Finite Group Databasebeta

← C2×#11733324 #13523404

Subgroups — C2×#11733324 #13523404

Order 1792.

2442 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic, complemented
2C2×#89765C211yesmaximal, characteristic, complemented
3C2×#89755C211yesmaximal, characteristic, complemented
4C2×#89728C211yesmaximal, characteristic
5C2×#89724C211yesmaximal, characteristic, complemented
6C2×#89733C211yesmaximal, characteristic
7C2×#89729C211yesmaximal, characteristic
8C2×#89716C211yesmaximal, characteristic, complemented
9C2×#89723C211yesmaximal, characteristic, complemented
10C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
11C2×#89704C211yesmaximal, characteristic, complemented
12#11733324C2116yesmaximal, direct product factor
13C2×#89439C211yesmaximal, characteristic, complemented
14C2×#89442C211yesmaximal, characteristic, complemented
15C2×#89427C211yesmaximal, characteristic, complemented
16C2×#89426C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C7×#388C2218yescomplemented
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89765C2218yescomplemented
54#89755C2218yescomplemented
55#89733C2218yes—
56#89729C2218yes—
57#89728C2218yes—
58#89724C2218yescomplemented
59#89723C2218yescomplemented
60#89716C2218yescomplemented
61C4×(C2×D7)⋊C4C2218yescomplemented
62#89704C2218yescomplemented
63#89442C2218yescomplemented
64#89439C2218yescomplemented
65#89427C2218yescomplemented
66#89426C2218yescomplemented
67C2×#2531—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C24×D7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C22×C22⋊D7—24no—
77C22×C22⋊D7—24no—
78C22×C22⋊D7—42no—
79C22×C22⋊D7C2314yes—
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C22×C4×D7—24no—
88C22×C4×D7—24no—
89C22×C4×D7—42no—
90C22×C4×D7C2314yes—
91C2×C7×C4⋊C4—42no—
92C2×C7×C4⋊C4C2314yes—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4C2314yes—
97C2×C7×C22⋊C4C2314yes—
98C2×C7×C22⋊C4C2314yes—
99C2×C42×C7—24no—
100C2×C42×C7C2314yes—
101C2×C22⋊Dic7—24no—
102C2×C22⋊Dic7—42no—
103C2×C22⋊Dic7—42no—
104C2×C22⋊Dic7C2314yes—
105C2×C22⋊Dic7C2314yes—
106C2×C22⋊Dic7C2314yes—
107C2×(C2×D7)⋊C4—24no—
108C2×(C2×D7)⋊C4—24no—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—42no—
111C2×(C2×D7)⋊C4—42no—
112C2×(C2×D7)⋊C4C2314yes—
113C2×(C2×D7)⋊C4C2314yes—
114C2×(C2×D7)⋊C4C2314yes—
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
117C2×C4⋊Dic7—24no—
118C2×C4⋊Dic7—42no—
119C2×C4⋊Dic7C2314yes—
120C2×C4⋊Dic7C2314yes—
121C2×Dic7⋊C4—24no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×C4×Dic7—24no—
128C2×C4×Dic7—24no—
129C2×C4×Dic7—42no—
130C2×C4×Dic7C2314yes—
131C2×C4×Dic7C2314yes—
132C2×C4×Dic7C2314yes—
133C7×#95C2314yes—
134C7×#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145#2531—716no—
146C2×#398—71no—
147C2×#397—71no—
148C2×#397—71no—
149C2×#394—71no—
150C2×#390—71no—
151C2×#388—71no—
152C2×#388—71no—
153C2×#388—71no—
154C2×#388D711yescharacteristic, complemented
155C2×#387—71no—
156C2×#387—71no—
157C2×#386—71no—
158C2×#380—71no—
159C2×C4×C22⋊C4—71no—
160C2×#376—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7C2412yes—
169C24×C7C2411yescharacteristic
