Finite Group Databasebeta

← #13526759

Subgroups — #13526759

Order 1792.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90335C212yesmaximal, complemented
2C7×#2440C211yesmaximal, characteristic, complemented
3#11740702C211yesmaximal, characteristic, complemented
4#11740696C211yesmaximal, characteristic, complemented
5#11740214C212yesmaximal, complemented
6#11739638C211yesmaximal, characteristic, complemented
7C2×#89760C211yesmaximal, characteristic, complemented
8#11735283C212yesmaximal, complemented
9#11735234C212yesmaximal, complemented
10#11734654C212yesmaximal, complemented
11#11734632C212yesmaximal, complemented
12#11733731C211yesmaximal, characteristic, complemented
13#11733665C211yesmaximal, characteristic, complemented
14#11733636C211yesmaximal, characteristic, complemented
15#11733449C211yesmaximal, characteristic, complemented
16#11732050C212yesmaximal, complemented
17#11732037C212yesmaximal, complemented
18#11731820C211yesmaximal, characteristic, complemented
19#11731778C211yesmaximal, characteristic, complemented
20#11731461C211yesmaximal, characteristic, complemented
21#11731310C211yesmaximal, characteristic, complemented
22#11731032C211yesmaximal, characteristic, complemented
23C4×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
24C23×D28C2211yescharacteristic
25C2×C7×C4⋊Q8C2211yescharacteristic, complemented
26C2×C7×C22⋊Q8C2212yes—
27C22×C7×C4⋊C4C2211yescharacteristic
28C2×#6510C2212yescomplemented
29C2×#6510C2212yescomplemented
30C2×#6510C2212yescomplemented
31C2×#6493C2212yes—
32C2×#6493C2211yescharacteristic
33C2×C4×C22⋊D7C2211yescharacteristic
34C22×(C2×D7)⋊C4C2212yes—
35C22×(C2×D7)⋊C4C2212yes—
36C22×C4×Dic7C2211yescharacteristic
37#90335—216no—
38C2×#6461C2212yescomplemented
39C2×#6461C2212yescomplemented
40C2×#6458C2211yescharacteristic
41C2×#6458C2211yescharacteristic
42C2×#6458C2212yescomplemented
43C2×#6458C2212yescomplemented
44C2×#6458C2212yescomplemented
45C2×#6458C2211yescharacteristic, complemented
46C2×#6457C2212yescomplemented
47C2×#6457C2212yescomplemented
48C2×#6456C2211yescharacteristic, complemented
49C2×#6445C2212yes—
50C2×#6445C2212yes—
51C2×#6445C2212yes—
52C2×(C22⋊D7)⋊C4C2212yes—
53C2×(C22⋊D7)⋊C4C2211yescharacteristic
54C2×(C22⋊D7)⋊C4C2211yescharacteristic
55C2×#6437C2211yescharacteristic
56C2×#6437C2211yescharacteristic
57C2×C42×D7C2211yescharacteristic, complemented
58C7×#398C2212yescomplemented
59C7×#395C2212yescomplemented
60C7×#389C2211yescharacteristic, complemented
61C7×#389C2211yescharacteristic, complemented
62C7×#385C2212yes—
63C7×#384C2211yescharacteristic, complemented
64C7×#380C2211yescharacteristic
65C4×C7×C22⋊C4C2211yescharacteristic
66#90003C2212yescomplemented
67#89985C2212yes—
68#89766C2212yescomplemented
69#89766C2212yescomplemented
70#89765C2212yescomplemented
71#89763C2212yescomplemented
72#89763C2212yescomplemented
73#89763C2212yescomplemented
74#89763C2212yescomplemented
75#89762C2212yescomplemented
76#89762C2212yescomplemented
77#89762C2212yescomplemented
78#89762C2212yescomplemented
79#89760C2211yescharacteristic
80#89760C2211yescharacteristic
81#89760C2211yescharacteristic
82#89760C2211yescharacteristic
83#89760C2211yescharacteristic
84#89760C2212yes—
85#89760C2211yescharacteristic
86#89760C2212yes—
87#89760C2212yescomplemented
88#89760C2212yescomplemented
89#89760C2211yescharacteristic, complemented
90#89760C2211yescharacteristic, complemented
91#89760C2212yescomplemented
92#89760C2212yescomplemented
93#89759C2211yescharacteristic, complemented
