Finite Group Databasebeta

← C2×#11734303 #13560134

Subgroups — C2×#11734303 #13560134

Order 1792.

2238 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#393C211yesmaximal, characteristic, complemented
2C2×#90003C211yesmaximal, characteristic, complemented
3C2×#90001C211yesmaximal, characteristic, complemented
4C2×#89731C211yesmaximal, characteristic
5C2×#89731C211yesmaximal, characteristic
6C2×#89731C211yesmaximal, characteristic
7C2×#89725C211yesmaximal, characteristic, complemented
8C2×#89719C211yesmaximal, characteristic, complemented
9C2×#89717C211yesmaximal, characteristic, complemented
10#11734303C2116yesmaximal, direct product factor
11C2×#89447C211yesmaximal, characteristic, complemented
12C2×#89445C211yesmaximal, characteristic, complemented
13C2×#89432C211yesmaximal, characteristic, complemented
14C2×#89430C211yesmaximal, characteristic, complemented
15C2×#89418C211yesmaximal, characteristic, complemented
16C2×#89442C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C7×#393C2218yescomplemented
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42#90003C2218yescomplemented
43#90001C2218yescomplemented
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
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89731C2218yes—
56#89731C2218yes—
57#89731C2218yes—
58#89725C2218yescomplemented
59#89719C2218yescomplemented
60#89717C2218yescomplemented
61#89447C2218yescomplemented
62#89445C2218yescomplemented
63#89442C2218yescomplemented
64#89432C2218yescomplemented
65#89430C2218yescomplemented
66#89418C2218yescomplemented
67C2×#2832—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C24×D7C2311yescharacteristic
70C22×C7×Q8—42no—
71C22×C7×Q8—42no—
72C22×C7×Q8—42no—
73C22×C7×Q8C2314yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—42no—
81C22×C22⋊D7—42no—
82C22×C22⋊D7—42no—
83C22×C22⋊D7C2314yes—
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C22×Dic14—24no—
92C22×Dic14—42no—
93C22×Dic14—42no—
94C22×Dic14C2314yes—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4—42no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4C2314yes—
99C2×C7×C22⋊C4C2314yes—
100C2×C7×C22⋊C4C2314yes—
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—42no—
109C2×(C2×D7)⋊C4—42no—
110C2×(C2×D7)⋊C4—42no—
111C2×(C2×D7)⋊C4—42no—
112C2×(C2×D7)⋊C4—42no—
113C2×(C2×D7)⋊C4C2314yes—
114C2×(C2×D7)⋊C4C2314yes—
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
117C2×(C2×D7)⋊C4C2314yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×C4⋊Dic7—42no—
120C2×C4⋊Dic7C2314yes—
121C2×Dic7⋊C4—42no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4—42no—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×C4×Dic7—42no—
130C2×C4×Dic7C2314yes—
131C7×#95C2314yes—
132C7×#95C2314yes—
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#2832—716no—
146C2×#400—71no—
147C2×#400—71no—
148C2×#397—71no—
149C2×#397—71no—
150C2×#395—71no—
151C2×#394—71no—
152C2×#394—71no—
153C2×#394—71no—
154C2×#393—71no—
155C2×#393—71no—
156C2×#393—71no—
157C2×#393D711yescharacteristic, complemented
158C2×#391—71no—
159C2×#388—71no—
160C2×#388—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—22no—
177C23×D7C2412yes—
178C2×C7×Q8—44no—
179C2×C7×Q8—44no—
180C2×C7×Q8—44no—
181C2×C7×Q8—416no—
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—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C22×C4×C7C2412yes—
203C22×C4×C7C2412yes—
204C22×C4×C7C2412yes—
205C22×C4×C7C2412yes—
206C2×C22⋊D7—44no—
207C2×C22⋊D7—44no—
208C2×C22⋊D7—44no—
209C2×C22⋊D7—416no—
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—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7#4114yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C2×Dic14—28no—
239C2×Dic14—44no—
240C2×Dic14—44no—
241C2×Dic14—416no—
242C7×C22⋊C4—44no—
243C7×C22⋊C4—44no—
244C7×C22⋊C4—44no—
245C22⋊Dic7—28no—
246C22⋊Dic7—44no—
247C22⋊Dic7—44no—
248(C2×D7)⋊C4—28no—
249(C2×D7)⋊C4—44no—
250(C2×D7)⋊C4—44no—
251(C2×D7)⋊C4—44no—
252(C2×D7)⋊C4—44no—
253(C2×D7)⋊C4—44no—
254C4⋊Dic7—44no—
255Dic7⋊C4—44no—
256Dic7⋊C4—44no—
257Dic7⋊C4—44no—
