Finite Group Databasebeta

← C2×#11732824 #13520205

Subgroups — C2×#11732824 #13520205

Order 1792.

2958 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
1C22×#6459C211yesmaximal, characteristic, complemented
2C22×C4×D28C211yesmaximal, characteristic
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×#89763C211yesmaximal, characteristic
5C2×#89761C211yesmaximal, characteristic, complemented
6C2×#89756C211yesmaximal, characteristic, complemented
7C2×#89705C211yesmaximal, characteristic, complemented
8#11732824C2116yesmaximal, direct product factor
9C2×#89447C211yesmaximal, characteristic, complemented
10C2×#89447C211yesmaximal, characteristic, complemented
11C2×#89445C211yesmaximal, characteristic, complemented
12C2×#89440C211yesmaximal, characteristic, complemented
13C2×#89436C211yesmaximal, characteristic, complemented
14C2×#89446C211yesmaximal, characteristic, complemented
15C2×#89428C211yesmaximal, characteristic, complemented
16C2×#89444C211yesmaximal, characteristic
17C23×D28C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
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×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C2×#6459—28no—
41C2×#6459C2218yescomplemented
42C2×C4×D28—28no—
43C2×C4×D28C2218yes—
44C7×#387C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
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#89763C2218yes—
58#89761C2218yescomplemented
59#89756C2218yescomplemented
60#89705C2218yescomplemented
61#89447C2218yescomplemented
62#89447C2218yescomplemented
63#89446C2218yescomplemented
64#89445C2218yescomplemented
65#89444C2218yes—
66#89440C2218yescomplemented
67#89436C2218yescomplemented
68#89428C2218yescomplemented
69C2×#2638—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—24no—
88C22×D28C2314yes—
89C22×C4×D7—24no—
90C22×C4×D7—42no—
91C22×C4×D7—42no—
92C22×C4×D7—42no—
93C22×C4×D7—42no—
94C22×C4×D7D418yes—
95C22×C4×D7C2314yes—
96C22×C4×D7C2314yes—
97C22×Dic14—24no—
98C22×Dic14—42no—
99C22×Dic14—42no—
100C22×Dic14C2314yes—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—24no—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C4⋊C4C2314yes—
105C2×C42×C7—24no—
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—42no—
114C2×(C2×D7)⋊C4—42no—
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×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×C4⋊Dic7—24no—
128C2×C4⋊Dic7—42no—
129C2×C4⋊Dic7C2314yes—
130C2×C4⋊Dic7C2314yes—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—24no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139#6459—232no—
140C4×D28—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×C22⋊Q8—71no—
154C22×C4×D4—71no—
155#2638—716no—
156C2×#398—71no—
157C2×#397—71no—
158C2×#397—71no—
159C2×#397—71no—
160C2×#395—71no—
161C2×#394—71no—
162C2×#394—71no—
163C2×#393—71no—
164C2×#387—71no—
165C2×#387D711yescharacteristic, complemented
166C2×#385—71no—
167C2×#385—71no—
168C2×#381—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×D7C2×D414yes—
183C23×D7#4114yes—
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×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7C2×D414yes—
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×Dic7—22no—
231C22×Dic7C2×D414yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C2×D28—232no—
239C2×D28—28no—
240C2×D28—28no—
241C2×D28—28no—
242C2×C4×D7—28no—
243C2×C4×D7—416no—
244C2×C4×D7—44no—
245C2×C4×D7—44no—
246C2×C4×D7—44no—
247C2×C4×D7—44no—
248C2×C4×D7—416no—
249C2×C4×D7C2×D4116yes—
250C2×Dic14—28no—
251C2×Dic14—44no—
252C2×Dic14—44no—
253C2×Dic14—416no—
254C7×C4⋊C4—28no—
255C7×C4⋊C4—28no—
256C42×C7—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—44no—
264(C2×D7)⋊C4—44no—
265(C2×D7)⋊C4—44no—
266(C2×D7)⋊C4—44no—
267C4⋊Dic7—28no—
268C4⋊Dic7—44no—
269Dic7⋊C4—28no—
270Dic7⋊C4—28no—
271Dic7⋊C4—28no—
272Dic7⋊C4—44no—
273C23×Q8—71no—
274C23×D4—71no—
275C24×C4—71no—
276C24×C4—71no—
277C2×C22⋊Q8—78no—
278C2×C22⋊Q8—148no—
279C2×C4×D4—78no—
280C2×C4×D4—148no—