94#89757C2211yescharacteristic, complemented
95C4⋊C4×Dic7C2211yescharacteristic, complemented
96#89745C2211yescharacteristic, complemented
97#89730C2212yes—
98#89727C2212yes—
99C22⋊C4×Dic7C2211yescharacteristic
100C22⋊C4×Dic7C2211yescharacteristic
101#89711C2211yescharacteristic
102#89711C2211yescharacteristic
103C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
104C4×Dic7⋊C4C2211yescharacteristic, complemented
105C42×Dic7C2211yescharacteristic, complemented
106#89444C2212yes—
107#89444C2212yescomplemented
108#89443C2212yes—
109#89443C2212yes—
110#89443C2212yes—
111#89443C2212yescomplemented
112#89442C2212yescomplemented
113#89441C2212yescomplemented
114#89441C2212yescomplemented
115#89441C2212yescomplemented
116#89438C2211yescharacteristic, complemented
117#89438C2212yescomplemented
118#89438C2211yescharacteristic, complemented
119#89437C2212yescomplemented
120#89437C2212yescomplemented
121#89437C2212yescomplemented
122#89421C2211yescharacteristic, complemented
123#89421C2211yescharacteristic, complemented
124#35007—71nomaximal, Sylow
125C24×D7C2312yes—
126C22×C7×Q8C2312yes—
127C23×C4×C7C2311yescharacteristic
128C23×C4×C7C2312yes—
129C22×C22⋊D7C2312yes—
130C22×C22⋊D7C2311yescharacteristic
131C23×Dic7C2311yescharacteristic
132C23×Dic7C2311yescharacteristic
133C22×D28—24no—
134C22×D28—42no—
135C22×D28—42no—
136C22×D28C2311yescharacteristic
137C22×D28C2311yescharacteristic
138C22×D28C2311yescharacteristic
139C22×D28C2312yes—
140C22×D28C2312yes—
141C22×D28C2312yes—
142C22×D28C2312yes—
143C22×D28C2312yes—
144C22×D28C2312yes—
145C22×D28C2312yes—
146C22×D28C2312yes—
147C22×C4×D7C2311yescharacteristic
148C22×C4×D7C2311yescharacteristic
149C22×C4×D7C2312yes—
150C22×C4×D7C2311yescharacteristic
151C7×C4⋊Q8—42no—
152C7×C22⋊Q8—28no—
153C2×C7×C4⋊C4—42no—
154C2×C7×C4⋊C4C2311yescharacteristic
155C2×C7×C4⋊C4C2312yes—
156C2×C7×C4⋊C4C2311yescharacteristic
157C2×C7×C4⋊C4C2312yes—
158C2×C7×C4⋊C4C2312yes—
159C2×C7×C4⋊C4C2311yescharacteristic
160C2×C7×C4⋊C4C2311yescharacteristic
161C2×C7×C4⋊C4C2312yes—
162C2×C7×C4⋊C4C2312yes—
163C2×C7×C4⋊C4C2312yes—
164C2×C7×C22⋊C4C2312yes—
165C2×C7×C22⋊C4C2311yescharacteristic
166C2×C7×C22⋊C4C2311yescharacteristic
167C2×C42×C7C2311yescharacteristic
168C2×C42×C7C2311yescharacteristic
169C2×C22⋊Dic7C2311yescharacteristic
170#6510—28no—
171#6510—28no—
172#6510—44no—
173#6493—24no—
174#6493—28no—
175C4×C22⋊D7—24no—
176C2×(C2×D7)⋊C4—28no—
177C2×(C2×D7)⋊C4—44no—
178C2×(C2×D7)⋊C4C2312yes—
179C2×(C2×D7)⋊C4C2311yescharacteristic
180C2×(C2×D7)⋊C4C2312yes—
181C2×(C2×D7)⋊C4C2312yes—
182C2×(C2×D7)⋊C4C2312yes—
183C2×(C2×D7)⋊C4C2312yes—
184C2×(C2×D7)⋊C4C2312yes—
185C2×(C2×D7)⋊C4C2312yes—
186C2×(C2×D7)⋊C4C2312yes—
187C2×(C2×D7)⋊C4C2312yes—
188C2×(C2×D7)⋊C4C2312yes—
189C2×(C2×D7)⋊C4C2312yes—
190C2×(C2×D7)⋊C4C2312yes—
191C2×(C2×D7)⋊C4C2312yes—
192C2×(C2×D7)⋊C4C2312yes—
193C2×(C2×D7)⋊C4C2312yes—
194C2×(C2×D7)⋊C4C2312yes—
195C2×(C2×D7)⋊C4C2311yescharacteristic
196C2×(C2×D7)⋊C4C2312yes—
197C2×(C2×D7)⋊C4C2312yes—
198C2×(C2×D7)⋊C4C2312yes—
199C2×(C2×D7)⋊C4C2312yes—
200C2×(C2×D7)⋊C4C2312yes—
201C2×(C2×D7)⋊C4C2312yes—
202C2×(C2×D7)⋊C4C2312yes—
203C2×(C2×D7)⋊C4C2312yes—
204C2×(C2×D7)⋊C4C2312yes—
205C2×(C2×D7)⋊C4C2312yes—
206C2×(C2×D7)⋊C4C2311yescharacteristic
207C2×C4⋊Dic7C2312yes—
208C2×C4⋊Dic7C2311yescharacteristic
209C2×Dic7⋊C4C2311yescharacteristic
210C2×Dic7⋊C4C2312yes—
211C2×Dic7⋊C4C2311yescharacteristic
212C2×Dic7⋊C4C2311yescharacteristic
213C2×C4×Dic7—42no—
214C2×C4×Dic7C2311yescharacteristic
