Finite Group Databasebeta

← #13526761

Subgroups — #13526761

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×#90348C212yesmaximal, complemented
2C7×#2445C211yesmaximal, characteristic, complemented
3#11740637C211yesmaximal, characteristic, complemented
4#11740620C211yesmaximal, characteristic, complemented
5#11740306C212yesmaximal, complemented
6#11739854C211yesmaximal, characteristic, complemented
7C4×#6501C211yesmaximal, characteristic, complemented
8#11734558C212yesmaximal, complemented
9#11734441C212yesmaximal, complemented
10#11734440C212yesmaximal, complemented
11#11734370C212yesmaximal, complemented
12#11733896C211yesmaximal, characteristic, complemented
13#11733884C211yesmaximal, characteristic, complemented
14#11733881C211yesmaximal, characteristic, complemented
15D7×#390C211yesmaximal, characteristic, complemented
16#11733870C211yesmaximal, characteristic, complemented
17#11733869C211yesmaximal, characteristic, complemented
18#11733731C211yesmaximal, characteristic, complemented
19#11733444C211yesmaximal, characteristic, complemented
20#11732321C212yesmaximal, complemented
21#11732201C212yesmaximal, complemented
22#11731137C211yesmaximal, characteristic, complemented
23C4×#6456C211yesmaximal, characteristic, complemented
24C22×D4×D7C2211yescharacteristic
25C2×C7×#127C2211yescharacteristic
26C2×C7×#123C2212yescomplemented
27C2×C4×C7×D4C2211yescharacteristic, complemented
28C2×#6503C2211yescharacteristic
29C2×#6501C2211yescharacteristic
30C2×#6501C2211yescharacteristic
31C2×#6501C2212yescomplemented
32C2×#6501C2212yescomplemented
33C2×#6501C2211yescharacteristic, complemented
34C2×#6500C2212yes—
35C2×#6500C2212yes—
36C2×#6493C2212yescomplemented
37C2×C4×C22⋊D7C2212yes—
38#90348—216no—
39C2×#6461C2212yescomplemented
40C2×#6460C2212yes—
41C2×#6458C2211yescharacteristic
42C2×#6457C2212yescomplemented
43C2×#6456C2211yescharacteristic
44C2×#6456C2211yescharacteristic
45C2×D7×C4⋊C4C2211yescharacteristic
46C2×#6451C2211yescharacteristic, complemented
47C2×#6448C2212yescomplemented
48C2×#6448C2212yescomplemented
49C2×#6448C2212yescomplemented
50C2×#6447C2212yes—
51C2×#6445C2212yes—
52C2×D7×C22⋊C4C2212yes—
53C2×D7×C22⋊C4C2212yes—
54C2×#6442C2212yescomplemented
55C2×C4×D28C2211yescharacteristic
56C2×C42×D7C2211yescharacteristic
57C2×C42×D7C2211yescharacteristic, complemented
58C7×#394C2212yescomplemented
59C7×#394C2212yescomplemented
60C7×#390C2211yescharacteristic
61C7×#390C2211yescharacteristic
62C7×#390C2211yescharacteristic, complemented
63C7×#389C2211yescharacteristic, complemented
64C7×#386C2212yescomplemented
65C4×C7×C4⋊C4C2211yescharacteristic, complemented
66#89995C2212yes—
67#89995C2212yes—
68#89993C2211yescharacteristic
69#89993C2211yescharacteristic
70#89993C2212yescomplemented
71#89993C2212yescomplemented
72#89993C2211yescharacteristic, complemented
73#89985C2212yescomplemented
74C4×C22⋊Dic7C2212yescomplemented
75#89766C2212yescomplemented
76#89762C2212yescomplemented
77#89760C2211yescharacteristic
78#89759C2211yescharacteristic
79#89759C2211yescharacteristic, complemented
80#89757C2211yescharacteristic, complemented
81#89755C2212yescomplemented
82C4⋊C4×Dic7C2211yescharacteristic, complemented
83C4⋊C4×Dic7C2211yescharacteristic, complemented
84#89745C2211yescharacteristic, complemented
85#89733C2212yes—
