Finite Group Databasebeta

← C2×#11733356 #13520366

Subgroups — C2×#11733356 #13520366

Order 1792.

2786 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×#6459C211yesmaximal, characteristic, complemented
2C22×#6446C211yesmaximal, characteristic
3C2×C7×#388C211yesmaximal, characteristic, complemented
4C2×#89744C211yesmaximal, characteristic, complemented
5C2×#89731C211yesmaximal, characteristic
6C2×#89721C211yesmaximal, characteristic, complemented
7C2×#89733C211yesmaximal, characteristic
8C2×#89719C211yesmaximal, characteristic, complemented
9C2×#89717C211yesmaximal, characteristic, complemented
10C2×#89700C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
12#11733356C2116yesmaximal, direct product factor
13C2×#89447C211yesmaximal, characteristic, complemented
14C2×#89432C211yesmaximal, characteristic, complemented
15C2×#89446C211yesmaximal, characteristic, complemented
16C2×#89428C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6459—28no—
43C2×#6459C2218yescomplemented
44C2×#6446—28no—
45C2×#6446C2218yes—
46C7×#388C2218yescomplemented
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#89744C2218yescomplemented
58#89733C2218yes—
59#89731C2218yes—
60#89721C2218yescomplemented
61#89719C2218yescomplemented
62#89717C2218yescomplemented
63C4×(C2×D7)⋊C4C2218yescomplemented
64#89700C2218yescomplemented
65#89447C2218yescomplemented
66#89446C2218yescomplemented
67#89432C2218yescomplemented
68#89428C2218yescomplemented
69C2×#2663—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C22×C22⋊D7—24no—
79C22×C22⋊D7—42no—
80C22×C22⋊D7—42no—
81C22×C22⋊D7C2314yes—
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C22×C4×D7—42no—
90C22×C4×D7—42no—
91C22×C4×D7D418yes—
92C22×C4×D7C2314yes—
93C22×Dic14—24no—
94C22×Dic14—42no—
95C22×Dic14—42no—
96C22×Dic14C2314yes—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4C2314yes—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4—42no—
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C42×C7—42no—
106C2×C42×C7C2314yes—
107C2×C22⋊Dic7—24no—
108C2×C22⋊Dic7—24no—
109C2×C22⋊Dic7—42no—
110C2×C22⋊Dic7C2314yes—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113C2×(C2×D7)⋊C4—24no—
114C2×(C2×D7)⋊C4—24no—
115C2×(C2×D7)⋊C4—24no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4—24no—
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—42no—
126C2×C4⋊Dic7C2314yes—
127C2×C4⋊Dic7C2314yes—
128C2×C4⋊Dic7C2314yes—
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#6459—232no—
142#6446—232no—
143C7×#95C2314yes—
144C7×#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#123—71no—
154C22×C22⋊Q8—71no—
155#2663—716no—
156C2×#400—71no—
157C2×#399—71no—
158C2×#397—71no—
159C2×#397—71no—
160C2×#395—71no—
161C2×#394—71no—
162C2×#394—71no—
163C2×#393—71no—
164C2×#389—71no—
165C2×#389—71no—
166C2×#388—71no—
167C2×#388D711yescharacteristic, complemented
168C2×C4×C22⋊C4—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7C2×D414yes—
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×C7C2×D414yes—
203C22×C4×C7#4114yes—
204C22×C4×C7C2412yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C2×C22⋊D7—28no—
211C2×C22⋊D7—44no—
212C2×C22⋊D7—44no—
213C2×C22⋊D7—416no—
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×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7C2×D414yes—
234C22×Dic7#4114yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C2×C4×D7—416no—
243C2×C4×D7—44no—
244C2×C4×D7—44no—
245C2×C4×D7C2×D4116yes—
246C2×Dic14—28no—
247C2×Dic14—44no—
248C2×Dic14—44no—
249C2×Dic14—416no—
250C7×C4⋊C4—28no—
251C7×C22⋊C4—28no—
252C7×C22⋊C4—28no—
253C7×C22⋊C4—44no—
254C42×C7—44no—
255C22⋊Dic7—28no—
256C22⋊Dic7—28no—
257C22⋊Dic7—44no—
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—
263C4⋊Dic7—28no—
264C4⋊Dic7—28no—
265C4⋊Dic7—44no—
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×#123—78no—
276C2×#123—148no—
277C2×C22⋊Q8—78no—
