Finite Group Databasebeta

← C2×#11732110 #13512547

Subgroups — C2×#11732110 #13512547

Order 1792.

3934 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6502C211yesmaximal, characteristic
2C22×C4×C22⋊D7C211yesmaximal, characteristic, complemented
3C22×#6440C211yesmaximal, characteristic, complemented
4C2×C7×#386C211yesmaximal, characteristic, complemented
5C2×#89993C211yesmaximal, characteristic, complemented
6C2×#89982C211yesmaximal, characteristic, complemented
7C2×#89728C211yesmaximal, characteristic, complemented
8C2×#89729C211yesmaximal, characteristic, complemented
9C2×#89729C211yesmaximal, characteristic, complemented
10C2×#89716C211yesmaximal, characteristic, complemented
11C2×#89714C211yesmaximal, characteristic, complemented
12#11732110C2116yesmaximal, direct product factor
13C2×#89440C211yesmaximal, characteristic, complemented
14C2×#89419C211yesmaximal, characteristic, complemented
15C2×#89441C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
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
31C2×#6502C4116yescomplemented
32C2×#6502C2218yes—
33C2×C4×C22⋊D7—28no—
34C2×C4×C22⋊D7C2218yescomplemented
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C22×C4×Dic7C2211yescharacteristic
49C22×C4×Dic7C2211yescharacteristic
50C2×#6440—28no—
51C2×#6440C2218yescomplemented
52C7×#386C2218yescomplemented
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55#89993C2218yescomplemented
56#89982C2218yescomplemented
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89729C2218yescomplemented
62#89729C2218yescomplemented
63#89728C2218yescomplemented
64#89716C2218yescomplemented
65#89714C2218yescomplemented
66#89441C2218yescomplemented
67#89440C2218yescomplemented
68#89421C2218yescomplemented
69#89419C2218yescomplemented
70C2×#2324—71nomaximal, Sylow
71C25×C7C2311yescharacteristic
72C25×C7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C22×C7×D4—42no—
75C22×C7×D4—42no—
76C22×C7×D4C2×C418yescomplemented
77C22×C7×D4C2314yes—
78C23×C4×C7—24no—
79C23×C4×C7—42no—
80C23×C4×C7—42no—
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2314yes—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7—42no—
91C22×C22⋊D7C2×C418yes—
92C22×C22⋊D7C2×C418yescomplemented
93C22×C22⋊D7C2314yes—
94C22×C22⋊D7C2314yes—
95C23×Dic7—24no—
96C23×Dic7—24no—
97C23×Dic7C2×C418yescomplemented
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2314yes—
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C22×C4×D7—24no—
107C22×C4×D7—42no—
108C22×C4×D7—42no—
109C22×C4×D7C2314yes—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4—42no—
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—42no—
119C2×C22⋊Dic7—42no—
120C2×C22⋊Dic7C2×C418yescomplemented
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126#6502C2×C4164yescomplemented
127C4×C22⋊D7—232no—
128C2×(C2×D7)⋊C4—24no—
129C2×(C2×D7)⋊C4—42no—
130C2×(C2×D7)⋊C4—42no—
131C2×(C2×D7)⋊C4C2×C418yescomplemented
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×C4⋊Dic7—42no—
137C2×C4⋊Dic7C2314yes—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—42no—
143C2×Dic7⋊C4C2×C418yescomplemented