86#89733C2212yescomplemented
87#89732C2212yes—
88#89732C2212yescomplemented
89#89731C2212yescomplemented
90#89731C2212yescomplemented
91#89729C2212yes—
92#89729C2212yes—
93#89729C2212yescomplemented
94#89729C2212yescomplemented
95#89728C2212yes—
96#89728C2212yes—
97#89727C2212yes—
98#89723C2212yescomplemented
99#89720C2212yescomplemented
100#89719C2212yescomplemented
101#89717C2212yescomplemented
102#89716C2212yescomplemented
103#89716C2212yescomplemented
104#89716C2212yescomplemented
105#89711C2211yescharacteristic
106#89711C2211yescharacteristic
107#89711C2211yescharacteristic
108C4×(C2×D7)⋊C4C2211yescharacteristic
109C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
110#89707C2211yescharacteristic, complemented
111C4×C4⋊Dic7C2211yescharacteristic, complemented
112C42×Dic7C2211yescharacteristic, complemented
113#89700C2211yescharacteristic, complemented
114#89446C2212yescomplemented
115#89442C2212yescomplemented
116#89441C2212yescomplemented
117#89440C2212yes—
118#89438C2211yescharacteristic
119#89438C2211yescharacteristic
120#89438C2211yescharacteristic, complemented
121#89438C2211yescharacteristic, complemented
122#89437C2212yescomplemented
123#89428C2212yescomplemented
124#35007—71nomaximal, Sylow
125C24×D7C2312yes—
126C22×C7×D4C2311yescharacteristic
127C22×C7×D4C2311yescharacteristic
128C22×C7×D4C2312yes—
129C22×C7×D4C2312yes—
130C23×C4×C7C2312yes—
131C22×C22⋊D7C2312yes—
132C22×C22⋊D7C2312yes—
133C22×C22⋊D7C2312yes—
134C22×C22⋊D7C2312yes—
135C22×C22⋊D7C2312yes—
136C22×C22⋊D7C2312yes—
137C2×D4×D7—24no—
138C2×D4×D7—42no—
139C2×D4×D7—42no—
140C22×D28C2311yescharacteristic
141C22×D28C2311yescharacteristic
142C22×D28C2312yes—
143C22×C4×D7C2311yescharacteristic
144C22×C4×D7C2311yescharacteristic
145C22×C4×D7C2311yescharacteristic
146C22×C4×D7C2311yescharacteristic
147C22×C4×D7C2312yes—
148C22×C4×D7C2311yescharacteristic
149C22×C4×D7C2311yescharacteristic
150C22×Dic14C2312yes—
151C7×#127—42no—
152C7×#123—28no—
153C4×C7×D4—42no—
154C2×C7×C4⋊C4C2311yescharacteristic
155C2×C7×C4⋊C4C2311yescharacteristic
156C2×C7×C4⋊C4C2312yes—
157C2×C7×C4⋊C4C2311yescharacteristic
158C2×C7×C4⋊C4C2311yescharacteristic
159C2×C7×C22⋊C4C2312yes—
160C2×C7×C22⋊C4C2312yes—
161C2×C7×C22⋊C4C2312yes—
162C2×C7×C22⋊C4C2312yes—
163C2×C7×C22⋊C4C2312yes—
164C2×C7×C22⋊C4C2312yes—
165C2×C7×C22⋊C4C2312yes—
166C2×C42×C7C2311yescharacteristic
167C2×C42×C7C2311yescharacteristic
168C2×C42×C7C2311yescharacteristic
169C2×C22⋊Dic7C2312yes—
170C2×C22⋊Dic7C2312yes—
171C2×C22⋊Dic7C2312yes—
172C2×C22⋊Dic7C2312yes—
173C2×C22⋊Dic7C2312yes—
174C2×C22⋊Dic7C2312yes—
175C2×C22⋊Dic7C2312yes—
176C2×C22⋊Dic7C2312yes—
177C2×C22⋊Dic7C2312yes—
178#6503—42no—
179#6501—28no—
180#6501—24no—
181#6501—42no—
182#6501—42no—
183#6501—44no—
184#6500—28no—
185#6500—28no—
186#6493—28no—
187C4×C22⋊D7—28no—
188C2×(C2×D7)⋊C4C2311yescharacteristic
189C2×(C2×D7)⋊C4C2311yescharacteristic
190C2×(C2×D7)⋊C4C2312yes—
191C2×(C2×D7)⋊C4C2312yes—
192C2×(C2×D7)⋊C4C2312yes—
193C2×(C2×D7)⋊C4C2312yes—
194C2×(C2×D7)⋊C4C2312yes—
195C2×(C2×D7)⋊C4C2312yes—
196C2×(C2×D7)⋊C4C2311yescharacteristic
197C2×(C2×D7)⋊C4C2312yes—
198C2×(C2×D7)⋊C4C2312yes—
199C2×(C2×D7)⋊C4C2312yes—
200C2×(C2×D7)⋊C4C2312yes—
201C2×(C2×D7)⋊C4C2312yes—
202C2×(C2×D7)⋊C4C2311yescharacteristic
203C2×(C2×D7)⋊C4C2311yescharacteristic
