Finite Group Databasebeta

← C2×#11731899 #13521428

Subgroups — C2×#11731899 #13521428

Order 1792.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic7C211yesmaximal, characteristic, complemented
2C22×#6461C211yesmaximal, characteristic, complemented
3C2×C7×#385C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic
5C2×#89766C211yesmaximal, characteristic, complemented
6C2×#89758C211yesmaximal, characteristic, complemented
7C2×#89753C211yesmaximal, characteristic, complemented
8C2×#89730C211yesmaximal, characteristic
9C2×#89730C211yesmaximal, characteristic
10C2×#89714C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
12#11731899C2116yesmaximal, direct product factor
13C2×#89432C211yesmaximal, characteristic, complemented
14C2×#89446C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89426C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×C4⋊Dic7—28no—
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4⋊Dic7C2218yescomplemented
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6461—28no—
43C2×#6461C2218yescomplemented
44C7×#385C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47#89985C2218yes—
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89766C2218yescomplemented
59#89758C2218yescomplemented
60#89753C2218yescomplemented
61#89730C2218yes—
62#89730C2218yes—
63#89714C2218yescomplemented
64C22⋊C4×Dic7C2218yescomplemented
65#89446C2218yescomplemented
66#89442C2218yescomplemented
67#89432C2218yescomplemented
68#89426C2218yescomplemented
69C2×#2481—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7—24no—
73C23×C4×C7—24no—
74C23×C4×C7—24no—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2314yes—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7C2314yes—
86C23×Dic7—24no—
87C23×Dic7—24no—
88C23×Dic7—24no—
89C23×Dic7—24no—
90C23×Dic7—42no—
91C23×Dic7—42no—
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2314yes—
98C23×Dic7C2314yes—
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—24no—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7C2314yes—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—24no—
114C2×(C2×D7)⋊C4—24no—
115C2×(C2×D7)⋊C4—42no—
116C2×(C2×D7)⋊C4—42no—
117C2×(C2×D7)⋊C4C2314yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×(C2×D7)⋊C4C2314yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×C4⋊Dic7—24no—
124C2×C4⋊Dic7—24no—
125C2×C4⋊Dic7—24no—
126C2×C4⋊Dic7—232no—
127C2×C4⋊Dic7D418yescomplemented
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×C4⋊Dic7C2314yes—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×C4×Dic7—24no—
137C2×C4×Dic7—42no—
138C2×C4×Dic7C2314yes—
139C2×C4×Dic7C2314yes—
140#6461—232no—
141C7×#95C2314yes—
142C7×#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#126—71no—
154C23×C4⋊C4—71no—
155#2481—716no—
156C2×#400—71no—
157C2×#400—71no—
158C2×#397—71no—
159C2×#396—71no—
160C2×#388—71no—
161C2×#387—71no—
162C2×#387—71no—
163C2×#386—71no—
164C2×#386—71no—
165C2×#386—71no—
166C2×#385D711yescharacteristic, complemented
167C2×#380—71no—
168C2×C4×C22⋊C4—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7#4114yes—
174C24×C7#4114yes—
175C24×C7#4114yes—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7—22no—
185C23×D7C2412yes—
186C22×C4×C7—232no—
187C22×C4×C7—22no—
188C22×C4×C7—28no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—28no—
193C22×C4×C7—28no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7C2×D414yes—
207C22×C4×C7#4114yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C2×C22⋊D7—28no—
215C2×C22⋊D7—28no—
216C2×C22⋊D7—28no—
217C2×C22⋊D7—416no—
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—22no—
227C22×Dic7—22no—
228C22×Dic7—28no—
229C22×Dic7—28no—
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—28no—
240C22×Dic7—28no—
241C22×Dic7—44no—
242C22×Dic7—44no—
243C22×Dic7—416no—
244C22×Dic7—416no—
245C22×Dic7C2×D414yes—
246C22×Dic7C2×D414yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C7×C4⋊C4—28no—
255C7×C4⋊C4—28no—
256C7×C22⋊C4—28no—
257C7×C22⋊C4—28no—
258C22⋊Dic7—28no—
259(C2×D7)⋊C4—28no—
260(C2×D7)⋊C4—28no—
261(C2×D7)⋊C4—28no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—44no—
264(C2×D7)⋊C4—44no—
265C4⋊Dic7—28no—
266C4⋊Dic7—28no—
267C4⋊Dic7—28no—
268C4⋊Dic7C2×D4116yescomplemented
269Dic7⋊C4—28no—
270Dic7⋊C4—44no—