215C2×C4×Dic7C2311yescharacteristic
216C2×C4×Dic7C2312yes—
217C2×C4×Dic7C2311yescharacteristic
218C2×C4×Dic7C2311yescharacteristic
219C2×C4×Dic7C2311yescharacteristic
220C2×C4×Dic7C2311yescharacteristic
221C2×C4×Dic7C2311yescharacteristic
222C2×C4×Dic7C2311yescharacteristic
223C2×C4×Dic7C2311yescharacteristic
224C2×C4×Dic7C2311yescharacteristic
225C2×C4×Dic7C2311yescharacteristic
226#6461—28no—
227#6461—28no—
228#6458—28no—
229#6458—28no—
230#6458—44no—
231#6458—42no—
232#6458—42no—
233#6458—42no—
234#6457—28no—
235#6457—28no—
236#6456—42no—
237#6445—28no—
238#6445—28no—
239#6445—28no—
240(C22⋊D7)⋊C4—28no—
241(C22⋊D7)⋊C4—24no—
242(C22⋊D7)⋊C4D418yescomplemented
243#6437—42no—
244#6437—42no—
245C42×D7—42no—
246C7×#95C2311yescharacteristic
247C7×#95C2311yescharacteristic
248C7×#95C2312yes—
249C7×#95C2312yes—
250C7×#95C2312yes—
251C7⋊#95C2311yescharacteristic
252C7⋊#95C2311yescharacteristic
253C7⋊#95C2311yescharacteristic
254C7⋊#95C2312yes—
255C7⋊#95C2311yescharacteristic
256C7⋊#95C2312yes—
257C7⋊#95C2312yes—
258C7⋊#95C2312yes—
259C2×#538—72no—
260#2860—71no—
261#2858—71no—
262#2856—71no—
263#2854—71no—
264#2662—72no—
265#2661—72no—
266#2555—72no—
267#2554—72no—
268#2512—71no—
269#2491—71no—
270#2472—72no—
271#2445—71no—
272#2440D711yescharacteristic, complemented
273#2433—71no—
274#2428—71no—
275#2424—72no—
276#2416—71no—
277#2408—71no—
278#2321—72no—
279C4×#121—71no—
280C2×#390—71no—
281C42×D4—71no—
282C24×C7C2411yescharacteristic
283C23×D7—24no—
284C23×D7—24no—
285C23×D7—24no—
286C23×D7—42no—
287C23×D7—42no—
288C23×D7—42no—
289C23×D7—42no—
290C23×D7C2412yes—
291C23×D7C2412yes—
292C23×D7C2412yes—
293C23×D7C2411yescharacteristic
294C2×C7×Q8—24no—
295C2×C7×Q8—42no—
296C2×C7×Q8—42no—
297C22×C4×C7—22no—
298C22×C4×C7—22no—
299C22×C4×C7—24no—
300C22×C4×C7—42no—
301C22×C4×C7—42no—
302C22×C4×C7#4114yes—
303C22×C4×C7C2412yes—
304C22×C4×C7C2412yes—
305C22×C4×C7C2412yes—
306C22×C4×C7C2412yes—
307C22×C4×C7C2411yescharacteristic
308C22×C4×C7C2411yescharacteristic
309C22×C4×C7C2411yescharacteristic
310C22×C4×C7C2411yescharacteristic
311C22×C4×C7C2411yescharacteristic
312C22×C4×C7C2411yescharacteristic
313C2×C22⋊D7—22no—
314C2×C22⋊D7—22no—
315C2×C22⋊D7—24no—
316C2×C22⋊D7—24no—
317C2×C22⋊D7—24no—
318C2×C22⋊D7C2×D414yes—
319C22×Dic7—22no—
320C22×Dic7—22no—
321C22×Dic7—41no—
322C22×Dic7—41no—
323C22×Dic7—41no—
324C22×Dic7C2×D414yes—
325C22×Dic7C2411yescharacteristic
326C22×Dic7C2411yescharacteristic
327C22×Dic7C2411yescharacteristic
328C22×Dic7C2412yes—
329C22×Dic7C2411yescharacteristic
330C22×Dic7C2411yescharacteristic
331C22×Dic7C2411yescharacteristic
332C22×Dic7C2411yescharacteristic
333C2×D28—22no—
334C2×D28—24no—
335C2×D28—22no—
336C2×D28—22no—
337C2×D28—22no—
338C2×D28—22no—
339C2×D28—22no—
340C2×D28—22no—
341C2×D28—22no—
342C2×D28—22no—
343C2×D28—24no—
344C2×D28—24no—
345C2×D28—24no—
346C2×D28—24no—
347C2×D28—24no—
348C2×D28—24no—
349C2×D28—24no—
350C2×D28—42no—
351C2×D28—42no—
352C2×D28—416no—
353C2×D28—42no—
354C2×D28—42no—
355C2×D28—42no—
356C2×D28—42no—
357C2×D28—42no—
358C2×D28—42no—
359C2×D28—42no—
360C2×D28—42no—
361C2×D28—42no—
362C2×D28—42no—
363C2×D28—42no—
364C2×D28—42no—
365C2×D28—42no—
366C2×D28—42no—
367C2×C4×D7—22no—
368C2×C4×D7—22no—
369C2×C4×D7—22no—
370C2×C4×D7—22no—
371C2×C4×D7—22no—
372C2×C4×D7—24no—
373C2×C4×D7—41no—
374C2×C4×D7—41no—
375C2×C4×D7—41no—
376C2×C4×D7—42no—
377C2×C4×D7—42no—
378C2×C4×D7C2×D414yescomplemented
379C7×C4⋊C4—24no—
380C7×C4⋊C4—24no—
381C7×C4⋊C4—24no—
382C7×C4⋊C4—22no—
383C7×C4⋊C4—22no—
384C7×C4⋊C4—22no—
