Finite Group Databasebeta

← C2×#11731241 #13522863

Subgroups — C2×#11731241 #13522863

Order 1792.

2898 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6439C211yesmaximal, characteristic, complemented
2C22×#6438C211yesmaximal, characteristic
3C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#89764C211yesmaximal, characteristic, complemented
5C2×#89765C211yesmaximal, characteristic, complemented
6C2×#89763C211yesmaximal, characteristic
7C2×#89751C211yesmaximal, characteristic, complemented
8C2×#89712C211yesmaximal, characteristic, complemented
9C2×#89712C211yesmaximal, characteristic, complemented
10C2×#89705C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
12#11731241C2116yesmaximal, direct product factor
13C2×#89437C211yesmaximal, characteristic
14C2×#89439C211yesmaximal, characteristic, complemented
15C2×#89418C211yesmaximal, characteristic, complemented
16C2×#89441C211yesmaximal, characteristic, complemented
17C23×D28C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6439—28no—
43C2×#6439C2218yescomplemented
44C2×#6438—28no—
45C2×#6438C2218yes—
46C4×C7×C4⋊C4C2218yescomplemented
47C2×C7×#95C2211yescharacteristic
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
57#89765C2218yescomplemented
58#89764C2218yescomplemented
59#89763C2218yes—
60#89751C2218yescomplemented
61#89712C2218yescomplemented
62#89712C2218yescomplemented
63C4×(C2×D7)⋊C4C2218yescomplemented
64#89705C2218yescomplemented
65#89441C2218yescomplemented
66#89439C2218yescomplemented
67#89437C2218yes—
68#89418C2218yescomplemented
69C2×#2521—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
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
85C22×D28—24no—
86C22×D28—24no—
87C22×D28—42no—
88C22×D28C2314yes—
89C22×C4×D7—24no—
90C22×C4×D7—24no—
91C22×C4×D7—42no—
92C22×C4×D7C2314yes—
93C22×Dic14—24no—
94C22×Dic14—24no—
95C22×Dic14—42no—
96C22×Dic14C2314yes—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4—24no—
99C2×C7×C4⋊C4C2314yes—
100C2×C7×C4⋊C4C2314yes—
101C2×C42×C7—24no—
102C2×C42×C7—24no—
103C2×C42×C7—24no—
104C2×C42×C7C2314yes—
105C2×C42×C7C2314yes—
106C2×C42×C7C2314yes—
107C2×(C2×D7)⋊C4—24no—
108C2×(C2×D7)⋊C4—24no—
109C2×(C2×D7)⋊C4—24no—
110C2×(C2×D7)⋊C4—24no—
111C2×(C2×D7)⋊C4—24no—
112C2×(C2×D7)⋊C4—24no—
113C2×(C2×D7)⋊C4—24no—
114C2×(C2×D7)⋊C4—24no—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—42no—
117C2×(C2×D7)⋊C4D418yes—
118C2×(C2×D7)⋊C4C2314yes—
119C2×(C2×D7)⋊C4C2314yes—
120C2×(C2×D7)⋊C4C2314yes—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×C4×Dic7—42no—
140C2×C4×Dic7C2314yes—
141#6439—232no—
142#6438—232no—
143C7×#95C2314yes—
144C7×#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#126—71no—
154C22×#124—71no—
155#2521—716no—
156C2×#399—71no—
157C2×#397—71no—
158C2×#395—71no—
159C2×#394—71no—
160C2×#391—71no—
161C2×#388—71no—
162C2×#388—71no—
163C2×#388—71no—
164C2×#387—71no—
165C2×#386—71no—
166C2×#380—71no—
167C2×C4×C4⋊C4D711yescharacteristic, complemented
168C2×C4×C22⋊C4—71no—
169C24×C7C2411yescharacteristic
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—22no—
174C23×D7—22no—
175C23×D7—22no—
176C23×D7—22no—
177C23×D7—22no—
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7C2×D414yes—
184C23×D7C2412yes—
185C23×D7C2412yes—
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×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7C2×D414yes—