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×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⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C42C2×D711yescharacteristic
300#398—78no—
301#397—78no—
302#397—78no—
303#397—78no—
304#395—78no—
305#394—78no—
306#394—78no—
307#393—78no—
308#387—78no—
309#387C2×D718yescomplemented
310#385—78no—
311#385—78no—
312#381—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×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C2×#95C2×D711yescharacteristic
324C2×#95C2×D711yescharacteristic
325C23×C7C22×D412yes—
326C23×C7C2×#4112yes—
327C23×C7C2×#4112yes—
328C23×C7H(5,𝔽2)12yes—
329C23×C7H(5,𝔽2)12yes—
330C23×C72−1+412yes—
331C23×C72−1+412yes—
332C23×C7C2511yescharacteristic
333C22×D7—28no—
334C22×D7—28no—
335C22×D7—28no—
336C22×D7—28no—
337C22×D7—28no—
338C22×D7—28no—
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—22no—
349C22×D7—22no—
350C22×D7—22no—
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—
360C22×D7C2×#4114yes—
361C2×C4×C7—28no—
362C2×C4×C7—28no—
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—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—44no—
383C2×C4×C7—44no—
384C2×C4×C7—44no—
385C2×C4×C7—44no—
386C2×C4×C7—44no—
387C2×C4×C7C22×D414yes—
388C2×C4×C7C2×#4114yes—
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—22no—
407C2×Dic7—44no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7—44no—
411C2×Dic7—44no—
412C2×Dic7C22×D414yes—
413D28—232no—
414C4×D7—416no—
415C4×D7—416no—
416Dic14—416no—
417C25—71no—
418C25—71no—
419C22×Q8—74no—
420C22×Q8—144no—
421C22×Q8—282no—
422C22×Q8—282no—
423C22×D4—74no—
424C22×D4—144no—
425C22×D4—144no—
426C22×D4—144no—
427C23×C4—71no—
428C23×C4—78no—
429C23×C4—74no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—74no—
436C23×C4—144no—
437C23×C4—282no—
438C23×C4—282no—
439C23×C4—282no—
440C23×C4—282no—
441C23×C4C22×D711yescharacteristic
442C23×C4C22×D711yescharacteristic
443C23×C4C22×D711yescharacteristic
444C23×C4C22×D711yescharacteristic
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C23×C4C22×D711yescharacteristic
448C22⋊Q8—1432no—
449C4×D4—1432no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
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—144no—
459C2×C4⋊C4—144no—
460C2×C4⋊C4—144no—
461C2×C4⋊C4—144no—
462C2×C4⋊C4—282no—
463C2×C4⋊C4—282no—
464C2×C4⋊C4C22×D714yes—
465C2×C4⋊C4C22×D714yes—
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—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—144no—
480C2×C22⋊C4—144no—
481C2×C22⋊C4—144no—
482C2×C22⋊C4—282no—
483C2×C22⋊C4—282no—
484C2×C22⋊C4—282no—
485C2×C22⋊C4—282no—
486C2×C42—24no—
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—
498#95C22×D714yes—
499#95C22×D714yes—
500C22×C7#52514yes—
501C22×C7#53414yes—
502C22×C7#53614yes—
503C22×C7#53914yes—
504C22×C7#53914yes—
505C22×C7#54214yes—
506C22×C7#54214yes—
507C22×C7C23×D411yescharacteristic
508C22×C7C22×#4111yescharacteristic
509C22×C7C22×#4111yescharacteristic
510C22×C7C2×H(5,𝔽2)11yescharacteristic
511C22×C7C2×H(5,𝔽2)11yescharacteristic
512C22×C7C2×2−1+411yescharacteristic
513C22×C7C2×2−1+411yescharacteristic
514C2×D7—24no—
515C2×D7—24no—
516C2×D7—24no—
517C2×D7—24no—
518C2×D7—24no—
519C2×D7—24no—
520C2×D7—416no—
521C2×D7—416no—
522C2×D7—42no—
523C2×D7—42no—
524C2×D7—42no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C2×D7—42no—
529C2×D7—42no—
530C4×C7—24no—
531C4×C7—24no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537Dic7—24no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—74no—
544C24—74no—
545C24—72no—
546C24—72no—
547C24—142no—
548C24—142no—
549C24—142no—
550C24—142no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24—142no—
557C24—142no—
558C24—142no—
559C24C23×D711yescharacteristic
560C2×Q8—148no—
561C2×Q8—284no—
562C2×Q8—284no—
563C2×Q8—2816no—
564C2×D4—148no—
565C2×D4—148no—
566C2×D4—1432no—
567C2×D4—148no—
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—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—74no—
