no—
276C2×#95—72no—
277C2×#95—72no—
278C2×#95C2×D712yes—
279C23×C7—22no—
280C23×C7—22no—
281C23×C7—22no—
282C23×C7—22no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—24no—
288C23×C7—24no—
289C23×C7—24no—
290C23×C7—24no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7—41no—
297C23×C7—42no—
298C23×C7—42no—
299C23×C7—41no—
300C23×C7—42no—
301C23×C7#11714yes—
302C23×C7C23×C411yescharacteristic
303C23×C7C22×D411yescharacteristic
304C23×C7C22×D411yescharacteristic
305C23×C7C22×D411yescharacteristic
306C23×C7C22×D411yescharacteristic
307C23×C7C2×#4112yes—
308C23×C7C2×#4111yescharacteristic
309C23×C7C2×#4112yes—
310C23×C7C2×#4111yescharacteristic
311C23×C7C2×#4112yes—
312C23×C7C2×#4112yes—
313C22×D7—22no—
314C22×D7—22no—
315C22×D7—22no—
316C22×D7—22no—
317C22×D7—22no—
318C22×D7—22no—
319C22×D7—24no—
320C22×D7—24no—
321C22×D7—24no—
322C22×D7—24no—
323C22×D7—24no—
324C22×D7—24no—
325C22×D7—41no—
326C22×D7—41no—
327C22×D7—42no—
328C22×D7—42no—
329C22×D7—42no—
330C22×D7—41no—
331C22×D7—42no—
332C22×D7—42no—
333C22×D7—41no—
334C22×D7—42no—
335C22×D7#11714yes—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—24no—
342C2×C4×C7—24no—
343C2×C4×C7—24no—
344C2×C4×C7—24no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7—41no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—41no—
356C2×C4×C7—42no—
357C2×C4×C7—416no—
358C2×C4×C7C2×C22⋊C414yes—
359C2×C4×C7C4×D414yes—
360C2×C4×C7C4×D414yes—
361C2×C4×C7#12114yes—
362C2×C4×C7#12114yes—
363C2×C4×C7#12414yes—
364C2×C4×C7#12714yes—
365C22⋊D7—232no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—24no—
371C2×Dic7—24no—
372C2×Dic7—24no—
373C2×Dic7—24no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—24no—
378C2×Dic7—24no—
379C2×Dic7—24no—
380C2×Dic7—24no—
381C2×Dic7—24no—
382C2×Dic7—24no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7—41no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—41no—
394C2×Dic7—42no—
395C2×Dic7C2×C22⋊C414yes—
396C2×Dic7C2×C22⋊C414yes—
397C4×D7—416no—
398C25—71no—
399C25C22×D711yescharacteristic
400C22×D4—74no—
401C22×D4—142no—
402C22×D4—142no—
403C22×D4—144no—
404C22×D4—144no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4—72no—
414C23×C4—72no—
415C23×C4—71no—
416C23×C4—74no—
417C23×C4—142no—
418C23×C4—142no—
419C23×C4—142no—
420C23×C4—142no—
421C23×C4—142no—
422C23×C4—142no—
423C23×C4C4×D714yes—
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D712yes—
426C23×C4C22×D712yes—
427C23×C4C22×D711yescharacteristic
428C4×D4—1432no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—142no—
431C2×C4⋊C4—142no—
432C2×C4⋊C4—144no—
433C2×C4⋊C4—144no—
434C2×C4⋊C4—144no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—142no—
441C2×C22⋊C4—142no—
442C2×C22⋊C4—144no—
443C2×C22⋊C4—144no—
444C2×C22⋊C4—144no—
445C2×C22⋊C4—144no—
446C2×C22⋊C4—142no—
447C2×C22⋊C4—142no—
448C2×C22⋊C4—144no—
449C2×C22⋊C4—144no—
450C2×C22⋊C4—144no—
451C2×C22⋊C4—144no—
452C2×C22⋊C4—144no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—74no—
459C2×C42—74no—
460C2×C42—74no—
461C2×C42—74no—
462C2×C42—142no—
463C2×C42—142no—
464C2×C42—142no—
465C2×C42—142no—
466C2×C42—142no—
467C2×C42C22⋊D714yescomplemented
468#95—24no—
469#95—144no—
470#95—144no—
471#95—144no—
