Finite Group Databasebeta

← #13526746

Subgroups — #13526746

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×#90185C212yesmaximal, complemented
2C2×C7×#390C211yesmaximal, characteristic, complemented
3#11741498C211yesmaximal, characteristic, complemented
4#11741494C211yesmaximal, characteristic, complemented
5#11739638C211yesmaximal, characteristic, complemented
6#11739616C211yesmaximal, characteristic, complemented
7#11739556C212yesmaximal, complemented
8#11739554C212yesmaximal, complemented
9#11739541C212yesmaximal, complemented
10C4×#6493C211yesmaximal, characteristic, complemented
11C42×C22⋊D7C211yesmaximal, characteristic, complemented
12#11733921C211yesmaximal, characteristic, complemented
13#11733920C211yesmaximal, characteristic, complemented
14#11733905C212yesmaximal, complemented
15#11733900C212yesmaximal, complemented
16#11733896C211yesmaximal, characteristic, complemented
17#11733889C211yesmaximal, characteristic, complemented
18#11733870C211yesmaximal, characteristic, complemented
19#11733869C211yesmaximal, characteristic, complemented
20#11733822C212yesmaximal, complemented
21#11733801C212yesmaximal, complemented
22#11733783C211yesmaximal, characteristic, complemented
23#11733761C211yesmaximal, characteristic, complemented
24C23×C7×D4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C42×C7C2211yescharacteristic
29C2×#6516C2212yes—
30C2×#6516C2212yes—
31C2×#6516C2212yes—
32C2×#6503C2211yescharacteristic
33C2×#6503C2211yescharacteristic
34C2×#6501C2211yescharacteristic
35C2×#6501C2211yescharacteristic
36C2×#6493C2212yes—
37C2×#6493C2211yescharacteristic
38C2×C4×C22⋊D7C2212yes—
39C2×C4×C22⋊D7C2211yescharacteristic
40C2×C4×C22⋊D7C2211yescharacteristic
41C2×C4×C22⋊D7C2211yescharacteristic
42C2×#6487C2212yes—
43C2×#6458C2211yescharacteristic, complemented
44C2×#6451C2211yescharacteristic, complemented
45#90185—216no—
46C2×#6448C2212yescomplemented
47C2×#6448C2212yescomplemented
48C2×#6448C2212yescomplemented
49C2×#6447C2212yescomplemented
50C2×#6447C2212yescomplemented
51C2×#6447C2212yescomplemented
52C2×#6446C2212yescomplemented
53C2×#6446C2212yescomplemented
54C2×#6442C2212yescomplemented
55C2×#6442C2212yescomplemented
56C2×C4×D28C2211yescharacteristic, complemented
57C2×C42×D7C2211yescharacteristic, complemented
58C7×#390C2211yescharacteristic
59C7×#390C2211yescharacteristic
60C7×#390C2212yes—
61C7×#390C2212yes—
62C7×#390C2211yescharacteristic
63C7×#390C2211yescharacteristic
64#90019C2212yes—
65#89995C2212yes—
66#89995C2212yes—
67#89995C2212yes—
68#89994C2212yes—
69#89993C2211yescharacteristic
70#89993C2211yescharacteristic
71#89993C2211yescharacteristic
72#89993C2211yescharacteristic
73#89985C2212yes—
74#89985C2212yes—
