Finite Group Databasebeta

← #13526760

Subgroups — #13526760

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×#2860C211yesmaximal, characteristic, complemented
3#11740558C212yesmaximal, complemented
4#11733921C211yesmaximal, characteristic, complemented
5#11733897C211yesmaximal, characteristic, complemented
6#11733881C211yesmaximal, characteristic, complemented
7D7×#390C211yesmaximal, characteristic, complemented
8#11733763C211yesmaximal, characteristic, complemented
9#11733759C211yesmaximal, characteristic, complemented
10#11733731C211yesmaximal, characteristic, complemented
11#11733665C211yesmaximal, characteristic, complemented
12#11733656C211yesmaximal, characteristic, complemented
13#11733492C211yesmaximal, characteristic, complemented
14#11733443C211yesmaximal, characteristic, complemented
15#11733409C211yesmaximal, characteristic, complemented
16#11733355C212yesmaximal, complemented
17#11733291C212yesmaximal, complemented
18#11733271C212yesmaximal, complemented
19#11733042C212yesmaximal, complemented
20#11733040C212yesmaximal, complemented
21#11732971C212yesmaximal, complemented
22#11730758C211yesmaximal, characteristic, complemented
23C42×D28C211yesmaximal, characteristic, complemented
24C22×D4×D7C2211yescharacteristic
25C2×C7×#126C2212yescomplemented
26C2×#6503C2211yescharacteristic
27C2×#6501C2211yescharacteristic
28#90395—216no—
29C2×#6461C2212yescomplemented
30C2×#6459C2212yes—
31C2×#6458C2212yes—
32C2×#6458C2211yescharacteristic
33C2×#6458C2211yescharacteristic
34C2×#6458C2212yescomplemented
35C2×#6458C2211yescharacteristic, complemented
36C2×#6457C2212yescomplemented
37C2×#6456C2212yes—
38C2×#6456C2211yescharacteristic, complemented
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×#6448C2212yescomplemented
41C2×#6447C2212yescomplemented
42C2×#6447C2212yescomplemented
43C2×#6446C2212yescomplemented
44C2×#6445C2212yes—
45C2×#6445C2212yes—
46C2×#6445C2212yes—
47C2×D7×C22⋊C4C2212yes—
48C2×D7×C22⋊C4C2212yes—
49C2×#6438C2212yescomplemented
50C2×#6438C2212yescomplemented
51C2×#6437C2211yescharacteristic
52C2×C4×D28C2211yescharacteristic
53C2×C4×D28C2211yescharacteristic
54C2×C4×D28C2211yescharacteristic
55C2×C42×D7C2211yescharacteristic
56C2×C42×D7C2211yescharacteristic, complemented
57C2×#6432C2211yescharacteristic, complemented
58C7×#390C2211yescharacteristic
59C7×#390C2211yescharacteristic
60C7×#390C2211yescharacteristic
61C7×#389C2211yescharacteristic, complemented
62C7×#389C2211yescharacteristic, complemented
63C7×#389C2211yescharacteristic, complemented
64C7×#388C2212yescomplemented
65C7×#388C2212yescomplemented
66C7×#388C2212yescomplemented
67C43×C7C2211yescharacteristic, complemented
68#89993C2211yescharacteristic
69#89766C2212yescomplemented
70#89766C2212yescomplemented
71#89763C2212yescomplemented
72#89762C2212yescomplemented
73#89762C2212yescomplemented
74#89760C2211yescharacteristic
75#89760C2211yescharacteristic
76#89759C2211yescharacteristic
77#89759C2211yescharacteristic, complemented
78#89751C2212yescomplemented
79#89748C2211yescharacteristic, complemented
80C4⋊C4×Dic7C2211yescharacteristic, complemented
81#89745C2211yescharacteristic, complemented
82#89733C2212yes—
83#89733C2212yescomplemented
84#89733C2212yescomplemented
85#89732C2212yes—
86#89732C2212yes—
87#89732C2212yes—
88#89731C2212yescomplemented
89#89729C2212yes—
90#89729C2212yes—
91#89729C2212yescomplemented
92#89729C2212yescomplemented