258Dic7⋊C4—44no—
259C4×Dic7—44no—
260C23×Q8—71no—
261C23×Q8C2×D711yescharacteristic
262C23×D4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4—71no—
267C22×C4⋊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⋊C4—71no—
276C22×C22⋊C4—71no—
277C22×C22⋊C4C2×D711yescharacteristic
278C22×C22⋊C4C2×D711yescharacteristic
279C22×C22⋊C4C2×D711yescharacteristic
280C22×C42—71no—
281#400—78no—
282#400—78no—
283#397—78no—
284#397—78no—
285#395—78no—
286#394—78no—
287#394—78no—
288#394—78no—
289#393—78no—
290#393—78no—
291#393—78no—
292#393C2×D718yescomplemented
293#391—78no—
294#388—78no—
295#388—78no—
296C2×#95—71no—
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
309C2×#95C2×D711yescharacteristic
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—44no—
318C23×C7—44no—
319C23×C7—44no—
320C23×C7—44no—
321C23×C7—44no—
322C23×C7—44no—
323C23×C7—44no—
324C23×C7C2×#4112yes—
325C23×C7H(5,𝔽2)12yes—
326C23×C7H(5,𝔽2)12yes—
327C23×C7H(5,𝔽2)12yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C72−1+412yes—
330C23×C72−1+412yes—
331C23×C7C2511yescharacteristic
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—44no—
340C22×D7—44no—
341C22×D7—44no—
342C22×D7—44no—
343C22×D7—44no—
344C22×D7—44no—
345C22×D7—44no—
346C7×Q8—416no—
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—22no—
364C2×C4×C7—22no—
365C2×C4×C7—44no—
366C2×C4×C7—44no—
367C2×C4×C7—44no—
368C2×C4×C7—44no—
369C2×C4×C7—44no—
370C2×C4×C7—44no—
371C22⋊D7—416no—
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—22no—
392C2×Dic7—22no—
393C2×Dic7—44no—
394C2×Dic7—44no—
395C2×Dic7—44no—
396C2×Dic7—44no—
397C2×Dic7—44no—
398C2×Dic7—44no—
399C2×Dic7C2×#4114yes—
400Dic14—416no—
401C25—71no—
402C25C22×D711yescharacteristic
403C22×Q8—42no—
404C22×Q8—42no—
405C22×Q8—42no—
406C22×Q8—74no—
407C22×Q8—144no—
408C22×Q8—282no—
409C22×Q8—282no—
410C22×Q8C22×D714yes—
411C22×D4—74no—
412C22×D4—282no—
413C22×D4—282no—
414C22×D4—282no—
415C23×C4—71no—
416C23×C4—71no—
417C23×C4—71no—
418C23×C4—71no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4C22×D711yescharacteristic
423C23×C4C22×D711yescharacteristic
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C2×C4⋊C4—74no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—74no—
431C2×C4⋊C4—74no—
432C2×C4⋊C4—74no—
433C2×C4⋊C4—282no—
434C2×C4⋊C4—282no—
435C2×C4⋊C4—282no—
436C2×C4⋊C4—282no—
437C2×C4⋊C4—282no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—74no—
442C2×C22⋊C4—74no—
443C2×C22⋊C4—74no—
444C2×C22⋊C4—74no—
445C2×C22⋊C4—74no—
446C2×C22⋊C4—74no—
447C2×C22⋊C4—74no—
448C2×C22⋊C4—74no—
449C2×C22⋊C4—74no—
450C2×C22⋊C4—144no—
451C2×C22⋊C4—144no—
452C2×C22⋊C4—282no—
453C2×C22⋊C4—282no—
454C2×C22⋊C4—282no—
455C2×C22⋊C4—282no—
456C2×C22⋊C4—282no—
457C2×C22⋊C4—282no—
458C2×C22⋊C4—282no—
459C2×C22⋊C4C22×D714yes—
460C2×C22⋊C4C22×D714yes—
461C2×C22⋊C4C22×D714yes—
462C2×C42—74no—
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#95—74no—
474#95—74no—
475#95C22×D714yes—
476#95C22×D714yes—
477#95C22×D714yes—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—88no—
486C22×C7#53814yes—
487C22×C7#54214yes—
488C22×C7#54214yes—
489C22×C7H(3,𝔽4)14yes—
490C22×C7#56214yes—
491C22×C7#56214yes—
492C22×C7#56314yes—
493C22×C7C22×#4111yescharacteristic
494C22×C7C2×H(5,𝔽2)11yescharacteristic
495C22×C7C2×H(5,𝔽2)11yescharacteristic
496C22×C7C2×H(5,𝔽2)11yescharacteristic
497C22×C7C2×H(5,𝔽2)11yescharacteristic
498C22×C7C2×2−1+411yescharacteristic
499C22×C7C2×2−1+411yescharacteristic
500C2×D7—42no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—42no—
504C2×D7—42no—
505C2×D7—42no—
506C2×D7—42no—
507C2×D7—88no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7—42no—
511C4×C7—42no—
512C4×C7—42no—
513C4×C7—42no—
514Dic7—24no—
515Dic7—42no—
516Dic7—42no—
517Dic7—42no—
518Dic7—42no—
519Dic7—42no—
520Dic7—42no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—72no—
529C24—142no—
530C24—142no—
531C24—142no—
532C24—142no—
533C24—142no—
534C24—142no—
535C24—142no—
536C24C23×D712yes—
537C24C23×D711yescharacteristic
538C2×Q8—44no—
539C2×Q8—44no—
540C2×Q8—44no—
541C2×Q8—416no—
