Finite Group Databasebeta

← #13277238

Subgroups — #13277238

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×C7×#390C211yesmaximal, characteristic
2C2×#89993C211yesmaximal, characteristic
3C2×#89993C211yesmaximal, characteristic
4C2×#89717C212yesmaximal, complemented
5C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
6C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729303C212yesmaximal, complemented
10#11729301C212yesmaximal, complemented
11#11729299C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C22⋊C4C2212yes—
15C22×C7×C22⋊C4C2212yes—
16C22×C42×C7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C22×C22⋊Dic7C2212yes—
19C22×C22⋊Dic7C2212yes—
20C22×C22⋊Dic7C2212yes—
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2212yes—
27C22×C4×Dic7C2211yescharacteristic
28C7×#390—24no—
29#89993—24no—
30#89993C418yescomplemented
31C2×C7⋊#95C2211yescharacteristic
32C2×C7⋊#95C2211yescharacteristic
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89717—28no—
39C4×C4⋊Dic7—24no—
40C4×Dic7⋊C4—24no—
41#14022—71nomaximal, Sylow
42C25×C7C2312yes—
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4C2×C414yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×Dic7C2312yes—
55C23×Dic7C2311yescharacteristic
56C23×Dic7C2311yescharacteristic
57C23×Dic7C2312yes—
58C23×Dic7C2311yescharacteristic
59C23×Dic7C2311yescharacteristic
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C22⋊C4—24no—
64C2×C7×C22⋊C4—24no—
65C2×C7×C22⋊C4—24no—
66C2×C7×C22⋊C4—24no—
67C2×C7×C22⋊C4—42no—
68C2×C7×C22⋊C4—42no—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×C42×C7D414yes—
72C2×C22⋊Dic7—24no—
73C2×C22⋊Dic7—24no—
74C2×C22⋊Dic7—24no—
75C2×C22⋊Dic7—24no—
76C2×C22⋊Dic7—24no—
77C2×C22⋊Dic7—24no—
78C2×C22⋊Dic7—42no—
79C2×C22⋊Dic7—42no—
80C2×C22⋊Dic7—42no—
81C2×C22⋊Dic7—42no—
82C2×C22⋊Dic7C2×C418yes—
83C2×C22⋊Dic7C2×C418yes—
84C2×C4⋊Dic7—22no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7C2×C414yes—
89C2×C4⋊Dic7D414yes—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4D414yescomplemented
96C2×C4×Dic7—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—24no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—24no—
103C2×C4×Dic7—42no—
104C2×C4×Dic7C2×C414yes—
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×#390D711yescharacteristic
115C2×#388—72no—
116C2×C4×C4⋊C4—71no—
117C2×C4×C4⋊C4—71no—
118#1440—72no—
119#1439—72no—
120#1437—72no—
121C4⋊#95—71no—
122C4⋊#95—71no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7C22×C414yes—
138C24×C7C2411yescharacteristic
139C2×C7×D4—28no—
140C2×C7×D4—28no—
141C2×C7×D4—28no—
142C2×C7×D4—44no—
143C2×C7×D4—44no—
144C2×C7×D4—44no—
145C2×C7×D4—44no—
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—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7C22×C412yes—
164C22×C4×C7C2×D412yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2×D412yes—
169C22×C4×C7#4112yes—
170C22×C4×C7#4112yes—
171C22×C4×C7#4112yes—
172C22×C4×C7#4112yes—
173C22×C4×C7#4112yes—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—21no—
197C22×Dic7—21no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7C22×C412yes—
209C22×Dic7C22×C414yes—
210C22×Dic7C22×C412yes—
211C22×Dic7C2×D412yes—
212C22×Dic7C2×D414yes—
213C22×Dic7C2×D412yes—
214C22×Dic7#4112yes—
215C22×Dic7#4112yes—
216C7×C4⋊C4—44no—
217C7×C22⋊C4—48no—
218C7×C22⋊C4—48no—
219C42×C7—28no—
220C22⋊Dic7—216no—
221C22⋊Dic7—48no—
222C22⋊Dic7—48no—
223C22⋊Dic7—48no—
224C4⋊Dic7—28no—
225C4⋊Dic7—28no—
226Dic7⋊C4—28no—
227Dic7⋊C4—28no—
228C4×Dic7—28no—
229C4×Dic7—48no—
