Finite Group Databasebeta

← #13526753

Subgroups — #13526753

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×#90395C212yesmaximal, complemented
2C7×#2512C211yesmaximal, characteristic, complemented
3#11740553C212yesmaximal, complemented
4#11735009C212yesmaximal, complemented
5#11734919C212yesmaximal, complemented
6#11734861C212yesmaximal, complemented
7#11734789C212yesmaximal, complemented
8#11733920C211yesmaximal, characteristic, complemented
9#11733889C211yesmaximal, characteristic, complemented
10#11733881C211yesmaximal, characteristic, complemented
11D7×#390C211yesmaximal, characteristic, complemented
12#11733869C211yesmaximal, characteristic, complemented
13#11733759C211yesmaximal, characteristic, complemented
14#11733656C211yesmaximal, characteristic, complemented
15#11733636C211yesmaximal, characteristic, complemented
16#11733272C212yesmaximal, complemented
17#11733042C212yesmaximal, complemented
18#11731820C211yesmaximal, characteristic, complemented
19#11731771C211yesmaximal, characteristic, complemented
20#11731233C211yesmaximal, characteristic, complemented
21#11731225C211yesmaximal, characteristic, complemented
22C4×#6458C211yesmaximal, characteristic, complemented
23C4×#6456C211yesmaximal, characteristic, complemented
24C22×D4×D7C2211yescharacteristic
25C2×C7×#126C2212yescomplemented
26C2×#6503C2211yescharacteristic
27C2×#6501C2211yescharacteristic
28#90395—216no—
29C2×#6461C2212yescomplemented
30C2×#6459C2212yes—
31C2×#6458C2211yescharacteristic
32C2×#6458C2212yes—
33C2×#6458C2211yescharacteristic
34C2×#6458C2212yescomplemented
35C2×#6458C2212yescomplemented
36C2×#6458C2211yescharacteristic, complemented
37C2×#6457C2212yescomplemented
38C2×#6456C2211yescharacteristic
39C2×#6456C2211yescharacteristic
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×#6451C2211yescharacteristic, complemented
42C2×#6448C2212yescomplemented
43C2×#6448C2212yescomplemented
44C2×#6447C2212yescomplemented
45C2×#6446C2212yescomplemented
46C2×#6445C2212yes—
47C2×#6445C2212yes—
48C2×#6445C2212yes—
49C2×D7×C22⋊C4C2212yes—
50C2×D7×C22⋊C4C2212yes—
51C2×#6438C2212yescomplemented
52C2×#6437C2211yescharacteristic
53C2×C4×D28C2212yes—
54C2×C4×D28C2211yescharacteristic
55C2×C4×D28C2211yescharacteristic, complemented
56C2×C42×D7C2211yescharacteristic
57C2×C42×D7C2211yescharacteristic, complemented
58C7×#397C2212yescomplemented
59C7×#396C2212yescomplemented
60C7×#390C2211yescharacteristic
61C7×#390C2211yescharacteristic
62C7×#390C2211yescharacteristic
63C7×#389C2211yescharacteristic, complemented
64C7×#388C2212yescomplemented
65C7×#384C2211yescharacteristic, complemented
66C4×C7×C4⋊C4C2211yescharacteristic, complemented
67C4×C7×C4⋊C4C2211yescharacteristic, complemented
68#89993C2211yescharacteristic
69#89766C2212yescomplemented
70#89763C2212yescomplemented
71#89762C2212yescomplemented
72#89761C2212yes—