278C2×C22⋊Q8—148no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C42—71no—
300C22×C42C2×D711yescharacteristic
301#400—78no—
302#399—78no—
303#397—78no—
304#397—78no—
305#395—78no—
306#394—78no—
307#394—78no—
308#393—78no—
309#389—78no—
310#389—78no—
311#388—78no—
312#388C2×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×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—44no—
332C23×C7—44no—
333C23×C7—44no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7—44no—
337C23×C7—44no—
338C23×C7C22×D412yes—
339C23×C7C2×#4112yes—
340C23×C7C2×#4112yes—
341C23×C7H(5,𝔽2)12yes—
342C23×C7H(5,𝔽2)12yes—
343C23×C72−1+412yes—
344C23×C72−1+412yes—
345C23×C7C2511yescharacteristic
346C22×D7—28no—
347C22×D7—28no—
348C22×D7—28no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
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—22no—
363C2×C4×C7—22no—
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—44no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7—44no—
382C2×C4×C7C22×D414yes—
383C2×C4×C7C2×#4114yes—
384C22⋊D7—416no—
385C2×Dic7—28no—
386C2×Dic7—28no—
387C2×Dic7—22no—
388C2×Dic7—22no—
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—44no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7—44no—
411C2×Dic7C22×D414yes—
412C2×Dic7C2×#4114yes—
413C4×D7—416no—
414Dic14—416no—
415C25—71no—
416C25C22×D711yescharacteristic
417C22×Q8—74no—
418C22×Q8—144no—
419C22×Q8—282no—
420C22×Q8—282no—
421C22×D4—74no—
422C22×D4—144no—
423C22×D4—282no—
424C22×D4—282no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—78no—
428C23×C4—74no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—282no—
435C23×C4—282no—
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439C23×C4C22×D711yescharacteristic
440C23×C4C22×D711yescharacteristic
441C23×C4C22×D711yescharacteristic
442#123—1432no—
443C22⋊Q8—1432no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—74no—
446C2×C4⋊C4—74no—
447C2×C4⋊C4—74no—
448C2×C4⋊C4—74no—
449C2×C4⋊C4—74no—
450C2×C4⋊C4—74no—
451C2×C4⋊C4—74no—
452C2×C4⋊C4—74no—
453C2×C4⋊C4—144no—
454C2×C4⋊C4—144no—
455C2×C4⋊C4—144no—
456C2×C4⋊C4—144no—
457C2×C4⋊C4—144no—
458C2×C4⋊C4—144no—
459C2×C4⋊C4—282no—
460C2×C4⋊C4—282no—
461C2×C4⋊C4C22×D714yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—74no—
466C2×C22⋊C4—74no—
467C2×C22⋊C4—74no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—74no—
470C2×C22⋊C4—74no—
471C2×C22⋊C4—74no—
472C2×C22⋊C4—74no—
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—144no—
480C2×C22⋊C4—282no—
481C2×C22⋊C4C22×D714yes—
482C2×C22⋊C4C22×D714yes—
483C2×C22⋊C4C22×D714yes—
484C2×C42—42no—
485C2×C42—74no—
486C2×C42—282no—
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—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—42no—
503C22×C7—42no—
504C22×C7—42no—
505C22×C7—88no—
506C22×C7#53214yes—
507C22×C7#53414yes—
508C22×C7#53614yes—
509C22×C7#53914yes—
510C22×C7#53914yes—
511C22×C7#54214yes—
512C22×C7#54214yes—
513C22×C7C23×D411yescharacteristic
514C22×C7C22×#4111yescharacteristic
515C22×C7C22×#4111yescharacteristic
516C22×C7C2×H(5,𝔽2)11yescharacteristic
517C22×C7C2×H(5,𝔽2)11yescharacteristic
518C22×C7C2×2−1+411yescharacteristic
519C22×C7C2×2−1+411yescharacteristic
520C2×D7—24no—
521C2×D7—24no—
522C2×D7—24no—
523C2×D7—416no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C4×C7—24no—
529C4×C7—24no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534Dic7—24no—
535Dic7—24no—
536Dic7—42no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—74no—
549C24—72no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24C23×D712yes—
557C24C23×D711yescharacteristic
558C2×Q8—148no—
559C2×Q8—284no—
560C2×Q8—284no—
561C2×Q8—2816no—
562C2×D4—148no—
563C2×D4—284no—
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—74no—
583C22×C4—74no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—716no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