230C4×Dic7—44no—
231C23×D4C2×D711yescharacteristic
232C22×C4⋊C4—71no—
233C22×C4⋊C4—71no—
234C22×C4⋊C4—71no—
235C22×C4⋊C4—71no—
236C22×C4⋊C4C2×D711yescharacteristic
237C22×C22⋊C4—72no—
238C22×C22⋊C4—72no—
239C22×C22⋊C4—72no—
240C22×C22⋊C4—72no—
241C22×C22⋊C4C2×D712yes—
242C22×C22⋊C4C2×D712yes—
243C22×C42—71no—
244C22×C42—71no—
245C22×C42—72no—
246C22×C42C2×D711yescharacteristic
247#390—24no—
248#390—78no—
249#390—144no—
250#388—148no—
251C4×C4⋊C4—144no—
252C4×C4⋊C4—144no—
253C2×#95—72no—
254C2×#95—72no—
255C2×#95—71no—
256C2×#95—72no—
257C2×#95—71no—
258C2×#95—72no—
259C2×#95—72no—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—24no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7—42no—
283C23×C7—42no—
284C23×C7—42no—
285C23×C7—42no—
286C23×C7—42no—
287C23×C7—42no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7C23×C411yescharacteristic
296C23×C7C22×D411yescharacteristic
297C23×C7C22×D411yescharacteristic
298C23×C7C22×D411yescharacteristic
299C23×C7C2×#4111yescharacteristic
300C23×C7C2×#4111yescharacteristic
301C23×C7C2×#4111yescharacteristic
302C23×C7C2×#4111yescharacteristic
303C23×C7C2×#4111yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C23×C7C2×#4111yescharacteristic
306C23×C7H(5,𝔽2)11yescharacteristic
307C23×C7H(5,𝔽2)11yescharacteristic
308C23×C7H(5,𝔽2)11yescharacteristic
309C23×C72−1+411yescharacteristic
310C7×D4—416no—
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—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7#11714yes—
332C2×C4×C7C4×D414yes—
333C2×C4×C7C4×D414yes—
334C2×C4×C7#12114yes—
335C2×C4×C7#12114yes—
336C2×C4×C7#12314yes—
337C2×C4×C7#12414yes—
338C2×C4×C7#12614yes—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—22no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—22no—
345C2×Dic7—22no—
346C2×Dic7—24no—
347C2×Dic7—24no—
348C2×Dic7—22no—
349C2×Dic7—24no—
350C2×Dic7—22no—
351C2×Dic7—22no—
352C2×Dic7—24no—
353C2×Dic7—22no—
354C2×Dic7—24no—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—24no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—42no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—42no—
369C2×Dic7—41no—
370C2×Dic7—42no—
371C2×Dic7—41no—
372C2×Dic7—42no—
373C2×Dic7—42no—
374C2×Dic7—42no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7C4×D414yes—
381C25C22×D712yes—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4C4×D714yes—
389C23×C4—71no—
390C23×C4—72no—
391C23×C4—71no—
392C23×C4—72no—
393C23×C4—71no—
394C23×C4—71no—
395C23×C4C22×D712yes—
396C23×C4C22×D711yescharacteristic
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—74no—
403C2×C4⋊C4—74no—
404C2×C4⋊C4—74no—
405C2×C4⋊C4—142no—
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⋊C4—142no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—78no—
421C2×C22⋊C4—78no—
422C2×C22⋊C4—144no—
423C2×C22⋊C4—144no—
424C2×C22⋊C4—144no—
425C2×C22⋊C4—144no—
426C2×C22⋊C4—144no—
427C2×C22⋊C4—144no—
428C2×C22⋊C4—282no—
429C2×C22⋊C4—282no—
430C2×C22⋊C4—282no—
431C2×C22⋊C4—282no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—74no—
435C2×C42—142no—
436C2×C42—142no—
437C2×C42—144no—
438C2×C42—144no—
439C2×C42—142no—
440C2×C42—142no—
441C2×C42—142no—
442C2×C42—282no—
443C2×C42C22⋊D714yes—
444#95—144no—
445#95—144no—
446#95—144no—
447#95—142no—
448#95—142no—
449#95—282no—
450#95—282no—
451C22×C7—44no—
452C22×C7—44no—
453C22×C7—44no—
454C22×C7—44no—
455C22×C7—44no—
456C22×C7—44no—
457C22×C7—44no—
458C22×C7—82no—
459C22×C7—82no—
460C22×C7—82no—
461C22×C7—82no—
462C22×C7—82no—
463C22×C7—82no—
464C22×C7—82no—