204C2×(C2×D7)⋊C4C2311yescharacteristic
205C2×C4⋊Dic7C2311yescharacteristic
206C2×C4⋊Dic7C2312yes—
207C2×C4⋊Dic7C2311yescharacteristic
208C2×C4⋊Dic7C2311yescharacteristic
209C2×C4⋊Dic7C2312yes—
210C2×C4⋊Dic7C2311yescharacteristic
211C2×C4⋊Dic7C2312yes—
212C2×Dic7⋊C4C2312yes—
213C2×Dic7⋊C4C2312yes—
214C2×Dic7⋊C4C2312yes—
215C2×Dic7⋊C4C2312yes—
216C2×C4×Dic7C2311yescharacteristic
217C2×C4×Dic7C2311yescharacteristic
218C2×C4×Dic7C2312yes—
219C2×C4×Dic7C2311yescharacteristic
220C2×C4×Dic7C2311yescharacteristic
221C2×C4×Dic7C2311yescharacteristic
222C2×C4×Dic7C2311yescharacteristic
223C2×C4×Dic7C2311yescharacteristic
224C2×C4×Dic7C2311yescharacteristic
225C2×C4×Dic7C2311yescharacteristic
226C2×C4×Dic7C2311yescharacteristic
227#6461—28no—
228#6460—28no—
229#6458—42no—
230#6457—28no—
231#6456—24no—
232#6456D418yescomplemented
233D7×C4⋊C4—42no—
234#6451—42no—
235#6448—28no—
236#6448—28no—
237#6448—44no—
238#6447—28no—
239#6445—28no—
240D7×C22⋊C4—28no—
241D7×C22⋊C4—44no—
242#6442—28no—
243C4×D28—24no—
244C42×D7—42no—
245C42×D7—42no—
246C7×#95C2312yes—
247C7×#95C2311yescharacteristic
248C7×#95C2311yescharacteristic
249C7⋊#95C2311yescharacteristic
250C7⋊#95C2312yes—
251C7⋊#95C2312yes—
252C7⋊#95C2311yescharacteristic
253C7⋊#95C2311yescharacteristic
254C7⋊#95C2311yescharacteristic
255C7⋊#95C2312yes—
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#2445D711yescharacteristic, complemented
272#2440—71no—
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×C7C2412yes—
283C24×C7C2412yes—
284C23×D7—24no—
285C23×D7—24no—
286C23×D7—24no—
287C23×D7—42no—
288C23×D7—42no—
289C23×D7—42no—
290C23×D7—42no—
291C23×D7C2412yes—
292C23×D7C2411yescharacteristic
293C23×D7C2411yescharacteristic
294C2×C7×D4—24no—
295C2×C7×D4—22no—
296C2×C7×D4—22no—
297C2×C7×D4—24no—
298C2×C7×D4—22no—
299C2×C7×D4—22no—
300C2×C7×D4—22no—
301C2×C7×D4—22no—
302C2×C7×D4—42no—
303C2×C7×D4—42no—
304C2×C7×D4—42no—
305C2×C7×D4—42no—
306C22×C4×C7—24no—
307C22×C4×C7—42no—
308C22×C4×C7—42no—
309C22×C4×C7C2411yescharacteristic
310C22×C4×C7C2412yes—
311C22×C4×C7C2411yescharacteristic
312C22×C4×C7C2412yes—
313C22×C4×C7C2411yescharacteristic
314C22×C4×C7C2411yescharacteristic
315C22×C4×C7C2411yescharacteristic
316C22×C4×C7C2411yescharacteristic
317C22×C4×C7C2411yescharacteristic
318C2×C22⋊D7—24no—
319C2×C22⋊D7—24no—
320C2×C22⋊D7—24no—
321C2×C22⋊D7—24no—
322C2×C22⋊D7—24no—
323C2×C22⋊D7—24no—
324C2×C22⋊D7—24no—
325C2×C22⋊D7—24no—
326C2×C22⋊D7—42no—
327C2×C22⋊D7—42no—
328C2×C22⋊D7—42no—
329C2×C22⋊D7—42no—
330C2×C22⋊D7—42no—
331C2×C22⋊D7—42no—
332C2×C22⋊D7—42no—
333C2×C22⋊D7—42no—
334C2×C22⋊D7—42no—
335C2×C22⋊D7—42no—
336C22×Dic7C2411yescharacteristic
337C22×Dic7C2412yes—
338C22×Dic7C2412yes—
339C22×Dic7C2412yes—
340C22×Dic7C2411yescharacteristic
341C22×Dic7C2411yescharacteristic
342C22×Dic7C2411yescharacteristic
343C22×Dic7C2411yescharacteristic
344C22×Dic7C2411yescharacteristic
345D4×D7—416no—
346C2×D28—22no—
347C2×D28—22no—
348C2×D28—22no—
349C2×D28—22no—
350C2×D28—22no—
351C2×D28—24no—
352C2×D28—42no—
353C2×D28—42no—
354C2×D28C2×D414yes—
355C2×C4×D7—22no—
356C2×C4×D7—22no—
357C2×C4×D7—22no—
358C2×C4×D7—22no—
359C2×C4×D7—22no—
360C2×C4×D7—22no—
361C2×C4×D7—22no—
362C2×C4×D7—22no—
363C2×C4×D7—22no—
364C2×C4×D7—24no—
365C2×C4×D7—41no—
366C2×C4×D7—41no—
367C2×C4×D7—41no—
368C2×C4×D7—41no—