588C22×C4—72no—
589C22×C4—716no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—72no—
594C22×C4—72no—
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—142no—
612C22×C4—148no—
613C22×C4—2816no—
614C22×C4—284no—
615C22×C4—284no—
616C22×C4—284no—
617C22×C4—284no—
618C22×C4—2816no—
619C22×C4#115714yes—
620C22×C4D4×D714yes—
621C22×C4C23×D712yes—
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—148no—
631C4⋊C4—148no—
632C4⋊C4—148no—
633C4⋊C4—148no—
634C4⋊C4—284no—
635C4⋊C4—284no—
636C22⋊C4—148no—
637C22⋊C4—148no—
638C22⋊C4—148no—
639C22⋊C4—148no—
640C22⋊C4—148no—
641C22⋊C4—148no—
642C22⋊C4—284no—
643C22⋊C4—284no—
644C22⋊C4—284no—
645C22⋊C4—284no—
646C42—28no—
647C2×C7#263818yescomplemented
648C2×C7C2×#52511yescharacteristic
649C2×C7C2×#53411yescharacteristic
650C2×C7C2×#53611yescharacteristic
651C2×C7C2×#53911yescharacteristic
652C2×C7C2×#53911yescharacteristic
653C2×C7C2×#54211yescharacteristic
654C2×C7C2×#54211yescharacteristic
655D7—44no—
656D7—44no—
657C23—74no—
658C23—74no—
659C23—148no—
660C23—148no—
661C23—148no—
662C23—148no—
663C23—148no—
664C23—148no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—142no—
673C23—142no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—284no—
678C23—284no—
679C23—284no—
680C23—284no—
681C23—284no—
682C23—284no—
683C23—284no—
684C23—284no—
685C23C2×#115712yes—
686C23C2×D4×D712yes—
687C23#655112yes—
688C23D7×#4112yes—
689C23#655312yes—
690C23#655312yes—
691C23#655412yes—
692C23C24×D711yescharacteristic
693Q8—2816no—
694D4—1432no—
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—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—74no—
722C2×C4—148no—
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×#115714yes—
748C2×C4C2×D4×D714yes—
749C7C2×#263811yescharacteristic, complemented, Sylow
750C22—144no—
751C22—144no—
752C22—144no—
753C22—144no—
754C22—144no—
755C22—144no—
756C22—282no—
757C22—282no—
758C22—282no—
759C22—2816no—
760C22—2816no—
761C22—282no—
762C22—282no—
763C22—282no—
764C22—282no—
765C22—282no—
766C22#9022514yes—
767C22#9023814yes—
768C22#9027314yes—
769C22#9031914yes—
770C22#9034414yes—
771C22#9038314yes—
772C22#9039814yes—
773C22C22×#115711yescharacteristic
774C22C22×D4×D711yescharacteristic
775C22C2×#655111yescharacteristic
776C22C2×D7×#4111yescharacteristic
777C22C2×#655311yescharacteristic
778C22C2×#655311yescharacteristic
779C22C2×#655411yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—144no—
788C4—282no—
789C4—282no—
790C4—282no—
791C4—282no—
792C4—282no—
793C2—284no—
794C2—284no—
795C2#1173282418yesdirect product factor
796C2C2×#9022511yescharacteristic
797C2C2×#9023811yescharacteristic
798C2C2×#9027311yescharacteristic
799C2C2×#9031911yescharacteristic
800C2C2×#9034411yescharacteristic
801C2C2×#9038311yescharacteristic
802C2C2×#9039811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#387C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC2×#387D7
hypocenterC7C2×#2638
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#6459C2semidirect
3. C2×C7×#387C2semidirect
5. C2×#89761C2semidirect
6. C2×#89756C2semidirect
7. C2×#89705C2semidirect
8. #11732824C2direct (N × H)
9. C2×#89447C2semidirect
10. C2×#89447C2semidirect
11. C2×#89445C2semidirect
12. C2×#89440C2semidirect
13. C2×#89436C2semidirect
14. C2×#89446C2semidirect
15. C2×#89428C2semidirect
41. C2×#6459C22semidirect
44. C7×#387C22semidirect
58. #89761C22semidirect
59. #89756C22semidirect
60. #89705C22semidirect
61. #89447C22semidirect
62. #89447C22semidirect
63. #89446C22semidirect
64. #89445C22semidirect
66. #89440C22semidirect
67. #89436C22semidirect
68. #89428C22semidirect
165. C2×#387D7semidirect
309. #387C2×D7semidirect
647. C2×C7#2638semidirect
749. C7C2×#2638semidirect
795. C2#11732824direct (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×C4×D282
C2×C7×#3872
C2×#897632
C2×#897612
C2×#897562
C2×#897052
#117328242
C2×#894472
C2×#894452
C2×#894402
C2×#894362
C2×#894462
C2×#894282
C2×#894442
C2×#26387