Finite Group Databasebeta

← C2×#11734849 #13560174

Subgroups — C2×#11734849 #13560174

Order 1792.

2174 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×#396C211yesmaximal, characteristic, complemented
2C2×#89765C211yesmaximal, characteristic, complemented
3C2×#89765C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89752C211yesmaximal, characteristic, complemented
6C2×#89751C211yesmaximal, characteristic, complemented
7C2×#89750C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic
9C2×#89731C211yesmaximal, characteristic
10C2×#89725C211yesmaximal, characteristic, complemented
11C2×#89724C211yesmaximal, characteristic, complemented
12C2×#89719C211yesmaximal, characteristic, complemented
13C2×#89729C211yesmaximal, characteristic
14#11734849C2116yesmaximal, direct product factor
15C2×#89445C211yesmaximal, characteristic, complemented
16C2×#89427C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C7×#396C2218yescomplemented
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#89766C2218yescomplemented
54#89765C2218yescomplemented
55#89765C2218yescomplemented
56#89752C2218yescomplemented
57#89751C2218yescomplemented
58#89750C2218yescomplemented
59#89731C2218yes—
60#89731C2218yes—
61#89729C2218yes—
62#89725C2218yescomplemented
63#89724C2218yescomplemented
64#89719C2218yescomplemented
65#89445C2218yescomplemented
66#89427C2218yescomplemented
67C2×#2830—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×Dic14—42no—
88C22×Dic14—42no—
89C22×Dic14—42no—
90C22×Dic14C2314yes—
91C2×C7×C4⋊C4—42no—
92C2×C7×C4⋊C4—42no—
93C2×C7×C4⋊C4—42no—
94C2×C7×C4⋊C4C2314yes—
95C2×C7×C4⋊C4C2314yes—
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—42no—
104C2×C22⋊Dic7—42no—
105C2×C22⋊Dic7—42no—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C22⋊Dic7C2314yes—
109C2×(C2×D7)⋊C4—42no—
110C2×(C2×D7)⋊C4—42no—
111C2×(C2×D7)⋊C4—42no—
112C2×(C2×D7)⋊C4—42no—
113C2×(C2×D7)⋊C4—42no—
114C2×(C2×D7)⋊C4—42no—
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
117C2×(C2×D7)⋊C4C2314yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×(C2×D7)⋊C4C2314yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×C4⋊Dic7—42no—
122C2×C4⋊Dic7C2314yes—
123C2×Dic7⋊C4—24no—
124C2×Dic7⋊C4—24no—
125C2×Dic7⋊C4—42no—
126C2×Dic7⋊C4—42no—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×C4×Dic7—42no—
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#2830—716no—
146C2×#398—71no—
147C2×#397—71no—
148C2×#397—71no—
149C2×#397—71no—
150C2×#397—71no—
151C2×#396—71no—
152C2×#396D711yescharacteristic, complemented
153C2×#395—71no—
154C2×#394—71no—
155C2×#394—71no—
156C2×#393—71no—
157C2×#393—71no—
158C2×#390—71no—
159C2×#387—71no—
160C2×#387—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—
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—22no—
226C22×Dic7#4114yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C2×Dic14—44no—
235C2×Dic14—44no—
236C2×Dic14—44no—
237C2×Dic14—416no—
238C7×C4⋊C4—44no—
239C7×C4⋊C4—44no—
240C7×C4⋊C4—44no—
241C7×C22⋊C4—44no—
242C7×C22⋊C4—44no—
243C7×C22⋊C4—44no—
244C22⋊Dic7—44no—
245C22⋊Dic7—44no—
246C22⋊Dic7—44no—
247(C2×D7)⋊C4—44no—
248(C2×D7)⋊C4—44no—
249(C2×D7)⋊C4—44no—
250(C2×D7)⋊C4—44no—
251(C2×D7)⋊C4—44no—
252(C2×D7)⋊C4—44no—
253C4⋊Dic7—44no—
254Dic7⋊C4—28no—
255Dic7⋊C4—28no—
256Dic7⋊C4—44no—
257Dic7⋊C4—44no—
258C4×Dic7—44no—
259C23×Q8—71no—
260C23×D4—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×C4⋊C4C2×D711yescharacteristic
268C22×C4⋊C4C2×D711yescharacteristic