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×Dic7⋊C4C2314yes—
148C2×Dic7⋊C4C2314yes—
149C2×Dic7⋊C4C2314yes—
150C2×C4×Dic7—24no—
151C2×C4×Dic7—42no—
152C2×C4×Dic7—42no—
153C2×C4×Dic7D418yescomplemented
154C2×C4×Dic7C2314yes—
155C2×C4×Dic7C2314yes—
156C2×C4×Dic7C2314yes—
157C2×C4×Dic7C2314yes—
158#6440—232no—
159C7×#95C2314yes—
160C7×#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C22×#121—71no—
166C22×C4×D4—71no—
167C22×#117—71no—
168#2324—716no—
169C2×#390—71no—
170C2×#390—71no—
171C2×#390—71no—
172C2×#389—71no—
173C2×#388—71no—
174C2×#388—71no—
175C2×#386—71no—
176C2×#386D711yescharacteristic, complemented
177C2×#385—71no—
178C2×#385—71no—
179C2×#380—71no—
180C2×C4×C4⋊C4—71no—
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×C7C22×C414yes—
194C24×C7C22×C414yes—
195C24×C7C2412yes—
196C24×C7C2412yes—
197C24×C7C2411yescharacteristic
198C23×D7—22no—
199C23×D7—22no—
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7C22×C414yes—
205C23×D7C2412yes—
206C2×C7×D4—416no—
207C2×C7×D4—44no—
208C2×C7×D4—44no—
209C2×C7×D4C22×C4116yescomplemented
210C22×C4×C7—22no—
211C22×C4×C7—22no—
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—28no—
224C22×C4×C7—44no—
225C22×C4×C7—44no—
226C22×C4×C7—416no—
227C22×C4×C7C22×C414yes—
228C22×C4×C7C2×D414yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C2×C22⋊D7—232no—
235C2×C22⋊D7—28no—
236C2×C22⋊D7—28no—
237C2×C22⋊D7—416no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—44no—
240C2×C22⋊D7C22×C4116yes—
241C2×C22⋊D7C22×C4116yescomplemented
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—232no—
249C22×Dic7—28no—
250C22×Dic7—28no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7C22×C414yes—
261C22×Dic7C22×C414yes—
262C22×Dic7C22×C414yes—
263C22×Dic7C22×C4116yescomplemented
264C22×Dic7C2×D414yes—
265C22×Dic7C2×D414yes—
266C22×Dic7#4114yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C2×C4×D7—28no—
275C2×C4×D7—44no—
276C2×C4×D7—44no—
277C2×C4×D7—416no—
278C7×C22⋊C4—28no—
279C7×C22⋊C4—44no—
280C7×C22⋊C4—44no—
281C22⋊Dic7—28no—
282C22⋊Dic7—28no—
283C22⋊Dic7—44no—
284C22⋊Dic7—44no—
285C22⋊Dic7C22×C4116yescomplemented
286(C2×D7)⋊C4—28no—
287(C2×D7)⋊C4—44no—
288(C2×D7)⋊C4—44no—
289(C2×D7)⋊C4C22×C4116yescomplemented
290C4⋊Dic7—44no—
291Dic7⋊C4—28no—
292Dic7⋊C4—28no—
293Dic7⋊C4—28no—
294Dic7⋊C4—28no—
295Dic7⋊C4—44no—
296Dic7⋊C4C22×C4116yescomplemented
297C4×Dic7—28no—
298C4×Dic7—44no—
299C4×Dic7—44no—
300C4×Dic7C2×D4116yescomplemented
301C23×D4—71no—
302C23×D4—71no—
303C23×D4C2×D711yescharacteristic
304C24×C4—71no—
305C24×C4—71no—
306C24×C4C2×D711yescharacteristic
307C2×#121—716no—
308C2×#121—78no—
309C2×C4×D4—78no—
310C2×C4×D4—148no—
311C2×#117—78no—
312C2×#117—148no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C22⋊C4—71no—
321C22×C22⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4C2×D711yescharacteristic
330C22×C22⋊C4C2×D711yescharacteristic
331C22×C22⋊C4C2×D711yescharacteristic
332C22×C42—71no—
333C22×C42—71no—
334C22×C42—71no—
335C22×C42—71no—
336#390—78no—
337#390—78no—
338#390—78no—
339#389—78no—
340#388—78no—
341#388—78no—
342#386—78no—
343#386C2×D718yescomplemented
344#385—78no—
345#385—78no—
346#380—78no—
