Finite Group Databasebeta

← C2×#11734136 #13523902

Subgroups — C2×#11734136 #13523902

Order 1792.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6499C211yesmaximal, characteristic, complemented
2C22×#6498C211yesmaximal, characteristic, complemented
3C2×C7×#392C211yesmaximal, characteristic
4C2×#89993C211yesmaximal, characteristic, complemented
5C2×#89992C211yesmaximal, characteristic, complemented
6C2×#89992C211yesmaximal, characteristic, complemented
7C2×#89992C211yesmaximal, characteristic, complemented
8C2×#89725C211yesmaximal, characteristic, complemented
9C2×#89724C211yesmaximal, characteristic, complemented
10C2×#89719C211yesmaximal, characteristic, complemented
11C2×#89716C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
14#11734136C2116yesmaximal, direct product factor
15C2×#89418C211yesmaximal, characteristic, complemented
16C2×#89426C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C22⋊Dic7C2211yescharacteristic
36C2×#6499—28no—
37C2×#6499C2218yescomplemented
38C2×#6498—28no—
39C2×#6498C2218yescomplemented
40C22×C4⋊Dic7C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C7×#392C2218yes—
47C2×C7×#95C2211yescharacteristic
48#89993C2218yescomplemented
49#89992C2218yescomplemented
50#89992C2218yescomplemented
51#89992C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89725C2218yescomplemented
62#89724C2218yescomplemented
63#89719C2218yescomplemented
64#89716C2218yescomplemented
65C22⋊C4×Dic7C2218yescomplemented
66C22⋊C4×Dic7C2218yescomplemented
67#89426C2218yescomplemented
68#89418C2218yescomplemented
69C2×#2557—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C25×C7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—24no—
78C22×C7×D4—24no—
79C22×C7×D4—42no—
80C22×C7×D4—42no—
81C22×C7×D4—42no—
82C22×C7×D4C2314yes—
83C22×C7×D4C2314yes—
84C22×C7×D4C2314yes—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×Dic7—24no—
90C23×Dic7—24no—
91C23×Dic7—24no—
92C23×Dic7—42no—
93C23×Dic7—42no—
94C23×Dic7—42no—
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2314yes—
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2314yes—
105C22×Dic14—24no—
106C22×Dic14—24no—
107C22×Dic14—42no—
108C22×Dic14C2314yes—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4C2314yes—
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—42no—
123C2×C22⋊Dic7—42no—
124C2×C22⋊Dic7D418yescomplemented
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133C2×C22⋊Dic7C2314yes—
134C2×C22⋊Dic7C2314yes—
135#6499—232no—
136#6498—232no—
137C2×C4⋊Dic7—24no—
138C2×C4⋊Dic7C2314yes—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×C4×Dic7—24no—
144C2×C4×Dic7—42no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148C2×C4×Dic7C2314yes—
149C7×#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#124—71no—
160C22×#123—71no—
161#2557—716no—
162C2×#397—71no—
163C2×#397—71no—
164C2×#393—71no—
165C2×#392D711yescharacteristic
166C2×#391—71no—
167C2×#390—71no—
168C2×#388—71no—
169C2×#387—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×C4×C22⋊C4—71no—
174C2×C4×C22⋊C4—71no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7C2×D414yes—
195C24×C7#4114yes—
196C24×C7C2412yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C2×C7×D4—28no—
201C2×C7×D4—28no—
202C2×C7×D4—28no—
203C2×C7×D4—28no—
204C2×C7×D4—28no—
205C2×C7×D4—28no—
206C2×C7×D4—44no—
207C2×C7×D4—44no—
208C2×C7×D4—44no—
209C2×C7×D4—416no—
210C2×C7×D4—416no—
211C2×C7×D4—416no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7#4114yes—
223C22×C4×C7#4114yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—28no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—28no—
251C22×Dic7—28no—
252C22×Dic7—44no—
253C22×Dic7—44no—
254C22×Dic7—44no—
255C22×Dic7—416no—
256C22×Dic7—416no—
257C22×Dic7C2×D414yes—
258C22×Dic7C2×D414yes—
259C22×Dic7#4114yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C2×Dic14—28no—
269C2×Dic14—28no—
270C2×Dic14—44no—
271C2×Dic14—416no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—44no—