472#95—144no—
473#95—144no—
474#95—144no—
475C22×C7—24no—
476C22×C7—24no—
477C22×C7—24no—
478C22×C7—44no—
479C22×C7—44no—
480C22×C7—44no—
481C22×C7—44no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7C22×C22⋊C411yescharacteristic
487C22×C7C2×#11711yescharacteristic
488C22×C7C2×#11711yescharacteristic
489C22×C7C2×C4×D411yescharacteristic
490C22×C7C2×C4×D411yescharacteristic
491C22×C7C4×#4111yescharacteristic
492C22×C7C4×#4111yescharacteristic
493C22×C7C2×#12111yescharacteristic
494C22×C7C2×#12111yescharacteristic
495C22×C7#52512yes—
496C22×C7#52512yes—
497C22×C7#52512yes—
498C22×C7#52512yes—
499C22×C7#52512yes—
500C22×C7#52512yes—
501C22×C7#52512yes—
502C22×C7C2×#12411yescharacteristic
503C22×C7#52912yes—
504C22×C7#52912yes—
505C22×C7#52912yes—
506C22×C7#52912yes—
507C22×C7C2×#12711yescharacteristic
508C22×C7#53212yes—
509C2×D7—24no—
510C2×D7—24no—
511C2×D7—24no—
512C2×D7—44no—
513C2×D7—44no—
514C2×D7—44no—
515C2×D7—44no—
516C2×D7—42no—
517C2×D7—42no—
518C2×D7—42no—
519C2×D7—42no—
520C4×C7—44no—
521C4×C7—44no—
522C4×C7—42no—
523C4×C7#39018yes—
524Dic7—24no—
525Dic7—24no—
526Dic7—44no—
527Dic7—44no—
528Dic7—42no—
529C24—22no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—72no—
539C24—74no—
540C24—142no—
541C24—141no—
542C24—142no—
543C24—141no—
544C24—141no—
545C24—141no—
546C24—141no—
547C24—142no—
548C24—141no—
549C24C2×C4×D712yes—
550C24#115714yes—
551C24C23×D711yescharacteristic
552C2×D4—148no—
553C2×D4—148no—
554C2×D4—1416no—
555C2×D4—1416no—
556C2×D4—148no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—72no—
583C22×C4—72no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—74no—
590C22×C4—74no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—141no—
601C22×C4—142no—
602C22×C4—141no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—141no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—141no—
612C22×C4—142no—
613C22×C4—148no—
614C22×C4—148no—
615C22×C4—148no—
616C22×C4—284no—
617C22×C4—284no—
618C22×C4—284no—
619C22×C4—284no—
620C22×C4C2×C4×D712yes—
621C22×C4C2×C4×D712yes—
622C22×C4#115714yes—
623C22×C4#115712yes—
624C22×C4D4×D712yes—
625C22×C4D4×D712yes—
626C22×C4D4×D712yes—
627C22×C4#115912yes—
628C22×C4C2×C22⋊D714yes—
629C22×C4C2×C22⋊D712yes—
630C4⋊C4—148no—
631C4⋊C4—1416no—
632C22⋊C4—216no—
633C22⋊C4—148no—
634C22⋊C4—1416no—
635C22⋊C4—1416no—
636C22⋊C4—148no—
637C22⋊C4—1416no—
638C42—28no—
639C42—44no—
640C42—716no—
641C42—148no—
642C42—284no—
643C2×C7—44no—
644C2×C7#228011yescharacteristic
645C2×C7#229011yescharacteristic
646C2×C7#229011yescharacteristic
647C2×C7#229011yescharacteristic
648C2×C7#229011yescharacteristic
649C2×C7C2×#39011yescharacteristic
650C2×C7#229711yescharacteristic
651C2×C7#239212yes—
652C2×C7#239212yes—
653C2×C7#239712yes—
654C2×C7#239812yes—
655D7—44no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—74no—
679C23—142no—
680C23—142no—
681C23—142no—
682C23—142no—
683C23—142no—
684C23—144no—
685C23—142no—
686C23—144no—
687C23—144no—
688C23—144no—
689C23—144no—
690C23—144no—
691C23—282no—
692C23—281no—
693C23—281no—
694C23—282no—
695C23—282no—
696C23—281no—
697C23—282no—
698C23—282no—
699C23—281no—
700C23—282no—
701C23#643514yes—
702C23C22×C4×D711yescharacteristic