369C2×C4×D7—41no—
370C2×C4×D7—41no—
371C2×C4×D7—42no—
372C2×C4×D7—42no—
373C2×C4×D7C2×D414yes—
374C2×C4×D7C2×D414yescomplemented
375C2×C4×D7#4114yes—
376C2×Dic14—24no—
377C2×Dic14—42no—
378C2×Dic14—42no—
379C7×C4⋊C4—24no—
380C7×C4⋊C4—22no—
381C7×C4⋊C4—22no—
382C7×C4⋊C4—22no—
383C7×C4⋊C4C2×D414yescomplemented
384C7×C22⋊C4—24no—
385C7×C22⋊C4—24no—
386C7×C22⋊C4—24no—
387C7×C22⋊C4—42no—
388C7×C22⋊C4—42no—
389C7×C22⋊C4—42no—
390C7×C22⋊C4—42no—
391C42×C7—22no—
392C42×C7—22no—
393C42×C7—22no—
394C22⋊Dic7—24no—
395C22⋊Dic7—24no—
396C22⋊Dic7—24no—
397C22⋊Dic7—24no—
398C22⋊Dic7—24no—
399C22⋊Dic7—24no—
400C22⋊Dic7—24no—
401C22⋊Dic7—42no—
402C22⋊Dic7—42no—
403(C2×D7)⋊C4—24no—
404(C2×D7)⋊C4—24no—
405(C2×D7)⋊C4—22no—
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—22no—
412(C2×D7)⋊C4—22no—
413(C2×D7)⋊C4—24no—
414(C2×D7)⋊C4—42no—
415(C2×D7)⋊C4—42no—
416(C2×D7)⋊C4—42no—
417(C2×D7)⋊C4C2×D414yes—
418(C2×D7)⋊C4C2×D414yescomplemented
419(C2×D7)⋊C4#4114yes—
420C4⋊Dic7—24no—
421C4⋊Dic7—22no—
422C4⋊Dic7—22no—
423C4⋊Dic7—22no—
424C4⋊Dic7—24no—
425C4⋊Dic7—22no—
426C4⋊Dic7—42no—
427Dic7⋊C4—24no—
428Dic7⋊C4—24no—
429Dic7⋊C4—42no—
430Dic7⋊C4—42no—
431C4×Dic7—24no—
432C4×Dic7—22no—
433C4×Dic7—22no—
434C4×Dic7—22no—
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⋊Q8—71no—
445C2×#127—71no—
446C2×#127C2×D711yescharacteristic
447C2×#126—72no—
448C2×#126—72no—
449C2×#124—72no—
450C2×#124—72no—
451C2×#124—72no—
452C2×#123—72no—
453C2×#123C2×D712yescomplemented
454C2×C22⋊Q8—72no—
455C2×#121—72no—
456C2×#121—71no—
457C2×#121—72no—
458C2×#121—71no—
459C2×#121—71no—
460C2×#121—72no—
461C2×#121—71no—
462C2×#121—72no—
463C2×#120—72no—
464C2×#120—72no—
465C2×#120—72no—
466C2×C4×D4—72no—
467C2×C4×D4—71no—
468C2×C4×D4—71no—
469C2×C4×D4—71no—
470C2×C4×D4C2×D711yescharacteristic, complemented
471C22×C4⋊C4—71no—
472C22×C22⋊C4—72no—
473C22×C22⋊C4—72no—
474C22×C42—71no—
475C22×C42—71no—
476#398—72no—
477#397—72no—
478#396—72no—
479#396—72no—
480#395—72no—
481#394—72no—
482#394—72no—
483#394—72no—
484#394—72no—
485#394C2×D712yescomplemented
486#394C2×D712yescomplemented
487#393—72no—
488#392—72no—
489#392—72no—
490#392—72no—
491#392—72no—
492#390—72no—
493#390—71no—
494#390—71no—
495#390—72no—
496#390—71no—
497#390—71no—
498#390—72no—
499#390—72no—
500#390—72no—
501#390—72no—
502#390—71no—
503#390—71no—
504#390—71no—
505#390C2×D711yescharacteristic
506#390C2×D711yescharacteristic
507#390C2×D711yescharacteristic, complemented
508#389—71no—
509#389—71no—
510#389—71no—
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#386C2×D712yescomplemented
525#385—72no—
526#384—71no—
527#380—71no—
528#380—71no—
529#379—72no—
530C4×C4⋊C4—71no—
531C4×C4⋊C4—71no—
532C4×C4⋊C4—71no—
533C4×C4⋊C4C2×D711yescharacteristic, complemented
534C4×C22⋊C4—72no—
535C4×C22⋊C4—71no—
536C4×C22⋊C4—71no—
537C4×C22⋊C4—71no—
538C4×C22⋊C4—71no—
539C4×C22⋊C4—71no—
540C4×C22⋊C4—71no—
541C43—71no—
542C23×C7—22no—
543C23×C7—22no—
544C23×C7—22no—
545C23×C7—22no—
546C23×C7—22no—
547C23×C7—22no—
548C23×C7—22no—
549C23×C7—22no—
550C23×C7—22no—
551C23×C7—22no—
552C23×C7—22no—
553C23×C7—22no—
554C23×C7—22no—
555C23×C7—22no—
556C23×C7C2511yescharacteristic
557C22×D7—21no—
558C22×D7—21no—
559C22×D7—21no—
560C22×D7—21no—
561C22×D7—21no—
562C22×D7—21no—
563C22×D7—21no—
564C22×D7—21no—
565C22×D7—21no—