73#89760C2211yescharacteristic
74#89760C2211yescharacteristic
75#89760C2211yescharacteristic, complemented
76#89760C2212yescomplemented
77#89760C2212yescomplemented
78#89759C2211yescharacteristic
79#89759C2211yescharacteristic, complemented
80#89757C2211yescharacteristic, complemented
81#89752C2212yescomplemented
82#89751C2212yescomplemented
83C4⋊C4×Dic7C2211yescharacteristic, complemented
84C4⋊C4×Dic7C2211yescharacteristic, complemented
85#89745C2211yescharacteristic, complemented
86#89733C2212yes—
87#89732C2212yes—
88#89732C2212yes—
89#89732C2212yes—
90#89732C2212yescomplemented
91#89731C2212yescomplemented
92#89729C2212yes—
93#89729C2212yes—
94#89729C2212yescomplemented
95#89729C2212yescomplemented
96#89728C2212yescomplemented
97#89728C2212yescomplemented
98#89727C2212yes—
99#89723C2212yescomplemented
100#89717C2212yescomplemented
101#89712C2212yescomplemented
102#89711C2211yescharacteristic
103#89711C2211yescharacteristic
104#89711C2211yescharacteristic, complemented
105C4×(C2×D7)⋊C4C2211yescharacteristic
106C4×(C2×D7)⋊C4C2212yescomplemented
107C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
108C42×Dic7C2211yescharacteristic, complemented
109#89700C2211yescharacteristic, complemented
110#89445C2212yescomplemented
111#89444C2212yescomplemented
112#89444C2212yescomplemented
113#89444C2212yescomplemented
114#89442C2212yescomplemented
115#89442C2212yescomplemented
116#89441C2212yescomplemented
117#89438C2211yescharacteristic
118#89438C2211yescharacteristic
119#89438C2211yescharacteristic, complemented
120#89438C2211yescharacteristic, complemented
121#89437C2212yes—
122#89437C2212yes—
123#89437C2212yescomplemented
124#35007—71nomaximal, Sylow
125C24×D7C2312yes—
126C22×C7×D4C2311yescharacteristic
127C22×C22⋊D7C2312yes—
128C22×C22⋊D7C2312yes—
129C22×C22⋊D7C2312yes—
130C22×C22⋊D7C2312yes—
131C2×D4×D7—24no—
132C2×D4×D7—42no—
133C2×D4×D7—42no—
134C22×D28C2312yes—
135C22×D28C2311yescharacteristic
136C22×D28C2311yescharacteristic
137C22×D28C2311yescharacteristic
138C22×D28C2312yes—
139C22×D28C2312yes—
140C22×D28C2312yes—
141C22×D28C2312yes—
142C22×C4×D7C2311yescharacteristic
143C22×C4×D7C2311yescharacteristic
144C22×C4×D7C2311yescharacteristic
145C22×C4×D7C2311yescharacteristic
146C22×C4×D7C2312yes—
147C22×C4×D7C2312yes—
148C22×C4×D7C2311yescharacteristic
149C22×C4×D7C2311yescharacteristic
150C22×Dic14C2312yes—
151C7×#126—28no—
152C2×C7×C4⋊C4C2311yescharacteristic
153C2×C7×C4⋊C4C2311yescharacteristic
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×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×C7C2312yes—
169C2×C42×C7C2311yescharacteristic
170C2×C22⋊Dic7C2312yes—
171C2×C22⋊Dic7C2312yes—
172C2×C22⋊Dic7C2312yes—
173#6503—42no—
174#6501—42no—
175C2×(C2×D7)⋊C4C2312yes—
176C2×(C2×D7)⋊C4C2312yes—
177C2×(C2×D7)⋊C4C2311yescharacteristic
178C2×(C2×D7)⋊C4C2311yescharacteristic
