Finite Group Databasebeta

← C2×#11734942 #13523219

Subgroups — C2×#11734942 #13523219

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×#397C211yesmaximal, characteristic, complemented
2C2×#89764C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
4C2×#89728C211yesmaximal, characteristic
5C2×#89733C211yesmaximal, characteristic
6C2×#89729C211yesmaximal, characteristic
7C2×#89717C211yesmaximal, characteristic, complemented
8C2×#89716C211yesmaximal, characteristic, complemented
9C2×#89723C211yesmaximal, characteristic, complemented
10#11734942C2116yesmaximal, direct product factor
11C2×#89436C211yesmaximal, characteristic, complemented
12C2×#89432C211yesmaximal, characteristic, complemented
13C2×#89442C211yesmaximal, characteristic, complemented
14C2×#89425C211yesmaximal, characteristic, complemented
15C2×#89424C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, 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×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C7×#397C2218yescomplemented
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#89764C2218yescomplemented
54C4⋊C4×Dic7C2218yescomplemented
55#89733C2218yes—
56#89729C2218yes—
57#89728C2218yes—
58#89723C2218yescomplemented
59#89717C2218yescomplemented
60#89716C2218yescomplemented
61#89442C2218yescomplemented
62#89438C2218yescomplemented
63#89436C2218yescomplemented
64#89432C2218yescomplemented
65#89425C2218yescomplemented
66#89424C2218yescomplemented
67C2×#2516—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—24no—
92C2×C7×C4⋊C4C2314yes—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4C2314yes—
97C2×C7×C22⋊C4C2314yes—
98C2×C7×C22⋊C4C2314yes—
99C2×C22⋊Dic7—24no—
100C2×C22⋊Dic7—24no—
101C2×C22⋊Dic7—42no—
102C2×C22⋊Dic7C2314yes—
103C2×C22⋊Dic7C2314yes—
104C2×C22⋊Dic7C2314yes—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—24no—
108C2×(C2×D7)⋊C4—42no—
109C2×(C2×D7)⋊C4—42no—
110C2×(C2×D7)⋊C4C2314yes—
111C2×(C2×D7)⋊C4C2314yes—
112C2×(C2×D7)⋊C4C2314yes—
113C2×(C2×D7)⋊C4C2314yes—
114C2×(C2×D7)⋊C4C2314yes—
115C2×C4⋊Dic7—24no—
116C2×C4⋊Dic7—24no—
117C2×C4⋊Dic7C2314yes—
118C2×C4⋊Dic7C2314yes—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—42no—
121C2×Dic7⋊C4—42no—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×C4×Dic7—24no—
126C2×C4×Dic7—42no—
127C2×C4×Dic7—42no—
128C2×C4×Dic7—42no—
129C2×C4×Dic7C2314yes—
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#2516—716no—
146C2×#400—71no—
147C2×#399—71no—
148C2×#397D711yescharacteristic, complemented
149C2×#394—71no—
150C2×#390—71no—
151C2×#388—71no—
152C2×#388—71no—
153C2×#388—71no—
154C2×#388—71no—
155C2×#387—71no—
156C2×#387—71no—
157C2×#386—71no—
158C2×#381—71no—
159C2×C4×C4⋊C4—71no—
160C2×C4×C22⋊C4—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—22no—
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#4114yes—
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—28no—
239C7×C22⋊C4—28no—
240C7×C22⋊C4—44no—
241C7×C22⋊C4—44no—
242C22⋊Dic7—28no—
243C22⋊Dic7—28no—
244C22⋊Dic7—44no—
245(C2×D7)⋊C4—28no—
246(C2×D7)⋊C4—28no—
247(C2×D7)⋊C4—28no—
248(C2×D7)⋊C4—44no—
249(C2×D7)⋊C4—44no—
250C4⋊Dic7—28no—
251C4⋊Dic7—28no—
252Dic7⋊C4—28no—
253Dic7⋊C4—44no—
254Dic7⋊C4—44no—
255C4×Dic7—28no—
256C4×Dic7—44no—
257C4×Dic7—44no—
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×C42—71no—
282#400—78no—
283#399—78no—
284#397C2×D718yescomplemented
285#394—78no—
286#390—78no—
287#388—78no—
288#388—78no—
289#388—78no—
290#388—78no—
291#387—78no—
292#387—78no—
293#386—78no—
294#381—78no—
295C4×C4⋊C4—78no—
296C4×C22⋊C4—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×#95C2×D711yescharacteristic
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—22no—
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×C7—44no—
368C2×C4×C7C2×#4114yes—
369C22⋊D7—416no—
370C2×Dic7—28no—
371C2×Dic7—28no—
372C2×Dic7—28no—
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×Dic7C2×#4114yes—
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—24no—
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—144no—
431C2×C4⋊C4—282no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4C22×D714yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—42no—
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—144no—
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—74no—
457C2×C42—74no—