566C22×D7—21no—
567C22×D7—22no—
568C22×D7—22no—
569C22×D7—22no—
570C22×D7—22no—
571C22×D7—22no—
572C22×D7—22no—
573C22×D7—22no—
574C22×D7—48no—
575C22×D7—48no—
576C22×D7—48no—
577C22×D7—84no—
578C22×D7—84no—
579C22×D7—84no—
580C22×D7—84no—
581C22×D7C22×D412yes—
582C22×D7C22×D412yes—
583C22×D7C2×#4112yes—
584C22×D7C2×#4112yes—
585C7×D4—44no—
586C7×D4—44no—
587C7×D4—84no—
588C7×D4—84no—
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—21no—
597C2×C4×C7—22no—
598C2×C4×C7—22no—
599C2×C4×C7—21no—
600C2×C4×C7—21no—
601C2×C4×C7—21no—
602C2×C4×C7—21no—
603C2×C4×C7—22no—
604C2×C4×C7—22no—
605C2×C4×C7—21no—
606C2×C4×C7—22no—
607C2×C4×C7—21no—
608C2×C4×C7—22no—
609C2×C4×C7—84no—
610C2×C4×C7C22×D412yes—
611C2×C4×C7C22×D412yes—
612C2×C4×C7C22×D412yes—
613C2×C4×C7C2×#4112yes—
614C2×C4×C7C2×#4112yes—
615C2×C4×C7H(5,𝔽2)12yes—
616C2×C4×C7H(5,𝔽2)12yes—
617C22⋊D7—48no—
618C22⋊D7—48no—
619C22⋊D7—84no—
620C22⋊D7—84no—
621C22⋊D7—84no—
622C22⋊D7—84no—
623C2×Dic7—21no—
624C2×Dic7—21no—
625C2×Dic7—21no—
626C2×Dic7—21no—
627C2×Dic7—21no—
628C2×Dic7—21no—
629C2×Dic7—21no—
630C2×Dic7—21no—
631C2×Dic7—21no—
632C2×Dic7—21no—
633C2×Dic7—22no—
634C2×Dic7—22no—
635C2×Dic7—22no—
636C2×Dic7—21no—
637C2×Dic7—22no—
638C2×Dic7—22no—
639C2×Dic7—21no—
640C2×Dic7—22no—
641C2×Dic7—22no—
642C2×Dic7—22no—
643C2×Dic7—22no—
644C2×Dic7—21no—
645C2×Dic7C22×D412yes—
646C2×Dic7C22×D412yes—
647C2×Dic7C2×#4112yes—
648C2×Dic7C2×#4112yes—
649C2×Dic7H(5,𝔽2)12yes—
650D28—28no—
651D28—44no—
652D28—84no—
653C4×D7—28no—
654C4×D7—44no—
655C4×D7—44no—
656C4×D7—44no—
657C4×D7—44no—
658C4×D7—44no—
659C4×D7—84no—
660Dic14—84no—
661C25—72no—
662C22×Q8—72no—
663C22×D4—72no—
664C22×D4—72no—
665C22×D4—72no—
666C22×D4—72no—
667C22×D4—72no—
668C22×D4—72no—
669C22×D4—71no—
670C22×D4—71no—
671C22×D4—72no—
672C22×D4—144no—
673C22×D4—282no—
674C22×D4—282no—
675C22×D4C22×D711yescharacteristic
676C22×D4C22×D711yescharacteristic
677C22×D4C22×D712yes—
678C22×D4C22×D712yes—
679C23×C4—71no—
680C23×C4—71no—
681C23×C4—71no—
682C23×C4—71no—
683C23×C4—71no—
684C23×C4—71no—
685C23×C4—72no—
686C23×C4C22×D712yes—
687C4⋊Q8—282no—
688#127—42no—
689#127—282no—
690#126—148no—
691#126—148no—
692#124—148no—
693#124—148no—
694#124—284no—
695#123—28no—
696#123—148no—
697C22⋊Q8—148no—
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—42no—
710C4×D4—78no—
711C4×D4—144no—
712C4×D4—144no—
713C4×D4—148no—
714C2×C4⋊C4—71no—
715C2×C4⋊C4—72no—
716C2×C4⋊C4—71no—
717C2×C4⋊C4—72no—
718C2×C4⋊C4—72no—
719C2×C4⋊C4—72no—
720C2×C4⋊C4—71no—
721C2×C4⋊C4—71no—
722C2×C4⋊C4—72no—
723C2×C4⋊C4—72no—
724C2×C4⋊C4—72no—
725C2×C4⋊C4—282no—
726C2×C4⋊C4C22×D711yescharacteristic
727C2×C4⋊C4C22×D711yescharacteristic
728C2×C4⋊C4C22×D711yescharacteristic
729C2×C4⋊C4C22×D712yes—
730C2×C4⋊C4C22×D711yescharacteristic
731C2×C22⋊C4—71no—
732C2×C22⋊C4—71no—
733C2×C22⋊C4—71no—
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—72no—
741C2×C22⋊C4—72no—
742C2×C22⋊C4—72no—
743C2×C22⋊C4—72no—
744C2×C22⋊C4—72no—
745C2×C22⋊C4—71no—
746C2×C22⋊C4—71no—
747C2×C22⋊C4—71no—
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—148no—
758C2×C22⋊C4—284no—
759C2×C22⋊C4C22×D712yes—
760C2×C22⋊C4C22×D712yes—
761C2×C22⋊C4C22×D712yes—
762C2×C22⋊C4C22×D712yes—
763C2×C22⋊C4C22×D712yes—
764C2×C22⋊C4C22×D712yes—
765C2×C22⋊C4C22×D712yes—