179C2×(C2×D7)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
196C2×(C2×D7)⋊C4C2311yescharacteristic
197C2×(C2×D7)⋊C4C2311yescharacteristic
198C2×(C2×D7)⋊C4C2311yescharacteristic
199C2×C4⋊Dic7C2312yes—
200C2×C4⋊Dic7C2311yescharacteristic
201C2×C4⋊Dic7C2311yescharacteristic
202C2×C4⋊Dic7C2311yescharacteristic
203C2×Dic7⋊C4C2312yes—
204C2×Dic7⋊C4C2312yes—
205C2×Dic7⋊C4C2312yes—
206C2×Dic7⋊C4C2312yes—
207C2×C4×Dic7C2311yescharacteristic
208C2×C4×Dic7C2311yescharacteristic
209C2×C4×Dic7C2311yescharacteristic
210C2×C4×Dic7C2311yescharacteristic
211C2×C4×Dic7C2311yescharacteristic
212C2×C4×Dic7C2311yescharacteristic
213C2×C4×Dic7C2311yescharacteristic
214C2×C4×Dic7C2311yescharacteristic
215C2×C4×Dic7C2311yescharacteristic
216C2×C4×Dic7C2311yescharacteristic
217#6461—28no—
218#6459—28no—
219#6458—28no—
220#6458—28no—
221#6458—24no—
222#6458—44no—
223#6458—42no—
224#6458—42no—
225#6457—28no—
226#6456—24no—
227#6456D418yescomplemented
228D7×C4⋊C4—42no—
229#6451—42no—
230#6448—28no—
231#6448—44no—
232#6447—28no—
233#6446—28no—
234#6445—28no—
235#6445—28no—
236#6445—28no—
237D7×C22⋊C4—28no—
238D7×C22⋊C4—44no—
239#6438—28no—
240#6437—42no—
241C4×D28—28no—
242C4×D28—24no—
243C4×D28—42no—
244C42×D7—42no—
245C42×D7—42no—
246C7×#95C2312yes—
247C7×#95C2312yes—
248C7×#95C2311yescharacteristic
249C7×#95C2311yescharacteristic
250C7⋊#95C2312yes—
251C7⋊#95C2312yes—
252C7⋊#95C2312yes—
253C7⋊#95C2311yescharacteristic
254C7⋊#95C2311yescharacteristic
255C7⋊#95C2311yescharacteristic
256C7⋊#95C2311yescharacteristic
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#2512D711yescharacteristic, complemented
269#2491—71no—
270#2472—72no—
271#2445—71no—
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—
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×D7C2411yescharacteristic
293C23×D7C2411yescharacteristic
294C2×C7×D4—22no—
295C2×C7×D4—22no—
296C2×C7×D4—22no—
297C22×C4×C7C2412yes—
298C22×C4×C7C2411yescharacteristic
299C22×C4×C7C2412yes—
300C22×C4×C7C2412yes—
301C22×C4×C7C2411yescharacteristic
302C22×C4×C7C2411yescharacteristic
303C22×C4×C7C2411yescharacteristic
304C22×C4×C7C2411yescharacteristic
305C22×C4×C7C2411yescharacteristic
306C22×C4×C7C2411yescharacteristic
307C2×C22⋊D7—24no—
308C2×C22⋊D7—24no—
309C2×C22⋊D7—24no—
310C2×C22⋊D7—24no—
311C2×C22⋊D7—42no—
312C2×C22⋊D7—42no—
313C2×C22⋊D7—42no—
314C2×C22⋊D7—42no—
315C2×C22⋊D7—42no—
316C2×C22⋊D7—42no—
317C2×C22⋊D7—42no—
318C2×C22⋊D7—42no—
319C22×Dic7C2411yescharacteristic
320C22×Dic7C2412yes—
321C22×Dic7C2412yes—
322C22×Dic7C2411yescharacteristic
323C22×Dic7C2411yescharacteristic
324C22×Dic7C2411yescharacteristic
325C22×Dic7C2411yescharacteristic
326C22×Dic7C2411yescharacteristic
327D4×D7—416no—
328C2×D28—22no—
329C2×D28—22no—
330C2×D28—24no—
331C2×D28—24no—
332C2×D28—24no—
333C2×D28—22no—
334C2×D28—22no—
335C2×D28—22no—
336C2×D28—22no—
337C2×D28—22no—
338C2×D28—22no—
339C2×D28—24no—
340C2×D28—24no—