385C7×C4⋊C4—22no—
386C7×C4⋊C4—42no—
387C7×C4⋊C4—42no—
388C7×C4⋊C4—42no—
389C7×C22⋊C4—24no—
390C7×C22⋊C4C2×D414yes—
391C7×C22⋊C4#4114yes—
392C42×C7—22no—
393C42×C7—22no—
394C22⋊Dic7—22no—
395(C2×D7)⋊C4—24no—
396(C2×D7)⋊C4—24no—
397(C2×D7)⋊C4—24no—
398(C2×D7)⋊C4—22no—
399(C2×D7)⋊C4—24no—
400(C2×D7)⋊C4—24no—
401(C2×D7)⋊C4—22no—
402(C2×D7)⋊C4—24no—
403(C2×D7)⋊C4—24no—
404(C2×D7)⋊C4—24no—
405(C2×D7)⋊C4—24no—
406(C2×D7)⋊C4—24no—
407(C2×D7)⋊C4—24no—
408(C2×D7)⋊C4—24no—
409(C2×D7)⋊C4—24no—
410(C2×D7)⋊C4—24no—
411(C2×D7)⋊C4—24no—
412(C2×D7)⋊C4—24no—
413(C2×D7)⋊C4—24no—
414(C2×D7)⋊C4—42no—
415(C2×D7)⋊C4—42no—
416(C2×D7)⋊C4—42no—
417(C2×D7)⋊C4—42no—
418(C2×D7)⋊C4—42no—
419(C2×D7)⋊C4—42no—
420(C2×D7)⋊C4—42no—
421(C2×D7)⋊C4—42no—
422(C2×D7)⋊C4—42no—
423(C2×D7)⋊C4C2×D414yescomplemented
424C4⋊Dic7—22no—
425C4⋊Dic7—24no—
426Dic7⋊C4—22no—
427Dic7⋊C4—22no—
428Dic7⋊C4—24no—
429Dic7⋊C4C2×D414yescomplemented
430C4×Dic7—22no—
431C4×Dic7—22no—
432C4×Dic7—22no—
433C4×Dic7—22no—
434C4×Dic7—24no—
435C4×Dic7—22no—
436C4×Dic7—41no—
437C4×Dic7—41no—
438C4×Dic7—41no—
439C4×Dic7—41no—
440C4×Dic7—41no—
441C4×Dic7C2×D414yescomplemented
442C23×D4—71no—
443#538—1416no—
444C2×C4⋊Q8C2×D711yescharacteristic, complemented
445C2×#127—71no—
446C2×#127—71no—
447C2×#126—72no—
448C2×#126—72no—
449C2×#124—72no—
450C2×#124—72no—
451C2×#124—72no—
452C2×#123—72no—
453C2×#123—72no—
454C2×C22⋊Q8C2×D712yes—
455C2×#121—72no—
456C2×#121—71no—
457C2×#121—72no—
458C2×#121—72no—
459C2×#121—71no—
460C2×#121—71no—
461C2×#121—71no—
462C2×#121—72no—
463C2×#120—72no—
464C2×#120—72no—
465C2×#120—72no—
466C2×C4×D4—71no—
467C2×C4×D4—71no—
468C2×C4×D4—71no—
469C2×C4×D4—72no—
470C2×C4×D4—71no—
471C22×C4⋊C4C2×D711yescharacteristic
472C22×C22⋊C4—72no—
473C22×C22⋊C4—72no—
474C22×C42—71no—
475C22×C42—71no—
476#398C2×D712yescomplemented
477#397—72no—
478#396—72no—
479#396—72no—
480#395C2×D712yescomplemented
481#394—72no—
482#394—72no—
483#394—72no—
484#394—72no—
485#394—72no—
486#394—72no—
487#393—72no—
488#392—72no—
489#392—72no—
490#392—72no—
491#392—72no—
492#390—72no—
493#390—72no—
494#390—71no—
495#390—71no—
496#390—71no—
497#390—72no—
498#390—71no—
499#390—71no—
500#390—72no—
501#390—71no—
502#390—72no—
503#390—71no—
504#390—71no—
505#390—72no—
506#390—71no—
507#390—71no—
508#389—71no—
509#389—71no—
510#389C2×D711yescharacteristic, complemented
511#389C2×D711yescharacteristic, complemented
512#388—72no—
513#388—72no—
514#388—72no—
515#388—72no—
516#388—72no—
517#388—72no—
518#388—72no—
519#388—72no—
520#386—72no—
521#386—72no—
522#386—72no—
523#386—72no—
524#386—72no—
525#385C2×D712yes—
526#384C2×D711yescharacteristic, complemented
527#380—71no—
528#380C2×D711yescharacteristic
529#379—72no—
530C4×C4⋊C4—71no—
531C4×C4⋊C4—71no—
532C4×C4⋊C4—71no—
533C4×C4⋊C4—71no—
534C4×C22⋊C4—71no—
535C4×C22⋊C4—71no—
536C4×C22⋊C4—71no—
537C4×C22⋊C4—71no—
538C4×C22⋊C4—71no—
539C4×C22⋊C4—72no—
540C4×C22⋊C4C2×D711yescharacteristic
541C43—71no—
542C23×C7—21no—
543C23×C7—21no—
544C23×C7—21no—
545C23×C7—21no—
546C23×C7C22×D412yes—
547C23×C7C2×#4112yes—
548C23×C7C2×#4112yes—
549C23×C7C2511yescharacteristic
550C22×D7—21no—
551C22×D7—21no—
552C22×D7—21no—
553C22×D7—21no—
554C22×D7—21no—
555C22×D7—21no—
556C22×D7—22no—
557C22×D7—22no—
558C22×D7—22no—
559C22×D7—22no—
560C22×D7—22no—
561C22×D7—22no—
562C22×D7—22no—
563C22×D7—22no—
564C22×D7—22no—
565C22×D7—22no—
566C22×D7—22no—
567C22×D7—22no—
568C22×D7—22no—
569C22×D7—22no—
570C22×D7—22no—
571C22×D7—22no—
572C22×D7—22no—
573C22×D7—22no—
574C22×D7—22no—