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—282no—
778C2×C42—282no—
779C2×C42C22×D711yescharacteristic
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#95—72no—
791#95—72no—
792#95C22×D711yescharacteristic
793#95C22×D711yescharacteristic
794#95C22×D712yes—
795C22×C7—42no—
796C22×C7—42no—
797C22×C7—42no—
798C22×C7—42no—
799C22×C7—42no—
800C22×C7—42no—
801C22×C7—42no—
802C22×C7—42no—
803C22×C7—42no—
804C22×C7—42no—
805C22×C7—42no—
806C22×C7—42no—
807C22×C7—42no—
808C22×C7—42no—
809C22×C7C23×D411yescharacteristic
810C22×C7C22×#4111yescharacteristic
811C22×C7C22×#4111yescharacteristic
812C22×C7C2×H(5,𝔽2)11yescharacteristic
813C22×C7C2×H(5,𝔽2)11yescharacteristic
814C22×C7C2×H(5,𝔽2)11yescharacteristic
815C22×C7#58511yescharacteristic
816C2×D7—22no—
817C2×D7—22no—
818C2×D7—22no—
819C2×D7—22no—
820C2×D7—22no—
821C2×D7—22no—
822C2×D7—22no—
823C2×D7—22no—
824C2×D7—22no—
825C2×D7—41no—
826C2×D7—41no—
827C2×D7—41no—
828C2×D7—41no—
829C2×D7—42no—
830C2×D7—42no—
831C2×D7—42no—
832C2×D7—42no—
833C2×D7—42no—
834C2×D7—42no—
835C2×D7—42no—
836C2×D7—816no—
837C2×D7#53214yes—
838C4×C7—22no—
839C4×C7—22no—
840C4×C7—22no—
841C4×C7—22no—
842C4×C7—41no—
843C4×C7—42no—
844C4×C7—42no—
845C4×C7—41no—
846C4×C7#53814yescomplemented
847Dic7—22no—
848Dic7—22no—
849Dic7—22no—
850Dic7—22no—
851Dic7—22no—
852Dic7—42no—
853Dic7—41no—
854Dic7—42no—
855Dic7—42no—
856C24—71no—
857C24—71no—
858C24—72no—
859C24—144no—
860C24—144no—
861C24—144no—
862C24—282no—
863C24—282no—
864C24—282no—
865C24—282no—
866C24C23×D712yes—
867C24C23×D712yes—
868C2×Q8—144no—
869C2×Q8—282no—
870C2×Q8—282no—
871C2×D4—24no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—24no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—74no—
884C2×D4—142no—
885C2×D4—142no—
886C2×D4—144no—
887C2×D4—144no—
888C2×D4—144no—
889C2×D4—144no—
890C2×D4—144no—
891C2×D4—144no—
892C2×D4—144no—
893C2×D4—144no—
894C2×D4—144no—
895C2×D4—142no—
896C2×D4—142no—
897C2×D4—142no—
898C2×D4—282no—
899C2×D4—282no—
900C2×D4—2816no—
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—24no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—71no—
915C22×C4—71no—
916C22×C4—71no—
917C22×C4—71no—
918C22×C4—71no—
919C22×C4—74no—
920C22×C4—74no—
921C22×C4—74no—
922C22×C4—71no—
923C22×C4—72no—
924C22×C4—72no—
925C22×C4—72no—
926C22×C4—142no—
927C22×C4—142no—
928C22×C4—142no—
929C22×C4—144no—
930C22×C4—142no—
931C22×C4—142no—
932C22×C4—142no—
933C22×C4—142no—
934C22×C4—142no—
935C22×C4—142no—
936C22×C4—281no—
937C22×C4—281no—
938C22×C4—281no—
939C22×C4—281no—
940C22×C4—281no—
941C22×C4—281no—
942C22×C4—282no—
943C22×C4—282no—
944C22×C4C23×D711yescharacteristic
945C22×C4C23×D712yes—
946C22×C4C23×D711yescharacteristic
947C22×C4C23×D712yes—
948C22×C4C23×D711yescharacteristic
949C22×C4C23×D711yescharacteristic
950C22×C4C23×D711yescharacteristic
951C22×C4C23×D711yescharacteristic
952C22×C4C23×D711yescharacteristic
953C4⋊C4—24no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—144no—
958C4⋊C4—142no—
959C4⋊C4—144no—
960C4⋊C4—144no—
961C4⋊C4—144no—
962C4⋊C4—142no—
963C4⋊C4—142no—
964C4⋊C4—142no—
965C4⋊C4—282no—
966C4⋊C4—282no—
967C4⋊C4—282no—
968C4⋊C4D4×D714yescomplemented
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—74no—
977C22⋊C4—74no—
978C22⋊C4—74no—
979C22⋊C4—144no—
980C22⋊C4—144no—
981C22⋊C4—142no—