75#89984C2211yescharacteristic
76#89982C2212yes—
77C4×C22⋊Dic7C2211yescharacteristic
78C4×C22⋊Dic7C2211yescharacteristic
79C4×C22⋊Dic7C2211yescharacteristic
80#89766C2212yescomplemented
81#89763C2212yescomplemented
82#89760C2211yescharacteristic, complemented
83#89759C2211yescharacteristic, complemented
84#89757C2211yescharacteristic, complemented
85#89757C2211yescharacteristic, complemented
86#89756C2212yescomplemented
87#89751C2212yescomplemented
88#89748C2211yescharacteristic, complemented
89#89745C2211yescharacteristic, complemented
90#89733C2212yescomplemented
91#89732C2212yescomplemented
92#89731C2212yescomplemented
93#89731C2212yescomplemented
94#89731C2212yescomplemented
95#89729C2212yescomplemented
96#89729C2212yescomplemented
97#89729C2212yescomplemented
98#89729C2212yescomplemented
99#89728C2212yescomplemented
100#89728C2212yescomplemented
101#89728C2212yescomplemented
102#89724C2212yescomplemented
103#89723C2212yescomplemented
104#89723C2212yescomplemented
105#89720C2212yescomplemented
106#89719C2212yescomplemented
107#89717C2212yescomplemented
108#89717C2212yescomplemented
109#89716C2212yescomplemented
110#89716C2212yescomplemented
111#89716C2212yescomplemented
112#89712C2212yescomplemented
113#89711C2211yescharacteristic, complemented
114C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
115C4×(C2×D7)⋊C4C2212yescomplemented
116C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
117C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
118C4×C4⋊Dic7C2211yescharacteristic, complemented
119C4×Dic7⋊C4C2211yescharacteristic, complemented
120C4×Dic7⋊C4C2211yescharacteristic, complemented
121C4×Dic7⋊C4C2211yescharacteristic, complemented
122C42×Dic7C2211yescharacteristic, complemented
123#89700C2211yescharacteristic, 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—
132C23×C4×C7C2311yescharacteristic
133C23×C4×C7C2311yescharacteristic
134C23×C4×C7C2312yes—
135C23×C4×C7C2311yescharacteristic
136C22×C22⋊D7C2312yes—
137C22×C22⋊D7C2311yescharacteristic
138C22×C22⋊D7C2312yes—
139C22×C22⋊D7C2312yes—
140C22×C22⋊D7C2312yes—
141C22×C22⋊D7C2312yes—
142C22×C22⋊D7C2312yes—
143C22×C22⋊D7C2312yes—
144C22×D28C2311yescharacteristic
145C22×D28C2312yes—
146C22×C4×D7C2311yescharacteristic
147C22×C4×D7C2311yescharacteristic
148C22×C4×D7C2312yes—
149C22×C4×D7C2311yescharacteristic
150C22×Dic14C2312yes—
151C2×C7×C4⋊C4—42no—
152C2×C7×C4⋊C4C2311yescharacteristic
153C2×C7×C4⋊C4C2311yescharacteristic
154C2×C7×C4⋊C4C2312yes—
155C2×C7×C22⋊C4—28no—
156C2×C7×C22⋊C4—44no—
157C2×C7×C22⋊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×C7×C22⋊C4C2312yes—
165C2×C42×C7—42no—
166C2×C42×C7C2311yescharacteristic
167C2×C42×C7C2311yescharacteristic
168C2×C42×C7C2311yescharacteristic