93#89728C2212yescomplemented
94#89727C2212yes—
95#89723C2212yescomplemented
96#89719C2212yescomplemented
97#89711C2211yescharacteristic
98#89711C2211yescharacteristic
99#89711C2211yescharacteristic, complemented
100#89711C2212yescomplemented
101#89711C2212yescomplemented
102#89711C2211yescharacteristic, complemented
103C4×(C2×D7)⋊C4C2211yescharacteristic
104C4×(C2×D7)⋊C4C2211yescharacteristic
105C4×(C2×D7)⋊C4C2211yescharacteristic
106C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
107C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
109C4×C4⋊Dic7C2211yescharacteristic, complemented
110C4×C4⋊Dic7C2211yescharacteristic, complemented
111C4×C4⋊Dic7C2211yescharacteristic, complemented
112#89447C2212yescomplemented
113#89444C2212yescomplemented
114#89443C2212yescomplemented
115#89441C2212yescomplemented
116#89441C2212yescomplemented
117#89440C2212yes—
118#89438C2212yescomplemented
119#89437C2212yes—
120#89437C2212yes—
121#89437C2212yescomplemented
122#89437C2212yescomplemented
123#89429C2212yescomplemented
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×D28C2311yescharacteristic
135C22×D28C2311yescharacteristic
136C22×D28C2312yes—
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⋊C4C2312yes—
154C2×C7×C4⋊C4C2311yescharacteristic
155C2×C7×C4⋊C4C2312yes—
156C2×C7×C4⋊C4C2311yescharacteristic
157C2×C7×C4⋊C4C2312yes—
158C2×C7×C22⋊C4C2312yes—
159C2×C7×C22⋊C4C2312yes—
160C2×C7×C22⋊C4C2312yes—
161C2×C7×C22⋊C4C2312yes—
162C2×C7×C22⋊C4C2312yes—
163C2×C7×C22⋊C4C2312yes—
164C2×C42×C7C2311yescharacteristic
165C2×C42×C7C2311yescharacteristic
166C2×C42×C7C2311yescharacteristic
167C2×C42×C7C2311yescharacteristic
168C2×C42×C7C2311yescharacteristic
169C2×C42×C7C2311yescharacteristic
170C2×C42×C7C2311yescharacteristic
171C2×C22⋊Dic7C2312yes—
172C2×C22⋊Dic7C2312yes—
173C2×C22⋊Dic7C2312yes—
174#6503—42no—
175#6501—42no—
176C2×(C2×D7)⋊C4C2311yescharacteristic
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)⋊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)⋊C4C2312yes—
196C2×(C2×D7)⋊C4C2312yes—
197C2×(C2×D7)⋊C4C2311yescharacteristic
198C2×(C2×D7)⋊C4C2311yescharacteristic
199C2×(C2×D7)⋊C4C2311yescharacteristic
200C2×C4⋊Dic7C2311yescharacteristic
201C2×C4⋊Dic7C2311yescharacteristic
202C2×C4⋊Dic7C2311yescharacteristic
203C2×C4⋊Dic7C2311yescharacteristic
204C2×C4⋊Dic7C2312yes—
205C2×C4⋊Dic7C2311yescharacteristic
206C2×Dic7⋊C4C2312yes—
207C2×Dic7⋊C4C2312yes—
208C2×Dic7⋊C4C2312yes—
209C2×Dic7⋊C4C2312yes—
210C2×C4×Dic7C2311yescharacteristic
211C2×C4×Dic7C2311yescharacteristic
212C2×C4×Dic7C2312yes—
213C2×C4×Dic7C2311yescharacteristic
214C2×C4×Dic7C2311yescharacteristic
215C2×C4×Dic7C2311yescharacteristic
216C2×C4×Dic7C2311yescharacteristic
217#6461—28no—
218#6459—28no—
219#6458—28no—
220#6458—24no—
221#6458—28no—
222#6458—42no—
223#6458—42no—
224#6457—28no—
225#6456—28no—
226#6456—42no—
227D7×C4⋊C4—42no—
228#6448—28no—
229#6447—28no—
230#6447—44no—
231#6446—28no—
232#6445—28no—
233#6445—28no—
234#6445—28no—
235D7×C22⋊C4—28no—
236D7×C22⋊C4—44no—
237#6438—28no—
238#6438—44no—
239#6437—42no—
240C4×D28—24no—
241C4×D28—24no—
242C4×D28D418yescomplemented
243C42×D7—42no—
244C42×D7—42no—
245#6432—42no—
246C7×#95C2312yes—
247C7×#95C2312yes—
248C7×#95C2312yes—
249C7⋊#95C2311yescharacteristic
250C7⋊#95C2312yes—
251C7⋊#95C2312yes—
252C7⋊#95C2312yes—
253C7⋊#95C2311yescharacteristic
254C7⋊#95C2312yes—
255C7⋊#95C2311yescharacteristic
256C7⋊#95C2311yescharacteristic
