Finite Group Databasebeta

← #13526747

Subgroups — #13526747

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×#90284C212yesmaximal, complemented
2C7×#2433C211yesmaximal, characteristic, complemented
3#11741498C211yesmaximal, characteristic, complemented
4C2×#89993C211yesmaximal, characteristic, complemented
5#11740637C211yesmaximal, characteristic, complemented
6#11740631C211yesmaximal, characteristic, complemented
7#11740629C211yesmaximal, characteristic, complemented
8#11740621C211yesmaximal, characteristic, complemented
9#11740150C211yesmaximal, characteristic, complemented
10Dic7×#121C211yesmaximal, characteristic, complemented
11#11740034C212yesmaximal, complemented
12#11740031C212yesmaximal, complemented
13#11740023C212yesmaximal, complemented
14#11734154C212yesmaximal, complemented
15#11734153C212yesmaximal, complemented
16#11734135C212yesmaximal, complemented
17#11734134C212yesmaximal, complemented
18#11733920C211yesmaximal, characteristic, complemented
19#11733897C211yesmaximal, characteristic, complemented
20#11733870C211yesmaximal, characteristic, complemented
21#11733782C211yesmaximal, characteristic, complemented
22#11730938C211yesmaximal, characteristic, complemented
23C4×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
24C23×C7×D4C2211yescharacteristic
25C2×C7×#127C2211yescharacteristic
26C2×C7×#127C2211yescharacteristic
27C2×C7×#121C2211yescharacteristic
28C2×C7×#120C2212yes—
29C2×C7×#120C2212yes—
30C2×#6516C2212yes—
31C22×C22⋊Dic7C2212yes—
32C22×C22⋊Dic7C2212yes—
33C2×#6502C2212yes—
34C2×#6502C2212yescomplemented
35C2×#6501C2211yescharacteristic
36C2×#6501C2211yescharacteristic
37C2×#6501C2212yescomplemented
38C2×#6501C2212yescomplemented
39C2×#6501C2211yescharacteristic, complemented
40C2×#6499C2212yescomplemented
41C2×#6499C2212yescomplemented
42C2×#6498C2212yescomplemented
43C2×D4×Dic7C2212yes—
44C2×D4×Dic7C2211yescharacteristic, complemented
45C2×C4×C22⋊D7C2211yescharacteristic
46C22×C4⋊Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48#90284—216no—
49C2×#6448C2212yescomplemented
50C2×#6446C2212yescomplemented
51C2×(C22⋊D7)⋊C4C2211yescharacteristic
52C2×(C22⋊D7)⋊C4C2211yescharacteristic
53C2×#6442C2212yescomplemented
54C2×#6442C2212yescomplemented
55C2×#6441C2212yes—
56C2×C42×D7C2211yescharacteristic, complemented
57C2×#6432C2211yescharacteristic, complemented
58C7×#392C2212yes—
59C7×#392C2212yes—
60C7×#390C2211yescharacteristic
61C7×#390C2211yescharacteristic
62C4×C7×C22⋊C4C2211yescharacteristic
63#90019C2212yes—
64#89995C2212yes—
65#89995C2212yescomplemented
66#89994C2212yes—
67#89994C2212yescomplemented
68#89994C2212yescomplemented
69#89994C2212yescomplemented
70#89993C2211yescharacteristic
71#89993C2211yescharacteristic
72#89993C2211yescharacteristic
73#89993C2212yes—
74#89993C2211yescharacteristic
75#89993C2212yes—
76#89993C2211yescharacteristic
77#89993C2211yescharacteristic
78#89993C2212yescomplemented
79#89993C2212yescomplemented
80#89993C2212yescomplemented
