Finite Group Databasebeta

← C2×#11735006 #13520286

Subgroups — C2×#11735006 #13520286

Order 1792.

2394 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×#397C211yesmaximal, characteristic, complemented
2C2×#89761C211yesmaximal, characteristic, complemented
3C2×#89755C211yesmaximal, characteristic, complemented
4C2×#89731C211yesmaximal, characteristic
5C2×#89728C211yesmaximal, characteristic
6C2×#89733C211yesmaximal, characteristic
7C2×#89719C211yesmaximal, characteristic, complemented
8C2×#89716C211yesmaximal, characteristic, complemented
9C2×#89716C211yesmaximal, characteristic, complemented
10#11735006C2116yesmaximal, direct product factor
11C2×#89447C211yesmaximal, characteristic, complemented
12C2×#89445C211yesmaximal, characteristic, complemented
13C2×C7⋊#401C211yesmaximal, characteristic, complemented
14C2×#89418C211yesmaximal, characteristic, complemented
15C2×#89427C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C7×#397C2218yescomplemented
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
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#89761C2218yescomplemented
54#89755C2218yescomplemented
55#89733C2218yes—
56#89731C2218yes—
57#89728C2218yes—
58#89719C2218yescomplemented
59#89716C2218yescomplemented
60#89716C2218yescomplemented
61#89447C2218yescomplemented
62#89445C2218yescomplemented
63#89438C2218yescomplemented
64C7⋊#401C2218yescomplemented
65#89427C2218yescomplemented
66#89418C2218yescomplemented
67C2×#2653—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—42no—
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—42no—
89C22×C4×D7—42no—
90C22×C4×D7C2314yes—
91C22×Dic14—24no—
92C22×Dic14—42no—
93C22×Dic14—42no—
94C22×Dic14C2314yes—
95C2×C7×C4⋊C4—42no—
96C2×C7×C4⋊C4C2314yes—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4—42no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4C2314yes—
101C2×C7×C22⋊C4C2314yes—
102C2×C7×C22⋊C4C2314yes—
103C2×C22⋊Dic7—24no—
104C2×C22⋊Dic7—24no—
105C2×C22⋊Dic7—42no—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C22⋊Dic7C2314yes—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—24no—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—42no—
113C2×(C2×D7)⋊C4—42no—
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—24no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×C4×Dic7—42no—
128C2×C4×Dic7—42no—
129C2×C4×Dic7C2314yes—
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#2653—716no—
146C2×#401—71no—
147C2×#398—71no—
148C2×#397—71no—
149C2×#397D711yescharacteristic, complemented
150C2×#394—71no—
151C2×#394—71no—
152C2×#393—71no—
153C2×#393—71no—
154C2×#391—71no—
155C2×#388—71no—
156C2×#388—71no—
157C2×#387—71no—
158C2×#386—71no—
159C2×#385—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—22no—
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—44no—
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—44no—
236C2×C4×D7—44no—
237C2×C4×D7—416no—
238C2×Dic14—28no—
239C2×Dic14—44no—
240C2×Dic14—44no—
241C2×Dic14—416no—
242C7×C4⋊C4—44no—
243C7×C22⋊C4—44no—
244C7×C22⋊C4—44no—
245C7×C22⋊C4—44no—
246C22⋊Dic7—28no—
247C22⋊Dic7—28no—
248C22⋊Dic7—44no—
249(C2×D7)⋊C4—28no—
250(C2×D7)⋊C4—28no—
251(C2×D7)⋊C4—28no—
252(C2×D7)⋊C4—44no—
253(C2×D7)⋊C4—44no—
254C4⋊Dic7—44no—
255Dic7⋊C4—28no—
256Dic7⋊C4—44no—
257Dic7⋊C4—44no—
258C4×Dic7—44no—
259C4×Dic7—44no—
260C23×Q8—71no—
261C23×D4—71no—
262C24×C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4—71no—
267C22×C4⋊C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
277C22×C22⋊C4C2×D711yescharacteristic
278C22×C22⋊C4C2×D711yescharacteristic