341C2×D28—24no—
342C2×D28—24no—
343C2×D28—42no—
344C2×D28—42no—
345C2×D28—42no—
346C2×D28—42no—
347C2×D28—42no—
348C2×D28—42no—
349C2×D28—42no—
350C2×D28—42no—
351C2×D28C2×D414yes—
352C2×C4×D7—22no—
353C2×C4×D7—22no—
354C2×C4×D7—22no—
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—24no—
362C2×C4×D7—24no—
363C2×C4×D7—41no—
364C2×C4×D7—41no—
365C2×C4×D7—41no—
366C2×C4×D7—41no—
367C2×C4×D7—41no—
368C2×C4×D7—41no—
369C2×C4×D7—42no—
370C2×C4×D7—42no—
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—24no—
381C7×C4⋊C4—22no—
382C7×C4⋊C4—22no—
383C7×C4⋊C4—22no—
384C7×C4⋊C4—22no—
385C7×C4⋊C4—42no—
386C7×C4⋊C4C2×D414yescomplemented
387C7×C22⋊C4—24no—
388C7×C22⋊C4—24no—
389C7×C22⋊C4—24no—
390C7×C22⋊C4—24no—
391C7×C22⋊C4—42no—
392C7×C22⋊C4—42no—
393C42×C7—24no—
394C42×C7—22no—
395C42×C7—22no—
396C42×C7—22no—
397C22⋊Dic7—24no—
398C22⋊Dic7—24no—
399C22⋊Dic7—42no—
400(C2×D7)⋊C4—24no—
401(C2×D7)⋊C4—24no—
402(C2×D7)⋊C4—22no—
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—22no—
410(C2×D7)⋊C4—24no—
411(C2×D7)⋊C4—22no—
412(C2×D7)⋊C4—24no—
413(C2×D7)⋊C4—24no—
414(C2×D7)⋊C4—24no—
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)⋊C4C2×D414yes—
422(C2×D7)⋊C4C2×D414yescomplemented
423(C2×D7)⋊C4#4114yes—
424C4⋊Dic7—22no—
425C4⋊Dic7—22no—
426C4⋊Dic7—24no—
427C4⋊Dic7—22no—
428Dic7⋊C4—24no—
429Dic7⋊C4—24no—
430Dic7⋊C4—42no—
431Dic7⋊C4—42no—
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×#127—71no—
447C2×#126—72no—
448C2×#126C2×D712yescomplemented
449C2×#124—72no—
450C2×#124—72no—
451C2×#124—72no—
452C2×#123—72no—
453C2×#123—72no—
454C2×C22⋊Q8—72no—
455C2×#121—71no—
456C2×#121—72no—
457C2×#121—72no—
458C2×#121—71no—
459C2×#121—71no—
460C2×#121—71no—
461C2×#121—72no—
462C2×#121—72no—
463C2×#120—72no—
464C2×#120—72no—
465C2×#120—72no—
466C2×C4×D4—71no—
467C2×C4×D4—71no—
468C2×C4×D4—72no—
469C2×C4×D4—71no—
470C2×C4×D4—71no—
471C22×C4⋊C4—71no—
472C22×C22⋊C4—72no—
473C22×C22⋊C4—72no—
474C22×C42—71no—
475C22×C42—71no—
476#398—72no—
477#397C2×D712yescomplemented
478#396—72no—
479#396C2×D712yescomplemented
480#395—72no—
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—71no—
493#390—72no—
494#390—71no—
495#390—71no—
496#390—72no—
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
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#388C2×D712yescomplemented
520#386—72no—
521#386—72no—
522#386—72no—
523#386—72no—
524#386—72no—
525#385—72no—
526#384C2×D711yescharacteristic, complemented
527#380—71no—
528#380—71no—
529#379—72no—
530C4×C4⋊C4—71no—
531C4×C4⋊C4—71no—
532C4×C4⋊C4C2×D711yescharacteristic, complemented
533C4×C4⋊C4C2×D711yescharacteristic, complemented
534C4×C22⋊C4—71no—
535C4×C22⋊C4—71no—
536C4×C22⋊C4—72no—
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×C7C2511yescharacteristic
550C22×D7—21no—
551C22×D7—21no—
552C22×D7—21no—
553C22×D7—21no—
554C22×D7—21no—
555C22×D7—21no—
556C22×D7—21no—