81#89993C2212yescomplemented
82#89993C2211yescharacteristic, complemented
83#89993C2211yescharacteristic, complemented
84#89992C2212yes—
85#89992C2212yes—
86#89992C2212yescomplemented
87#89992C2212yescomplemented
88#89984C2211yescharacteristic
89#89759C2211yescharacteristic, complemented
90#89757C2211yescharacteristic, complemented
91C4⋊C4×Dic7C2211yescharacteristic, complemented
92#89745C2211yescharacteristic, complemented
93#89733C2212yescomplemented
94#89733C2212yescomplemented
95#89728C2212yescomplemented
96#89725C2212yescomplemented
97#89723C2212yescomplemented
98#89723C2212yescomplemented
99#89723C2212yescomplemented
100#89723C2212yescomplemented
101#89723C2212yescomplemented
102#89722C2212yes—
103#89720C2212yescomplemented
104#89720C2212yescomplemented
105#89719C2212yescomplemented
106#89717C2212yescomplemented
107#89717C2212yescomplemented
108#89716C2212yescomplemented
109C22⋊C4×Dic7C2211yescharacteristic
110C22⋊C4×Dic7C2211yescharacteristic
111C22⋊C4×Dic7C2212yescomplemented
112C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
113#89707C2211yescharacteristic, complemented
114C4×Dic7⋊C4C2211yescharacteristic, complemented
115C42×Dic7C2211yescharacteristic, complemented
116#89700C2211yescharacteristic, complemented
117#89700C2211yescharacteristic, complemented
118#89438C2211yescharacteristic, complemented
119#89438C2211yescharacteristic, complemented
120#89433C2212yescomplemented
121#89428C2212yescomplemented
122#89421C2211yescharacteristic, complemented
123#89421C2211yescharacteristic, complemented
124#35007—71nomaximal, Sylow
125C25×C7C2312yes—
126C22×C7×D4—24no—
127C22×C7×D4—42no—
128C22×C7×D4—42no—
129C22×C7×D4C2311yescharacteristic
130C22×C7×D4C2311yescharacteristic
131C22×C7×D4C2312yes—
132C22×C7×D4C2311yescharacteristic
133C22×C7×D4C2312yes—
134C22×C7×D4C2312yes—
135C22×C7×D4C2312yes—
136C22×C7×D4C2312yes—
137C22×C7×D4C2312yes—
138C23×C4×C7C2311yescharacteristic
139C22×C22⋊D7C2311yescharacteristic
140C22×C22⋊D7C2312yes—
141C22×C22⋊D7C2312yes—
142C22×C22⋊D7C2312yes—
143C23×Dic7C2311yescharacteristic
144C23×Dic7C2312yes—
145C23×Dic7C2312yes—
146C23×Dic7C2311yescharacteristic
147C22×C4×D7C2311yescharacteristic
148C22×C4×D7C2311yescharacteristic
149C22×C4×D7C2311yescharacteristic
150C22×Dic14C2312yes—
151C7×#127—42no—
152C7×#127—42no—
153C7×#121—24no—
154C7×#120—28no—
155C7×#120—28no—
156C2×C7×C4⋊C4C2311yescharacteristic
157C2×C7×C22⋊C4C2312yes—
158C2×C7×C22⋊C4C2312yes—
159C2×C7×C22⋊C4C2312yes—
160C2×C7×C22⋊C4C2312yes—
161C2×C7×C22⋊C4C2312yes—
162C2×C7×C22⋊C4C2311yescharacteristic
163C2×C7×C22⋊C4C2311yescharacteristic
164C2×C42×C7C2311yescharacteristic
165C2×C42×C7C2311yescharacteristic
166#6516—28no—
167C2×C22⋊Dic7—28no—
168C2×C22⋊Dic7—44no—
169C2×C22⋊Dic7C2312yes—
170C2×C22⋊Dic7C2312yes—
171C2×C22⋊Dic7C2312yes—
172C2×C22⋊Dic7C2312yes—
173C2×C22⋊Dic7C2312yes—
174C2×C22⋊Dic7C2312yes—
175C2×C22⋊Dic7C2312yes—
176C2×C22⋊Dic7C2311yescharacteristic
177C2×C22⋊Dic7C2312yes—
178C2×C22⋊Dic7C2312yes—
179C2×C22⋊Dic7C2312yes—