257C7⋊#95C2311yescharacteristic
258C7⋊#95C2311yescharacteristic
259C2×#538—72no—
260#2860D711yescharacteristic, complemented
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#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×C7C2412yes—
299C22×C4×C7C2411yescharacteristic
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×Dic7C2411yescharacteristic
321C22×Dic7C2412yes—
322C22×Dic7C2412yes—
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—24no—
382C7×C4⋊C4—22no—
383C7×C4⋊C4—22no—
384C7×C4⋊C4—22no—
385C7×C22⋊C4—24no—
386C7×C22⋊C4—24no—
387C7×C22⋊C4—24no—
388C7×C22⋊C4—24no—
389C7×C22⋊C4—24no—
390C7×C22⋊C4—42no—
391C42×C7—22no—
392C42×C7—22no—
393C42×C7—22no—
394C42×C7—22no—
395C42×C7—22no—
396C42×C7—41no—
397C42×C7C2×D414yescomplemented
398C22⋊Dic7—24no—
399C22⋊Dic7—42no—
400C22⋊Dic7—42no—
401(C2×D7)⋊C4—24no—
402(C2×D7)⋊C4—24no—
403(C2×D7)⋊C4—22no—
404(C2×D7)⋊C4—24no—
405(C2×D7)⋊C4—24no—
406(C2×D7)⋊C4—24no—
407(C2×D7)⋊C4—24no—
408(C2×D7)⋊C4—22no—
409(C2×D7)⋊C4—24no—
410(C2×D7)⋊C4—24no—
411(C2×D7)⋊C4—24no—
412(C2×D7)⋊C4—24no—
413(C2×D7)⋊C4—22no—
414(C2×D7)⋊C4—24no—
415(C2×D7)⋊C4—24no—
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)⋊C4C2×D414yes—
423(C2×D7)⋊C4C2×D414yescomplemented
424(C2×D7)⋊C4#4114yes—
425C4⋊Dic7—22no—
426C4⋊Dic7—22no—
427C4⋊Dic7—22no—
428C4⋊Dic7—22no—
429C4⋊Dic7—42no—
430C4⋊Dic7C2×D414yescomplemented
431Dic7⋊C4—24no—
432Dic7⋊C4—24no—
433Dic7⋊C4—42no—
434Dic7⋊C4—42no—
435C4×Dic7—22no—
436C4×Dic7—22no—
437C4×Dic7—24no—
438C4×Dic7—41no—
439C4×Dic7—41no—
440C4×Dic7—41no—
441C4×Dic7—41no—
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—71no—
458C2×#121—72no—
459C2×#121—71no—
460C2×#121—71no—
461C2×#121—72no—
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×D4—71no—
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#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—71no—
494#390—71no—
495#390—72no—
496#390—72no—
497#390—72no—
498#390—72no—
499#390—72no—
500#390—71no—
501#390—71no—
502#390—71no—
503#390—71no—
504#390—72no—
505#390C2×D711yescharacteristic
506#390C2×D711yescharacteristic
507#390C2×D711yescharacteristic
508#389—71no—
509#389C2×D711yescharacteristic, complemented
510#389C2×D711yescharacteristic, complemented
511#389C2×D711yescharacteristic, complemented
512#388—72no—
513#388—72no—
514#388—72no—
515#388—72no—
516#388—72no—
517#388C2×D712yescomplemented
518#388C2×D712yescomplemented
519#388C2×D712yescomplemented
520#386—72no—
521#386—72no—
522#386—72no—
523#386—72no—
524#386—72no—
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⋊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—71no—
540C4×C22⋊C4—72no—
541C43C2×D711yescharacteristic, complemented
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—21no—
595C2×C4×C7—21no—
596C2×C4×C7—22no—
597C2×C4×C7—22no—
598C2×C4×C7—22no—
599C2×C4×C7—21no—
600C2×C4×C7—22no—
601C2×C4×C7—22no—
602C2×C4×C7—22no—
603C2×C4×C7—22no—
604C2×C4×C7—21no—
605C2×C4×C7—22no—
606C2×C4×C7—21no—
607C2×C4×C7—22no—
608C2×C4×C7C22×D412yes—
609C2×C4×C7C22×D412yes—
610C2×C4×C7C22×D412yes—
611C2×C4×C7C2×#4112yes—
612C2×C4×C7C2×#4112yes—
613C2×C4×C7H(5,𝔽2)12yes—
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—22no—
629C2×Dic7—22no—
630C2×Dic7—21no—
631C2×Dic7—21no—
632C2×Dic7—21no—
633C2×Dic7—21no—
634C2×Dic7—22no—
635C2×Dic7—22no—
636C2×Dic7—22no—
637C2×Dic7—22no—
638C2×Dic7—21no—
639C2×Dic7—21no—
640C2×Dic7C22×D412yes—
641C2×Dic7C22×D412yes—