703C23C2×#115712yes—
704C23C2×#115712yes—
705C23C2×#115711yescharacteristic
706C23C2×D4×D711yescharacteristic
707C23C2×D4×D711yescharacteristic
708C23C2×D4×D711yescharacteristic
709C23C2×#115911yescharacteristic
710C23D7×#4112yes—
711C23D7×#4112yes—
712C23C22×C22⋊D711yescharacteristic
713D4—1432no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—416no—
736C2×C4—74no—
737C2×C4—74no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—144no—
743C2×C4—144no—
744C2×C4—144no—
745C2×C4—144no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—144no—
749C2×C4—142no—
750C2×C4—144no—
751C2×C4—144no—
752C2×C4—144no—
753C2×C4—144no—
754C2×C4—144no—
755C2×C4—282no—
756C2×C4—281no—
757C2×C4—281no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4—281no—
761C2×C4—282no—
762C2×C4—282no—
763C2×C4—282no—
764C2×C4—282no—
765C2×C4—281no—
766C2×C4—282no—
767C2×C4—2816no—
768C2×C4D7×C22⋊C414yes—
769C2×C4(C22⋊D7)⋊C414yes—
770C2×C4#644714yes—
771C2×C4#644814yes—
772C2×C4C4×C22⋊D714yes—
773C2×C4#650214yes—
774C2×C4#650314yes—
775C7#1384711yescharacteristic, complemented, Sylow
776C22—24no—
777C22—24no—
778C22—24no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—42no—
786C22—44no—
787C22—144no—
788C22—144no—
789C22—144no—
790C22—282no—
791C22—284no—
792C22—282no—
793C22—284no—
794C22—284no—
795C22—282no—
796C22—282no—
797C22—284no—
798C22C2×#643511yescharacteristic
799C22C4×#115711yescharacteristic
800C22#9017012yes—
801C22C2×D7×C22⋊C411yescharacteristic
802C22C2×(C22⋊D7)⋊C411yescharacteristic
803C22C2×#644711yescharacteristic
804C22C2×#644811yescharacteristic
805C22D7×#11711yescharacteristic
806C22#9021311yescharacteristic
807C22#9021912yes—
808C22#9022912yes—
809C22#9023812yes—
810C22#9023812yes—
811C22#9023812yes—
812C22#9023812yes—
813C22#9023812yes—
814C22#9023912yes—
815C22#9024812yes—
816C22C2×C4×C22⋊D711yescharacteristic
817C22#9048212yes—
818C22C2×#650211yescharacteristic
819C22C2×#650311yescharacteristic
820C22#9051912yes—
821C4—44no—
822C4—44no—
823C4—42no—
824C4—144no—
825C4—144no—
826C4—284no—
827C4—284no—
828C4—282no—
829C4#8972918yes—
830C2—44no—
831C2—284no—
832C2#1173088311yescharacteristic
833C2#1173092612yes—
834C2#1173100611yescharacteristic
835C2#1173100711yescharacteristic
836C2#1173100811yescharacteristic
837C2#1173102612yes—
838C2#1173951011yescharacteristic
839C2C2×#8972911yescharacteristic
840C2#1173971311yescharacteristic
841C2#1173979012yes—
842C2#1173979212yes—
subgroupG/H
centerC23×C4C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#13847
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C22⋊C4C2semidirect
3. C2×C4×C22⋊Dic7C2semidirect
4. C2×C4×Dic7⋊C4C2semidirect
5. C2×C4×(C2×D7)⋊C4C2semidirect
6. C2×C4×(C2×D7)⋊C4C2semidirect
7. C2×#89704C2semidirect
9. #11729301C2semidirect
10. #11727182C2semidirect
11. #11727175C2semidirect
22. C2×C4×C22⋊D7C4semidirect
83. C2×C42×C7D4semidirect
114. C2×C4×Dic7D4semidirect
127. C2×C4×C22⋊C4D7semidirect
246. C4×Dic7C22⋊C4semidirect
467. C2×C42C22⋊D7semidirect
775. C7#13847semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C2×C4×C7×C22⋊C42
C2×C4×C22⋊Dic72
C2×C4×Dic7⋊C42
C2×C4×(C2×D7)⋊C42
C2×#897042
#117293042
#117293012
#117271822
#117271752
#138477