542C2×Q8—148no—
543C2×Q8—284no—
544C2×Q8—284no—
545C2×Q8—2816no—
546C2×D4—284no—
547C2×D4—284no—
548C2×D4—284no—
549C2×D4—2816no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—74no—
569C22×C4—72no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—72no—
574C22×C4—72no—
575C22×C4—72no—
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—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4C23×D712yes—
597C22×C4C23×D712yes—
598C22×C4C23×D712yes—
599C22×C4C23×D712yes—
600C22×C4C23×D712yes—
601C22×C4C23×D712yes—
602C4⋊C4—284no—
603C4⋊C4—284no—
604C4⋊C4—284no—
605C4⋊C4—284no—
606C4⋊C4—284no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—148no—
611C22⋊C4—148no—
612C22⋊C4—284no—
613C22⋊C4—284no—
614C22⋊C4—284no—
615C22⋊C4—284no—
616C22⋊C4—284no—
617C22⋊C4—284no—
618C22⋊C4—284no—
619C42—284no—
620C2×C7—82no—
621C2×C7#283218yescomplemented
622C2×C7C2×#53811yescharacteristic
623C2×C7C2×#54211yescharacteristic
624C2×C7C2×#54211yescharacteristic
625C2×C7C2×H(3,𝔽4)11yescharacteristic
626C2×C7C2×#56211yescharacteristic
627C2×C7C2×#56211yescharacteristic
628C2×C7C2×#56311yescharacteristic
629D7—82no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—142no—
645C23—142no—
646C23—142no—
647C23—142no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—284no—
652C23—284no—
653C23—284no—
654C23—284no—
655C23—284no—
656C23—284no—
657C23—284no—
658C23#654812yes—
659C23#654812yes—
660C23#654812yes—
661C23#655112yes—
662C23D7×#4112yes—
663C23#655312yes—
664C23#655412yes—
665C23C24×D711yescharacteristic
666Q8—416no—
667Q8—2816no—
668D4—2816no—
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—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—74no—
694C2×C4—148no—
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—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—284no—
716C2×C4—284no—
717C2×C4—284no—
718C2×C4—284no—
719C2×C4—284no—
720C2×C4—284no—
721C7C2×#283211yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—88no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—282no—
734C22—282no—
735C22—282no—
736C22—282no—
737C22—568no—
738C22#9028514yes—
739C22#9033114yes—
740C22#9033714yes—
741C22#9033814yes—
742C22#9036014yes—
743C22#9036914yes—
744C22#9037514yes—
745C22C2×#654811yescharacteristic
746C22C2×#654811yescharacteristic
747C22C2×#654811yescharacteristic
748C22C2×#655111yescharacteristic
749C22C2×D7×#4111yescharacteristic
750C22C2×#655311yescharacteristic
751C22C2×#655411yescharacteristic
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—144no—
759C4—282no—
760C4—282no—
761C4—282no—
762C4—282no—
763C4—282no—
764C4—282no—
765C2—82no—
766C2—562no—
767C2#1173430318yesdirect product factor
768C2C2×#9028511yescharacteristic
769C2C2×#9033111yescharacteristic
770C2C2×#9033711yescharacteristic
771C2C2×#9033811yescharacteristic
772C2C2×#9036011yescharacteristic
773C2C2×#9037511yescharacteristic
774C2C2×#9036911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#393C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#393D7
hypocenterC7C2×#2832
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C2×C7×#393C2semidirect
2. C2×#90003C2semidirect
3. C2×#90001C2semidirect
7. C2×#89725C2semidirect
8. C2×#89719C2semidirect
9. C2×#89717C2semidirect
10. #11734303C2direct (N × H)
11. C2×#89447C2semidirect
12. C2×#89445C2semidirect
13. C2×#89432C2semidirect
14. C2×#89430C2semidirect
15. C2×#89418C2semidirect
16. C2×#89442C2semidirect
38. C7×#393C22semidirect
42. #90003C22semidirect
43. #90001C22semidirect
58. #89725C22semidirect
59. #89719C22semidirect
60. #89717C22semidirect
61. #89447C22semidirect
62. #89445C22semidirect
63. #89442C22semidirect
64. #89432C22semidirect
65. #89430C22semidirect
66. #89418C22semidirect
157. C2×#393D7semidirect
292. #393C2×D7semidirect
621. C2×C7#2832semidirect
721. C7C2×#2832semidirect
767. C2#11734303direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3932
C2×#900032
C2×#900012
C2×#897312
C2×#897252
C2×#897192
C2×#897172
#117343032
C2×#894472
C2×#894452
C2×#894322
C2×#894302
C2×#894182
C2×#894422
C2×#28327