Finite Group Databasebeta

← C2×#11734546 #13560128

Subgroups — C2×#11734546 #13560128

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×#394C211yesmaximal, characteristic
2C2×#89994C211yesmaximal, characteristic
3C2×#89994C211yesmaximal, characteristic
4C2×#89754C211yesmaximal, characteristic, complemented
5C2×#89751C211yesmaximal, characteristic, complemented
6C2×#89724C211yesmaximal, characteristic, complemented
7C2×#89724C211yesmaximal, characteristic, complemented
8C2×#89719C211yesmaximal, characteristic, complemented
9C2×#89719C211yesmaximal, characteristic, complemented
10C2×#89719C211yesmaximal, characteristic, complemented
11C2×#89719C211yesmaximal, characteristic, complemented
12C2×#89717C211yesmaximal, characteristic, complemented
13C2×#89716C211yesmaximal, characteristic, complemented
14#11734546C2116yesmaximal, direct product factor
15C2×#89430C211yesmaximal, characteristic, complemented
16C2×#89418C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C7×#394C2218yes—
39C2×C7×#95C2211yescharacteristic
40#89994C2218yes—
41#89994C2218yes—
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
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89754C2218yescomplemented
56#89751C2218yescomplemented
57#89724C2218yescomplemented
58#89724C2218yescomplemented
59#89719C2218yescomplemented
60#89719C2218yescomplemented
61#89719C2218yescomplemented
62#89719C2218yescomplemented
63#89717C2218yescomplemented
64#89716C2218yescomplemented
65#89430C2218yescomplemented
66#89418C2218yescomplemented
67C2×#2832—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C22×C7×D4—42no—
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×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C22×Dic14—24no—
88C22×Dic14—42no—
89C22×Dic14—42no—
90C22×Dic14—42no—
91C22×Dic14—42no—
92C22×Dic14—42no—
93C22×Dic14C2314yes—
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⋊C4—42no—
101C2×C7×C22⋊C4C2314yes—
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C22⋊Dic7—24no—
106C2×C22⋊Dic7—24no—
107C2×C22⋊Dic7—42no—
108C2×C22⋊Dic7—42no—
109C2×C22⋊Dic7—42no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7—42no—
112C2×C22⋊Dic7—42no—
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊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×#394D711yescharacteristic
154C2×#393—71no—
155C2×#393—71no—
156C2×#393—71no—
157C2×#393—71no—
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×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7C2412yes—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C2×C7×D4—44no—
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#4114yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C2×Dic14—28no—
235C2×Dic14—44no—
236C2×Dic14—44no—
237C2×Dic14—44no—
238C2×Dic14—44no—
239C2×Dic14—44no—
240C2×Dic14—416no—
241C2×Dic14—416no—
242C7×C4⋊C4—44no—
243C7×C22⋊C4—44no—
244C7×C22⋊C4—44no—
245C7×C22⋊C4—44no—
246C7×C22⋊C4—44no—
247C22⋊Dic7—28no—
248C22⋊Dic7—28no—
249C22⋊Dic7—44no—
250C22⋊Dic7—44no—
251C22⋊Dic7—44no—
252C22⋊Dic7—44no—
253C22⋊Dic7—44no—
254C22⋊Dic7—44no—
255Dic7⋊C4—44no—
256Dic7⋊C4—44no—
257Dic7⋊C4—44no—
258Dic7⋊C4—44no—
259C4×Dic7—44no—
260C23×Q8—71no—
261C23×Q8—71no—
262C23×D4C2×D711yescharacteristic
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×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#394C2×D718yes—
289#393—78no—
290#393—78no—
291#393—78no—
292#393—78no—
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×#95—71no—
308C2×#95—71no—
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—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—44no—
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×C7—44no—
337C23×C7—44no—
338C23×C7C2×#4112yes—
339C23×C7H(5,𝔽2)12yes—
340C23×C7H(5,𝔽2)12yes—
341C23×C7H(5,𝔽2)12yes—
342C23×C7H(5,𝔽2)12yes—
343C23×C72−1+412yes—
344C23×C72−1+412yes—
345C23×C7C2511yescharacteristic
346C7×D4—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—44no—
363C2×C4×C7—44no—
364C2×C4×C7—44no—
365C2×C4×C7—44no—
366C2×C4×C7—44no—
367C2×Dic7—28no—
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—22no—
391C2×Dic7—44no—
392C2×Dic7—44no—
393C2×Dic7—44no—
394C2×Dic7—44no—
395C2×Dic7—44no—
396C2×Dic7—44no—
397C2×Dic7—44no—
398C2×Dic7C2×#4114yes—
399Dic14—416no—
400Dic14—416no—
401C25C22×D711yescharacteristic
402C25C22×D711yescharacteristic
403C22×Q8—74no—
404C22×Q8—74no—
405C22×Q8—144no—
406C22×Q8—282no—
407C22×Q8—282no—
408C22×Q8—282no—
409C22×Q8—282no—
410C22×Q8—282no—
411C22×D4—42no—
412C22×D4—42no—
413C22×D4—42no—
414C22×D4C22×D714yes—
415C23×C4—71no—
416C23×C4—71no—
417C23×C4—71no—