642C2×Dic7C2×#4112yes—
643C2×Dic7C2×#4112yes—
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—144no—
711C4×D4—144no—
712C4×D4—148no—
713C4×D4—282no—
714C2×C4⋊C4—71no—
715C2×C4⋊C4—71no—
716C2×C4⋊C4—71no—
717C2×C4⋊C4—71no—
718C2×C4⋊C4—72no—
719C2×C4⋊C4—71no—
720C2×C4⋊C4—72no—
721C2×C4⋊C4—72no—
722C2×C4⋊C4—72no—
723C2×C4⋊C4—72no—
724C2×C4⋊C4—282no—
725C2×C4⋊C4C22×D711yescharacteristic
726C2×C4⋊C4C22×D711yescharacteristic
727C2×C4⋊C4C22×D712yes—
728C2×C4⋊C4C22×D712yes—
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—71no—
741C2×C22⋊C4—71no—
742C2×C22⋊C4—71no—
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—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—72no—
767C2×C42—71no—
768C2×C42—71no—
769C2×C42—71no—
770C2×C42—71no—
771C2×C42—71no—
772C2×C42—71no—
773C2×C42—282no—
774C2×C42—282no—
775C2×C42C22×D711yescharacteristic
776C2×C42C22×D711yescharacteristic
777C2×C42C22×D711yescharacteristic
778C2×C42C22×D711yescharacteristic
779C2×C42C22×D711yescharacteristic
780C2×C42C22×D711yescharacteristic
781C2×C42C22×D711yescharacteristic
782#95—71no—
783#95—71no—
784#95—71no—
785#95—71no—
786#95—71no—
787#95—71no—
788#95—72no—
789#95—72no—
790#95—72no—
791#95—72no—
792#95C22×D712yes—
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—22no—
843C4×C7—42no—
844C4×C7—41no—
845C4×C7—42no—
846C4×C7—42no—
847C4×C7#53814yescomplemented
848Dic7—22no—
849Dic7—22no—
850Dic7—22no—
851Dic7—22no—
852Dic7—41no—
853Dic7—42no—
854Dic7—42no—
855Dic7—41no—
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—74no—
916C22×C4—74no—
917C22×C4—74no—
918C22×C4—71no—
919C22×C4—71no—
920C22×C4—72no—
921C22×C4—72no—
922C22×C4—142no—
923C22×C4—144no—
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—142no—
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—24no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—74no—
960C4⋊C4—144no—
961C4⋊C4—144no—
962C4⋊C4—142no—
963C4⋊C4—142no—
964C4⋊C4—142no—
965C4⋊C4—142no—
966C4⋊C4—282no—
967C4⋊C4—282no—
968C4⋊C4—282no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—42no—
975C22⋊C4—74no—
976C22⋊C4—74no—
977C22⋊C4—74no—
978C22⋊C4—144no—
979C22⋊C4—142no—
980C22⋊C4—144no—
981C22⋊C4—144no—
982C22⋊C4—144no—
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—142no—
992C22⋊C4—144no—
993C22⋊C4—144no—
994C22⋊C4—282no—
995C22⋊C4—282no—
996C22⋊C4—282no—
997C22⋊C4—282no—
998C22⋊C4—282no—
999C22⋊C4—282no—
1000C22⋊C4—282no—
1001C22⋊C4—282no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—41no—
1008C42—144no—
1009C42—142no—
1010C42—142no—
1011C42—281no—
1012C42—281no—
1013C42—281no—
1014C42—281no—
1015C42D4×D714yescomplemented
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—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—72no—
1108C2×C4—72no—
1109C2×C4—72no—
1110C2×C4—72no—
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—148no—
1120C2×C4—142no—
1121C2×C4—142no—
1122C2×C4—141no—
1123C2×C4—141no—
1124C2×C4—141no—
1125C2×C4—141no—
1126C2×C4—142no—
1127C2×C4—142no—
1128C2×C4—141no—
1129C2×C4—141no—
1130C2×C4—142no—
1131C2×C4—142no—
1132C2×C4—284no—
1133C2×C4—284no—
1134C2×C4—284no—
1135C2×C4—284no—
1136C2×C4—284no—
1137C2×C4—564no—
1138C2×C4—564no—
1139C2×C4C2×D4×D712yes—
1140C2×C4C2×D4×D712yes—
1141C2×C4C2×D4×D712yes—
1142C2×C4D7×#4112yes—
1143C2×C4D7×#4112yes—
1144C2×C4#655312yes—
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
1189C22C2×#655311yescharacteristic