169C2×C42×C7C2311yescharacteristic
170#6516—28no—
171#6516—28no—
172#6516—28no—
173C2×C22⋊Dic7C2312yes—
174C2×C22⋊Dic7C2312yes—
175C2×C22⋊Dic7C2312yes—
176C2×C22⋊Dic7C2312yes—
177C2×C22⋊Dic7C2312yes—
178C2×C22⋊Dic7C2311yescharacteristic
179C2×C22⋊Dic7C2312yes—
180C2×C22⋊Dic7C2312yes—
181C2×C22⋊Dic7C2312yes—
182C2×C22⋊Dic7C2312yes—
183C2×C22⋊Dic7C2312yes—
184C2×C22⋊Dic7C2312yes—
185C2×C22⋊Dic7C2311yescharacteristic
186C2×C22⋊Dic7C2311yescharacteristic
187#6503—42no—
188#6503—42no—
189#6501—42no—
190#6501—42no—
191#6493—24no—
192#6493—28no—
193C4×C22⋊D7—28no—
194C4×C22⋊D7—24no—
195C4×C22⋊D7—24no—
196C4×C22⋊D7D418yescomplemented
197C2×(C2×D7)⋊C4C2312yes—
198C2×(C2×D7)⋊C4C2312yes—
199C2×(C2×D7)⋊C4C2312yes—
200C2×(C2×D7)⋊C4C2312yes—
201C2×(C2×D7)⋊C4C2311yescharacteristic
202C2×(C2×D7)⋊C4C2311yescharacteristic
203C2×(C2×D7)⋊C4C2312yes—
204C2×(C2×D7)⋊C4C2312yes—
205C2×(C2×D7)⋊C4C2312yes—
206C2×(C2×D7)⋊C4C2312yes—
207C2×(C2×D7)⋊C4C2311yescharacteristic
208C2×C4⋊Dic7C2311yescharacteristic
209C2×C4⋊Dic7C2312yes—
210C2×C4⋊Dic7C2312yes—
211C2×C4⋊Dic7C2311yescharacteristic
212C2×C4⋊Dic7C2311yescharacteristic
213#6487—28no—
214C2×Dic7⋊C4C2312yes—
215C2×Dic7⋊C4C2312yes—
216C2×Dic7⋊C4C2312yes—
217C2×Dic7⋊C4C2311yescharacteristic
218C2×Dic7⋊C4C2311yescharacteristic
219C2×Dic7⋊C4C2312yes—
220C2×Dic7⋊C4C2312yes—
221C2×Dic7⋊C4C2311yescharacteristic
222C2×C4×Dic7C2311yescharacteristic
223C2×C4×Dic7C2312yes—
224C2×C4×Dic7C2311yescharacteristic
225C2×C4×Dic7C2311yescharacteristic
226C2×C4×Dic7C2311yescharacteristic
227C2×C4×Dic7C2311yescharacteristic
228C2×C4×Dic7C2311yescharacteristic
229C2×C4×Dic7C2311yescharacteristic
230C2×C4×Dic7C2311yescharacteristic
231C2×C4×Dic7C2311yescharacteristic
232#6458—42no—
233#6451—42no—
234#6448—28no—
235#6448—28no—
236#6448—44no—
237#6447—28no—
238#6447—28no—
239#6447—44no—
240#6446—28no—
241#6446—28no—
242#6442—28no—
243#6442—28no—
244C4×D28—42no—
245C42×D7—42no—
246C7⋊#95C2312yes—
247C7⋊#95C2311yescharacteristic
248C7⋊#95C2311yescharacteristic
249C7⋊#95C2311yescharacteristic
250C7⋊#95C2311yescharacteristic
251C7⋊#95C2311yescharacteristic
252C7⋊#95C2311yescharacteristic
253C7⋊#95C2312yes—
254C7⋊#95C2312yes—
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#2433—71no—
274#2428—71no—
275#2424—72no—
276#2416—71no—
277#2408—71no—
278#2321—72no—
279C4×#121—71no—
280C2×#390D711yescharacteristic, complemented
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×C7C2411yescharacteristic
292C23×D7C2412yes—
293C23×D7C2411yescharacteristic
294C2×C7×D4—24no—
295C2×C7×D4—22no—
296C2×C7×D4—22no—
297C2×C7×D4—22no—
298C2×C7×D4—22no—
299C2×C7×D4—22no—
300C2×C7×D4—22no—
301C2×C7×D4—42no—
302C2×C7×D4—42no—
303C2×C7×D4—416no—
304C22×C4×C7—22no—