557C22×D7—21no—
558C22×D7—21no—
559C22×D7—21no—
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—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—
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—22no—
595C2×C4×C7—22no—
596C2×C4×C7—22no—
597C2×C4×C7—21no—
598C2×C4×C7—22no—
599C2×C4×C7—21no—
600C2×C4×C7—22no—
601C2×C4×C7—21no—
602C2×C4×C7—21no—
603C2×C4×C7—22no—
604C2×C4×C7—22no—
605C2×C4×C7—22no—
606C2×C4×C7—22no—
607C2×C4×C7—21no—
608C2×C4×C7—21no—
609C2×C4×C7C22×D412yes—
610C2×C4×C7C22×D412yes—
611C2×C4×C7C22×D412yes—
612C2×C4×C7C2×#4112yes—
613C2×C4×C7C2×#4112yes—
614C2×C4×C7H(5,𝔽2)12yes—
615C2×C4×C7H(5,𝔽2)12yes—
616C22⋊D7—48no—
617C22⋊D7—84no—
618C22⋊D7—84no—
619C22⋊D7—84no—
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—21no—
629C2×Dic7—21no—
630C2×Dic7—22no—
631C2×Dic7—22no—
632C2×Dic7—21no—
633C2×Dic7—21no—
634C2×Dic7—22no—
635C2×Dic7—22no—
636C2×Dic7—21no—
637C2×Dic7—22no—
638C2×Dic7—22no—
639C2×Dic7C22×D412yes—
640C2×Dic7C22×D412yes—
641C2×Dic7C2×#4112yes—
642C2×Dic7C2×#4112yes—
643C2×Dic7H(5,𝔽2)12yes—
644D28—28no—
645D28—48no—
646D28—44no—
647D28—44no—
648D28—84no—
649D28—84no—
650D28—84no—
651D28—84no—
652C4×D7—28no—
653C4×D7—44no—
654C4×D7—44no—
655C4×D7—44no—
656C4×D7—44no—
657C4×D7—44no—
658C4×D7—84no—
659C4×D7—84no—
660Dic14—84no—
661C25—72no—
662C22×Q8—72no—
663C22×D4—72no—
664C22×D4—72no—
665C22×D4—72no—
666C22×D4—72no—
667C22×D4—71no—
668C22×D4—72no—
669C22×D4—71no—
670C22×D4—71no—
671C22×D4—72no—
672C22×D4—72no—
673C22×D4—72no—
674C22×D4—72no—
675C22×D4—144no—
676C22×D4—282no—
677C22×D4—282no—
678C22×D4C22×D711yescharacteristic
679C23×C4—71no—
680C23×C4—71no—
681C23×C4—71no—
682C23×C4—71no—
683C23×C4—71no—
684C23×C4—71no—
685C23×C4—72no—
686C23×C4—72no—
687C4⋊Q8—282no—
688#127—282no—
689#127—282no—
690#126—28no—
691#126—148no—
692#124—148no—
693#124—148no—
694#124—284no—
695#123—148no—
696#123—148no—
697C22⋊Q8—148no—
698#121—148no—
699#121—148no—
700#121—144no—
701#121—148no—
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—71no—
715C2×C4⋊C4—71no—
716C2×C4⋊C4—72no—
717C2×C4⋊C4—71no—
718C2×C4⋊C4—72no—
719C2×C4⋊C4—72no—
720C2×C4⋊C4—72no—
721C2×C4⋊C4—72no—
722C2×C4⋊C4—282no—
723C2×C4⋊C4C22×D711yescharacteristic
724C2×C4⋊C4C22×D711yescharacteristic
725C2×C4⋊C4C22×D712yes—
726C2×C4⋊C4C22×D712yes—
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—71no—
742C2×C22⋊C4—71no—
743C2×C22⋊C4—71no—
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—148no—
759C2×C22⋊C4—284no—
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—71no—
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—282no—
777C2×C42—282no—
778C2×C42C22×D712yes—
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#95C22×D711yescharacteristic
792#95C22×D711yescharacteristic
793#95C22×D712yes—
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×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—22no—