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⋊C4—71no—
278C22×C22⋊C4C2×D711yescharacteristic
279C22×C22⋊C4C2×D711yescharacteristic
280C22×C22⋊C4C2×D711yescharacteristic
281C22×C42—71no—
282#398—78no—
283#397—78no—
284#397—78no—
285#397—78no—
286#397—78no—
287#396—78no—
288#396C2×D718yescomplemented
289#395—78no—
290#394—78no—
291#394—78no—
292#393—78no—
293#393—78no—
294#390—78no—
295#387—78no—
296#387—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×#95—71no—
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×C7H(5,𝔽2)12yes—
325C23×C7H(5,𝔽2)12yes—
326C23×C7H(5,𝔽2)12yes—
327C23×C7H(5,𝔽2)12yes—
328C23×C72−1+412yes—
329C23×C72−1+412yes—
330C23×C7C2511yescharacteristic
331C22×D7—22no—
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—44no—
339C22×D7—44no—
340C22×D7—44no—
341C22×D7—44no—
342C22×D7—44no—
343C22×D7—44no—
344C22×D7—44no—
345C2×C4×C7—22no—
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×C7—44no—
369C22⋊D7—416no—
370C2×Dic7—28no—
371C2×Dic7—22no—
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×Dic7—44no—
397C2×Dic7C2×#4114yes—
398Dic14—416no—
399C25—71no—
400C25C22×D711yescharacteristic
401C22×Q8—74no—
402C22×Q8—282no—
403C22×Q8—282no—
404C22×Q8—282no—
405C22×D4—74no—
406C22×D4—144no—
407C22×D4—282no—
408C22×D4—282no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4—71no—
414C23×C4—71no—
415C23×C4—71no—
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—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—74no—
426C2×C4⋊C4—74no—
427C2×C4⋊C4—74no—
428C2×C4⋊C4—74no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—144no—
431C2×C4⋊C4—144no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4—282no—
434C2×C4⋊C4—282no—
435C2×C4⋊C4C22×D714yes—
436C2×C4⋊C4C22×D714yes—
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—74no—
450C2×C22⋊C4—282no—
451C2×C22⋊C4—282no—
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—
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#53814yes—
485C22×C7#54214yes—
486C22×C7#54214yes—
487C22×C7#56014yes—
488C22×C7#56214yes—
489C22×C7#56214yes—
490C22×C7#56314yes—
491C22×C7C22×#4111yescharacteristic
492C22×C7C2×H(5,𝔽2)11yescharacteristic
493C22×C7C2×H(5,𝔽2)11yescharacteristic
494C22×C7C2×H(5,𝔽2)11yescharacteristic
495C22×C7C2×H(5,𝔽2)11yescharacteristic
496C22×C7C2×2−1+411yescharacteristic
497C22×C7C2×2−1+411yescharacteristic
498C2×D7—42no—
499C2×D7—42no—
500C2×D7—42no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—42no—
504C2×D7—42no—
505C2×D7—88no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7—42no—
511C4×C7—42no—
512Dic7—24no—
513Dic7—42no—
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—72no—
527C24—142no—
528C24—142no—
529C24—142no—
530C24—142no—
531C24—142no—
532C24—142no—
533C24—142no—
534C24C23×D712yes—
535C24C23×D711yescharacteristic
536C2×Q8—284no—
537C2×Q8—284no—
538C2×Q8—284no—
539C2×Q8—2816no—
540C2×D4—148no—
541C2×D4—284no—
542C2×D4—284no—
543C2×D4—2816no—
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—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—74no—
563C22×C4—72no—
564C22×C4—72no—
565C22×C4—72no—
566C22×C4—72no—
567C22×C4—72no—
568C22×C4—72no—
569C22×C4—72no—
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—142no—
588C22×C4—142no—
589C22×C4—142no—
590C22×C4C23×D712yes—
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C22×C4C23×D712yes—
594C22×C4C23×D712yes—
595C22×C4C23×D712yes—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—148no—