465C22×C7—82no—
466C22×C7C2×#11711yescharacteristic
467C22×C7C2×C4×D411yescharacteristic
468C22×C7C2×C4×D411yescharacteristic
469C22×C7C2×C4×D411yescharacteristic
470C22×C7C4×#4111yescharacteristic
471C22×C7#51811yescharacteristic
472C22×C7#52011yescharacteristic
473C22×C7C2×#12111yescharacteristic
474C22×C7C2×#12111yescharacteristic
475C22×C7C2×#12311yescharacteristic
476C22×C7#52511yescharacteristic
477C22×C7C2×#12411yescharacteristic
478C22×C7C2×#12611yescharacteristic
479C22×C7#52911yescharacteristic
480C22×C7#53211yescharacteristic
481C22×C7#53511yescharacteristic
482C22×C7#53711yescharacteristic
483C22×C7#54011yescharacteristic
484C22×C7#54211yescharacteristic
485C22×C7D4211yescharacteristic
486C22×C7#54611yescharacteristic
487C22×C7#54711yescharacteristic
488C22×C7#54811yescharacteristic
489C22×C7#55011yescharacteristic
490C22×C7#55011yescharacteristic
491C22×C7#55011yescharacteristic
492C22×C7#55311yescharacteristic
493C22×C7#55311yescharacteristic
494C22×C7#55511yescharacteristic
495C22×C7#55611yescharacteristic
496C22×C7#55611yescharacteristic
497C22×C7#55911yescharacteristic
498C22×C7#55911yescharacteristic
499C22×C7#55911yescharacteristic
500C22×C7#55911yescharacteristic
501C4×C7—24no—
502C4×C7—42no—
503C4×C7—82no—
504C4×C7#38818yescomplemented
505Dic7—24no—
506Dic7—42no—
507Dic7—44no—
508Dic7—42no—
509Dic7—42no—
510Dic7—44no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24C2×C4×D714yes—
526C24C23×D711yescharacteristic
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
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—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—72no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—74no—
556C22×C4—72no—
557C22×C4—74no—
558C22×C4—72no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—141no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—141no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—141no—
584C22×C4—142no—
585C22×C4—142no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4C2×C4×D712yes—
594C22×C4#115712yes—
595C22×C4D4×D712yes—
596C22×C4D4×D712yes—
597C22×C4#115912yes—
598C22×C4#115912yes—
599C22×C4#115912yes—
600C22×C4#115912yes—
601C22×C4C2×C22⋊D712yes—
602C22×C4C2×C22⋊D712yes—
603C22×C4C2×C22⋊D712yes—
604C4⋊C4—44no—
605C4⋊C4—148no—
606C4⋊C4—148no—
607C4⋊C4—148no—
608C4⋊C4—148no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—1416no—
612C22⋊C4—288no—
613C22⋊C4—288no—
614C22⋊C4—288no—
615C42—28no—
616C42—148no—
617C42—288no—
618C42—284no—
619C2×C7—84no—
620C2×C7C2×#38811yescharacteristic
621C2×C7C4×#12111yescharacteristic
622C2×C7#232411yescharacteristic
623C2×C7#235411yescharacteristic
624C2×C7#235711yescharacteristic
625C2×C7#236611yescharacteristic
626C2×C7#236711yescharacteristic
627C2×C7#241411yescharacteristic
628C2×C7#241611yescharacteristic
629C2×C7#244511yescharacteristic
630C2×C7#244811yescharacteristic
631C2×C7#251211yescharacteristic
632C2×C7#251311yescharacteristic
633C2×C7#254811yescharacteristic
634C2×C7#259211yescharacteristic
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23C22×C4×D711yescharacteristic
671C23C2×#115711yescharacteristic
672C23C2×D4×D711yescharacteristic
673C23C2×D4×D711yescharacteristic
674C23C2×#115911yescharacteristic
675C23C2×#115911yescharacteristic
676C23C2×#115911yescharacteristic
677C23C2×#115911yescharacteristic
678C23#654811yescharacteristic
679C23#654811yescharacteristic
680C23D7×#4111yescharacteristic
681C23D7×#4111yescharacteristic
682C23#655311yescharacteristic
683C23#655411yescharacteristic