180C2×C22⋊Dic7C2312yes—
181C2×C22⋊Dic7C2312yes—
182C2×C22⋊Dic7C2312yes—
183C2×C22⋊Dic7C2312yes—
184C2×C22⋊Dic7C2312yes—
185C2×C22⋊Dic7C2312yes—
186C2×C22⋊Dic7C2312yes—
187C2×C22⋊Dic7C2312yes—
188C2×C22⋊Dic7C2312yes—
189C2×C22⋊Dic7C2312yes—
190C2×C22⋊Dic7C2312yes—
191#6502—28no—
192#6502—28no—
193#6501—28no—
194#6501—42no—
195#6501—42no—
196#6501—42no—
197#6501—44no—
198#6499—28no—
199#6499—44no—
200#6498—28no—
201D4×Dic7—28no—
202D4×Dic7—42no—
203C4×C22⋊D7—24no—
204C2×(C2×D7)⋊C4C2311yescharacteristic
205C2×(C2×D7)⋊C4C2312yes—
206C2×(C2×D7)⋊C4C2311yescharacteristic
207C2×(C2×D7)⋊C4C2311yescharacteristic
208C2×C4⋊Dic7—42no—
209C2×C4⋊Dic7C2311yescharacteristic
210C2×C4⋊Dic7C2311yescharacteristic
211C2×C4⋊Dic7C2312yes—
212C2×C4⋊Dic7C2312yes—
213C2×C4⋊Dic7C2311yescharacteristic
214C2×C4⋊Dic7C2311yescharacteristic
215C2×C4⋊Dic7C2312yes—
216C2×C4⋊Dic7C2312yes—
217C2×C4⋊Dic7C2312yes—
218C2×Dic7⋊C4C2312yes—
219C2×Dic7⋊C4C2312yes—
220C2×Dic7⋊C4C2312yes—
221C2×Dic7⋊C4C2311yescharacteristic
222C2×Dic7⋊C4C2311yescharacteristic
223C2×Dic7⋊C4C2311yescharacteristic
224C2×C4×Dic7—42no—
225C2×C4×Dic7C2311yescharacteristic
226C2×C4×Dic7C2312yes—
227C2×C4×Dic7C2311yescharacteristic
228C2×C4×Dic7C2311yescharacteristic
229C2×C4×Dic7C2311yescharacteristic
230C2×C4×Dic7C2311yescharacteristic
231C2×C4×Dic7C2311yescharacteristic
232C2×C4×Dic7C2311yescharacteristic
233C2×C4×Dic7C2311yescharacteristic
234C2×C4×Dic7C2311yescharacteristic
235C2×C4×Dic7C2311yescharacteristic
236C2×C4×Dic7C2311yescharacteristic
237#6448—28no—
238#6446—28no—
239(C22⋊D7)⋊C4—24no—
240(C22⋊D7)⋊C4D418yescomplemented
241#6442—28no—
242#6442—28no—
243#6441—28no—
244C42×D7—42no—
245#6432—42no—
246C7×#95C2311yescharacteristic
247C7×#95C2311yescharacteristic
248C7⋊#95C2311yescharacteristic
249C7⋊#95C2311yescharacteristic
250C7⋊#95C2312yes—
251C7⋊#95C2312yes—
252C7⋊#95C2312yes—
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#2445—71no—
272#2440—71no—
273#2433D711yescharacteristic, complemented
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×C7—24no—
283C24×C7—24no—
284C24×C7—24no—
285C24×C7—42no—
286C24×C7—42no—
287C24×C7—42no—
288C24×C7—42no—
289C24×C7C2412yes—
290C24×C7C2412yes—
291C24×C7C2412yes—
292C24×C7C2411yescharacteristic
293C23×D7C2411yescharacteristic
294C2×C7×D4—24no—
295C2×C7×D4—24no—
296C2×C7×D4—24no—
297C2×C7×D4—24no—
298C2×C7×D4—24no—
299C2×C7×D4—22no—
300C2×C7×D4—24no—
301C2×C7×D4—22no—
302C2×C7×D4—22no—
303C2×C7×D4—24no—
304C2×C7×D4—24no—
305C2×C7×D4—22no—
306C2×C7×D4—22no—
307C2×C7×D4—22no—
308C2×C7×D4—22no—
309C2×C7×D4—22no—
310C2×C7×D4—22no—
311C2×C7×D4—42no—
312C2×C7×D4—42no—
313C2×C7×D4—416no—
314C2×C7×D4—42no—
315C2×C7×D4—42no—
316C2×C7×D4—42no—
317C2×C7×D4—42no—
318C2×C7×D4—42no—
319C2×C7×D4—42no—
320C2×C7×D4—42no—
321C2×C7×D4—42no—
322C22×C4×C7—22no—
323C22×C4×C7—22no—
324C22×C4×C7#4114yes—
325C22×C4×C7C2412yes—
326C22×C4×C7C2411yescharacteristic
327C22×C4×C7C2411yescharacteristic
328C22×C4×C7C2411yescharacteristic