305C22×C4×C7—22no—
306C22×C4×C7—22no—
307C22×C4×C7—24no—
308C22×C4×C7—22no—
309C22×C4×C7—41no—
310C22×C4×C7—41no—
311C22×C4×C7—41no—
312C22×C4×C7—42no—
313C22×C4×C7—42no—
314C22×C4×C7C2×D414yes—
315C22×C4×C7#4114yes—
316C22×C4×C7C2411yescharacteristic
317C22×C4×C7C2412yes—
318C22×C4×C7C2412yes—
319C22×C4×C7C2411yescharacteristic
320C22×C4×C7C2411yescharacteristic
321C22×C4×C7C2411yescharacteristic
322C22×C4×C7C2411yescharacteristic
323C22×C4×C7C2411yescharacteristic
324C2×C22⋊D7—22no—
325C2×C22⋊D7—22no—
326C2×C22⋊D7—24no—
327C2×C22⋊D7—24no—
328C2×C22⋊D7—24no—
329C2×C22⋊D7—24no—
330C2×C22⋊D7—24no—
331C2×C22⋊D7—24no—
332C2×C22⋊D7—24no—
333C2×C22⋊D7—24no—
334C2×C22⋊D7—24no—
335C2×C22⋊D7—42no—
336C2×C22⋊D7—42no—
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⋊D7—42no—
344C2×C22⋊D7—42no—
345C2×C22⋊D7—42no—
346C2×C22⋊D7—42no—
347C2×C22⋊D7C2×D414yes—
348C22×Dic7C2411yescharacteristic
349C22×Dic7C2411yescharacteristic
350C22×Dic7C2412yes—
351C22×Dic7C2412yes—
352C22×Dic7C2412yes—
353C22×Dic7C2411yescharacteristic
354C22×Dic7C2411yescharacteristic
355C22×Dic7C2411yescharacteristic
356C22×Dic7C2411yescharacteristic
357C22×Dic7C2411yescharacteristic
358C2×D28—22no—
359C2×D28—22no—
360C2×D28—22no—
361C2×D28—24no—
362C2×D28—42no—
363C2×D28—42no—
364C2×C4×D7—22no—
365C2×C4×D7—22no—
366C2×C4×D7—22no—
367C2×C4×D7—22no—
368C2×C4×D7—22no—
369C2×C4×D7—24no—
370C2×C4×D7—41no—
371C2×C4×D7—41no—
372C2×C4×D7—41no—
373C2×C4×D7—42no—
374C2×C4×D7—42no—
375C2×C4×D7C2×D414yescomplemented
376C2×Dic14—24no—
377C2×Dic14—42no—
378C2×Dic14—42no—
379C7×C4⋊C4—22no—
380C7×C4⋊C4—22no—
381C7×C4⋊C4—42no—
382C7×C22⋊C4—24no—
383C7×C22⋊C4—24no—
384C7×C22⋊C4—24no—
385C7×C22⋊C4—24no—
386C7×C22⋊C4—24no—
387C7×C22⋊C4—24no—
388C7×C22⋊C4—42no—
389C7×C22⋊C4—42no—
390C42×C7—22no—
391C42×C7—22no—
392C42×C7—41no—
393C42×C7—41no—
394C22⋊Dic7—24no—
395C22⋊Dic7—22no—
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⋊Dic7C2×D414yes—
407C22⋊Dic7#4114yes—
408(C2×D7)⋊C4—24no—
409(C2×D7)⋊C4—24no—
410(C2×D7)⋊C4—22no—
411(C2×D7)⋊C4—24no—
412(C2×D7)⋊C4—24no—
413(C2×D7)⋊C4—24no—
414(C2×D7)⋊C4—22no—
415(C2×D7)⋊C4—42no—
416(C2×D7)⋊C4—42no—
417(C2×D7)⋊C4—42no—
418(C2×D7)⋊C4C2×D414yescomplemented
419C4⋊Dic7—22no—
420C4⋊Dic7—22no—
421C4⋊Dic7—22no—
422C4⋊Dic7—24no—
423C4⋊Dic7—24no—
424Dic7⋊C4—24no—
425Dic7⋊C4—22no—
426Dic7⋊C4—24no—
427Dic7⋊C4—24no—
428Dic7⋊C4—22no—
429Dic7⋊C4—42no—
430Dic7⋊C4—42no—
431Dic7⋊C4C2×D414yescomplemented
432C4×Dic7—24no—
433C4×Dic7—22no—
434C4×Dic7—22no—
435C4×Dic7—22no—
436C4×Dic7—22no—
437C4×Dic7—22no—
438C4×Dic7—41no—
439C4×Dic7—41no—
440C4×Dic7—41no—
441C4×Dic7C2×D414yescomplemented
442C23×D4C2×D711yescharacteristic
443#538—1416no—
444C2×C4⋊Q8—71no—
445C2×#127—71no—