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—22no—
174C23×D7—22no—
175C23×D7—22no—
176C23×D7#4114yes—
177C23×D7C2412yes—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
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—22no—
194C22×C4×C7#4114yes—
195C22×C4×C7#4114yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C2×C22⋊D7—28no—
203C2×C22⋊D7—28no—
204C2×C22⋊D7—44no—
205C2×C22⋊D7—416no—
206C22×Dic7—22no—
207C22×Dic7—22no—
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—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7#4114yes—
226C22×Dic7#4114yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C2×C4×D7—28no—
235C2×C4×D7—28no—
236C2×C4×D7—44no—
237C2×C4×D7—416no—
238C7×C4⋊C4—44no—
239C7×C22⋊C4—28no—
240C7×C22⋊C4—28no—
241C7×C22⋊C4—44no—
242C42×C7—28no—
243C22⋊Dic7—28no—
244C22⋊Dic7—44no—
245C22⋊Dic7—44no—
246(C2×D7)⋊C4—28no—
247(C2×D7)⋊C4—28no—
248(C2×D7)⋊C4—28no—
249(C2×D7)⋊C4—44no—
250(C2×D7)⋊C4—44no—
251C4⋊Dic7—28no—
252C4⋊Dic7—44no—
253Dic7⋊C4—28no—
254Dic7⋊C4—44no—
255Dic7⋊C4—44no—
256C4×Dic7—28no—
257C4×Dic7—28no—
258C4×Dic7—44no—
259C23×D4—71no—
260C24×C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4C2×D711yescharacteristic
267C22×C22⋊C4—71no—
268C22×C22⋊C4—71no—
269C22×C22⋊C4—71no—
270C22×C22⋊C4—71no—
271C22×C22⋊C4—71no—
272C22×C22⋊C4—71no—
273C22×C22⋊C4—71no—
274C22×C22⋊C4—71no—
275C22×C22⋊C4C2×D711yescharacteristic
276C22×C22⋊C4C2×D711yescharacteristic
277C22×C22⋊C4C2×D711yescharacteristic
278C22×C42—71no—
279C22×C42—71no—
280C22×C42—71no—
281C22×C42C2×D711yescharacteristic
282#398—78no—
283#397—78no—
284#397—78no—
285#394—78no—
286#390—78no—
287#388—78no—
288#388—78no—
289#388—78no—
290#388C2×D718yescomplemented
291#387—78no—
292#387—78no—
293#386—78no—
294#380—78no—
295C4×C22⋊C4—78no—
296#376—78no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95C2×D711yescharacteristic
308C2×#95C2×D711yescharacteristic
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—44no—
317C23×C7—44no—
318C23×C7—44no—
319C23×C7—44no—
320C23×C7—44no—
321C23×C7—44no—
322C23×C7—44no—
323C23×C7C2×#4112yes—
324C23×C7C2×#4112yes—
325C23×C7C2×#4112yes—
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C7H(5,𝔽2)12yes—
330C23×C7C2511yescharacteristic
331C22×D7—28no—
332C22×D7—28no—
333C22×D7—28no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—22no—
340C22×D7—44no—
341C22×D7—44no—
342C22×D7—44no—
343C22×D7—44no—
344C22×D7C2×#4114yes—
345C2×C4×C7—28no—
346C2×C4×C7—28no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—44no—
364C2×C4×C7—44no—
365C2×C4×C7—44no—
366C2×C4×C7—44no—
367C2×C4×C7C2×#4114yes—
368C2×C4×C7C2×#4114yes—
369C22⋊D7—416no—
370C2×Dic7—28no—
371C2×Dic7—28no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—44no—
392C2×Dic7—44no—
393C2×Dic7—44no—
394C2×Dic7—44no—
395C2×Dic7—44no—
396C2×Dic7C2×#4114yes—
397C2×Dic7C2×#4114yes—
398C4×D7—416no—
399C25—71no—
400C25C22×D711yescharacteristic
401C22×D4—74no—
402C22×D4—144no—
403C22×D4—144no—
404C22×D4—282no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4—71no—
412C23×C4—74no—
413C23×C4—144no—
414C23×C4—144no—
415C23×C4—282no—
416C23×C4C22×D711yescharacteristic