329C22×C4×C7C2411yescharacteristic
330C22×C4×C7C2411yescharacteristic
331C22×C4×C7C2411yescharacteristic
332C2×C22⋊D7—22no—
333C2×C22⋊D7—22no—
334C2×C22⋊D7—24no—
335C2×C22⋊D7—24no—
336C2×C22⋊D7—24no—
337C2×C22⋊D7—42no—
338C2×C22⋊D7—42no—
339C2×C22⋊D7—42no—
340C2×C22⋊D7—42no—
341C2×C22⋊D7—42no—
342C2×C22⋊D7—42no—
343C2×C22⋊D7C2×D414yes—
344C22×Dic7—22no—
345C22×Dic7—24no—
346C22×Dic7—22no—
347C22×Dic7—24no—
348C22×Dic7—41no—
349C22×Dic7—41no—
350C22×Dic7—41no—
351C22×Dic7—42no—
352C22×Dic7—42no—
353C22×Dic7—42no—
354C22×Dic7—42no—
355C22×Dic7C2×D414yes—
356C22×Dic7C2411yescharacteristic
357C22×Dic7C2411yescharacteristic
358C22×Dic7C2411yescharacteristic
359C22×Dic7C2412yes—
360C22×Dic7C2412yes—
361C22×Dic7C2412yes—
362C22×Dic7C2412yes—
363C22×Dic7C2411yescharacteristic
364C22×Dic7C2411yescharacteristic
365C22×Dic7C2411yescharacteristic
366C22×Dic7C2411yescharacteristic
367C2×C4×D7—22no—
368C2×C4×D7—22no—
369C2×C4×D7—22no—
370C2×C4×D7—22no—
371C2×C4×D7—22no—
372C2×C4×D7—41no—
373C2×C4×D7—41no—
374C2×C4×D7—41no—
375C2×C4×D7C2×D414yescomplemented
376C2×Dic14—24no—
377C2×Dic14—42no—
378C2×Dic14—42no—
379C7×C4⋊C4—22no—
380C7×C22⋊C4—24no—
381C7×C22⋊C4—24no—
382C7×C22⋊C4—24no—
383C7×C22⋊C4—24no—
384C7×C22⋊C4—24no—
385C7×C22⋊C4C2×D414yes—
386C7×C22⋊C4#4114yes—
387C42×C7—22no—
388C42×C7—22no—
389C22⋊Dic7—24no—
390C22⋊Dic7—22no—
391C22⋊Dic7—24no—
392C22⋊Dic7—24no—
393C22⋊Dic7—24no—
394C22⋊Dic7—24no—
395C22⋊Dic7—24no—
396C22⋊Dic7—24no—
397C22⋊Dic7—24no—
398C22⋊Dic7—24no—
399C22⋊Dic7—24no—
400C22⋊Dic7—24no—
401C22⋊Dic7—24no—
402C22⋊Dic7—42no—
403C22⋊Dic7—42no—
404C22⋊Dic7—42no—
405C22⋊Dic7—42no—
406C22⋊Dic7—42no—
407C22⋊Dic7—42no—
408C22⋊Dic7—42no—
409C22⋊Dic7—42no—
410C22⋊Dic7—42no—
411(C2×D7)⋊C4—24no—
412(C2×D7)⋊C4—22no—
413(C2×D7)⋊C4—22no—
414(C2×D7)⋊C4C2×D414yescomplemented
415C4⋊Dic7—24no—
416C4⋊Dic7—22no—
417C4⋊Dic7—22no—
418C4⋊Dic7—22no—
419C4⋊Dic7—22no—
420C4⋊Dic7—24no—
421C4⋊Dic7—42no—
422C4⋊Dic7—42no—
423C4⋊Dic7—42no—
424Dic7⋊C4—24no—
425Dic7⋊C4—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×D4C2×D711yescharacteristic
443#538—1416no—
444C2×C4⋊Q8—71no—
445C2×#127C2×D711yescharacteristic
446C2×#127C2×D711yescharacteristic
447C2×#126—72no—
448C2×#126—72no—
449C2×#124—72no—
450C2×#124—72no—
451C2×#124—72no—
452C2×#123—72no—
453C2×#123—72no—
454C2×C22⋊Q8—72no—
455C2×#121—72no—
456C2×#121—72no—
457C2×#121—72no—
458C2×#121—71no—
459C2×#121—71no—
460C2×#121—71no—
461C2×#121—72no—
462C2×#121C2×D711yescharacteristic
463C2×#120—72no—
464C2×#120C2×D712yes—
465C2×#120C2×D712yes—
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#392C2×D712yes—
491#392C2×D712yes—
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#390C2×D711yescharacteristic
507#390C2×D711yescharacteristic
508#389—71no—
509#389—71no—
510#389—71no—
511#389—71no—
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#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—72no—
537C4×C22⋊C4—71no—
538C4×C22⋊C4—71no—
539C4×C22⋊C4—71no—
540C4×C22⋊C4C2×D711yescharacteristic