458C2×C42—74no—
459C2×C42—74no—
460C2×C42—144no—
461C2×C42—282no—
462C2×C42—282no—
463C2×C42—282no—
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#95C22×D714yes—
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#55914yes—
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—42no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7—42no—
511C4×C7—42no—
512Dic7—24no—
513Dic7—24no—
514Dic7—24no—
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—22no—
557C22×C4—74no—
558C22×C4—74no—
559C22×C4—74no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—72no—
565C22×C4—72no—
566C22×C4—72no—
567C22×C4—148no—
568C22×C4—148no—
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—142no—
586C22×C4—142no—
587C22×C4—284no—
588C22×C4—2816no—
589C22×C4#115914yes—
590C22×C4C23×D712yes—
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C22×C4C23×D712yes—
594C22×C4C23×D712yes—
595C22×C4C23×D712yes—
596C4⋊C4—28no—
597C4⋊C4—148no—
598C4⋊C4—148no—
599C4⋊C4—148no—
600C4⋊C4—284no—
601C4⋊C4—284no—
602C22⋊C4—28no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—148no—
606C22⋊C4—148no—
607C22⋊C4—148no—
608C22⋊C4—148no—
609C22⋊C4—148no—
610C22⋊C4—284no—
611C22⋊C4—284no—
612C22⋊C4—284no—
613C42—148no—
614C42—284no—
615C42—284no—
616C42—284no—
617C2×C7—82no—
618C2×C7#251618yescomplemented
619C2×C7C2×#52911yescharacteristic
620C2×C7C2×#52911yescharacteristic
621C2×C7C2×#54011yescharacteristic
622C2×C7C2×#55111yescharacteristic
623C2×C7C2×#55111yescharacteristic
624C2×C7C2×#55311yescharacteristic
625C2×C7C2×#55911yescharacteristic
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×#115912yes—
656C23#654812yes—
657C23D7×#4112yes—
658C23D7×#4112yes—
659C23D7×#4112yes—
660C23D7×#4112yes—
661C23#655312yes—
662C23C24×D711yescharacteristic
663D4—2816no—
664C2×C4—28no—
665C2×C4—22no—
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—44no—
687C2×C4—74no—
688C2×C4—74no—
689C2×C4—74no—
690C2×C4—148no—
691C2×C4—148no—
692C2×C4—148no—
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—142no—
710C2×C4—142no—
711C2×C4—2816no—
712C2×C4—284no—
713C2×C4—284no—
714C2×C4—284no—
715C2×C4—284no—
716C2×C4C2×#115914yes—
717C7C2×#251611yescharacteristic, 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—282no—
730C22—282no—
731C22—282no—
732C22—2816no—
733C22—282no—
734C22#9031014yes—
735C22#9034014yes—
736C22#9035014yes—
737C22#9035514yes—
738C22#9037114yes—
739C22#9039614yes—
740C22#9040014yes—
741C22C22×#115911yescharacteristic
742C22C2×#654811yescharacteristic
743C22C2×D7×#4111yescharacteristic
744C22C2×D7×#4111yescharacteristic
745C22C2×D7×#4111yescharacteristic
746C22C2×D7×#4111yescharacteristic
747C22C2×#655311yescharacteristic
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—144no—
755C4—144no—
756C4—144no—
757C4—282no—
758C4—282no—
759C4—282no—
760C4—282no—
761C2—82no—
762C2—284no—
763C2#1173494218yesdirect product factor
764C2C2×#9031011yescharacteristic
765C2C2×#9034011yescharacteristic
766C2C2×#9035511yescharacteristic
767C2C2×#9035011yescharacteristic
768C2C2×#9037111yescharacteristic
769C2C2×#9040011yescharacteristic
770C2C2×#9039611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#397C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#397D7
hypocenterC7C2×#2516
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×C7×#397C2semidirect
2. C2×#89764C2semidirect
3. C2×C4⋊C4×Dic7C2semidirect
7. C2×#89717C2semidirect
8. C2×#89716C2semidirect
9. C2×#89723C2semidirect
10. #11734942C2direct (N × H)
11. C2×#89436C2semidirect
12. C2×#89432C2semidirect
13. C2×#89442C2semidirect
14. C2×#89425C2semidirect
15. C2×#89424C2semidirect
16. C2×#89438C2semidirect
40. C7×#397C22semidirect
53. #89764C22semidirect
54. C4⋊C4×Dic7C22semidirect
58. #89723C22semidirect
59. #89717C22semidirect
60. #89716C22semidirect
61. #89442C22semidirect
62. #89438C22semidirect
63. #89436C22semidirect
64. #89432C22semidirect
65. #89425C22semidirect
66. #89424C22semidirect
148. C2×#397D7semidirect
284. #397C2×D7semidirect
618. C2×C7#2516semidirect
717. C7C2×#2516semidirect
763. C2#11734942direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3972
C2×#897642
C2×C4⋊C4×Dic72
C2×#897282
C2×#897332
C2×#897292
C2×#897172
C2×#897162
C2×#897232
#117349422
C2×#894362
C2×#894322
C2×#894422
C2×#894252
C2×#894242
C2×#894382
C2×#25167