271C4×Dic7—28no—
272C4×Dic7—44no—
273C23×D4—71no—
274C24×C4—71no—
275C24×C4—71no—
276C24×C4C2×D711yescharacteristic
277C2×#126—78no—
278C2×#126—148no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—78no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—148no—
287C22×C4⋊C4C2×D711yescharacteristic
288C22×C4⋊C4C2×D711yescharacteristic
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C42—71no—
299C22×C42—71no—
300#400—78no—
301#400—78no—
302#397—78no—
303#396—78no—
304#388—78no—
305#387—78no—
306#387—78no—
307#386—78no—
308#386—78no—
309#386—78no—
310#385C2×D718yescomplemented
311#380—78no—
312C4×C22⋊C4—78no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95C2×D711yescharacteristic
324C2×#95C2×D711yescharacteristic
325C23×C7—28no—
326C23×C7—28no—
327C23×C7—28no—
328C23×C7—28no—
329C23×C7—28no—
330C23×C7—28no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7#126116yescomplemented
336C23×C7C22×D412yes—
337C23×C7C2×#4114yes—
338C23×C7C2×#4112yes—
339C23×C7C2×#4114yes—
340C23×C7C2×#4112yes—
341C23×C7C2×#4112yes—
342C23×C7C2×#4114yes—
343C23×C7C2×#4112yes—
344C23×C7H(5,𝔽2)12yes—
345C23×C72−1+412yes—
346C23×C7C2511yescharacteristic
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7—44no—
358C22×D7—44no—
359C22×D7—44no—
360C22×D7—44no—
361C2×C4×C7—232no—
362C2×C4×C7—28no—
363C2×C4×C7—28no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—44no—
381C2×C4×C7—44no—
382C2×C4×C7—44no—
383C2×C4×C7—44no—
384C2×C4×C7C22×D414yes—
385C2×C4×C7C2×#4114yes—
386C22⋊D7—416no—
387C2×Dic7—28no—
388C2×Dic7—28no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—416no—
409C2×Dic7—416no—
410C2×Dic7—44no—
411C2×Dic7—44no—
412C2×Dic7—44no—
413C2×Dic7—44no—
414C2×Dic7—44no—
415C2×Dic7C22×D414yes—
416C2×Dic7C22×D414yes—
417C25—71no—
418C25C22×D711yescharacteristic
419C22×D4—74no—
420C22×D4—144no—
421C22×D4—144no—
422C22×D4—144no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—74no—
434C23×C4—74no—
435C23×C4—144no—
436C23×C4—144no—
437C23×C4—144no—
438C23×C4—144no—
439C23×C4—282no—
440C23×C4—282no—
441C23×C4C22×D714yes—
442C23×C4C22×D711yescharacteristic
443C23×C4C22×D711yescharacteristic
444C23×C4C22×D711yescharacteristic
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C23×C4C22×D711yescharacteristic
448#126—1432no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—78no—
452C2×C4⋊C4—74no—
453C2×C4⋊C4—74no—
454C2×C4⋊C4—74no—
455C2×C4⋊C4—74no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—1432no—
459C2×C4⋊C4—144no—
460C2×C4⋊C4—144no—
461C2×C4⋊C4—144no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—282no—
464C2×C4⋊C4C22×D714yes—
465C2×C4⋊C4C22×D714yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—74no—
470C2×C22⋊C4—74no—
471C2×C22⋊C4—74no—
472C2×C22⋊C4—74no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—144no—
480C2×C22⋊C4—282no—
481C2×C22⋊C4—282no—
482C2×C22⋊C4C22×D714yes—
483C2×C22⋊C4C22×D714yes—
484C2×C42—74no—
485C2×C42—74no—
486C2×C42—144no—
487C2×C42—282no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
495#95—74no—
496#95—74no—
497#95—74no—
498#95C22×D714yes—
499#95C22×D714yes—
500C22×C7—24no—
501C22×C7—24no—
502C22×C7—24no—
503C22×C7—24no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—232no—
507C22×C7#52514yes—
508C22×C7C2×#12614yes—
509C22×C7C2×#12618yescomplemented
510C22×C7#53914yes—
511C22×C7#54614yes—
512C22×C7#54814yes—
513C22×C7#55214yes—
514C22×C7#55314yes—
515C22×C7C23×D411yescharacteristic
516C22×C7C22×#4111yescharacteristic
517C22×C7C22×#4111yescharacteristic
518C22×C7C22×#4111yescharacteristic
519C22×C7C22×#4111yescharacteristic
520C22×C7C2×H(5,𝔽2)11yescharacteristic
521C22×C7C2×2−1+411yescharacteristic
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C2×D7—42no—
529C2×D7—88no—
530C4×C7—24no—
531C4×C7—24no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536Dic7—24no—
537Dic7—24no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—72no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24#115714yes—
556C24#115914yes—
557C24#116114yes—
558C24C23×D712yes—
559C24C23×D711yescharacteristic
560C2×D4—148no—
561C2×D4—148no—
562C2×D4—148no—
563C2×D4—2816no—
564C22×C4—232no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—74no—
585C22×C4—74no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—148no—