541C43—71no—
542C23×C7—21no—
543C23×C7—21no—
544C23×C7—21no—
545C23×C7—21no—
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×C7—22no—
557C23×C7—22no—
558C23×C7—22no—
559C23×C7—22no—
560C23×C7—22no—
561C23×C7—22no—
562C23×C7—22no—
563C23×C7—22no—
564C23×C7—22no—
565C23×C7—22no—
566C23×C7—22no—
567C23×C7—48no—
568C23×C7—48no—
569C23×C7—48no—
570C23×C7—84no—
571C23×C7—84no—
572C23×C7—84no—
573C23×C7—84no—
574C23×C7C22×D412yes—
575C23×C7C2×#4112yes—
576C23×C7C2×#4112yes—
577C23×C7C2511yescharacteristic
578C22×D7—21no—
579C22×D7—21no—
580C22×D7—21no—
581C22×D7—21no—
582C22×D7—21no—
583C22×D7—21no—
584C22×D7C22×D412yes—
585C7×D4—48no—
586C7×D4—48no—
587C7×D4—44no—
588C7×D4—44no—
589C7×D4—44no—
590C7×D4—84no—
591C7×D4—84no—
592C7×D4—84no—
593C7×D4—84no—
594C2×C4×C7—21no—
595C2×C4×C7—21no—
596C2×C4×C7—21no—
597C2×C4×C7—21no—
598C2×C4×C7—21no—
599C2×C4×C7—21no—
600C2×C4×C7—21no—
601C2×C4×C7—21no—
602C2×C4×C7—21no—
603C2×C4×C7—21no—
604C2×C4×C7—28no—
605C2×C4×C7—22no—
606C2×C4×C7—22no—
607C2×C4×C7—22no—
608C2×C4×C7C22×D412yes—
609C2×C4×C7C22×D412yes—
610C2×C4×C7C2×#4112yes—
611C2×C4×C7C2×#4112yes—
612C2×C4×C7C2×#4112yes—
613C2×C4×C7C2×#4112yes—
614C2×C4×C7H(5,𝔽2)12yes—
615C2×C4×C7H(5,𝔽2)12yes—
616C22⋊D7—28no—
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—22no—
631C2×Dic7—22no—
632C2×Dic7—21no—
633C2×Dic7—21no—
634C2×Dic7—21no—
635C2×Dic7—21no—
636C2×Dic7—21no—
637C2×Dic7—21no—
638C2×Dic7—22no—
639C2×Dic7—22no—
640C2×Dic7—22no—
641C2×Dic7—22no—
642C2×Dic7—22no—
643C2×Dic7—22no—
644C2×Dic7—22no—
645C2×Dic7—21no—
646C2×Dic7—21no—
647C2×Dic7—21no—
648C2×Dic7—22no—
649C2×Dic7—44no—
650C2×Dic7—44no—
651C2×Dic7—84no—
652C2×Dic7—84no—
653C2×Dic7C22×D412yes—
654C2×Dic7C22×D412yes—
655C2×Dic7C22×D412yes—
656C2×Dic7H(5,𝔽2)12yes—
657C4×D7—44no—
658C4×D7—44no—
659C4×D7—44no—
660Dic14—84no—
661C25C22×D712yes—
662C22×Q8—72no—
663C22×D4—24no—
664C22×D4—42no—
665C22×D4—42no—
666C22×D4—71no—
667C22×D4—72no—
668C22×D4—72no—
669C22×D4—72no—
670C22×D4C22×D712yes—
671C22×D4C22×D711yescharacteristic
672C22×D4C22×D711yescharacteristic
673C22×D4C22×D711yescharacteristic
674C22×D4C22×D712yes—
675C22×D4C22×D712yes—
676C22×D4C22×D712yes—
677C22×D4C22×D712yes—
678C22×D4C22×D712yes—
679C23×C4—71no—
680C23×C4—71no—
681C23×C4—71no—
682C23×C4—72no—
683C23×C4—72no—
684C23×C4—71no—
685C23×C4—71no—
686C23×C4C22×D711yescharacteristic
687C4⋊Q8—282no—
688#127—42no—
689#127—42no—
690#126—148no—
691#126—148no—
692#124—148no—
693#124—148no—
694#124—284no—
695#123—148no—
696#123—148no—
697C22⋊Q8—148no—
698#121—24no—
699#121—148no—
700#121—148no—
701#121—148no—
702#121—284no—
703#121—282no—
704#121—282no—
705#121—282no—
706#120—28no—
707#120—28no—
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—71no—
717C2×C4⋊C4—71no—
718C2×C4⋊C4—72no—
719C2×C4⋊C4—71no—
720C2×C4⋊C4—71no—
721C2×C4⋊C4—72no—
722C2×C4⋊C4—72no—
723C2×C4⋊C4—72no—
724C2×C4⋊C4—71no—
725C2×C4⋊C4—72no—
726C2×C4⋊C4—72no—
727C2×C4⋊C4—72no—
728C2×C4⋊C4—72no—
729C2×C4⋊C4—282no—
730C2×C4⋊C4C22×D711yescharacteristic