813C2×D7—22no—
814C2×D7—22no—
815C2×D7—22no—
816C2×D7—22no—
817C2×D7—22no—
818C2×D7—41no—
819C2×D7—41no—
820C2×D7—41no—
821C2×D7—41no—
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—816no—
837C2×D7#53214yes—
838C4×C7—22no—
839C4×C7—22no—
840C4×C7—22no—
841C4×C7—22no—
842C4×C7—42no—
843C4×C7—41no—
844C4×C7—42no—
845C4×C7—42no—
846C4×C7—41no—
847C4×C7#53814yescomplemented
848Dic7—22no—
849Dic7—22no—
850Dic7—22no—
851Dic7—22no—
852Dic7—22no—
853Dic7—41no—
854Dic7—42no—
855Dic7—42no—
856C24—71no—
857C24—71no—
858C24—72no—
859C24—72no—
860C24—144no—
861C24—144no—
862C24—144no—
863C24—282no—
864C24—282no—
865C24—282no—
866C24—282no—
867C24C23×D712yes—
868C2×Q8—144no—
869C2×Q8—282no—
870C2×Q8—282no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—74no—
875C2×D4—142no—
876C2×D4—142no—
877C2×D4—144no—
878C2×D4—144no—
879C2×D4—144no—
880C2×D4—144no—
881C2×D4—144no—
882C2×D4—144no—
883C2×D4—144no—
884C2×D4—144no—
885C2×D4—144no—
886C2×D4—144no—
887C2×D4—142no—
888C2×D4—142no—
889C2×D4—144no—
890C2×D4—142no—
891C2×D4—142no—
892C2×D4—142no—
893C2×D4—142no—
894C2×D4—282no—
895C2×D4—282no—
896C2×D4—282no—
897C2×D4—282no—
898C2×D4—282no—
899C2×D4—282no—
900C2×D4—282no—
901C2×D4—282no—
902C2×D4—2816no—
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—71no—
912C22×C4—71no—
913C22×C4—71no—
914C22×C4—71no—
915C22×C4—71no—
916C22×C4—74no—
917C22×C4—74no—
918C22×C4—74no—
919C22×C4—71no—
920C22×C4—72no—
921C22×C4—72no—
922C22×C4—142no—
923C22×C4—142no—
924C22×C4—142no—
925C22×C4—144no—
926C22×C4—142no—
927C22×C4—142no—
928C22×C4—142no—
929C22×C4—142no—
930C22×C4—142no—
931C22×C4—142no—
932C22×C4—144no—
933C22×C4—281no—
934C22×C4—281no—
935C22×C4—281no—
936C22×C4—281no—
937C22×C4—281no—
938C22×C4—281no—
939C22×C4—282no—
940C22×C4—282no—
941C22×C4—282no—
942C22×C4—282no—
943C22×C4C23×D712yes—
944C22×C4C23×D711yescharacteristic
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—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—42no—
960C4⋊C4—144no—
961C4⋊C4—142no—
962C4⋊C4—144no—
963C4⋊C4—144no—
964C4⋊C4—142no—
965C4⋊C4—142no—
966C4⋊C4—282no—
967C4⋊C4—282no—
968C4⋊C4D4×D714yescomplemented
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—74no—
976C22⋊C4—74no—
977C22⋊C4—74no—
978C22⋊C4—144no—
979C22⋊C4—144no—
980C22⋊C4—142no—
981C22⋊C4—142no—
982C22⋊C4—144no—
983C22⋊C4—144no—
984C22⋊C4—144no—
985C22⋊C4—144no—
986C22⋊C4—144no—
987C22⋊C4—142no—
988C22⋊C4—144no—
989C22⋊C4—144no—
990C22⋊C4—144no—
991C22⋊C4—144no—
992C22⋊C4—144no—
993C22⋊C4—144no—
994C22⋊C4—144no—
995C22⋊C4—282no—
996C22⋊C4—282no—
997C22⋊C4—282no—
998C22⋊C4—282no—
999C22⋊C4—282no—
1000C22⋊C4—282no—
1001C22⋊C4—282no—
1002C42—24no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—74no—
1007C42—142no—
1008C42—142no—
1009C42—142no—
1010C42—142no—
1011C42—281no—
1012C42—281no—
1013C42—281no—
1014C42—281no—
1015C42—281no—