417C23×C4C22×D711yescharacteristic
418C23×C4C22×D711yescharacteristic
419C23×C4C22×D711yescharacteristic
420C23×C4C22×D711yescharacteristic
421C23×C4C22×D711yescharacteristic
422C2×C4⋊C4—42no—
423C2×C4⋊C4—74no—
424C2×C4⋊C4—74no—
425C2×C4⋊C4—74no—
426C2×C4⋊C4—74no—
427C2×C4⋊C4—74no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—144no—
430C2×C4⋊C4—282no—
431C2×C4⋊C4—282no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4C22×D714yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—74no—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—74no—
441C2×C22⋊C4—74no—
442C2×C22⋊C4—74no—
443C2×C22⋊C4—74no—
444C2×C22⋊C4—74no—
445C2×C22⋊C4—144no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—144no—
449C2×C22⋊C4—282no—
450C2×C22⋊C4—282no—
451C2×C22⋊C4—282no—
452C2×C22⋊C4—282no—
453C2×C22⋊C4C22×D714yes—
454C2×C22⋊C4C22×D714yes—
455C2×C22⋊C4C22×D714yes—
456C2×C42—24no—
457C2×C42—74no—
458C2×C42—74no—
459C2×C42—74no—
460C2×C42—144no—
461C2×C42—144no—
462C2×C42—282no—
463C2×C42C22×D714yes—
464#95—74no—
465#95—74no—
466#95—74no—
467#95—74no—
468#95—74no—
469#95—74no—
470#95—74no—
471#95—74no—
472#95—74no—
473#95—74no—
474#95C22×D714yes—
475#95C22×D714yes—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—42no—
483C22×C7—88no—
484C22×C7#52914yes—
485C22×C7#52914yes—
486C22×C7#54014yes—
487C22×C7#55114yes—
488C22×C7#55114yes—
489C22×C7#55314yes—
490C22×C7#55514yes—
491C22×C7C22×#4111yescharacteristic
492C22×C7C22×#4111yescharacteristic
493C22×C7C22×#4111yescharacteristic
494C22×C7C22×#4111yescharacteristic
495C22×C7C22×#4111yescharacteristic
496C22×C7C2×H(5,𝔽2)11yescharacteristic
497C22×C7C2×H(5,𝔽2)11yescharacteristic
498C2×D7—24no—
499C2×D7—24no—
500C2×D7—24no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—42no—
504C2×D7—42no—
505C2×D7—416no—
506C4×C7—24no—
507C4×C7—24no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7—42no—
511C4×C7—42no—
512Dic7—24no—
513Dic7—24no—
514Dic7—42no—
515Dic7—42no—
516Dic7—42no—
517Dic7—42no—
518Dic7—42no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—74no—
527C24—72no—
528C24—142no—
529C24—142no—
530C24—142no—
531C24—142no—
532C24—142no—
533C24—142no—
534C24C23×D712yes—
535C24C23×D711yescharacteristic
536C2×D4—148no—
537C2×D4—148no—
538C2×D4—284no—
539C2×D4—2816no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—74no—
557C22×C4—74no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—72no—
565C22×C4—148no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—142no—
585C22×C4—148no—
586C22×C4—284no—
587C22×C4—2816no—
588C22×C4#115714yes—
589C22×C4#115914yes—
590C22×C4C23×D712yes—
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C22×C4C23×D712yes—
594C22×C4C23×D712yes—
595C22×C4C23×D712yes—
596C4⋊C4—44no—
597C4⋊C4—148no—
598C4⋊C4—148no—
599C4⋊C4—284no—
600C4⋊C4—284no—
601C4⋊C4—284no—
602C22⋊C4—28no—
603C22⋊C4—28no—
604C22⋊C4—44no—
605C22⋊C4—148no—
606C22⋊C4—148no—
607C22⋊C4—148no—
608C22⋊C4—148no—
609C22⋊C4—284no—
610C22⋊C4—284no—
611C22⋊C4—284no—
612C22⋊C4—284no—
613C42—28no—
614C42—148no—
615C42—148no—
616C42—284no—
617C2×C7—82no—
618C2×C7#253118yescomplemented
619C2×C7C2×#52911yescharacteristic