731C2×C22⋊C4—71no—
732C2×C22⋊C4—72no—
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—72no—
742C2×C22⋊C4—72no—
743C2×C22⋊C4—72no—
744C2×C22⋊C4—72no—
745C2×C22⋊C4—71no—
746C2×C22⋊C4—71no—
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—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×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#95—72no—
791#95—72no—
792#95—72no—
793#95C22×D711yescharacteristic
794#95C22×D711yescharacteristic
795C22×C7—22no—
796C22×C7—22no—
797C22×C7—22no—
798C22×C7—22no—
799C22×C7—22no—
800C22×C7—22no—
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×C7—42no—
810C22×C7—42no—
811C22×C7—42no—
812C22×C7—42no—
813C22×C7—42no—
814C22×C7—42no—
815C22×C7—42no—
816C22×C7—42no—
817C22×C7—42no—
818C22×C7—42no—
819C22×C7—42no—
820C22×C7—42no—
821C22×C7—42no—
822C22×C7—816no—
823C22×C7#53214yes—
824C22×C7C23×D411yescharacteristic
825C22×C7C22×#4111yescharacteristic
826C22×C7C22×#4111yescharacteristic
827C22×C7C2×H(5,𝔽2)11yescharacteristic
828C22×C7C2×H(5,𝔽2)11yescharacteristic
829C22×C7C2×H(5,𝔽2)11yescharacteristic
830C22×C7#58511yescharacteristic
831C2×D7—22no—
832C2×D7—22no—
833C2×D7—22no—
834C2×D7—41no—
835C2×D7—41no—
836C2×D7—41no—
837C2×D7—41no—
838C4×C7—22no—
839C4×C7—22no—
840C4×C7—22no—
841C4×C7—22no—
842C4×C7—22no—
843C4×C7—42no—
844C4×C7#53814yescomplemented
845Dic7—22no—
846Dic7—22no—
847Dic7—22no—
848Dic7—22no—
849Dic7—41no—
850Dic7—41no—
851Dic7—42no—
852Dic7—42no—
853Dic7—42no—
854Dic7—42no—
855Dic7—41no—
856C24—24no—
857C24—24no—
858C24—24no—
859C24—42no—
860C24—42no—
861C24—42no—
862C24—42no—
863C24—71no—
864C24C23×D712yes—
865C24C23×D712yes—
866C24C23×D712yes—
867C24C23×D711yescharacteristic
868C2×Q8—144no—
869C2×Q8—282no—
870C2×Q8—282no—
871C2×D4—24no—
872C2×D4—24no—
873C2×D4—24no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—22no—
877C2×D4—24no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—24no—
881C2×D4—24no—
882C2×D4—22no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—416no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—74no—
900C2×D4—142no—
901C2×D4—142no—
902C2×D4—144no—
903C2×D4—144no—
904C2×D4—144no—
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—71no—
914C22×C4—71no—
915C22×C4—71no—
916C22×C4—71no—
917C22×C4—74no—
918C22×C4—74no—
919C22×C4—71no—
920C22×C4—71no—
921C22×C4—71no—
922C22×C4—72no—
923C22×C4—72no—
924C22×C4—72no—
925C22×C4—72no—
926C22×C4—142no—
927C22×C4—142no—
928C22×C4—144no—
929C22×C4—142no—
930C22×C4—144no—
931C22×C4—142no—
932C22×C4—142no—
933C22×C4—142no—
934C22×C4—142no—
935C22×C4—281no—
936C22×C4—281no—
937C22×C4—281no—
938C22×C4—281no—
939C22×C4—281no—
940C22×C4—281no—
941C22×C4—282no—
942C22×C4—282no—
943C22×C4—282no—
944C22×C4—282no—
945C22×C4#115914yes—
946C22×C4C23×D712yes—
947C22×C4C23×D711yescharacteristic
948C22×C4C23×D711yescharacteristic
949C22×C4C23×D711yescharacteristic
950C22×C4C23×D711yescharacteristic
951C22×C4C23×D711yescharacteristic
952C22×C4C23×D711yescharacteristic