575C22×D7—22no—
576C22×D7—22no—
577C22×D7—48no—
578C22×D7—48no—
579C22×D7—48no—
580C22×D7—84no—
581C22×D7—84no—
582C22×D7—84no—
583C22×D7—84no—
584C22×D7C22×D412yes—
585C7×Q8—84no—
586C2×C4×C7—21no—
587C2×C4×C7—21no—
588C2×C4×C7—21no—
589C2×C4×C7—21no—
590C2×C4×C7—21no—
591C2×C4×C7—21no—
592C2×C4×C7—21no—
593C2×C4×C7—21no—
594C2×C4×C7—21no—
595C2×C4×C7—21no—
596C2×C4×C7—28no—
597C2×C4×C7—22no—
598C2×C4×C7—22no—
599C2×C4×C7—22no—
600C2×C4×C7—22no—
601C2×C4×C7—22no—
602C2×C4×C7—22no—
603C2×C4×C7—22no—
604C2×C4×C7—22no—
605C2×C4×C7—22no—
606C2×C4×C7—22no—
607C2×C4×C7—22no—
608C2×C4×C7—22no—
609C2×C4×C7—84no—
610C2×C4×C7C22×D412yes—
611C2×C4×C7C22×D412yes—
612C2×C4×C7C2×#4112yes—
613C2×C4×C7C2×#4112yes—
614C2×C4×C7C2×#4112yes—
615C2×C4×C7C2×#4112yes—
616C2×C4×C7H(5,𝔽2)12yes—
617C2×C4×C7H(5,𝔽2)12yes—
618C22⋊D7—28no—
619C22⋊D7—48no—
620C2×Dic7—21no—
621C2×Dic7—21no—
622C2×Dic7—21no—
623C2×Dic7—21no—
624C2×Dic7—21no—
625C2×Dic7—21no—
626C2×Dic7—21no—
627C2×Dic7—21no—
628C2×Dic7—22no—
629C2×Dic7—21no—
630C2×Dic7—21no—
631C2×Dic7—21no—
632C2×Dic7—22no—
633C2×Dic7—22no—
634C2×Dic7—21no—
635C2×Dic7—21no—
636C2×Dic7—21no—
637C2×Dic7—21no—
638C2×Dic7—21no—
639C2×Dic7—21no—
640C2×Dic7—44no—
641C2×Dic7—44no—
642C2×Dic7C22×D412yes—
643C2×Dic7C22×D412yes—
644C2×Dic7C22×D412yes—
645C2×Dic7H(5,𝔽2)12yes—
646D28—48no—
647D28—44no—
648D28—44no—
649D28—44no—
650D28—84no—
651D28—84no—
652D28—84no—
653D28—84no—
654D28—84no—
655D28—84no—
656D28—84no—
657C4×D7—44no—
658C4×D7—44no—
659C4×D7—44no—
660C4×D7—84no—
661C25—72no—
662C22×Q8C22×D712yes—
663C22×D4—71no—
664C22×D4—72no—
665C22×D4—71no—
666C22×D4—71no—
667C22×D4—71no—
668C22×D4—72no—
669C22×D4—72no—
670C22×D4—72no—
671C22×D4—72no—
672C22×D4—72no—
673C22×D4—72no—
674C22×D4—72no—
675C22×D4—72no—
676C22×D4—144no—
677C22×D4—282no—
678C22×D4—282no—
679C23×C4—71no—
680C23×C4—71no—
681C23×C4—71no—
682C23×C4—71no—
683C23×C4—71no—
684C23×C4—72no—
685C23×C4C22×D711yescharacteristic
686C23×C4C22×D712yes—
687C4⋊Q8—42no—
688#127—282no—
689#127—282no—
690#126—148no—
691#126—148no—
692#124—148no—
693#124—148no—
694#124—284no—
695#123—148no—
696#123—148no—
697C22⋊Q8—28no—
698#121—148no—
699#121—148no—
700#121—148no—
701#121—144no—
702#121—284no—
703#121—282no—
704#121—282no—
705#121—282no—
706#120—148no—
707#120—148no—
708#120—148no—
709C4×D4—78no—
710C4×D4—148no—
711C4×D4—144no—
712C4×D4—144no—
713C4×D4—282no—
714C2×C4⋊C4—42no—
715C2×C4⋊C4—71no—
716C2×C4⋊C4—72no—
717C2×C4⋊C4—71no—
718C2×C4⋊C4—71no—
719C2×C4⋊C4—72no—
720C2×C4⋊C4—71no—
721C2×C4⋊C4C22×D711yescharacteristic
722C2×C4⋊C4C22×D711yescharacteristic
723C2×C4⋊C4C22×D711yescharacteristic
724C2×C4⋊C4C22×D712yes—
725C2×C4⋊C4C22×D712yes—
726C2×C4⋊C4C22×D711yescharacteristic
727C2×C4⋊C4C22×D712yes—
728C2×C4⋊C4C22×D712yes—
729C2×C4⋊C4C22×D712yes—
730C2×C4⋊C4C22×D712yes—
731C2×C22⋊C4—71no—
732C2×C22⋊C4—71no—
733C2×C22⋊C4—72no—
734C2×C22⋊C4—72no—
735C2×C22⋊C4—72no—
736C2×C22⋊C4—72no—
737C2×C22⋊C4—72no—
738C2×C22⋊C4—72no—
739C2×C22⋊C4—72no—
740C2×C22⋊C4—71no—
741C2×C22⋊C4—71no—
742C2×C22⋊C4—72no—
743C2×C22⋊C4—72no—
744C2×C22⋊C4—72no—
745C2×C22⋊C4—72no—
746C2×C22⋊C4—72no—
747C2×C22⋊C4—72no—
748C2×C22⋊C4—72no—
749C2×C22⋊C4—72no—
750C2×C22⋊C4—72no—
751C2×C22⋊C4—72no—
752C2×C22⋊C4—72no—
753C2×C22⋊C4—72no—
754C2×C22⋊C4—72no—
755C2×C22⋊C4—72no—
756C2×C22⋊C4—72no—
757C2×C22⋊C4—72no—
758C2×C22⋊C4—72no—
759C2×C22⋊C4—72no—
760C2×C22⋊C4—72no—
761C2×C22⋊C4—148no—
762C2×C22⋊C4—284no—
763C2×C22⋊C4C22×D712yes—
764C2×C22⋊C4C22×D711yescharacteristic