418C23×C4—71no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
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—282no—
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—42no—
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⋊C4C22×D714yes—
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#95—74no—
476#95—74no—
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—42no—
486C22×C7—42no—
487C22×C7—42no—
488C22×C7—42no—
489C22×C7—42no—
490C22×C7—42no—
491C22×C7—42no—
492C22×C7—88no—
493C22×C7—88no—
494C22×C7#53814yes—
495C22×C7#54214yes—
496C22×C7#54214yes—
497C22×C7H(3,𝔽4)14yes—
498C22×C7#56214yes—
499C22×C7#56214yes—
500C22×C7#56314yes—
501C22×C7C22×#4111yescharacteristic
502C22×C7C2×H(5,𝔽2)11yescharacteristic
503C22×C7C2×H(5,𝔽2)11yescharacteristic
504C22×C7C2×H(5,𝔽2)11yescharacteristic
505C22×C7C2×H(5,𝔽2)11yescharacteristic
506C22×C7C2×2−1+411yescharacteristic
507C22×C7C2×2−1+411yescharacteristic
508C4×C7—42no—
509C4×C7—42no—
510C4×C7—42no—
511C4×C7—42no—
512C4×C7—42no—
513Dic7—24no—
514Dic7—42no—
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—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24C23×D712yes—
536C24C23×D712yes—
537C24C23×D711yescharacteristic
538C2×Q8—148no—
539C2×Q8—284no—
540C2×Q8—284no—
541C2×Q8—284no—
542C2×Q8—284no—
543C2×Q8—284no—
544C2×Q8—2816no—
545C2×Q8—2816no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—416no—
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—74no—
566C22×C4—72no—
567C22×C4—72no—
568C22×C4—72no—
569C22×C4—72no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—72no—
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—142no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4C23×D712yes—
598C22×C4C23×D712yes—
599C22×C4C23×D712yes—
600C22×C4C23×D712yes—
601C22×C4C23×D712yes—
602C4⋊C4—44no—
603C4⋊C4—284no—
604C4⋊C4—284no—
605C4⋊C4—284no—
606C4⋊C4—284no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—148no—
612C22⋊C4—148no—
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—82no—
622C2×C7#283218yescomplemented
623C2×C7C2×#53811yescharacteristic
624C2×C7C2×#54211yescharacteristic
625C2×C7C2×#54211yescharacteristic
626C2×C7C2×H(3,𝔽4)11yescharacteristic
627C2×C7C2×#56211yescharacteristic
628C2×C7C2×#56211yescharacteristic
629C2×C7C2×#56311yescharacteristic
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23#654812yes—
659C23#654812yes—
660C23#654812yes—
661C23#654812yes—
662C23D7×#4112yes—
663C23#655412yes—
664C23#655412yes—
665C23C24×D711yescharacteristic
666Q8—2816no—
667Q8—2816no—
668D4—416no—
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—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—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—284no—
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—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—88no—
737C22—88no—
738C22#9028514yes—
739C22#9030414yes—
740C22#9031214yes—
741C22#9031214yes—
742C22#9034214yes—
743C22#9035314yes—
744C22#9036014yes—
745C22C2×#654811yescharacteristic
746C22C2×#654811yescharacteristic
747C22C2×#654811yescharacteristic
748C22C2×#654811yescharacteristic
749C22C2×D7×#4111yescharacteristic
750C22C2×#655411yescharacteristic
751C22C2×#655411yescharacteristic
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—144no—
758C4—282no—
759C4—282no—
760C4—282no—
761C4—282no—
762C4—282no—
763C4—282no—
764C4—282no—
765C2—82no—
766C2—82no—
767C2#1173454618yesdirect product factor
768C2C2×#9028511yescharacteristic
769C2C2×#9030411yescharacteristic
770C2C2×#9031211yescharacteristic
771C2C2×#9031211yescharacteristic
772C2C2×#9035311yescharacteristic
773C2C2×#9034211yescharacteristic
774C2C2×#9036011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#394D7
hypocenterC7C2×#2832
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×#89751C2semidirect
6. C2×#89724C2semidirect
7. C2×#89724C2semidirect
8. C2×#89719C2semidirect
9. C2×#89719C2semidirect
10. C2×#89719C2semidirect
11. C2×#89719C2semidirect
12. C2×#89717C2semidirect
13. C2×#89716C2semidirect
14. #11734546C2direct (N × H)
15. C2×#89430C2semidirect
16. C2×#89418C2semidirect
55. #89754C22semidirect
56. #89751C22semidirect
57. #89724C22semidirect
58. #89724C22semidirect
59. #89719C22semidirect
60. #89719C22semidirect
61. #89719C22semidirect
62. #89719C22semidirect
63. #89717C22semidirect
64. #89716C22semidirect
65. #89430C22semidirect
66. #89418C22semidirect
622. C2×C7#2832semidirect
721. C7C2×#2832semidirect
767. C2#11734546direct (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×#897542
C2×#897512
C2×#897242
C2×#897192
C2×#897172
C2×#897162
#117345462
C2×#894302
C2×#894182
C2×#28327