275C22⋊Dic7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—28no—
279C22⋊Dic7—28no—
280C22⋊Dic7—28no—
281C22⋊Dic7—28no—
282C22⋊Dic7—44no—
283C22⋊Dic7—44no—
284C22⋊Dic7C2×D4116yescomplemented
285C4⋊Dic7—28no—
286Dic7⋊C4—28no—
287Dic7⋊C4—28no—
288C4×Dic7—28no—
289C4×Dic7—44no—
290C4×Dic7—44no—
291C23×Q8—71no—
292C23×D4C2×D711yescharacteristic
293C23×D4C2×D711yescharacteristic
294C23×D4C2×D711yescharacteristic
295C24×C4—71no—
296C24×C4—71no—
297C2×#124—78no—
298C2×#124—148no—
299C2×#123—78no—
300C2×#123—148no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
320#397—78no—
321#397—78no—
322#393—78no—
323#392C2×D718yes—
324#391—78no—
325#390—78no—
326#388—78no—
327#387—78no—
328#386—78no—
329#386—78no—
330#386—78no—
331C4×C22⋊C4—78no—
332C4×C22⋊C4—78no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95C2×D711yescharacteristic
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—28no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—44no—
369C23×C7—44no—
370C23×C7—44no—
371C23×C7—44no—
372C23×C7—44no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7C22×D414yes—
384C23×C7C22×D412yes—
385C23×C7C2×#4114yes—
386C23×C7C2×#4112yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C7H(5,𝔽2)12yes—
392C23×C7C2511yescharacteristic
393C7×D4—416no—
394C7×D4—416no—
395C7×D4—416no—
396C2×C4×C7—28no—
397C2×C4×C7—28no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—44no—
409C2×C4×C7—44no—
410C2×C4×C7C2×#4114yes—
411C2×C4×C7C2×#4114yes—
412C2×Dic7—28no—
413C2×Dic7—28no—
414C2×Dic7—28no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—416no—
437C2×Dic7—416no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7C22×D414yes—
444C2×Dic7C22×D414yes—
445C2×Dic7C2×#4114yes—
446Dic14—416no—
447C25C22×D711yescharacteristic
448C25C22×D711yescharacteristic
449C25C22×D711yescharacteristic
450C22×Q8—74no—
451C22×Q8—144no—
452C22×Q8—144no—
453C22×Q8—282no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—24no—
457C22×D4—24no—
458C22×D4—24no—
459C22×D4—24no—
460C22×D4—42no—
461C22×D4—42no—
462C22×D4—42no—
463C22×D4C22×D714yes—
464C22×D4C22×D714yes—
465C22×D4C22×D714yes—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—74no—
475C23×C4—74no—
476C23×C4—144no—
477C23×C4—144no—
478C23×C4—144no—
479C23×C4—282no—
480C23×C4—282no—
481C23×C4—282no—
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#124—1432no—
487#123—1432no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—144no—
493C2×C4⋊C4—144no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—78no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—282no—
525C2×C42—282no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95—74no—
534#95—74no—
535#95C22×D714yes—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—24no—
541C22×C7—24no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—416no—
551C22×C7—416no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—88no—
560C22×C7#52914yes—
561C22×C7#53214yes—
562C22×C7#53814yes—
563C22×C7#54614yes—
564C22×C7#54614yes—
565C22×C7#55114yes—
566C22×C7#55914yes—
567C22×C7C23×D411yescharacteristic
568C22×C7C22×#4111yescharacteristic
569C22×C7C22×#4111yescharacteristic
570C22×C7C22×#4111yescharacteristic
571C22×C7C22×#4111yescharacteristic
572C22×C7C2×H(5,𝔽2)11yescharacteristic
573C22×C7C2×H(5,𝔽2)11yescharacteristic
574C4×C7—24no—
575C4×C7—24no—
576C4×C7—42no—
577C4×C7—42no—
578Dic7—24no—
579Dic7—24no—
580Dic7—24no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584Dic7—42no—
585Dic7—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24D4×D714yes—
606C24#115914yes—
607C24C23×D712yes—
608C24C23×D712yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×Q8—148no—
612C2×Q8—148no—
613C2×Q8—284no—
614C2×Q8—2816no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—28no—
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—28no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—416no—
625C2×D4—416no—
626C2×D4—416no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—74no—
