Finite Group Databasebeta

← C2×#11734123 #13521908

Subgroups — C2×#11734123 #13521908

Order 1792.

3438 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×#6498C211yesmaximal, characteristic, complemented
2C22×D4×Dic7C211yesmaximal, characteristic, complemented
3C2×C7×#392C211yesmaximal, characteristic
4C2×#89994C211yesmaximal, characteristic, complemented
5C2×#89992C211yesmaximal, characteristic, complemented
6C2×#89992C211yesmaximal, characteristic, complemented
7C2×#89992C211yesmaximal, characteristic, complemented
8C2×#89720C211yesmaximal, characteristic, complemented
9C2×#89717C211yesmaximal, characteristic, complemented
10C2×#89716C211yesmaximal, characteristic, complemented
11C2×#89715C211yesmaximal, characteristic, complemented
12C2×#89714C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
14#11734123C2116yesmaximal, direct product factor
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89424C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C24×Dic7C2211yescharacteristic
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
35C2×#6498—28no—
36C2×#6498C2218yescomplemented
37C2×D4×Dic7—28no—
38C2×D4×Dic7C2218yescomplemented
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C7×#392C2218yes—
47C2×C7×#95C2211yescharacteristic
48#89994C2218yescomplemented
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#89720C2218yescomplemented
62#89717C2218yescomplemented
63#89716C2218yescomplemented
64#89715C2218yescomplemented
65#89714C2218yescomplemented
66C22⋊C4×Dic7C2218yescomplemented
67#89432C2218yescomplemented
68#89424C2218yescomplemented
69C2×#2457—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—24no—
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—24no—
93C23×Dic7—24no—
94C23×Dic7—24no—
95C23×Dic7—42no—
96C23×Dic7—42no—
97C23×Dic7—42no—
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2314yes—
104C23×Dic7C2314yes—
105C23×Dic7C2314yes—
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2311yescharacteristic
108C23×Dic7C2311yescharacteristic
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—42no—
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—42no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7—42no—
123C2×C22⋊Dic7D418yescomplemented
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133#6498—232no—
134D4×Dic7—232no—
135C2×C4⋊Dic7—24no—
136C2×C4⋊Dic7C2314yes—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—42no—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×C4×Dic7—24no—
146C2×C4×Dic7—42no—
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×#123—71no—
160C22×C4×D4—71no—
161#2457—716no—
162C2×#400—71no—
163C2×#396—71no—
164C2×#394—71no—
165C2×#392D711yescharacteristic
166C2×#388—71no—
167C2×#388—71no—
168C2×#387—71no—
169C2×#386—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#381—71no—
173C2×#380—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×C7C2×D414yes—
194C24×C7#4114yes—
195C24×C7#4114yes—
196C24×C7C2412yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C2×C7×D4—232no—
201C2×C7×D4—28no—
202C2×C7×D4—28no—
203C2×C7×D4—28no—
204C2×C7×D4—28no—
205C2×C7×D4—28no—
206C2×C7×D4—28no—
207C2×C7×D4—28no—
208C2×C7×D4—44no—
209C2×C7×D4—44no—
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—22no—
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—28no—
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—22no—
251C22×Dic7—28no—
252C22×Dic7—28no—
253C22×Dic7—28no—
254C22×Dic7—28no—
255C22×Dic7—44no—
256C22×Dic7—44no—
257C22×Dic7—44no—
258C22×Dic7—416no—
259C22×Dic7—416no—
260C22×Dic7—416no—
261C22×Dic7C2×D414yes—
262C22×Dic7C2×D414yes—
263C22×Dic7#4114yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—44no—
274C7×C22⋊C4—44no—
275C22⋊Dic7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—28no—
279C22⋊Dic7—28no—
280C22⋊Dic7—44no—
281C22⋊Dic7—44no—
282C22⋊Dic7—44no—
283C22⋊Dic7C2×D4116yescomplemented
284C4⋊Dic7—28no—
285Dic7⋊C4—28no—
286Dic7⋊C4—28no—
287Dic7⋊C4—28no—
288Dic7⋊C4—44no—
289C4×Dic7—28no—
290C4×Dic7—44no—
291C23×D4C2×D711yescharacteristic
292C23×D4C2×D711yescharacteristic
293C23×D4C2×D711yescharacteristic
294C24×C4—71no—
295C24×C4—71no—
296C24×C4—71no—
297C2×#123—78no—
298C2×#123—148no—
299C2×C4×D4—78no—
300C2×C4×D4—148no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊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⋊C4—71no—
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320#400—78no—
321#396—78no—
322#394—78no—
323#392C2×D718yes—
324#388—78no—
325#388—78no—
326#387—78no—
327#386—78no—
328#386—78no—
329#386—78no—
330#381—78no—
331#380—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—28no—
350C23×C7—28no—
351C23×C7—28no—
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—22no—
369C23×C7—22no—
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×C7C22×D414yes—
383C23×C7C22×D412yes—
384C23×C7C2×#4114yes—
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—232no—
394C7×D4—416no—
395C7×D4—416no—
396C2×C4×C7—28no—
397C2×C4×C7—22no—
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×C7—44no—
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—416no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7—44no—
444C2×Dic7C22×D414yes—
445C2×Dic7C22×D414yes—
446C2×Dic7C2×#4114yes—
447C25C22×D711yescharacteristic
448C25C22×D711yescharacteristic
449C25C22×D711yescharacteristic
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—24no—
457C22×D4—42no—
458C22×D4—42no—
459C22×D4C22×D714yes—
460C22×D4C22×D714yes—
461C22×D4C22×D714yes—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—74no—