953C4⋊C4—22no—
954C4⋊C4—74no—
955C4⋊C4—144no—
956C4⋊C4—144no—
957C4⋊C4—144no—
958C4⋊C4—144no—
959C4⋊C4—144no—
960C4⋊C4—142no—
961C4⋊C4—142no—
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—74no—
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—144no—
984C22⋊C4—144no—
985C22⋊C4—144no—
986C22⋊C4—144no—
987C22⋊C4—144no—
988C22⋊C4—142no—
989C22⋊C4—142no—
990C22⋊C4—142no—
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#115914yes—
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×C7—82no—
1018C2×C7—82no—
1019C2×C7—82no—
1020C2×C7C2×#53211yescharacteristic
1021C2×C7C2×#53811yescharacteristic
1022C2×C7#346011yescharacteristic
1023C2×C7#349611yescharacteristic
1024C2×C7#349811yescharacteristic
1025C2×C7#351411yescharacteristic
1026C2×C7#351911yescharacteristic
1027D7—42no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—48no—
1054C23—48no—
1055C23—48no—
1056C23—72no—
1057C23—84no—
1058C23—84no—
1059C23—84no—
1060C23—84no—
1061C23—141no—
1062C23—141no—
1063C23—141no—
1064C23—141no—
1065C23—141no—
1066C23—141no—
1067C23C2×D4×D712yes—
1068C23C2×#115912yes—
1069C23C2×#115912yes—
1070C23C24×D711yescharacteristic
1071Q8—564no—
1072D4—48no—
1073D4—48no—
1074D4—44no—
1075D4—44no—
1076D4—44no—
1077D4—84no—
1078D4—84no—
1079D4—84no—
1080D4—84no—
1081D4—148no—
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—72no—
1100C2×C4—72no—
1101C2×C4—72no—
1102C2×C4—72no—
1103C2×C4—141no—
1104C2×C4—141no—
1105C2×C4—141no—
1106C2×C4—141no—
1107C2×C4—141no—
1108C2×C4—141no—
1109C2×C4—141no—
1110C2×C4—141no—
1111C2×C4—142no—
1112C2×C4—142no—
1113C2×C4—142no—
1114C2×C4—142no—
1115C2×C4—141no—
1116C2×C4—141no—
1117C2×C4—141no—
1118C2×C4—141no—
1119C2×C4—141no—
1120C2×C4—141no—
1121C2×C4—142no—
1122C2×C4—142no—
1123C2×C4—142no—
1124C2×C4—142no—
1125C2×C4—141no—
1126C2×C4—142no—
1127C2×C4—142no—
1128C2×C4—142no—
1129C2×C4—141no—
1130C2×C4—141no—
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×#115912yes—
1142C2×C4C2×#115912yes—
1143C2×C4C2×#115912yes—
1144C2×C4C2×#115912yes—
1145C2×C4#654812yes—
1146C2×C4#654812yes—
1147C7#3500711yescharacteristic, complemented, Sylow
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—816no—
1176C22—142no—
1177C22—142no—
1178C22—142no—
1179C22—281no—
1180C22—281no—
1181C22—281no—
1182C22—281no—
1183C22#9040714yes—
1184C22C22×D4×D711yescharacteristic
1185C22C22×#115911yescharacteristic
1186C22C22×#115911yescharacteristic
1187C22C2×#654811yescharacteristic
1188C22C2×#654811yescharacteristic
1189C22D7×H(5,𝔽2)11yescharacteristic
1190C22#9061811yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—142no—
1198C4—142no—
1199C4—142no—
1200C4—142no—
1201C4—281no—
1202C4—281no—
1203C4—282no—
1204C4—282no—
1205C4—282no—
1206C4—281no—
1207C4—282no—
1208C4#9028414yescomplemented
1209C2—24no—
1210C2—82no—
1211C2—82no—
1212C2—82no—
1213C2—282no—
1214C2C2×#9028411yescharacteristic
1215C2C2×#9040711yescharacteristic
1216C2#1174338211yescharacteristic
1217C2#1174367611yescharacteristic