1190C22#9061611yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—41no—
1200C4—142no—
1201C4—142no—
1202C4—142no—
1203C4—142no—
1204C4—281no—
1205C4—282no—
1206C4—282no—
1207C4—281no—
1208C4#9039514yescomplemented
1209C2—82no—
1210C2—144no—
1211C2—282no—
1212C2—562no—
1213C2—562no—
1214C2C2×#9039511yescharacteristic
1215C2#1174321611yescharacteristic
1216C2#1174323011yescharacteristic
1217C2#1174323411yescharacteristic
1218C2D7×#53211yescharacteristic
1219C2#1174330911yescharacteristic
1220C2#1174331011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2860C2
hypercenter#2860D7
hypocenterC7#35007
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. C2×#90395C2semidirect
2. C7×#2860C2semidirect
3. #11740558C2semidirect
4. #11733921C2semidirect
5. #11733897C2semidirect
6. #11733881C2semidirect
7. D7×#390C2semidirect
8. #11733763C2semidirect
9. #11733759C2semidirect
10. #11733731C2semidirect
11. #11733665C2semidirect
12. #11733656C2semidirect
13. #11733492C2semidirect
14. #11733443C2semidirect
15. #11733409C2semidirect
16. #11733355C2semidirect
17. #11733291C2semidirect
18. #11733271C2semidirect
19. #11733042C2semidirect
20. #11733040C2semidirect
21. #11732971C2semidirect
22. #11730758C2semidirect
23. C42×D28C2semidirect
25. C2×C7×#126C22semidirect
29. C2×#6461C22semidirect
34. C2×#6458C22semidirect
35. C2×#6458C22semidirect
36. C2×#6457C22semidirect
38. C2×#6456C22semidirect
40. C2×#6448C22semidirect
41. C2×#6447C22semidirect
42. C2×#6447C22semidirect
43. C2×#6446C22semidirect
49. C2×#6438C22semidirect
50. C2×#6438C22semidirect
56. C2×C42×D7C22semidirect
57. C2×#6432C22semidirect
61. C7×#389C22semidirect
62. C7×#389C22semidirect
63. C7×#389C22semidirect
64. C7×#388C22semidirect
65. C7×#388C22semidirect
66. C7×#388C22semidirect
67. C43×C7C22semidirect
69. #89766C22semidirect
70. #89766C22semidirect
71. #89763C22semidirect
72. #89762C22semidirect
73. #89762C22semidirect
77. #89759C22semidirect
78. #89751C22semidirect
79. #89748C22semidirect
80. C4⋊C4×Dic7C22semidirect
81. #89745C22semidirect
83. #89733C22semidirect
84. #89733C22semidirect
88. #89731C22semidirect
91. #89729C22semidirect
92. #89729C22semidirect
93. #89728C22semidirect
95. #89723C22semidirect
96. #89719C22semidirect
99. #89711C22semidirect
100. #89711C22semidirect
101. #89711C22semidirect
102. #89711C22semidirect
106. C4×(C2×D7)⋊C4C22semidirect
107. C4×(C2×D7)⋊C4C22semidirect
108. C4×(C2×D7)⋊C4C22semidirect
109. C4×C4⋊Dic7C22semidirect
110. C4×C4⋊Dic7C22semidirect
111. C4×C4⋊Dic7C22semidirect
112. #89447C22semidirect
113. #89444C22semidirect
114. #89443C22semidirect
115. #89441C22semidirect
116. #89441C22semidirect
118. #89438C22semidirect
121. #89437C22semidirect
122. #89437C22semidirect
123. #89429C22semidirect
242. C4×D28D4semidirect
260. #2860D7semidirect
374. C2×C4×D7C2×D4semidirect
397. C42×C7C2×D4semidirect
423. (C2×D7)⋊C4C2×D4semidirect
430. C4⋊Dic7C2×D4semidirect
448. C2×#126C2×D7semidirect
509. #389C2×D7semidirect
510. #389C2×D7semidirect
511. #389C2×D7semidirect
517. #388C2×D7semidirect
518. #388C2×D7semidirect
519. #388C2×D7semidirect
541. C43C2×D7semidirect
847. C4×C7#538semidirect
1015. C42D4×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×#28602
#117405582
#117339212
#117338972
#117338812
D7×#3902
#117337632
#117337592
#117337312
#117336652
#117336562
#117334922
#117334432
#117334092
#117333552
#117332912
#117332712
#117330422
#117330402
#117329712
#117307582
C42×D282
#350077