765C2×C22⋊C4C22×D711yescharacteristic
766C2×C42—71no—
767C2×C42—72no—
768C2×C42—71no—
769C2×C42—71no—
770C2×C42—71no—
771C2×C42—71no—
772C2×C42—71no—
773C2×C42—71no—
774C2×C42—71no—
775C2×C42—71no—
776C2×C42—71no—
777C2×C42—71no—
778C2×C42—282no—
779C2×C42—282no—
780C2×C42C22×D711yescharacteristic
781C2×C42C22×D711yescharacteristic
782#95—71no—
783#95—71no—
784#95—71no—
785#95—71no—
786#95—72no—
787#95—72no—
788#95—72no—
789#95—72no—
790#95C22×D711yescharacteristic
791#95C22×D711yescharacteristic
792#95C22×D712yes—
793#95C22×D712yes—
794#95C22×D712yes—
795C22×C7—22no—
796C22×C7—22no—
797C22×C7—22no—
798C22×C7—22no—
799C22×C7—22no—
800C22×C7—22no—
801C22×C7#53214yes—
802C22×C7C23×D411yescharacteristic
803C22×C7C22×#4111yescharacteristic
804C22×C7C22×#4111yescharacteristic
805C22×C7C2×H(5,𝔽2)11yescharacteristic
806C22×C7C2×H(5,𝔽2)11yescharacteristic
807C22×C7C2×H(5,𝔽2)11yescharacteristic
808C22×C7#58511yescharacteristic
809C2×D7—22no—
810C2×D7—22no—
811C2×D7—22no—
812C2×D7—41no—
813C2×D7—41no—
814C2×D7—41no—
815C2×D7—41no—
816C2×D7—42no—
817C2×D7—42no—
818C2×D7—42no—
819C2×D7—42no—
820C2×D7—42no—
821C2×D7—42no—
822C2×D7—42no—
823C2×D7—42no—
824C2×D7—42no—
825C2×D7—42no—
826C2×D7—42no—
827C2×D7—42no—
828C2×D7—42no—
829C2×D7—42no—
830C2×D7—42no—
831C2×D7—42no—
832C2×D7—42no—
833C2×D7—42no—
834C2×D7—42no—
835C2×D7—42no—
836C2×D7—42no—
837C2×D7—816no—
838C4×C7—22no—
839C4×C7—22no—
840C4×C7—22no—
841C4×C7—22no—
842C4×C7—22no—
843C4×C7—42no—
844C4×C7—42no—
845C4×C7—42no—
846C4×C7—42no—
847C4×C7#53814yescomplemented
848Dic7—22no—
849Dic7—22no—
850Dic7—22no—
851Dic7—22no—
852Dic7—42no—
853Dic7—41no—
854Dic7—41no—
855Dic7—41no—
856C24—71no—
857C24—72no—
858C24—72no—
859C24—72no—
860C24—144no—
861C24—144no—
862C24—144no—
863C24—282no—
864C24—282no—
865C24—282no—
866C24—282no—
867C24C23×D711yescharacteristic
868C2×Q8—24no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×D4—74no—
872C2×D4—144no—
873C2×D4—144no—
874C2×D4—144no—
875C2×D4—142no—
876C2×D4—142no—
877C2×D4—144no—
878C2×D4—144no—
879C2×D4—144no—
880C2×D4—144no—
881C2×D4—144no—
882C2×D4—142no—
883C2×D4—142no—
884C2×D4—142no—
885C2×D4—142no—
886C2×D4—144no—
887C2×D4—142no—
888C2×D4—142no—
889C2×D4—144no—
890C2×D4—144no—
891C2×D4—142no—
892C2×D4—142no—
893C2×D4—142no—
894C2×D4—282no—
895C2×D4—282no—
896C2×D4—2816no—
897C2×D4—282no—
898C2×D4—282no—
899C2×D4—282no—
900C2×D4—282no—
901C2×D4—282no—
902C2×D4—282no—
903C2×D4—282no—
904C2×D4—282no—
905C2×D4—282no—
906C2×D4—282no—
907C2×D4—282no—
908C2×D4—282no—
909C2×D4—282no—
910C2×D4—282no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—71no—
917C22×C4—71no—
918C22×C4—71no—
919C22×C4—71no—
920C22×C4—74no—
921C22×C4—74no—
922C22×C4—71no—
923C22×C4—71no—
924C22×C4—71no—
925C22×C4—72no—
926C22×C4—142no—
927C22×C4—144no—
928C22×C4—142no—
929C22×C4—142no—
930C22×C4—142no—
931C22×C4—142no—
932C22×C4—142no—
933C22×C4—142no—
934C22×C4—281no—
935C22×C4—281no—
936C22×C4—281no—
937C22×C4—282no—
938C22×C4—282no—
939C22×C4—281no—
940C22×C4—281no—
941C22×C4—281no—
942C22×C4#116114yes—
943C22×C4C23×D712yes—
944C22×C4C23×D712yes—
945C22×C4C23×D712yes—
946C22×C4C23×D712yes—
947C22×C4C23×D711yescharacteristic
948C22×C4C23×D711yescharacteristic
949C22×C4C23×D711yescharacteristic
950C22×C4C23×D711yescharacteristic
951C22×C4C23×D711yescharacteristic
952C22×C4C23×D711yescharacteristic
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—74no—
964C4⋊C4—144no—
965C4⋊C4—144no—
966C4⋊C4—142no—
967C4⋊C4—142no—
968C4⋊C4—142no—
969C22⋊C4—24no—
970C22⋊C4—74no—