204C22×C4×C7#4114yes—
205C22×C4×C7#4114yes—
206C22×C4×C7#4114yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
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—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7C2×D414yes—
231C22×Dic7#4114yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C2×D28—28no—
239C2×D28—28no—
240C2×D28—44no—
241C2×D28—416no—
242C2×C4×D7—28no—
243C2×C4×D7—28no—
244C2×C4×D7—44no—
245C2×C4×D7—416no—
246C2×Dic14—28no—
247C2×Dic14—28no—
248C2×Dic14—44no—
249C2×Dic14—416no—
250C7×C4⋊C4—28no—
251C7×C4⋊C4—28no—
252C42×C7—28no—
253C42×C7—28no—
254C42×C7—28no—
255(C2×D7)⋊C4—28no—
256(C2×D7)⋊C4—28no—
257(C2×D7)⋊C4—28no—
258(C2×D7)⋊C4—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—28no—
264(C2×D7)⋊C4—44no—
265(C2×D7)⋊C4C2×D4116yes—
266Dic7⋊C4—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4—28no—
269Dic7⋊C4—28no—
270Dic7⋊C4—44no—
271C4×Dic7—44no—
272C23×Q8—71no—
273C23×D4—71no—
274C24×C4—71no—
275C2×#126—78no—
276C2×#126—148no—
277C2×#124—78no—
278C2×#124—148no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4C2×D711yescharacteristic
285C22×C4⋊C4C2×D711yescharacteristic
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
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⋊C4—71no—
297C22×C42—71no—
298C22×C42C2×D711yescharacteristic
299C22×C42C2×D711yescharacteristic
300C22×C42C2×D711yescharacteristic
301#399—78no—
302#397—78no—
303#395—78no—
304#394—78no—
305#391—78no—
306#388—78no—
307#388—78no—
308#388—78no—
309#387—78no—
310#386—78no—
311#380—78no—
312C4×C4⋊C4C2×D718yescomplemented
313C4×C22⋊C4—78no—
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×#95C2×D711yescharacteristic
323C2×#95C2×D711yescharacteristic
324C23×C7C22×D412yes—
325C23×C7C2×#4112yes—
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7C2×#4112yes—
329C23×C7H(5,𝔽2)12yes—
330C23×C72−1+412yes—
331C23×C7C2511yescharacteristic
332C22×D7—28no—
333C22×D7—28no—
334C22×D7—28no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—22no—
338C22×D7—22no—
339C22×D7—22no—
340C22×D7—22no—
341C22×D7—22no—
342C22×D7—22no—
343C22×D7—22no—
344C22×D7—22no—
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—44no—
349C22×D7—44no—
350C22×D7—44no—
351C22×D7—44no—
352C22×D7—44no—
353C22×D7—44no—
354C22×D7—44no—
355C22×D7—44no—
356C22×D7—44no—
357C22×D7—44no—
358C22×D7—44no—
359C22×D7C22×D414yes—
360C2×C4×C7—28no—
361C2×C4×C7—28no—
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—22no—
381C2×C4×C7—44no—
382C2×C4×C7—44no—
383C2×C4×C7—44no—
384C2×C4×C7C22×D414yes—
385C2×C4×C7C2×#4114yes—
386C2×C4×C7C2×#4114yes—
387C2×C4×C7C2×#4114yes—
388C2×Dic7—28no—
389C2×Dic7—28no—
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—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7C22×D414yes—
411C2×Dic7C2×#4114yes—
412D28—416no—
413C4×D7—416no—
414Dic14—416no—
415C25—71no—
416C25—71no—
417C22×Q8—74no—
418C22×Q8—144no—
419C22×Q8—144no—
420C22×Q8—282no—
421C22×D4—74no—
422C22×D4—144no—
423C22×D4—144no—
424C22×D4—282no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—74no—
432C23×C4—144no—
433C23×C4—144no—
434C23×C4—282no—
435C23×C4C22×D711yescharacteristic
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439C23×C4C22×D711yescharacteristic
440C23×C4C22×D711yescharacteristic