600C4⋊C4—148no—
601C4⋊C4—284no—
602C4⋊C4—284no—
603C4⋊C4—284no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—284no—
608C22⋊C4—284no—
609C22⋊C4—284no—
610C22⋊C4—284no—
611C22⋊C4—284no—
612C22⋊C4—284no—
613C22⋊C4—284no—
614C22⋊C4—284no—
615C22⋊C4—284no—
616C42—284no—
617C2×C7—82no—
618C2×C7#283018yescomplemented
619C2×C7C2×#53811yescharacteristic
620C2×C7C2×#54211yescharacteristic
621C2×C7C2×#54211yescharacteristic
622C2×C7C2×#56011yescharacteristic
623C2×C7C2×#56211yescharacteristic
624C2×C7C2×#56211yescharacteristic
625C2×C7C2×#56311yescharacteristic
626D7—82no—
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—142no—
642C23—142no—
643C23—142no—
644C23—142no—
645C23—142no—
646C23—142no—
647C23—142no—
648C23—284no—
649C23—284no—
650C23—284no—
651C23—284no—
652C23—284no—
653C23—284no—
654C23—284no—
655C23#654812yes—
656C23#654812yes—
657C23#654812yes—
658C23#655112yes—
659C23D7×#4112yes—
660C23#655312yes—
661C23#655412yes—
662C23C24×D711yescharacteristic
663Q8—2816no—
664D4—2816no—
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—22no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—74no—
690C2×C4—148no—
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—142no—
710C2×C4—142no—
711C2×C4—284no—
712C2×C4—284no—
713C2×C4—284no—
714C2×C4—284no—
715C2×C4—284no—
716C2×C4—284no—
717C7C2×#283011yescharacteristic, complemented, Sylow
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—88no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—282no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—568no—
734C22#9030414yes—
735C22#9031114yes—
736C22#9031214yes—
737C22#9033114yes—
738C22#9033714yes—
739C22#9033814yes—
740C22#9040114yes—
741C22C2×#654811yescharacteristic
742C22C2×#654811yescharacteristic
743C22C2×#654811yescharacteristic
744C22C2×#655111yescharacteristic
745C22C2×D7×#4111yescharacteristic
746C22C2×#655311yescharacteristic
747C22C2×#655411yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—144no—
755C4—282no—
756C4—282no—
757C4—282no—
758C4—282no—
759C4—282no—
760C4—282no—
761C2—82no—
762C2—562no—
763C2#1173484918yesdirect product factor
764C2C2×#9030411yescharacteristic
765C2C2×#9031111yescharacteristic
766C2C2×#9031211yescharacteristic
767C2C2×#9033111yescharacteristic
768C2C2×#9033711yescharacteristic
769C2C2×#9033811yescharacteristic
770C2C2×#9040111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#396D7
hypocenterC7C2×#2830
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C2×C7×#396C2semidirect
2. C2×#89765C2semidirect
3. C2×#89765C2semidirect
4. C2×#89766C2semidirect
5. C2×#89752C2semidirect
6. C2×#89751C2semidirect
7. C2×#89750C2semidirect
10. C2×#89725C2semidirect
11. C2×#89724C2semidirect
12. C2×#89719C2semidirect
14. #11734849C2direct (N × H)
15. C2×#89445C2semidirect
16. C2×#89427C2semidirect
40. C7×#396C22semidirect
53. #89766C22semidirect
54. #89765C22semidirect
55. #89765C22semidirect
56. #89752C22semidirect
57. #89751C22semidirect
58. #89750C22semidirect
62. #89725C22semidirect
63. #89724C22semidirect
64. #89719C22semidirect
65. #89445C22semidirect
66. #89427C22semidirect
152. C2×#396D7semidirect
288. #396C2×D7semidirect
618. C2×C7#2830semidirect
717. C7C2×#2830semidirect
763. C2#11734849direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×#897652
C2×#897662
C2×#897522
C2×#897512
C2×#897502
C2×#897312
C2×#897252
C2×#897242
C2×#897192
C2×#897292
#117348492
C2×#894452
C2×#894272
C2×#28307