971C22⋊C4—144no—
972C22⋊C4—144no—
973C22⋊C4—144no—
974C22⋊C4—144no—
975C22⋊C4—144no—
976C22⋊C4—144no—
977C22⋊C4—144no—
978C22⋊C4—144no—
979C22⋊C4—144no—
980C22⋊C4—144no—
981C22⋊C4—144no—
982C22⋊C4—144no—
983C22⋊C4—142no—
984C22⋊C4—144no—
985C22⋊C4—144no—
986C22⋊C4—142no—
987C22⋊C4—142no—
988C22⋊C4—144no—
989C22⋊C4—144no—
990C22⋊C4—144no—
991C22⋊C4—282no—
992C22⋊C4—282no—
993C22⋊C4—282no—
994C22⋊C4—282no—
995C22⋊C4—282no—
996C22⋊C4—282no—
997C22⋊C4—282no—
998C22⋊C4—282no—
999C22⋊C4—282no—
1000C22⋊C4D4×D714yes—
1001C22⋊C4#116114yes—
1002C42—22no—
1003C42—22no—
1004C42—74no—
1005C42—144no—
1006C42—142no—
1007C42—142no—
1008C42—142no—
1009C42—142no—
1010C42—142no—
1011C42—281no—
1012C42—281no—
1013C42—281no—
1014C42—281no—
1015C42—281no—
1016C2×C7—24no—
1017C2×C7C2×#53211yescharacteristic
1018C2×C7C2×#53811yescharacteristic
1019C2×C7#346011yescharacteristic
1020C2×C7#349611yescharacteristic
1021C2×C7#349811yescharacteristic
1022C2×C7#351411yescharacteristic
1023C2×C7#351911yescharacteristic
1024D7—42no—
1025D7—82no—
1026D7—82no—
1027D7—82no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—72no—
1033C23—141no—
1034C23—141no—
1035C23—141no—
1036C23—141no—
1037C23—141no—
1038C23—141no—
1039C23—142no—
1040C23—142no—
1041C23—142no—
1042C23—142no—
1043C23—142no—
1044C23—142no—
1045C23—142no—
1046C23—142no—
1047C23—142no—
1048C23—142no—
1049C23—142no—
1050C23—142no—
1051C23—142no—
1052C23—142no—
1053C23—142no—
1054C23—142no—
1055C23—142no—
1056C23—142no—
1057C23—142no—
1058C23—142no—
1059C23—142no—
1060C23—288no—
1061C23—288no—
1062C23—288no—
1063C23—564no—
1064C23—564no—
1065C23—564no—
1066C23—564no—
1067C23C2×D4×D712yes—
1068C23C2×#116112yes—
1069C23C2×#116112yes—
1070C23C24×D711yescharacteristic
1071Q8—84no—
1072D4—148no—
1073D4—288no—
1074D4—288no—
1075D4—284no—
1076D4—284no—
1077D4—284no—
1078D4—564no—
1079D4—564no—
1080D4—564no—
1081D4—564no—
1082D4—564no—
1083D4—564no—
1084D4—564no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—28no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—72no—
1109C2×C4—72no—
1110C2×C4—72no—
1111C2×C4—72no—
1112C2×C4—84no—
1113C2×C4—141no—
1114C2×C4—141no—
1115C2×C4—141no—
1116C2×C4—141no—
1117C2×C4—141no—
1118C2×C4—141no—
1119C2×C4—141no—
1120C2×C4—141no—
1121C2×C4—142no—
1122C2×C4—141no—
1123C2×C4—141no—
1124C2×C4—142no—
1125C2×C4—141no—
1126C2×C4—141no—
1127C2×C4—142no—
1128C2×C4—141no—
1129C2×C4—141no—
1130C2×C4—141no—
1131C2×C4—141no—
1132C2×C4—141no—
1133C2×C4—284no—
1134C2×C4—284no—
1135C2×C4—284no—
1136C2×C4—284no—
1137C2×C4—284no—
1138C2×C4—564no—
1139C2×C4C2×D4×D712yes—
1140C2×C4C2×D4×D712yes—
1141C2×C4#654812yes—
1142C2×C4C2×#116112yes—
1143C2×C4C2×#116112yes—
1144C2×C4C2×#116112yes—
1145C2×C4C2×#116112yes—
1146C2×C4#655312yes—
1147C7#3500711yescharacteristic, complemented, Sylow
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—142no—
1155C22—142no—
1156C22—142no—
1157C22—281no—
1158C22—281no—
1159C22—281no—
1160C22—281no—
1161C22—282no—
1162C22—282no—
1163C22—282no—
1164C22—282no—
1165C22—282no—
1166C22—282no—
1167C22—282no—
1168C22—282no—
1169C22—282no—
1170C22—282no—
1171C22—282no—
1172C22—282no—
1173C22—282no—
1174C22—282no—
1175C22—282no—
1176C22—282no—
1177C22—282no—
1178C22—282no—
1179C22—282no—
1180C22—282no—
1181C22—282no—
1182C22—5616no—
1183C22#9041614yes—
1184C22C22×D4×D711yescharacteristic
1185C22C2×#654811yescharacteristic
1186C22C22×#116111yescharacteristic
1187C22C22×#116111yescharacteristic
1188C22C2×#655311yescharacteristic
1189C22D7×H(5,𝔽2)11yescharacteristic