684C23C22×C22⋊D711yescharacteristic
685D4—416no—
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—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—74no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—144no—
714C2×C4—144no—
715C2×C4—142no—
716C2×C4—144no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—144no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—144no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—144no—
727C2×C4—142no—
728C2×C4—282no—
729C2×C4—282no—
730C2×C4—282no—
731C2×C4—282no—
732C2×C4—281no—
733C2×C4—281no—
734C2×C4—282no—
735C2×C4—281no—
736C2×C4—281no—
737C2×C4—281no—
738C2×C4—282no—
739C2×C4—281no—
740C2×C4—281no—
741C2×C4—281no—
742C2×C4—281no—
743C2×C4—281no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4#644014yes—
749C2×C4#644214yes—
750C2×C4(C22⋊D7)⋊C414yes—
751C2×C4#644614yes—
752C2×C4C4×C22⋊D714yes—
753C2×C4#649914yes—
754C2×C4#650114yes—
755C2×C4#650214yes—
756C7#1402211yescharacteristic, complemented, Sylow
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C2×#644011yescharacteristic
773C22C2×#644211yescharacteristic
774C22C2×(C22⋊D7)⋊C411yescharacteristic
775C22C2×#644611yescharacteristic
776C22C4×#115911yescharacteristic
777C22C4×D4×D711yescharacteristic
778C22#9023611yescharacteristic
779C22#9023711yescharacteristic
780C22#9023911yescharacteristic
781C22#9024811yescharacteristic
782C22#9025211yescharacteristic
783C22#9025311yescharacteristic
784C22#9028911yescharacteristic
785C22#9029011yescharacteristic
786C22#9030011yescharacteristic
787C22#9030211yescharacteristic
788C22#9030311yescharacteristic
789C22#9030511yescharacteristic
790C22#9030711yescharacteristic
791C22#9030911yescharacteristic
792C22#9036211yescharacteristic
793C22#9036211yescharacteristic
794C22#9037211yescharacteristic
795C22#9037211yescharacteristic
796C22#9040411yescharacteristic
797C22#9040411yescharacteristic
798C22#9040911yescharacteristic
799C22#9040911yescharacteristic
800C22C2×C4×C22⋊D711yescharacteristic
801C22C2×#649911yescharacteristic
802C22C2×#650111yescharacteristic
803C22C2×#650211yescharacteristic
804C22#9049611yescharacteristic
805C22#9051911yescharacteristic
806C22#9052411yescharacteristic
807C4—24no—
808C4—42no—
809C4—82no—
810C4—144no—
811C4—284no—
812C4—282no—
813C4—282no—
814C4—282no—
815C4—284no—
816C4#8971718yescomplemented
817C2—84no—
818C2#1173374711yescharacteristic
819C2#1173374811yescharacteristic
820C2#1173375111yescharacteristic
821C2#1173375211yescharacteristic
822C2#1173376111yescharacteristic
823C2#1173376511yescharacteristic
824C2#1173378311yescharacteristic
825C2#1173378611yescharacteristic
826C2C2×#8971711yescharacteristic
827C2C4×#650111yescharacteristic
828C2#1173984111yescharacteristic
829C2#1174014911yescharacteristic
830C2#1174015011yescharacteristic
831C2#1174042111yescharacteristic
832C2#1174062411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#390C2
socle, cosocleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#390D7
hypocenterC7#14022
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#89717C2semidirect
5. C2×C4×C4⋊Dic7C2semidirect
6. C2×C4×Dic7⋊C4C2semidirect
7. #11729317C2semidirect
8. #11729317C2semidirect
9. #11729303C2semidirect
10. #11729301C2semidirect
11. #11729299C2semidirect
30. #89993C4semidirect
95. C2×Dic7⋊C4D4semidirect
504. C4×C7#388semidirect
756. C7#14022semidirect
816. C4#89717semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3902
C2×#899932
C2×#897172
C2×C4×C4⋊Dic72
C2×C4×Dic7⋊C42
#117293172
#117293032
#117293012
#117292992
#140227