982C22⋊C4—142no—
983C22⋊C4—142no—
984C22⋊C4—144no—
985C22⋊C4—144no—
986C22⋊C4—144no—
987C22⋊C4—144no—
988C22⋊C4—144no—
989C22⋊C4—144no—
990C22⋊C4—144no—
991C22⋊C4—144no—
992C22⋊C4—144no—
993C22⋊C4—144no—
994C22⋊C4—144no—
995C22⋊C4—144no—
996C22⋊C4—144no—
997C22⋊C4—282no—
998C22⋊C4—282no—
999C22⋊C4—282no—
1000C22⋊C4—282no—
1001C22⋊C4—282no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—74no—
1006C42—142no—
1007C42—142no—
1008C42—144no—
1009C42—142no—
1010C42—142no—
1011C42—281no—
1012C42—281no—
1013C42—281no—
1014C42—281no—
1015C42—281no—
1016C2×C7—82no—
1017C2×C7—82no—
1018C2×C7C2×#53211yescharacteristic
1019C2×C7C2×#53811yescharacteristic
1020C2×C7#346011yescharacteristic
1021C2×C7#349611yescharacteristic
1022C2×C7#349811yescharacteristic
1023C2×C7#351411yescharacteristic
1024C2×C7#351911yescharacteristic
1025D7—24no—
1026D7—42no—
1027D7—82no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—72no—
1043C23—72no—
1044C23—72no—
1045C23—72no—
1046C23—141no—
1047C23—141no—
1048C23—141no—
1049C23—141no—
1050C23—141no—
1051C23—141no—
1052C23—141no—
1053C23—141no—
1054C23—141no—
1055C23—141no—
1056C23—142no—
1057C23—142no—
1058C23—142no—
1059C23—142no—
1060C23—142no—
1061C23—142no—
1062C23—142no—
1063C23—288no—
1064C23—288no—
1065C23—288no—
1066C23—564no—
1067C23—564no—
1068C23—564no—
1069C23—564no—
1070C23C24×D711yescharacteristic
1071Q8—564no—
1072D4—44no—
1073D4—44no—
1074D4—84no—
1075D4—84no—
1076D4—148no—
1077D4—288no—
1078D4—288no—
1079D4—284no—
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—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—72no—
1106C2×C4—72no—
1107C2×C4—72no—
1108C2×C4—72no—
1109C2×C4—72no—
1110C2×C4—84no—
1111C2×C4—141no—
1112C2×C4—141no—
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—148no—
1122C2×C4—142no—
1123C2×C4—142no—
1124C2×C4—142no—
1125C2×C4—141no—
1126C2×C4—142no—
1127C2×C4—141no—
1128C2×C4—142no—
1129C2×C4—141no—
1130C2×C4—142no—
1131C2×C4—142no—
1132C2×C4—142no—
1133C2×C4—142no—
1134C2×C4—284no—
1135C2×C4—284no—
1136C2×C4—284no—
1137C2×C4—284no—
1138C2×C4—284no—
1139C2×C4—564no—
1140C2×C4C2×D4×D712yes—
1141C2×C4C2×D4×D712yes—
1142C2×C4C2×D4×D712yes—
1143C2×C4#654812yes—
1144C2×C4D7×#4112yes—
1145C2×C4D7×#4112yes—
1146C2×C4#655312yes—
1147C7#3500711yescharacteristic, complemented, Sylow
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—74no—
1163C22—142no—
1164C22—142no—
1165C22—142no—
1166C22—142no—
1167C22—142no—
1168C22—142no—
1169C22—142no—
1170C22—142no—
1171C22—142no—
1172C22—281no—
1173C22—281no—
1174C22—281no—
1175C22—281no—
1176C22—282no—
1177C22—282no—
1178C22—282no—
1179C22—282no—
1180C22—282no—
1181C22—282no—
1182C22—282no—
1183C22—5616no—
1184C22C22×D4×D711yescharacteristic
1185C22C2×#654811yescharacteristic
1186C22C2×D7×#4111yescharacteristic
1187C22C2×D7×#4111yescharacteristic
1188C22C2×#655311yescharacteristic
1189C22D7×H(5,𝔽2)11yescharacteristic
1190C22#9061811yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—41no—
1196C4—42no—
1197C4—42no—
1198C4—41no—
1199C4—142no—
1200C4—142no—
1201C4—142no—
1202C4—142no—
1203C4—142no—
1204C4—282no—
1205C4—282no—
1206C4—282no—
1207C4—281no—
1208C4#9034814yescomplemented
1209C2—82no—
1210C2—82no—
1211C2—144no—
1212C2—282no—
1213C2—562no—
1214C2C2×#9034811yescharacteristic
1215C2D7×#53211yescharacteristic