1190C22#9062011yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—42no—
1200C4—142no—
1201C4—142no—
1202C4—142no—
1203C4—142no—
1204C4—281no—
1205C4—282no—
1206C4—281no—
1207C4—281no—
1208C4#9033514yescomplemented
1209C2—24no—
1210C2—282no—
1211C2—562no—
1212C2—562no—
1213C2—562no—
1214C2C2×#9033511yescharacteristic
1215C2C2×#9041611yescharacteristic
1216C2#1174365011yescharacteristic
1217C2#1174367611yescharacteristic
1218C2#1174377011yescharacteristic
1219C2#1174381611yescharacteristic
1220C2#1174400111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2440C2
hypercenter#2440D7
hypocenterC7#35007
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#90335C2semidirect
2. C7×#2440C2semidirect
3. #11740702C2semidirect
4. #11740696C2semidirect
5. #11740214C2semidirect
6. #11739638C2semidirect
7. C2×#89760C2semidirect
8. #11735283C2semidirect
9. #11735234C2semidirect
10. #11734654C2semidirect
11. #11734632C2semidirect
12. #11733731C2semidirect
13. #11733665C2semidirect
14. #11733636C2semidirect
15. #11733449C2semidirect
16. #11732050C2semidirect
17. #11732037C2semidirect
18. #11731820C2semidirect
19. #11731778C2semidirect
20. #11731461C2semidirect
21. #11731310C2semidirect
22. #11731032C2semidirect
23. C4×(C22⋊D7)⋊C4C2semidirect
25. C2×C7×C4⋊Q8C22semidirect
28. C2×#6510C22semidirect
29. C2×#6510C22semidirect
30. C2×#6510C22semidirect
38. C2×#6461C22semidirect
39. C2×#6461C22semidirect
42. C2×#6458C22semidirect
43. C2×#6458C22semidirect
44. C2×#6458C22semidirect
45. C2×#6458C22semidirect
46. C2×#6457C22semidirect
47. C2×#6457C22semidirect
48. C2×#6456C22semidirect
57. C2×C42×D7C22semidirect
58. C7×#398C22semidirect
59. C7×#395C22semidirect
60. C7×#389C22semidirect
61. C7×#389C22semidirect
63. C7×#384C22semidirect
66. #90003C22semidirect
68. #89766C22semidirect
69. #89766C22semidirect
70. #89765C22semidirect
71. #89763C22semidirect
72. #89763C22semidirect
73. #89763C22semidirect
74. #89763C22semidirect
75. #89762C22semidirect
76. #89762C22semidirect
77. #89762C22semidirect
78. #89762C22semidirect
87. #89760C22semidirect
88. #89760C22semidirect
89. #89760C22semidirect
90. #89760C22semidirect
91. #89760C22semidirect
92. #89760C22semidirect
93. #89759C22semidirect
94. #89757C22semidirect
95. C4⋊C4×Dic7C22semidirect
96. #89745C22semidirect
103. C4×(C2×D7)⋊C4C22semidirect
104. C4×Dic7⋊C4C22semidirect
105. C42×Dic7C22semidirect
107. #89444C22semidirect
111. #89443C22semidirect
112. #89442C22semidirect
113. #89441C22semidirect
114. #89441C22semidirect
115. #89441C22semidirect
116. #89438C22semidirect
117. #89438C22semidirect
118. #89438C22semidirect
119. #89437C22semidirect
120. #89437C22semidirect
121. #89437C22semidirect
122. #89421C22semidirect
123. #89421C22semidirect
242. (C22⋊D7)⋊C4D4semidirect
272. #2440D7semidirect
378. C2×C4×D7C2×D4semidirect
423. (C2×D7)⋊C4C2×D4semidirect
429. Dic7⋊C4C2×D4semidirect
441. C4×Dic7C2×D4semidirect
444. C2×C4⋊Q8C2×D7semidirect
476. #398C2×D7semidirect
480. #395C2×D7semidirect
510. #389C2×D7semidirect
511. #389C2×D7semidirect
526. #384C2×D7semidirect
847. C4×C7#538semidirect
1147. C7#35007semidirect
1208. C4#90335semidirect

Maximal subgroups

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

subgroupindex
C2×#903352
C7×#24402
#117407022
#117406962
#117402142
#117396382
C2×#897602
#117352832
#117352342
#117346542
#117346322
#117337312
#117336652
#117336362
#117334492
#117320502
#117320372
#117318202
#117317782
#117314612
#117313102
#117310322
C4×(C22⋊D7)⋊C42
#350077