638C22×C4—74no—
639C22×C4—74no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—148no—
649C22×C4—148no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—148no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—142no—
669C22×C4—142no—
670C22×C4—142no—
671C22×C4—142no—
672C22×C4—284no—
673C22×C4—284no—
674C22×C4—284no—
675C22×C4—2816no—
676C22×C4—2816no—
677C22×C4#115914yes—
678C22×C4#115914yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—148no—
684C4⋊C4—148no—
685C4⋊C4—148no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—44no—
689C22⋊C4—716no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—148no—
696C22⋊C4—148no—
697C22⋊C4—284no—
698C22⋊C4—284no—
699C42—148no—
700C42—284no—
701C42—284no—
702C2×C7—44no—
703C2×C7—44no—
704C2×C7—82no—
705C2×C7#255718yescomplemented
706C2×C7C2×#52911yescharacteristic
707C2×C7C2×#53211yescharacteristic
708C2×C7C2×#53811yescharacteristic
709C2×C7C2×#54611yescharacteristic
710C2×C7C2×#54611yescharacteristic
711C2×C7C2×#55111yescharacteristic
712C2×C7C2×#55911yescharacteristic
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23C2×D4×D714yes—
754C23C2×D4×D712yes—
755C23C2×#115914yes—
756C23C2×#115912yes—
757C23C2×#115912yes—
758C23C2×#115912yes—
759C23#654812yes—
760C23#654812yes—
761C23D7×#4112yes—
762C23C24×D711yescharacteristic
763Q8—2816no—
764D4—416no—
765D4—416no—
766D4—416no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—74no—
782C2×C4—74no—
783C2×C4—74no—
784C2×C4—148no—
785C2×C4—148no—
786C2×C4—148no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—142no—
808C2×C4—2816no—
809C2×C4—2816no—
810C2×C4—284no—
811C2×C4—284no—
812C2×C4—284no—
813C2×C4—284no—
814C2×C4—284no—
815C2×C4C2×#115914yes—
816C2×C4C2×#115914yes—
817C7C2×#255711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—416no—
833C22—416no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—88no—
842C22#9027814yes—
843C22#9028214yes—
844C22#9028214yes—
845C22#9028714yes—
846C22#9029114yes—
847C22#9030414yes—
848C22#9040414yes—
849C22C22×D4×D711yescharacteristic
850C22C22×#115911yescharacteristic
851C22C22×#115911yescharacteristic
852C22C22×#115911yescharacteristic
853C22C2×#654811yescharacteristic
854C22C2×#654811yescharacteristic
855C22C2×D7×#4111yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—144no—
861C4—144no—
862C4—144no—
863C4—282no—
864C4—282no—
865C4—282no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—44no—
870C2—82no—
871C2#1173413618yesdirect product factor
872C2C2×#9027811yescharacteristic
873C2C2×#9028211yescharacteristic
874C2C2×#9028211yescharacteristic
875C2C2×#9029111yescharacteristic
876C2C2×#9028711yescharacteristic
877C2C2×#9030411yescharacteristic
878C2C2×#9040411yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC2×C7×#392C2
socleC24×C7C24
hypercenterC2×#392D7
hypocenterC7C2×#2557
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#6499C2semidirect
2. C22×#6498C2semidirect
4. C2×#89993C2semidirect
5. C2×#89992C2semidirect
6. C2×#89992C2semidirect
7. C2×#89992C2semidirect
8. C2×#89725C2semidirect
9. C2×#89724C2semidirect
10. C2×#89719C2semidirect
11. C2×#89716C2semidirect
12. C2×C22⋊C4×Dic7C2semidirect
13. C2×C22⋊C4×Dic7C2semidirect
14. #11734136C2direct (N × H)
15. C2×#89418C2semidirect
16. C2×#89426C2semidirect
37. C2×#6499C22semidirect
39. C2×#6498C22semidirect
48. #89993C22semidirect
49. #89992C22semidirect
50. #89992C22semidirect
51. #89992C22semidirect
61. #89725C22semidirect
62. #89724C22semidirect
63. #89719C22semidirect
64. #89716C22semidirect
65. C22⋊C4×Dic7C22semidirect
66. C22⋊C4×Dic7C22semidirect
67. #89426C22semidirect
68. #89418C22semidirect
124. C2×C22⋊Dic7D4semidirect
284. C22⋊Dic7C2×D4semidirect
705. C2×C7#2557semidirect
817. C7C2×#2557semidirect
871. C2#11734136direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64992
C22×#64982
C2×C7×#3922
C2×#899932
C2×#899922
C2×#897252
C2×#897242
C2×#897192
C2×#897162
C2×C22⋊C4×Dic72
#117341362
C2×#894182
C2×#894262
C2×#25577