1216C2#1174353611yescharacteristic
1217C2#1174368911yescharacteristic
1218C2#1174370811yescharacteristic
1219C2#1174383811yescharacteristic
1220C2#1174412211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2445C2
hypercenter#2445D7
hypocenterC7#35007
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2445

Complements

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

NH ≅ G/Ntype
1. C2×#90348C2semidirect
2. C7×#2445C2semidirect
3. #11740637C2semidirect
4. #11740620C2semidirect
5. #11740306C2semidirect
6. #11739854C2semidirect
7. C4×#6501C2semidirect
8. #11734558C2semidirect
9. #11734441C2semidirect
10. #11734440C2semidirect
11. #11734370C2semidirect
12. #11733896C2semidirect
13. #11733884C2semidirect
14. #11733881C2semidirect
15. D7×#390C2semidirect
16. #11733870C2semidirect
17. #11733869C2semidirect
18. #11733731C2semidirect
19. #11733444C2semidirect
20. #11732321C2semidirect
21. #11732201C2semidirect
22. #11731137C2semidirect
23. C4×#6456C2semidirect
26. C2×C7×#123C22semidirect
27. C2×C4×C7×D4C22semidirect
31. C2×#6501C22semidirect
32. C2×#6501C22semidirect
33. C2×#6501C22semidirect
36. C2×#6493C22semidirect
39. C2×#6461C22semidirect
42. C2×#6457C22semidirect
46. C2×#6451C22semidirect
47. C2×#6448C22semidirect
48. C2×#6448C22semidirect
49. C2×#6448C22semidirect
54. C2×#6442C22semidirect
57. C2×C42×D7C22semidirect
58. C7×#394C22semidirect
59. C7×#394C22semidirect
62. C7×#390C22semidirect
63. C7×#389C22semidirect
64. C7×#386C22semidirect
65. C4×C7×C4⋊C4C22semidirect
70. #89993C22semidirect
71. #89993C22semidirect
72. #89993C22semidirect
73. #89985C22semidirect
74. C4×C22⋊Dic7C22semidirect
75. #89766C22semidirect
76. #89762C22semidirect
79. #89759C22semidirect
80. #89757C22semidirect
81. #89755C22semidirect
82. C4⋊C4×Dic7C22semidirect
83. C4⋊C4×Dic7C22semidirect
84. #89745C22semidirect
86. #89733C22semidirect
88. #89732C22semidirect
89. #89731C22semidirect
90. #89731C22semidirect
93. #89729C22semidirect
94. #89729C22semidirect
98. #89723C22semidirect
99. #89720C22semidirect
100. #89719C22semidirect
101. #89717C22semidirect
102. #89716C22semidirect
103. #89716C22semidirect
104. #89716C22semidirect
109. C4×(C2×D7)⋊C4C22semidirect
110. #89707C22semidirect
111. C4×C4⋊Dic7C22semidirect
112. C42×Dic7C22semidirect
113. #89700C22semidirect
114. #89446C22semidirect
115. #89442C22semidirect
116. #89441C22semidirect
120. #89438C22semidirect
121. #89438C22semidirect
122. #89437C22semidirect
123. #89428C22semidirect
232. #6456D4semidirect
271. #2445D7semidirect
374. C2×C4×D7C2×D4semidirect
383. C7×C4⋊C4C2×D4semidirect
418. (C2×D7)⋊C4C2×D4semidirect
441. C4×Dic7C2×D4semidirect
453. C2×#123C2×D7semidirect
470. C2×C4×D4C2×D7semidirect
485. #394C2×D7semidirect
486. #394C2×D7semidirect
507. #390C2×D7semidirect
511. #389C2×D7semidirect
524. #386C2×D7semidirect
533. C4×C4⋊C4C2×D7semidirect
846. C4×C7#538semidirect
968. C4⋊C4D4×D7semidirect
1147. C7#35007semidirect
1208. C4#90348semidirect

Maximal subgroups

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

subgroupindex
C2×#903482
C7×#24452
#117406372
#117406202
#117403062
#117398542
C4×#65012
#117345582
#117344412
#117344402
#117343702
#117338962
#117338842
#117338812
D7×#3902
#117338702
#117338692
#117337312
#117334442
#117323212
#117322012
#117311372
C4×#64562
#350077