279C22×C42—71no—
280C22×C42—71no—
281#401—78no—
282#398—78no—
283#397—78no—
284#397C2×D718yescomplemented
285#394—78no—
286#394—78no—
287#393—78no—
288#393—78no—
289#391—78no—
290#388—78no—
291#388—78no—
292#387—78no—
293#386—78no—
294#385—78no—
295C4×C22⋊C4—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×C7C2×#4112yes—
326C23×C7C2×#4112yes—
327C23×C7H(5,𝔽2)12yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C7H(5,𝔽2)12yes—
330C23×C72−1+412yes—
331C23×C7C2511yescharacteristic
332C22×D7—28no—
333C22×D7—28no—
334C22×D7—28no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—44no—
342C22×D7—44no—
343C22×D7—44no—
344C22×D7—44no—
345C22×D7C2×#4114yes—
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—22no—
364C2×C4×C7—44no—
365C2×C4×C7—44no—
366C2×C4×C7—44no—
367C2×C4×C7—44no—
368C2×C4×C7—44no—
369C2×C4×C7—44no—
370C22⋊D7—416no—
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—22no—
392C2×Dic7—44no—
393C2×Dic7—44no—
394C2×Dic7—44no—
395C2×Dic7—44no—
396C2×Dic7—44no—
397C2×Dic7C2×#4114yes—
398C2×Dic7C2×#4114yes—
399C4×D7—416no—
400Dic14—416no—
401C25—71no—
402C25C22×D711yescharacteristic
403C22×Q8—74no—
404C22×Q8—144no—
405C22×Q8—282no—
406C22×Q8—282no—
407C22×D4—74no—
408C22×D4—144no—
409C22×D4—282no—
410C22×D4—282no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4—71no—
414C23×C4—71no—
415C23×C4—71no—
416C23×C4—71no—
417C23×C4—71no—
418C23×C4—74no—
419C23×C4—144no—
420C23×C4—282no—
421C23×C4—282no—
422C23×C4C22×D711yescharacteristic
423C23×C4C22×D711yescharacteristic
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C2×C4⋊C4—42no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—74no—
431C2×C4⋊C4—74no—
432C2×C4⋊C4—74no—
433C2×C4⋊C4—144no—
434C2×C4⋊C4—282no—
435C2×C4⋊C4—282no—
436C2×C4⋊C4—282no—
437C2×C4⋊C4C22×D714yes—
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—144no—
450C2×C22⋊C4—144no—
451C2×C22⋊C4—144no—
452C2×C22⋊C4—144no—
453C2×C22⋊C4—144no—
454C2×C22⋊C4—282no—
455C2×C22⋊C4—282no—
456C2×C22⋊C4—282no—
457C2×C22⋊C4C22×D714yes—
458C2×C22⋊C4C22×D714yes—
459C2×C22⋊C4C22×D714yes—
460C2×C42—74no—
461C2×C42—74no—
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#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#52914yes—
487C22×C7#53814yes—
488C22×C7#53814yes—
489C22×C7#53814yes—
490C22×C7#53914yes—
491C22×C7#54214yes—
492C22×C7#54214yes—
493C22×C7C22×#4111yescharacteristic
494C22×C7C22×#4111yescharacteristic
495C22×C7C22×#4111yescharacteristic
496C22×C7C2×H(5,𝔽2)11yescharacteristic
497C22×C7C2×H(5,𝔽2)11yescharacteristic
498C22×C7C2×H(5,𝔽2)11yescharacteristic
499C22×C7C2×2−1+411yescharacteristic
500C2×D7—24no—
501C2×D7—24no—
502C2×D7—24no—
503C2×D7—416no—
504C2×D7—42no—
505C2×D7—42no—
506C2×D7—42no—
507C2×D7—42no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7—42no—
511C4×C7—42no—
512C4×C7—42no—
513C4×C7—42no—
514Dic7—24no—
515Dic7—24no—
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—74no—
529C24—72no—
530C24—142no—
531C24—142no—
532C24—142no—
533C24—142no—
534C24—142no—
535C24—142no—
536C24C23×D712yes—
537C24C23×D711yescharacteristic
538C2×Q8—148no—
539C2×Q8—284no—
540C2×Q8—284no—
541C2×Q8—2816no—
542C2×D4—148no—
543C2×D4—284no—
544C2×D4—284no—
545C2×D4—2816no—
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—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—74no—
565C22×C4—74no—
566C22×C4—72no—
567C22×C4—72no—
568C22×C4—72no—
569C22×C4—72no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—148no—
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—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—284no—
