Finite Group Databasebeta

← C2×#11734536 #13559986

Subgroups — C2×#11734536 #13559986

Order 1792.

2218 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×#394C211yesmaximal, characteristic
2C2×#89994C211yesmaximal, characteristic
3C2×#89992C211yesmaximal, characteristic
4C2×#89754C211yesmaximal, characteristic, complemented
5C2×#89756C211yesmaximal, characteristic, complemented
6C2×#89721C211yesmaximal, characteristic, complemented
7C2×#89725C211yesmaximal, characteristic, complemented
8C2×#89724C211yesmaximal, characteristic, complemented
9C2×#89724C211yesmaximal, characteristic, complemented
10C2×#89720C211yesmaximal, characteristic, complemented
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89722C211yesmaximal, characteristic, complemented
13C2×#89718C211yesmaximal, characteristic, complemented
14#11734536C2116yesmaximal, direct product factor
15C2×#89431C211yesmaximal, characteristic, complemented
16C2×#89429C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C7×#394C2218yes—
41C2×C7×#95C2211yescharacteristic
42#89994C2218yes—
43#89992C2218yes—
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#89756C2218yescomplemented
56#89754C2218yescomplemented
57#89725C2218yescomplemented
58#89724C2218yescomplemented
59#89724C2218yescomplemented
60#89722C2218yescomplemented
61#89721C2218yescomplemented
62#89720C2218yescomplemented
63#89720C2218yescomplemented
64#89718C2218yescomplemented
65#89431C2218yescomplemented
66#89429C2218yescomplemented
67C2×#2827—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C22×C7×D4—24no—
71C22×C7×D4—42no—
72C22×C7×D4—42no—
73C22×C7×D4C2314yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×Dic7—42no—
80C23×Dic7—42no—
81C23×Dic7—42no—
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2314yes—
91C2×C7×C4⋊C4—42no—
92C2×C7×C4⋊C4C2314yes—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4—42no—
97C2×C7×C22⋊C4C2314yes—
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⋊Dic7—42no—
105C2×C22⋊Dic7—42no—
106C2×C22⋊Dic7—42no—
107C2×C22⋊Dic7—42no—
108C2×C22⋊Dic7C2314yes—
109C2×C22⋊Dic7C2314yes—
110C2×C22⋊Dic7C2314yes—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×C4⋊Dic7—42no—
116C2×C4⋊Dic7—42no—
117C2×C4⋊Dic7—42no—
118C2×C4⋊Dic7C2314yes—
119C2×C4⋊Dic7C2314yes—
120C2×C4⋊Dic7C2314yes—
121C2×Dic7⋊C4—42no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4—42no—
125C2×Dic7⋊C4—42no—
126C2×Dic7⋊C4—42no—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
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#2827—716no—
146C2×#400—71no—
147C2×#400—71no—
148C2×#399—71no—
149C2×#398—71no—
150C2×#398—71no—
151C2×#397—71no—
152C2×#397—71no—
153C2×#397—71no—
154C2×#396—71no—
155C2×#396—71no—
156C2×#394—71no—
157C2×#394D711yescharacteristic
158C2×#386—71no—
159C2×#385—71no—
160C2×#385—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7#4114yes—
175C24×C7C2412yes—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C2×C7×D4—28no—
179C2×C7×D4—44no—
180C2×C7×D4—44no—
181C2×C7×D4—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×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
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—44no—
227C22×Dic7—44no—
228C22×Dic7—44no—
229C22×Dic7—416no—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C7×C4⋊C4—44no—
239C7×C22⋊C4—28no—
240C7×C22⋊C4—44no—
241C7×C22⋊C4—44no—
242C7×C22⋊C4—44no—
243C22⋊Dic7—28no—
244C22⋊Dic7—44no—
245C22⋊Dic7—44no—
246C22⋊Dic7—44no—
247C22⋊Dic7—44no—
248C22⋊Dic7—44no—
249C22⋊Dic7—44no—
250C4⋊Dic7—44no—
251C4⋊Dic7—44no—
252C4⋊Dic7—44no—
253Dic7⋊C4—44no—
254Dic7⋊C4—44no—
255Dic7⋊C4—44no—