1016C2×C7—82no—
1017C2×C7C2×#53211yescharacteristic
1018C2×C7C2×#53811yescharacteristic
1019C2×C7#346011yescharacteristic
1020C2×C7#349611yescharacteristic
1021C2×C7#349811yescharacteristic
1022C2×C7#351411yescharacteristic
1023C2×C7#351911yescharacteristic
1024D7—24no—
1025D7—42no—
1026D7—82no—
1027D7—82no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—72no—
1036C23—72no—
1037C23—72no—
1038C23—72no—
1039C23—141no—
1040C23—141no—
1041C23—141no—
1042C23—141no—
1043C23—141no—
1044C23—141no—
1045C23—141no—
1046C23—141no—
1047C23—141no—
1048C23—141no—
1049C23—142no—
1050C23—142no—
1051C23—142no—
1052C23—142no—
1053C23—142no—
1054C23—142no—
1055C23—142no—
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—148no—
1074D4—288no—
1075D4—288no—
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—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—72no—
1109C2×C4—72no—
1110C2×C4—72no—
1111C2×C4—72no—
1112C2×C4—72no—
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—141no—
1122C2×C4—141no—
1123C2×C4—148no—
1124C2×C4—142no—
1125C2×C4—142no—
1126C2×C4—141no—
1127C2×C4—141no—
1128C2×C4—141no—
1129C2×C4—142no—
1130C2×C4—142no—
1131C2×C4—142no—
1132C2×C4—142no—
1133C2×C4—284no—
1134C2×C4—284no—
1135C2×C4—284no—
1136C2×C4—284no—
1137C2×C4—284no—
1138C2×C4—564no—
1139C2×C4—564no—
1140C2×C4C2×D4×D712yes—
1141C2×C4C2×D4×D712yes—
1142C2×C4C2×D4×D712yes—
1143C2×C4D7×#4112yes—
1144C2×C4D7×#4112yes—
1145C2×C4#655312yes—
1146C2×C4#655312yes—
1147C7#3500711yescharacteristic, complemented, Sylow
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—74no—
1156C22—142no—
1157C22—142no—
1158C22—142no—
1159C22—142no—
1160C22—142no—
1161C22—142no—
1162C22—142no—
1163C22—142no—
1164C22—142no—
1165C22—281no—
1166C22—281no—
1167C22—281no—
1168C22—281no—
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—282no—
1183C22—5616no—
1184C22C22×D4×D711yescharacteristic
1185C22C2×D7×#4111yescharacteristic
1186C22C2×D7×#4111yescharacteristic
1187C22C2×#655311yescharacteristic
1188C22C2×#655311yescharacteristic
1189C22D7×H(5,𝔽2)11yescharacteristic
1190C22#9062011yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—41no—
1199C4—41no—
1200C4—142no—
1201C4—142no—
1202C4—142no—
1203C4—142no—
1204C4—142no—
1205C4—282no—
1206C4—282no—
1207C4—281no—
1208C4#9039514yescomplemented
1209C2—82no—
1210C2—144no—
1211C2—282no—
1212C2—562no—
1213C2—562no—
1214C2C2×#9039511yescharacteristic
1215C2D7×#53211yescharacteristic
1216C2#1174359211yescharacteristic
1217C2#1174377011yescharacteristic
1218C2#1174383811yescharacteristic
1219C2#1174395511yescharacteristic
1220C2#1174405411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2512C2
hypercenter#2512D7
hypocenterC7#35007
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2512

Complements

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

NH ≅ G/Ntype
1. C2×#90395C2semidirect