347C4×C4⋊C4—78no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95C2×D711yescharacteristic
353C2×#95C2×D711yescharacteristic
354C23×C7—28no—
355C23×C7—28no—
356C23×C7—28no—
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
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—22no—
371C23×C7—22no—
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×C7C23×C414yes—
381C23×C7C23×C414yes—
382C23×C7C23×C412yes—
383C23×C7C22×D412yes—
384C23×C7C2×#4112yes—
385C23×C7H(5,𝔽2)12yes—
386C23×C7H(5,𝔽2)12yes—
387C23×C7H(5,𝔽2)12yes—
388C23×C72−1+412yes—
389C23×C7C2511yescharacteristic
390C22×D7—28no—
391C22×D7—28no—
392C22×D7—28no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—44no—
400C22×D7—44no—
401C22×D7—44no—
402C22×D7—44no—
403C22×D7C23×C414yes—
404C7×D4—416no—
405C2×C4×C7—28no—
406C2×C4×C7—28no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—416no—
421C2×C4×C7—44no—
422C2×C4×C7—44no—
423C2×C4×C7—44no—
424C2×C4×C7C23×C414yes—
425C2×C4×C7C22×D414yes—
426C22⋊D7—232no—
427C22⋊D7—416no—
428C2×Dic7—28no—
429C2×Dic7—28no—
430C2×Dic7—28no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—232no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—44no—
448C2×Dic7—44no—
449C2×Dic7—44no—
450C2×Dic7C4×D4116yes—
451C2×Dic7C23×C414yes—
452C2×Dic7C23×C414yes—
453C2×Dic7C23×C414yes—
454C2×Dic7C22×D414yes—
455C2×Dic7C22×D414yes—
456C2×Dic7C2×#4114yes—
457C4×D7—416no—
458C25—71no—
459C25C22×D711yescharacteristic
460C25C22×D711yescharacteristic
461C22×D4—42no—
462C22×D4—42no—
463C22×D4—78no—
464C22×D4—74no—
465C22×D4—78no—
466C22×D4—74no—
467C22×D4—144no—
468C22×D4—144no—
469C22×D4—282no—
470C22×D4—282no—
471C22×D4C4×D718yescomplemented
472C22×D4C22×D714yes—
473C23×C4—24no—
474C23×C4—42no—
475C23×C4—42no—
476C23×C4—71no—
477C23×C4—78no—
478C23×C4—74no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—74no—
486C23×C4—144no—
487C23×C4—144no—
488C23×C4—144no—
489C23×C4—282no—
490C23×C4—282no—
491C23×C4C22×D711yescharacteristic
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D714yes—
497#121—764no—
498C4×D4—1432no—
499#117—1432no—
500C2×C4⋊C4—78no—
501C2×C4⋊C4—74no—
502C2×C4⋊C4—74no—
503C2×C4⋊C4—74no—
504C2×C4⋊C4—74no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—144no—
509C2×C4⋊C4—144no—
510C2×C4⋊C4—144no—
511C2×C4⋊C4—144no—
512C2×C4⋊C4—282no—
513C2×C4⋊C4—282no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—78no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—78no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—144no—
529C2×C22⋊C4—144no—
530C2×C22⋊C4—144no—
531C2×C22⋊C4—282no—
532C2×C22⋊C4—282no—
533C2×C22⋊C4—282no—
534C2×C22⋊C4—282no—
535C2×C22⋊C4C22×D714yes—
536C2×C22⋊C4C22×D714yes—
537C2×C22⋊C4C22×D714yes—
538C2×C42—78no—
539C2×C42—74no—
540C2×C42—74no—
541C2×C42—74no—
542C2×C42—74no—
543C2×C42—144no—
544C2×C42—282no—
545C2×C42—282no—
546#95—74no—
547#95—74no—
548#95—74no—
549#95—74no—
550#95C22×D714yes—
551#95C22×D714yes—
552C22×C7—24no—
553C22×C7—24no—
554C22×C7—24no—
555C22×C7—24no—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—416no—
559C22×C7—416no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7C2×C4×D414yes—