441C23×C4C22×D711yescharacteristic
442#126—1432no—
443#124—1432no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—74no—
450C2×C4⋊C4—74no—
451C2×C4⋊C4—144no—
452C2×C4⋊C4—144no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4—144no—
455C2×C4⋊C4—282no—
456C2×C4⋊C4C22×D714yes—
457C2×C4⋊C4C22×D714yes—
458C2×C22⋊C4—78no—
459C2×C22⋊C4—74no—
460C2×C22⋊C4—74no—
461C2×C22⋊C4—74no—
462C2×C22⋊C4—74no—
463C2×C22⋊C4—74no—
464C2×C22⋊C4—74no—
465C2×C22⋊C4—74no—
466C2×C22⋊C4—74no—
467C2×C22⋊C4—74no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—74no—
470C2×C22⋊C4—144no—
471C2×C22⋊C4—144no—
472C2×C22⋊C4—144no—
473C2×C22⋊C4—144no—
474C2×C22⋊C4—144no—
475C2×C22⋊C4—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—282no—
480C2×C42—24no—
481C2×C42—24no—
482C2×C42—24no—
483C2×C42—74no—
484C2×C42—282no—
485C2×C42C22×D714yes—
486C2×C42C22×D714yes—
487C2×C42C22×D714yes—
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#95C22×D714yes—
497#95C22×D714yes—
498C22×C7#52914yes—
499C22×C7#53214yes—
500C22×C7#54214yes—
501C22×C7#54614yes—
502C22×C7#54714yes—
503C22×C7#55114yes—
504C22×C7#55614yes—
505C22×C7C23×D411yescharacteristic
506C22×C7C22×#4111yescharacteristic
507C22×C7C22×#4111yescharacteristic
508C22×C7C22×#4111yescharacteristic
509C22×C7C22×#4111yescharacteristic
510C22×C7C2×H(5,𝔽2)11yescharacteristic
511C22×C7C2×2−1+411yescharacteristic
512C2×D7—24no—
513C2×D7—24no—
514C2×D7—24no—
515C2×D7—42no—
516C2×D7—42no—
517C2×D7—42no—
518C2×D7—42no—
519C2×D7—416no—
520C2×D7—42no—
521C2×D7—42no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—88no—
528C4×C7—24no—
529C4×C7—24no—
530C4×C7—24no—
531C4×C7—24no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535Dic7—24no—
536Dic7—24no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541C24—74no—
542C24—72no—
543C24—72no—
544C24—142no—
545C24—142no—
546C24—142no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24—142no—
557C24C23×D711yescharacteristic
558C2×Q8—148no—
559C2×Q8—148no—
560C2×Q8—284no—
561C2×Q8—2816no—
562C2×D4—148no—
563C2×D4—148no—
564C2×D4—284no—
565C2×D4—2816no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
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—74no—
584C22×C4—74no—
585C22×C4—72no—
586C22×C4—72no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—148no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—142no—
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—142no—
608C22×C4—148no—
609C22×C4—284no—
610C22×C4—2816no—
611C22×C4#115714yes—
612C22×C4#115714yes—
613C22×C4#115714yes—
614C22×C4D4×D714yes—
615C22×C4C23×D712yes—
616C22×C4C23×D712yes—
617C22×C4C23×D712yes—
618C22×C4C23×D712yes—
619C22×C4C23×D712yes—
620C22×C4C23×D712yes—
621C22×C4C23×D712yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—148no—
625C4⋊C4—148no—
626C4⋊C4—148no—
627C4⋊C4—148no—
628C4⋊C4—284no—
629C22⋊C4—716no—
630C22⋊C4—148no—
631C22⋊C4—148no—
632C22⋊C4—148no—
633C22⋊C4—148no—
634C22⋊C4—148no—
635C22⋊C4—148no—
636C22⋊C4—148no—
637C22⋊C4—148no—
638C22⋊C4—148no—
639C22⋊C4—284no—
640C42—28no—
641C42—28no—
642C42—28no—
643C42—284no—
644C2×C7#252118yescomplemented
645C2×C7C2×#52911yescharacteristic
646C2×C7C2×#53211yescharacteristic
647C2×C7C2×#54211yescharacteristic
648C2×C7C2×#54611yescharacteristic
649C2×C7C2×#54711yescharacteristic