256Dic7⋊C4—44no—
257Dic7⋊C4—44no—
258Dic7⋊C4—44no—
259C23×D4C2×D711yescharacteristic
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⋊C4—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4C2×D711yescharacteristic
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×C22⋊C4C2×D711yescharacteristic
282#400—78no—
283#400—78no—
284#399—78no—
285#398—78no—
286#398—78no—
287#397—78no—
288#397—78no—
289#397—78no—
290#396—78no—
291#396—78no—
292#394—78no—
293#394C2×D718yes—
294#386—78no—
295#385—78no—
296#385—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—28no—
310C23×C7—28no—
311C23×C7—28no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—44no—
326C23×C7—44no—
327C23×C7—44no—
328C23×C7—44no—
329C23×C7—44no—
330C23×C7—44no—
331C23×C7—44no—
332C23×C7—44no—
333C23×C7—44no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7C2×#4114yes—
337C23×C7C2×#4112yes—
338C23×C7H(5,𝔽2)12yes—
339C23×C7H(5,𝔽2)12yes—
340C23×C7H(5,𝔽2)12yes—
341C23×C7H(5,𝔽2)12yes—
342C23×C72−1+412yes—
343C23×C72−1+412yes—
344C23×C7C2511yescharacteristic
345C7×D4—416no—
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—44no—
362C2×C4×C7—44no—
363C2×C4×C7—44no—
364C2×C4×C7—44no—
365C2×C4×C7—44no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
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—416no—
391C2×Dic7—44no—
392C2×Dic7—44no—
393C2×Dic7—44no—
394C2×Dic7—44no—
395C2×Dic7—44no—
396C2×Dic7—44no—
397C2×Dic7—44no—
398C2×Dic7—44no—
399C25C22×D711yescharacteristic
400C25C22×D711yescharacteristic
401C22×D4—24no—
402C22×D4—42no—
403C22×D4—42no—
404C22×D4C22×D714yes—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4—74no—
414C23×C4—282no—
415C23×C4—282no—
416C23×C4—282no—
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—74no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—74no—
431C2×C4⋊C4—74no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4—282no—
434C2×C4⋊C4—282no—
435C2×C4⋊C4—282no—
436C2×C4⋊C4—282no—
437C2×C4⋊C4—282no—
438C2×C4⋊C4—282no—
439C2×C4⋊C4—282no—
440C2×C4⋊C4—282no—
441C2×C4⋊C4C22×D714yes—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4—74no—
447C2×C22⋊C4—74no—
448C2×C22⋊C4—74no—
449C2×C22⋊C4—74no—
450C2×C22⋊C4—74no—
451C2×C22⋊C4—74no—
452C2×C22⋊C4—74no—
453C2×C22⋊C4—144no—
454C2×C22⋊C4—282no—
455C2×C22⋊C4—282no—
456C2×C22⋊C4—282no—
457C2×C22⋊C4—282no—
458C2×C22⋊C4—282no—
459C2×C22⋊C4—282no—
460C2×C22⋊C4C22×D714yes—
461C2×C22⋊C4C22×D714yes—
462C2×C22⋊C4C22×D714yes—
463C2×C22⋊C4C22×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#95—74no—
475#95C22×D714yes—
476C22×C7—24no—
477C22×C7—24no—
478C22×C7—24no—
479C22×C7—416no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—42no—
487C22×C7—42no—
488C22×C7—42no—
489C22×C7—42no—
490C22×C7—42no—
491C22×C7—88no—
492C22×C7#53814yes—
493C22×C7#53914yes—
494C22×C7#53914yes—
495C22×C7#56014yes—
496C22×C7#56214yes—
497C22×C7#56214yes—
498C22×C7#56314yes—
499C22×C7C22×#4111yescharacteristic
500C22×C7C2×H(5,𝔽2)11yescharacteristic
501C22×C7C2×H(5,𝔽2)11yescharacteristic
502C22×C7C2×H(5,𝔽2)11yescharacteristic
503C22×C7C2×H(5,𝔽2)11yescharacteristic
504C22×C7C2×2−1+411yescharacteristic
505C22×C7C2×2−1+411yescharacteristic
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—42no—
509C4×C7—42no—
510C4×C7—42no—
511Dic7—42no—
512Dic7—42no—
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—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24#115914yes—
533C24C23×D712yes—
534C24C23×D712yes—
535C24C23×D711yescharacteristic
536C2×D4—28no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—416no—