594C22×C4—148no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—148no—
608C22×C4—148no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—284no—
617C22×C4—284no—
618C22×C4—2816no—
619C22×C4—2816no—
620C22×C4D4×D714yes—
621C22×C4#115914yes—
622C22×C4C23×D712yes—
623C22×C4C23×D712yes—
624C22×C4C23×D712yes—
625C22×C4C23×D712yes—
626C22×C4C23×D712yes—
627C22×C4C23×D712yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—716no—
631C4⋊C4—148no—
632C4⋊C4—148no—
633C4⋊C4—148no—
634C4⋊C4—148no—
635C4⋊C4—284no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—148no—
639C22⋊C4—148no—
640C22⋊C4—148no—
641C22⋊C4—148no—
642C22⋊C4—148no—
643C22⋊C4—284no—
644C22⋊C4—284no—
645C42—148no—
646C42—284no—
647C2×C7—28no—
648C2×C7#248118yescomplemented
649C2×C7C2×#52511yescharacteristic
650C2×C7C22×#12611yescharacteristic
651C2×C7C2×#53911yescharacteristic
652C2×C7C2×#54611yescharacteristic
653C2×C7C2×#54811yescharacteristic
654C2×C7C2×#55211yescharacteristic
655C2×C7C2×#55311yescharacteristic
656D7—82no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—22no—
663C23—22no—
664C23—28no—
665C23—22no—
666C23—22no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—142no—
673C23—142no—
674C23—284no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23—284no—
679C23—284no—
680C23—284no—
681C23#6461116yescomplemented
682C23C2×#115714yes—
683C23C2×#115712yes—
684C23C2×D4×D712yes—
685C23C2×#115914yes—
686C23C2×#115912yes—
687C23C2×#115912yes—
688C23C2×#116114yes—
689C23C2×#116112yes—
690C23#655312yes—
691C23#655412yes—
692C23C24×D711yescharacteristic
693D4—2816no—
694C2×C4—232no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—74no—
718C2×C4—74no—
719C2×C4—148no—
720C2×C4—148no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—2816no—
741C2×C4—2816no—
742C2×C4—284no—
743C2×C4—284no—
744C2×C4—284no—
745C2×C4—284no—
746C2×C4—284no—
747C2×C4C2×D4×D714yes—
748C2×C4C2×#115914yes—
749C7C2×#248111yescharacteristic, complemented, Sylow
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—232no—
757C22—282no—
758C22—282no—
759C22—282no—
760C22—282no—
761C22—282no—
762C22—282no—
763C22—282no—
764C22—568no—
765C22C2×#646114yes—
766C22C2×#646118yescomplemented
767C22#9024314yes—
768C22#9025614yes—
769C22#9027714yes—
770C22#9032114yes—
771C22#9033314yes—
772C22#9035614yes—
773C22C22×#115711yescharacteristic
774C22C22×D4×D711yescharacteristic
775C22C22×#115911yescharacteristic
776C22C22×#115911yescharacteristic
777C22C22×#116111yescharacteristic
778C22C2×#655311yescharacteristic
779C22C2×#655411yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—144no—
787C4—144no—
788C4—282no—
789C4—282no—
790C4—282no—
791C4—282no—
792C4—282no—
793C2—28no—
794C2—562no—
795C2#1173189918yesdirect product factor
796C2C22×#646111yescharacteristic
797C2C2×#9024311yescharacteristic
798C2C2×#9025611yescharacteristic
799C2C2×#9027711yescharacteristic
800C2C2×#9033311yescharacteristic
801C2C2×#9032111yescharacteristic
802C2C2×#9035611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#385D7
hypocenterC7C2×#2481
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊Dic7C2semidirect
2. C22×#6461C2semidirect
3. C2×C7×#385C2semidirect
5. C2×#89766C2semidirect
6. C2×#89758C2semidirect
7. C2×#89753C2semidirect
10. C2×#89714C2semidirect
11. C2×C22⋊C4×Dic7C2semidirect
12. #11731899C2direct (N × H)
13. C2×#89432C2semidirect
14. C2×#89446C2semidirect
15. C2×#89442C2semidirect
16. C2×#89426C2semidirect
37. C22×C4⋊Dic7C22semidirect
43. C2×#6461C22semidirect
44. C7×#385C22semidirect
58. #89766C22semidirect
59. #89758C22semidirect
60. #89753C22semidirect
63. #89714C22semidirect
64. C22⋊C4×Dic7C22semidirect
65. #89446C22semidirect
66. #89442C22semidirect
67. #89432C22semidirect
68. #89426C22semidirect
127. C2×C4⋊Dic7D4semidirect
166. C2×#385D7semidirect
268. C4⋊Dic7C2×D4semidirect
310. #385C2×D7semidirect
335. C23×C7#126semidirect
509. C22×C7C2×#126semidirect
648. C2×C7#2481semidirect
681. C23#6461semidirect
749. C7C2×#2481semidirect
766. C22C2×#6461semidirect
795. C2#11731899direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic72
C22×#64612
C2×C7×#3852
C2×#899852
C2×#897662
C2×#897582
C2×#897532
C2×#897302
C2×#897142
C2×C22⋊C4×Dic72
#117318992
C2×#894322
C2×#894462
C2×#894422
C2×#894262
C2×#24817