569C22×C7#51814yes—
570C22×C7#52014yes—
571C22×C7#53514yes—
572C22×C7#53714yes—
573C22×C7#54014yes—
574C22×C7#54214yes—
575C22×C7C24×C411yescharacteristic
576C22×C7C23×D411yescharacteristic
577C22×C7C22×#4111yescharacteristic
578C22×C7C2×H(5,𝔽2)11yescharacteristic
579C22×C7C2×H(5,𝔽2)11yescharacteristic
580C22×C7C2×H(5,𝔽2)11yescharacteristic
581C22×C7C2×2−1+411yescharacteristic
582C2×D7—24no—
583C2×D7—24no—
584C2×D7—24no—
585C2×D7—416no—
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C4×C7—24no—
591C4×C7—24no—
592C4×C7—42no—
593C4×C7—42no—
594C4×C7—42no—
595Dic7—24no—
596Dic7—24no—
597Dic7—24no—
598Dic7—42no—
599Dic7—42no—
600Dic7—42no—
601Dic7C2×C4×D418yes—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—74no—
615C24—72no—
616C24—142no—
617C24—142no—
618C24—142no—
619C24—142no—
620C24—142no—
621C24—142no—
622C24C2×C4×D714yes—
623C24C2×C4×D714yes—
624C24C23×D712yes—
625C24C23×D712yes—
626C24C23×D711yescharacteristic
627C2×D4—416no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—716no—
631C2×D4—716no—
632C2×D4—148no—
633C2×D4—1432no—
634C2×D4—148no—
635C2×D4—2816no—
636C2×D4—284no—
637C2×D4—284no—
638C2×D4C2×C4×D7116yescomplemented
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—28no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—416no—
656C22×C4—74no—
657C22×C4—74no—
658C22×C4—74no—
659C22×C4—72no—
660C22×C4—74no—
661C22×C4—74no—
662C22×C4—716no—
663C22×C4—74no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—148no—
671C22×C4—1432no—
672C22×C4—148no—
673C22×C4—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—148no—
689C22×C4—284no—
690C22×C4—284no—
691C22×C4—2816no—
692C22×C4C2×C4×D714yes—
693C22×C4D4×D714yes—
694C22×C4C23×D712yes—
695C22×C4C23×D712yes—
696C22×C4C23×D712yes—
697C22×C4C23×D712yes—
698C22×C4C23×D712yes—
699C4⋊C4—716no—
700C4⋊C4—148no—
701C4⋊C4—148no—
702C4⋊C4—148no—
703C4⋊C4—148no—
704C4⋊C4—284no—
705C4⋊C4—284no—
706C22⋊C4—28no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—716no—
710C22⋊C4—716no—
711C22⋊C4—148no—
712C22⋊C4—148no—
713C22⋊C4—148no—
714C22⋊C4—284no—
715C22⋊C4—284no—
716C22⋊C4—284no—
717C22⋊C4—284no—
718C42—716no—
719C42—148no—
720C42—284no—
721C42—284no—
722C2×C7—44no—
723C2×C7—44no—
724C2×C7#232418yescomplemented
725C2×C7C22×C4×D411yescharacteristic
726C2×C7C2×#51811yescharacteristic
727C2×C7C2×#52011yescharacteristic
728C2×C7C2×#53511yescharacteristic
729C2×C7C2×#53711yescharacteristic
730C2×C7C2×#54011yescharacteristic
731C2×C7C2×#54211yescharacteristic
732D7—44no—
733C23—28no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—74no—
760C23—148no—
761C23—148no—
762C23—148no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—284no—
770C23—284no—
771C23—284no—
772C23—284no—
773C23C22×C4×D714yes—
774C23C22×C4×D714yes—
775C23C22×C4×D712yes—
776C23C2×D4×D712yes—
777C23#654812yes—
778C23#654812yes—
779C23#654812yes—
780C23D7×#4112yes—
781C23#655412yes—
782C23C24×D711yescharacteristic
783D4—416no—
784D4—1432no—
785D4—2816no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—416no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—716no—
806C2×C4—74no—
807C2×C4—74no—