620C2×C7C2×#52911yescharacteristic
621C2×C7C2×#54011yescharacteristic
622C2×C7C2×#55111yescharacteristic
623C2×C7C2×#55111yescharacteristic
624C2×C7C2×#55311yescharacteristic
625C2×C7C2×#55511yescharacteristic
626D7—44no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—74no—
642C23—148no—
643C23—148no—
644C23—148no—
645C23—142no—
646C23—142no—
647C23—142no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—284no—
652C23—284no—
653C23—284no—
654C23—284no—
655C23C2×#115712yes—
656C23C2×#115912yes—
657C23#654812yes—
658C23D7×#4112yes—
659C23D7×#4112yes—
660C23D7×#4112yes—
661C23#655312yes—
662C23C24×D711yescharacteristic
663D4—2816no—
664C2×C4—28no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—74no—
687C2×C4—74no—
688C2×C4—148no—
689C2×C4—148no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—2816no—
710C2×C4—284no—
711C2×C4—284no—
712C2×C4—284no—
713C2×C4—284no—
714C2×C4—284no—
715C2×C4C2×#115714yes—
716C2×C4C2×#115914yes—
717C7C2×#253111yescharacteristic, complemented, Sylow
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—88no—
726C22—144no—
727C22—144no—
728C22—144no—
729C22—2816no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—282no—
734C22#9021914yes—
735C22#9022914yes—
736C22#9025314yes—
737C22#9030514yes—
738C22#9034914yes—
739C22#9036114yes—
740C22#9039614yes—
741C22C22×#115711yescharacteristic
742C22C22×#115911yescharacteristic
743C22C2×#654811yescharacteristic
744C22C2×D7×#4111yescharacteristic
745C22C2×D7×#4111yescharacteristic
746C22C2×D7×#4111yescharacteristic
747C22C2×#655311yescharacteristic
748C4—24no—
749C4—24no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—144no—
755C4—144no—
756C4—282no—
757C4—282no—
758C4—282no—
759C4—282no—
760C4—282no—
761C2—82no—
762C2—284no—
763C2#1173332418yesdirect product factor
764C2C2×#9021911yescharacteristic
765C2C2×#9022911yescharacteristic
766C2C2×#9025311yescharacteristic
767C2C2×#9030511yescharacteristic
768C2C2×#9034911yescharacteristic
769C2C2×#9036111yescharacteristic
770C2C2×#9039611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#388D7
hypocenterC7C2×#2531
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×C7×#388C2semidirect
2. C2×#89765C2semidirect
3. C2×#89755C2semidirect
5. C2×#89724C2semidirect
8. C2×#89716C2semidirect
9. C2×#89723C2semidirect
10. C2×C4×(C2×D7)⋊C4C2semidirect
11. C2×#89704C2semidirect
12. #11733324C2direct (N × H)
13. C2×#89439C2semidirect
14. C2×#89442C2semidirect
15. C2×#89427C2semidirect
16. C2×#89426C2semidirect
40. C7×#388C22semidirect
53. #89765C22semidirect
54. #89755C22semidirect
58. #89724C22semidirect
59. #89723C22semidirect
60. #89716C22semidirect
61. C4×(C2×D7)⋊C4C22semidirect
62. #89704C22semidirect
63. #89442C22semidirect
64. #89439C22semidirect
65. #89427C22semidirect
66. #89426C22semidirect
154. C2×#388D7semidirect
290. #388C2×D7semidirect
618. C2×C7#2531semidirect
717. C7C2×#2531semidirect
763. C2#11733324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×#897652
C2×#897552
C2×#897282
C2×#897242
C2×#897332
C2×#897292
C2×#897162
C2×#897232
C2×C4×(C2×D7)⋊C42
C2×#897042
#117333242
C2×#894392
C2×#894422
C2×#894272
C2×#894262
C2×#25317