2. C7×#2512C2semidirect
3. #11740553C2semidirect
4. #11735009C2semidirect
5. #11734919C2semidirect
6. #11734861C2semidirect
7. #11734789C2semidirect
8. #11733920C2semidirect
9. #11733889C2semidirect
10. #11733881C2semidirect
11. D7×#390C2semidirect
12. #11733869C2semidirect
13. #11733759C2semidirect
14. #11733656C2semidirect
15. #11733636C2semidirect
16. #11733272C2semidirect
17. #11733042C2semidirect
18. #11731820C2semidirect
19. #11731771C2semidirect
20. #11731233C2semidirect
21. #11731225C2semidirect
22. C4×#6458C2semidirect
23. C4×#6456C2semidirect
25. C2×C7×#126C22semidirect
29. C2×#6461C22semidirect
34. C2×#6458C22semidirect
35. C2×#6458C22semidirect
36. C2×#6458C22semidirect
37. C2×#6457C22semidirect
41. C2×#6451C22semidirect
42. C2×#6448C22semidirect
43. C2×#6448C22semidirect
44. C2×#6447C22semidirect
45. C2×#6446C22semidirect
51. C2×#6438C22semidirect
55. C2×C4×D28C22semidirect
57. C2×C42×D7C22semidirect
58. C7×#397C22semidirect
59. C7×#396C22semidirect
63. C7×#389C22semidirect
64. C7×#388C22semidirect
65. C7×#384C22semidirect
66. C4×C7×C4⋊C4C22semidirect
67. C4×C7×C4⋊C4C22semidirect
69. #89766C22semidirect
70. #89763C22semidirect
71. #89762C22semidirect
75. #89760C22semidirect
76. #89760C22semidirect
77. #89760C22semidirect
79. #89759C22semidirect
80. #89757C22semidirect
81. #89752C22semidirect
82. #89751C22semidirect
83. C4⋊C4×Dic7C22semidirect
84. C4⋊C4×Dic7C22semidirect
85. #89745C22semidirect
90. #89732C22semidirect
91. #89731C22semidirect
94. #89729C22semidirect
95. #89729C22semidirect
96. #89728C22semidirect
97. #89728C22semidirect
99. #89723C22semidirect
100. #89717C22semidirect
101. #89712C22semidirect
104. #89711C22semidirect
106. C4×(C2×D7)⋊C4C22semidirect
107. C4×(C2×D7)⋊C4C22semidirect
108. C42×Dic7C22semidirect
109. #89700C22semidirect
110. #89445C22semidirect
111. #89444C22semidirect
112. #89444C22semidirect
113. #89444C22semidirect
114. #89442C22semidirect
115. #89442C22semidirect
116. #89441C22semidirect
119. #89438C22semidirect
120. #89438C22semidirect
123. #89437C22semidirect
227. #6456D4semidirect
268. #2512D7semidirect
374. C2×C4×D7C2×D4semidirect
386. C7×C4⋊C4C2×D4semidirect
422. (C2×D7)⋊C4C2×D4semidirect
441. C4×Dic7C2×D4semidirect
448. C2×#126C2×D7semidirect
477. #397C2×D7semidirect
479. #396C2×D7semidirect
511. #389C2×D7semidirect
519. #388C2×D7semidirect
526. #384C2×D7semidirect
532. C4×C4⋊C4C2×D7semidirect
533. C4×C4⋊C4C2×D7semidirect
847. C4×C7#538semidirect
968. C4⋊C4D4×D7semidirect
1147. C7#35007semidirect
1208. C4#90395semidirect

Maximal subgroups

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

subgroupindex
C2×#903952
C7×#25122
#117405532
#117350092
#117349192
#117348612
#117347892
#117339202
#117338892
#117338812
D7×#3902
#117338692
#117337592
#117336562
#117336362
#117332722
#117330422
#117318202
#117317712
#117312332
#117312252
C4×#64582
C4×#64562
#350077