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—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—2816no—
612C22×C4—284no—
613C22×C4—284no—
614C22×C4#115714yes—
615C22×C4D4×D714yes—
616C22×C4C23×D712yes—
617C22×C4C23×D712yes—
618C22×C4C23×D712yes—
619C22×C4C23×D712yes—
620C22×C4C23×D712yes—
621C22×C4C23×D712yes—
622C4⋊C4—28no—
623C4⋊C4—148no—
624C4⋊C4—148no—
625C4⋊C4—148no—
626C4⋊C4—148no—
627C4⋊C4—148no—
628C4⋊C4—148no—
629C4⋊C4—284no—
630C4⋊C4—284no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—44no—
634C22⋊C4—148no—
635C22⋊C4—148no—
636C22⋊C4—148no—
637C22⋊C4—148no—
638C22⋊C4—148no—
639C22⋊C4—148no—
640C22⋊C4—148no—
641C22⋊C4—284no—
642C42—44no—
643C42—284no—
644C2×C7—82no—
645C2×C7#266318yescomplemented
646C2×C7C2×#53211yescharacteristic
647C2×C7C2×#53411yescharacteristic
648C2×C7C2×#53611yescharacteristic
649C2×C7C2×#53911yescharacteristic
650C2×C7C2×#53911yescharacteristic
651C2×C7C2×#54211yescharacteristic
652C2×C7C2×#54211yescharacteristic
653D7—44no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—74no—
669C23—148no—
670C23—148no—
671C23—142no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—148no—
678C23—284no—
679C23—284no—
680C23—284no—
681C23—284no—
682C23C2×#115712yes—
683C23C2×D4×D712yes—
684C23#654812yes—
685C23D7×#4112yes—
686C23#655312yes—
687C23#655412yes—
688C23#655412yes—
689C23C24×D711yescharacteristic
690Q8—2816no—
691D4—2816no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—74no—
715C2×C4—74no—
716C2×C4—148no—
717C2×C4—148no—
718C2×C4—142no—
719C2×C4—142no—
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—142no—
737C2×C4—2816no—
738C2×C4—284no—
739C2×C4—284no—
740C2×C4—284no—
741C2×C4—284no—
742C2×C4—284no—
743C2×C4C2×#115714yes—
744C2×C4C2×D4×D714yes—
745C7C2×#266311yescharacteristic, complemented, Sylow
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—88no—
754C22—144no—
755C22—144no—
756C22—144no—
757C22—282no—
758C22—282no—
759C22—282no—
760C22—2816no—
761C22—282no—
762C22#9022514yes—
763C22#9023914yes—
764C22#9025514yes—
765C22#9029614yes—
766C22#9035314yes—
767C22#9036614yes—
768C22#9039814yes—
769C22C22×#115711yescharacteristic
770C22C22×D4×D711yescharacteristic
771C22C2×#654811yescharacteristic
772C22C2×D7×#4111yescharacteristic
773C22C2×#655311yescharacteristic
774C22C2×#655411yescharacteristic
775C22C2×#655411yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—144no—
783C4—144no—
784C4—282no—
785C4—282no—
786C4—282no—
787C4—282no—
788C4—282no—
789C2—82no—
790C2—284no—
791C2#1173335618yesdirect product factor
792C2C2×#9022511yescharacteristic
793C2C2×#9025511yescharacteristic
794C2C2×#9023911yescharacteristic
795C2C2×#9029611yescharacteristic
796C2C2×#9035311yescharacteristic
797C2C2×#9036611yescharacteristic
798C2C2×#9039811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#388D7
hypocenterC7C2×#2663
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#6459C2semidirect
3. C2×C7×#388C2semidirect
4. C2×#89744C2semidirect
6. C2×#89721C2semidirect
8. C2×#89719C2semidirect
9. C2×#89717C2semidirect
10. C2×#89700C2semidirect
11. C2×C4×(C2×D7)⋊C4C2semidirect
12. #11733356C2direct (N × H)
13. C2×#89447C2semidirect
14. C2×#89432C2semidirect
15. C2×#89446C2semidirect
16. C2×#89428C2semidirect
43. C2×#6459C22semidirect
46. C7×#388C22semidirect
57. #89744C22semidirect
60. #89721C22semidirect
61. #89719C22semidirect
62. #89717C22semidirect
63. C4×(C2×D7)⋊C4C22semidirect
64. #89700C22semidirect
65. #89447C22semidirect
66. #89446C22semidirect
67. #89432C22semidirect
68. #89428C22semidirect
167. C2×#388D7semidirect
312. #388C2×D7semidirect
645. C2×C7#2663semidirect
745. C7C2×#2663semidirect
791. C2#11733356direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64592
C22×#64462
C2×C7×#3882
C2×#897442
C2×#897312
C2×#897212
C2×#897332
C2×#897192
C2×#897172
C2×#897002
C2×C4×(C2×D7)⋊C42
#117333562
C2×#894472
C2×#894322
C2×#894462
C2×#894282
C2×#26637