808C2×C4—74no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—74no—
812C2×C4—1432no—
813C2×C4—148no—
814C2×C4—148no—
815C2×C4—148no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—2816no—
832C2×C4—284no—
833C2×C4—284no—
834C2×C4—284no—
835C2×C4C22×C4×D714yes—
836C2×C4C2×D4×D714yes—
837C7C2×#232411yescharacteristic, complemented, Sylow
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—416no—
853C22—416no—
854C22—144no—
855C22—144no—
856C22—144no—
857C22—282no—
858C22—282no—
859C22—282no—
860C22—282no—
861C22—2816no—
862C22#9017714yes—
863C22C4×D4×D714yes—
864C22#9023714yes—
865C22#9028314yes—
866C22#9029914yes—
867C22#9030614yes—
868C22#9035314yes—
869C22C23×C4×D711yescharacteristic
870C22C22×D4×D711yescharacteristic
871C22C2×#654811yescharacteristic
872C22C2×#654811yescharacteristic
873C22C2×#654811yescharacteristic
874C22C2×D7×#4111yescharacteristic
875C22C2×#655411yescharacteristic
876C4—24no—
877C4—24no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—78no—
882C4—144no—
883C4—144no—
884C4—144no—
885C4—282no—
886C4—282no—
887C4—282no—
888C2—44no—
889C2—44no—
890C2—284no—
891C2#1173211018yesdirect product factor
892C2C2×#9017711yescharacteristic
893C2C2×#9023711yescharacteristic
894C2C2×C4×D4×D711yescharacteristic
895C2C2×#9028311yescharacteristic
896C2C2×#9030611yescharacteristic
897C2C2×#9029911yescharacteristic
898C2C2×#9035311yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC22×#6502C2
cosocleC23×C7C25
hypercenterC2×#386D7
hypocenterC7C2×#2324
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D7C2semidirect
3. C22×#6440C2semidirect
4. C2×C7×#386C2semidirect
5. C2×#89993C2semidirect
6. C2×#89982C2semidirect
7. C2×#89728C2semidirect
8. C2×#89729C2semidirect
9. C2×#89729C2semidirect
10. C2×#89716C2semidirect
11. C2×#89714C2semidirect
12. #11732110C2direct (N × H)
13. C2×#89440C2semidirect
14. C2×#89419C2semidirect
15. C2×#89441C2semidirect
16. C2×#89421C2semidirect
31. C2×#6502C4semidirect
34. C2×C4×C22⋊D7C22semidirect
51. C2×#6440C22semidirect
52. C7×#386C22semidirect
55. #89993C22semidirect
56. #89982C22semidirect
61. #89729C22semidirect
62. #89729C22semidirect
63. #89728C22semidirect
64. #89716C22semidirect
65. #89714C22semidirect
66. #89441C22semidirect
67. #89440C22semidirect
68. #89421C22semidirect
69. #89419C22semidirect
76. C22×C7×D4C2×C4semidirect
92. C22×C22⋊D7C2×C4semidirect
97. C23×Dic7C2×C4semidirect
120. C2×C22⋊Dic7C2×C4semidirect
126. #6502C2×C4semidirect
131. C2×(C2×D7)⋊C4C2×C4semidirect
143. C2×Dic7⋊C4C2×C4semidirect
153. C2×C4×Dic7D4semidirect
176. C2×#386D7semidirect
209. C2×C7×D4C22×C4semidirect
241. C2×C22⋊D7C22×C4semidirect
263. C22×Dic7C22×C4semidirect
285. C22⋊Dic7C22×C4semidirect
289. (C2×D7)⋊C4C22×C4semidirect
296. Dic7⋊C4C22×C4semidirect
300. C4×Dic7C2×D4semidirect
343. #386C2×D7semidirect
471. C22×D4C4×D7semidirect
638. C2×D4C2×C4×D7semidirect
724. C2×C7#2324semidirect
837. C7C2×#2324semidirect
891. C2#11732110direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65022
C22×C4×C22⋊D72
C22×#64402
C2×C7×#3862
C2×#899932
C2×#899822
C2×#897282
C2×#897292
C2×#897162
C2×#897142
#117321102
C2×#894402
C2×#894192
C2×#894412
C2×#894212
C2×#23247