471C23×C4—74no—
472C23×C4—74no—
473C23×C4—144no—
474C23×C4—144no—
475C23×C4—144no—
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#123—1432no—
487C4×D4—1432no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—74no—
492C2×C4⋊C4—74no—
493C2×C4⋊C4—144no—
494C2×C4⋊C4—144no—
495C2×C4⋊C4—144no—
496C2×C4⋊C4—144no—
497C2×C4⋊C4—282no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—78no—
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—74no—
509C2×C22⋊C4—74no—
510C2×C22⋊C4—74no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—144no—
515C2×C22⋊C4—144no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4—282no—
518C2×C22⋊C4—282no—
519C2×C22⋊C4C22×D714yes—
520C2×C22⋊C4C22×D714yes—
521C2×C22⋊C4C22×D714yes—
522C2×C42—74no—
523C2×C42—74no—
524C2×C42—144no—
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—24no—
543C22×C7—24no—
544C22×C7—24no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—416no—
558C22×C7—416no—
559C22×C7—416no—
560C22×C7#52514yes—
561C22×C7#52914yes—
562C22×C7#54014yes—
563C22×C7#54614yes—
564C22×C7#54614yes—
565C22×C7#55114yes—
566C22×C7#55314yes—
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—42no—
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—
604C24D4×D714yes—
605C24#115914yes—
606C24#115914yes—
607C24C23×D712yes—
608C24C23×D712yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×D4—232no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—28no—
618C2×D4—28no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—416no—
622C2×D4—416no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—74no—
635C22×C4—74no—
636C22×C4—74no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—72no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—148no—
646C22×C4—148no—
647C22×C4—148no—
648C22×C4—148no—
649C22×C4—142no—
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—148no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—148no—
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—2816no—
678C22×C4#115914yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—148no—
684C4⋊C4—148no—
685C4⋊C4—148no—
686C4⋊C4—148no—
687C4⋊C4—284no—
688C22⋊C4—28no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—716no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—148no—
696C22⋊C4—148no—
697C22⋊C4—284no—
698C22⋊C4—284no—
699C22⋊C4—284no—
700C42—148no—
701C42—284no—
702C2×C7—44no—
703C2×C7—44no—
704C2×C7—44no—
705C2×C7#245718yescomplemented
706C2×C7C2×#52511yescharacteristic
707C2×C7C2×#52911yescharacteristic
708C2×C7C2×#54011yescharacteristic
709C2×C7C2×#54611yescharacteristic
710C2×C7C2×#54611yescharacteristic
711C2×C7C2×#55111yescharacteristic
712C2×C7C2×#55311yescharacteristic
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
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—22no—
739C23—22no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23C2×D4×D714yes—
753C23C2×D4×D712yes—
754C23C2×#115914yes—
755C23C2×#115914yes—
756C23C2×#115912yes—
757C23C2×#115912yes—
758C23C2×#115912yes—
759C23#654812yes—
760C23#654812yes—
761C23D7×#4112yes—
762C23C24×D711yescharacteristic
763D4—232no—
764D4—416no—
765D4—416no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
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—44no—
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—2816no—
811C2×C4—284no—
812C2×C4—284no—
813C2×C4—284no—
814C2×C4—284no—
815C2×C4—284no—
816C2×C4C2×#115914yes—
817C7C2×#245711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—416no—
840C22—416no—
841C22—416no—
842C22#9027714yes—
843C22#9027814yes—
844C22#9028214yes—
845C22#9029114yes—
846C22#9029214yes—
847C22#9030114yes—
848C22#9041014yes—
849C22C22×D4×D711yescharacteristic
850C22C22×#115911yescharacteristic
851C22C22×#115911yescharacteristic
852C22C22×#115911yescharacteristic
853C22C2×#654811yescharacteristic
854C22C2×#654811yescharacteristic
855C22C2×D7×#4111yescharacteristic
856C4—24no—
857C4—42no—
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—44no—
871C2#1173412318yesdirect product factor
872C2C2×#9027711yescharacteristic
873C2C2×#9027811yescharacteristic
874C2C2×#9028211yescharacteristic
875C2C2×#9029111yescharacteristic
876C2C2×#9029211yescharacteristic
877C2C2×#9030111yescharacteristic
878C2C2×#9041011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC2×C7×#392C2
socleC24×C7C24
hypercenterC2×#392D7
hypocenterC7C2×#2457
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#6498C2semidirect
2. C22×D4×Dic7C2semidirect
4. C2×#89994C2semidirect
5. C2×#89992C2semidirect
6. C2×#89992C2semidirect
7. C2×#89992C2semidirect
8. C2×#89720C2semidirect
9. C2×#89717C2semidirect
10. C2×#89716C2semidirect
11. C2×#89715C2semidirect
12. C2×#89714C2semidirect
13. C2×C22⋊C4×Dic7C2semidirect
14. #11734123C2direct (N × H)
15. C2×#89432C2semidirect
16. C2×#89424C2semidirect
36. C2×#6498C22semidirect
38. C2×D4×Dic7C22semidirect
48. #89994C22semidirect
49. #89992C22semidirect
50. #89992C22semidirect
51. #89992C22semidirect
61. #89720C22semidirect
62. #89717C22semidirect
63. #89716C22semidirect
64. #89715C22semidirect
65. #89714C22semidirect
66. C22⋊C4×Dic7C22semidirect
67. #89432C22semidirect
68. #89424C22semidirect
123. C2×C22⋊Dic7D4semidirect
283. C22⋊Dic7C2×D4semidirect
705. C2×C7#2457semidirect
817. C7C2×#2457semidirect
871. C2#11734123direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64982
C22×D4×Dic72
C2×C7×#3922
C2×#899942
C2×#899922
C2×#897202
C2×#897172
C2×#897162
C2×#897152
C2×#897142
C2×C22⋊C4×Dic72
#117341232
C2×#894322
C2×#894242
C2×#24577