594C22×C4—284no—
595C22×C4—2816no—
596C22×C4C23×D712yes—
597C22×C4C23×D712yes—
598C22×C4C23×D712yes—
599C22×C4C23×D712yes—
600C22×C4C23×D712yes—
601C22×C4C23×D712yes—
602C4⋊C4—44no—
603C4⋊C4—148no—
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—148no—
613C22⋊C4—148no—
614C22⋊C4—148no—
615C22⋊C4—284no—
616C22⋊C4—284no—
617C22⋊C4—284no—
618C42—284no—
619C42—284no—
620C2×C7—82no—
621C2×C7#265318yescomplemented
622C2×C7C2×#52911yescharacteristic
623C2×C7C2×#53811yescharacteristic
624C2×C7C2×#53811yescharacteristic
625C2×C7C2×#53811yescharacteristic
626C2×C7C2×#53911yescharacteristic
627C2×C7C2×#54211yescharacteristic
628C2×C7C2×#54211yescharacteristic
629D7—44no—
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—74no—
645C23—148no—
646C23—148no—
647C23—148no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—142no—
652C23—142no—
653C23—142no—
654C23—284no—
655C23—284no—
656C23—284no—
657C23—284no—
658C23#654812yes—
659C23#654812yes—
660C23D7×#4112yes—
661C23D7×#4112yes—
662C23D7×#4112yes—
663C23#655312yes—
664C23#655412yes—
665C23C24×D711yescharacteristic
666Q8—2816no—
667D4—2816no—
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—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—74no—
693C2×C4—74no—
694C2×C4—148no—
695C2×C4—148no—
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—2816no—
716C2×C4—284no—
717C2×C4—284no—
718C2×C4—284no—
719C2×C4—284no—
720C2×C4—284no—
721C7C2×#265311yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—88no—
730C22—144no—
731C22—144no—
732C22—144no—
733C22—282no—
734C22—282no—
735C22—282no—
736C22—282no—
737C22—2816no—
738C22#9030414yes—
739C22#9034814yes—
740C22#9034814yes—
741C22#9035114yes—
742C22#9036014yes—
743C22#9039714yes—
744C22#9040114yes—
745C22C2×#654811yescharacteristic
746C22C2×#654811yescharacteristic
747C22C2×D7×#4111yescharacteristic
748C22C2×D7×#4111yescharacteristic
749C22C2×D7×#4111yescharacteristic
750C22C2×#655311yescharacteristic
751C22C2×#655411yescharacteristic
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—144no—
759C4—144no—
760C4—282no—
761C4—282no—
762C4—282no—
763C4—282no—
764C4—282no—
765C2—82no—
766C2—284no—
767C2#1173500618yesdirect product factor
768C2C2×#9030411yescharacteristic
769C2C2×#9034811yescharacteristic
770C2C2×#9034811yescharacteristic
771C2C2×#9035111yescharacteristic
772C2C2×#9036011yescharacteristic
773C2C2×#9039711yescharacteristic
774C2C2×#9040111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#397C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#397D7
hypocenterC7C2×#2653
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×#89761C2semidirect
3. C2×#89755C2semidirect
7. C2×#89719C2semidirect
8. C2×#89716C2semidirect
9. C2×#89716C2semidirect
10. #11735006C2direct (N × H)
11. C2×#89447C2semidirect
12. C2×#89445C2semidirect
13. C2×C7⋊#401C2semidirect
14. C2×#89418C2semidirect
15. C2×#89427C2semidirect
16. C2×#89438C2semidirect
38. C7×#397C22semidirect
53. #89761C22semidirect
54. #89755C22semidirect
58. #89719C22semidirect
59. #89716C22semidirect
60. #89716C22semidirect
61. #89447C22semidirect
62. #89445C22semidirect
63. #89438C22semidirect
64. C7⋊#401C22semidirect
65. #89427C22semidirect
66. #89418C22semidirect
149. C2×#397D7semidirect
284. #397C2×D7semidirect
621. C2×C7#2653semidirect
721. C7C2×#2653semidirect
767. C2#11735006direct (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×#897612
C2×#897552
C2×#897312
C2×#897282
C2×#897332
C2×#897192
C2×#897162
#117350062
C2×#894472
C2×#894452
C2×C7⋊#4012
C2×#894182
C2×#894272
C2×#894382
C2×#26537