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—72no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
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—142no—
586C22×C4—142no—
587C22×C4—284no—
588C22×C4—284no—
589C22×C4—284no—
590C22×C4—2816no—
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C22×C4C23×D712yes—
594C22×C4C23×D712yes—
595C22×C4C23×D712yes—
596C4⋊C4—44no—
597C4⋊C4—284no—
598C4⋊C4—284no—
599C4⋊C4—284no—
600C4⋊C4—284no—
601C4⋊C4—284no—
602C4⋊C4—284no—
603C4⋊C4—284no—
604C4⋊C4—284no—
605C4⋊C4—284no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—148no—
611C22⋊C4—284no—
612C22⋊C4—284no—
613C22⋊C4—284no—
614C22⋊C4—284no—
615C22⋊C4—284no—
616C22⋊C4—284no—
617C2×C7—44no—
618C2×C7—82no—
619C2×C7#282718yescomplemented
620C2×C7C2×#53811yescharacteristic
621C2×C7C2×#53911yescharacteristic
622C2×C7C2×#53911yescharacteristic
623C2×C7C2×#56011yescharacteristic
624C2×C7C2×#56211yescharacteristic
625C2×C7C2×#56211yescharacteristic
626C2×C7C2×#56311yescharacteristic
627C23—28no—
628C23—28no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—28no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23C2×#115914yes—
655C23C2×#115912yes—
656C23#654812yes—
657C23#654812yes—
658C23#654812yes—
659C23#655312yes—
660C23#655412yes—
661C23#655412yes—
662C23C24×D711yescharacteristic
663D4—416no—
664C2×C4—22no—
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—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
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—2816no—
709C2×C4—284no—
710C2×C4—284no—
711C2×C4—284no—
712C2×C4—284no—
713C2×C4—284no—
714C2×C4—284no—
715C2×C4—284no—
716C2×C4—284no—
717C7C2×#282711yescharacteristic, complemented, Sylow
718C22—24no—
719C22—24no—
720C22—24no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22#9028414yes—
735C22#9029314yes—
736C22#9031114yes—
737C22#9031214yes—
738C22#9034214yes—
739C22#9035614yes—
740C22#9037514yes—
741C22C22×#115911yescharacteristic
742C22C2×#654811yescharacteristic
743C22C2×#654811yescharacteristic
744C22C2×#654811yescharacteristic
745C22C2×#655311yescharacteristic
746C22C2×#655411yescharacteristic
747C22C2×#655411yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—282no—
754C4—282no—
755C4—282no—
756C4—282no—
757C4—282no—
758C4—282no—
759C4—282no—
760C4—282no—
761C2—44no—
762C2—82no—
763C2#1173453618yesdirect product factor
764C2C2×#9028411yescharacteristic
765C2C2×#9029311yescharacteristic
766C2C2×#9031111yescharacteristic
767C2C2×#9031211yescharacteristic
768C2C2×#9035611yescharacteristic
769C2C2×#9034211yescharacteristic
770C2C2×#9037511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#394D7
hypocenterC7C2×#2827
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
4. C2×#89754C2semidirect
5. C2×#89756C2semidirect
6. C2×#89721C2semidirect
7. C2×#89725C2semidirect
8. C2×#89724C2semidirect
9. C2×#89724C2semidirect
10. C2×#89720C2semidirect
11. C2×#89720C2semidirect
12. C2×#89722C2semidirect
13. C2×#89718C2semidirect
14. #11734536C2direct (N × H)
15. C2×#89431C2semidirect
16. C2×#89429C2semidirect
55. #89756C22semidirect
56. #89754C22semidirect
57. #89725C22semidirect
58. #89724C22semidirect
59. #89724C22semidirect
60. #89722C22semidirect
61. #89721C22semidirect
62. #89720C22semidirect
63. #89720C22semidirect
64. #89718C22semidirect
65. #89431C22semidirect
66. #89429C22semidirect
619. C2×C7#2827semidirect
717. C7C2×#2827semidirect
763. C2#11734536direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3942
C2×#899942
C2×#899922
C2×#897542
C2×#897562
C2×#897212
C2×#897252
C2×#897242
C2×#897202
C2×#897222
C2×#897182
#117345362
C2×#894312
C2×#894292
C2×#28277