1218C2#1174367811yescharacteristic
1219C2#1174368011yescharacteristic
1220C2#1174368911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2433C2
hypercenter#2433D7
hypocenterC7#35007
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2433

Complements

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

NH ≅ G/Ntype
1. C2×#90284C2semidirect
2. C7×#2433C2semidirect
3. #11741498C2semidirect
4. C2×#89993C2semidirect
5. #11740637C2semidirect
6. #11740631C2semidirect
7. #11740629C2semidirect
8. #11740621C2semidirect
9. #11740150C2semidirect
10. Dic7×#121C2semidirect
11. #11740034C2semidirect
12. #11740031C2semidirect
13. #11740023C2semidirect
14. #11734154C2semidirect
15. #11734153C2semidirect
16. #11734135C2semidirect
17. #11734134C2semidirect
18. #11733920C2semidirect
19. #11733897C2semidirect
20. #11733870C2semidirect
21. #11733782C2semidirect
22. #11730938C2semidirect
23. C4×(C22⋊D7)⋊C4C2semidirect
34. C2×#6502C22semidirect
37. C2×#6501C22semidirect
38. C2×#6501C22semidirect
39. C2×#6501C22semidirect
40. C2×#6499C22semidirect
41. C2×#6499C22semidirect
42. C2×#6498C22semidirect
44. C2×D4×Dic7C22semidirect
49. C2×#6448C22semidirect
50. C2×#6446C22semidirect
53. C2×#6442C22semidirect
54. C2×#6442C22semidirect
56. C2×C42×D7C22semidirect
57. C2×#6432C22semidirect
65. #89995C22semidirect
67. #89994C22semidirect
68. #89994C22semidirect
69. #89994C22semidirect
78. #89993C22semidirect
79. #89993C22semidirect
80. #89993C22semidirect
81. #89993C22semidirect
82. #89993C22semidirect
83. #89993C22semidirect
86. #89992C22semidirect
87. #89992C22semidirect
89. #89759C22semidirect
90. #89757C22semidirect
91. C4⋊C4×Dic7C22semidirect
92. #89745C22semidirect
93. #89733C22semidirect
94. #89733C22semidirect
95. #89728C22semidirect
96. #89725C22semidirect
97. #89723C22semidirect
98. #89723C22semidirect
99. #89723C22semidirect
100. #89723C22semidirect
101. #89723C22semidirect
103. #89720C22semidirect
104. #89720C22semidirect
105. #89719C22semidirect
106. #89717C22semidirect
107. #89717C22semidirect
108. #89716C22semidirect
111. C22⋊C4×Dic7C22semidirect
112. C4×(C2×D7)⋊C4C22semidirect
113. #89707C22semidirect
114. C4×Dic7⋊C4C22semidirect
115. C42×Dic7C22semidirect
116. #89700C22semidirect
117. #89700C22semidirect
118. #89438C22semidirect
119. #89438C22semidirect
120. #89433C22semidirect
121. #89428C22semidirect
122. #89421C22semidirect
123. #89421C22semidirect
240. (C22⋊D7)⋊C4D4semidirect
273. #2433D7semidirect
375. C2×C4×D7C2×D4semidirect
414. (C2×D7)⋊C4C2×D4semidirect
429. Dic7⋊C4C2×D4semidirect
441. C4×Dic7C2×D4semidirect
844. C4×C7#538semidirect
1147. C7#35007semidirect
1208. C4#90284semidirect

Maximal subgroups

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

subgroupindex
C2×#902842
C7×#24332
#117414982
C2×#899932
#117406372
#117406312
#117406292
#117406212
#117401502
Dic7×#1212
#117400342
#117400312
#117400232
#117341542
#117341532
#117341352
#117341342
#117339202
#117338972
#117338702
#117337822
#117309382
C4×(C22⋊D7)⋊C42
#350077