650C2×C7C2×#55111yescharacteristic
651C2×C7C2×#55611yescharacteristic
652D7—44no—
653D7—82no—
654C23—74no—
655C23—148no—
656C23—148no—
657C23—148no—
658C23—142no—
659C23—142no—
660C23—142no—
661C23—142no—
662C23—142no—
663C23—142no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—284no—
672C23—284no—
673C23—284no—
674C23—284no—
675C23—284no—
676C23—284no—
677C23—284no—
678C23—284no—
679C23—284no—
680C23—284no—
681C23—284no—
682C23C2×#115712yes—
683C23C2×#115712yes—
684C23C2×#115712yes—
685C23C2×D4×D712yes—
686C23#655112yes—
687C23D7×#4112yes—
688C23#655312yes—
689C23C24×D711yescharacteristic
690Q8—2816no—
691D4—2816no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
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—74no—
717C2×C4—74no—
718C2×C4—148no—
719C2×C4—148no—
720C2×C4—142no—
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—2816no—
737C2×C4—284no—
738C2×C4—284no—
739C2×C4—284no—
740C2×C4—284no—
741C2×C4C2×#115714yes—
742C2×C4C2×#115714yes—
743C2×C4C2×#115714yes—
744C2×C4C2×D4×D714yes—
745C7C2×#252111yescharacteristic, complemented, Sylow
746C22—144no—
747C22—144no—
748C22—144no—
749C22—282no—
750C22—2816no—
751C22—282no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—282no—
756C22—282no—
757C22—282no—
758C22—282no—
759C22—282no—
760C22—282no—
761C22—568no—
762C22#9017014yes—
763C22#9019814yes—
764C22#9021814yes—
765C22#9023914yes—
766C22#9024114yes—
767C22#9025914yes—
768C22#9027314yes—
769C22C22×#115711yescharacteristic
770C22C22×#115711yescharacteristic
771C22C22×#115711yescharacteristic
772C22C22×D4×D711yescharacteristic
773C22C2×#655111yescharacteristic
774C22C2×D7×#4111yescharacteristic
775C22C2×#655311yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—144no—
784C4—144no—
785C4—282no—
786C4—282no—
787C4—282no—
788C4—282no—
789C2—284no—
790C2—562no—
791C2#1173124118yesdirect product factor
792C2C2×#9017011yescharacteristic
793C2C2×#9019811yescharacteristic
794C2C2×#9021811yescharacteristic
795C2C2×#9023911yescharacteristic
796C2C2×#9024111yescharacteristic
797C2C2×#9025911yescharacteristic
798C2C2×#9027311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C4×C7×C4⋊C4C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×C4×C4⋊C4D7
hypocenterC7C2×#2521
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6439C2semidirect
3. C2×C4×C7×C4⋊C4C2semidirect
4. C2×#89764C2semidirect
5. C2×#89765C2semidirect
7. C2×#89751C2semidirect
8. C2×#89712C2semidirect
9. C2×#89712C2semidirect
10. C2×#89705C2semidirect
11. C2×C4×(C2×D7)⋊C4C2semidirect
12. #11731241C2direct (N × H)
14. C2×#89439C2semidirect
15. C2×#89418C2semidirect
16. C2×#89441C2semidirect
43. C2×#6439C22semidirect
46. C4×C7×C4⋊C4C22semidirect
57. #89765C22semidirect
58. #89764C22semidirect
60. #89751C22semidirect
61. #89712C22semidirect
62. #89712C22semidirect
63. C4×(C2×D7)⋊C4C22semidirect
64. #89705C22semidirect
65. #89441C22semidirect
66. #89439C22semidirect
68. #89418C22semidirect
167. C2×C4×C4⋊C4D7semidirect
312. C4×C4⋊C4C2×D7semidirect
644. C2×C7#2521semidirect
745. C7C2×#2521semidirect
791. C2#11731241direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64392
C22×#64382
C2×C4×C7×C4⋊C42
C2×#897642
C2×#897652
C2×#897632
C2×#897512
C2×#897122
C2×#897052
C2×C4×(C2×D7)⋊C42
#117312412
C2×#894372
C2×#894392
C2×#894182
C2×#894412
C2×#25217