446C2×#127—71no—
447C2×#126—72no—
448C2×#126—72no—
449C2×#124—72no—
450C2×#124—72no—
451C2×#124—72no—
452C2×#123—72no—
453C2×#123—72no—
454C2×C22⋊Q8—72no—
455C2×#121—72no—
456C2×#121—71no—
457C2×#121—71no—
458C2×#121—71no—
459C2×#121—71no—
460C2×#121—72no—
461C2×#121—72no—
462C2×#121—72no—
463C2×#120—72no—
464C2×#120—72no—
465C2×#120—72no—
466C2×C4×D4—71no—
467C2×C4×D4—72no—
468C2×C4×D4—71no—
469C2×C4×D4—71no—
470C2×C4×D4—71no—
471C22×C4⋊C4C2×D711yescharacteristic
472C22×C22⋊C4C2×D712yes—
473C22×C22⋊C4C2×D712yes—
474C22×C42—71no—
475C22×C42C2×D711yescharacteristic
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—71no—
496#390—71no—
497#390—72no—
498#390—72no—
499#390—72no—
500#390—72no—
501#390—71no—
502#390C2×D711yescharacteristic
503#390C2×D711yescharacteristic
504#390C2×D712yes—
505#390C2×D711yescharacteristic
506#390C2×D711yescharacteristic
507#390C2×D712yes—
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—71no—
537C4×C22⋊C4—71no—
538C4×C22⋊C4—71no—
539C4×C22⋊C4—71no—
540C4×C22⋊C4—72no—
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—48no—
561C23×C7—48no—
562C23×C7—48no—
563C23×C7—84no—
564C23×C7—84no—
565C23×C7—84no—
566C23×C7—84no—
567C23×C7C22×D412yes—
568C23×C7C2×#4112yes—
569C23×C7C2×#4112yes—
570C23×C7C2511yescharacteristic
571C22×D7—21no—
572C22×D7—21no—
573C22×D7—21no—
574C22×D7—21no—
575C22×D7—21no—
576C22×D7—21no—
577C22×D7—22no—
578C22×D7—22no—
579C22×D7—22no—
580C22×D7—22no—
581C22×D7—22no—
582C22×D7—22no—
583C22×D7—22no—
584C22×D7C22×D412yes—
585C7×D4—48no—
586C7×D4—44no—
587C7×D4—44no—
588C2×C4×C7—21no—
589C2×C4×C7—21no—
590C2×C4×C7—21no—
591C2×C4×C7—21no—
592C2×C4×C7—21no—
593C2×C4×C7—21no—
594C2×C4×C7—21no—
595C2×C4×C7—21no—
596C2×C4×C7—28no—
597C2×C4×C7—22no—
598C2×C4×C7—22no—
599C2×C4×C7—21no—
600C2×C4×C7—22no—
601C2×C4×C7—22no—
602C2×C4×C7—21no—
603C2×C4×C7—22no—
604C2×C4×C7—22no—
605C2×C4×C7—21no—
606C2×C4×C7—44no—
607C2×C4×C7—44no—
608C2×C4×C7—84no—
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—28no—
617C22⋊D7—48no—
618C22⋊D7—84no—
619C22⋊D7—84no—
620C22⋊D7—84no—
621C22⋊D7—84no—
622C22⋊D7—84no—
623C22⋊D7—84no—
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—21no—
634C2×Dic7—22no—
635C2×Dic7—22no—
636C2×Dic7—22no—
637C2×Dic7—21no—
638C2×Dic7—21no—
639C2×Dic7—22no—
640C2×Dic7—22no—
641C2×Dic7—21no—
642C2×Dic7—21no—
643C2×Dic7—22no—
644C2×Dic7—22no—
645C2×Dic7—22no—
646C2×Dic7—21no—
647C2×Dic7—21no—
648C2×Dic7—22no—
649C2×Dic7C22×D412yes—
650C2×Dic7C22×D412yes—
651C2×Dic7C22×D412yes—
652C2×Dic7C2×#4112yes—
653C2×Dic7C2×#4112yes—
654D28—44no—
655D28—84no—
656C4×D7—44no—
657C4×D7—44no—
658C4×D7—44no—
659C4×D7—84no—
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×D4—72no—
671C22×D4—72no—
672C22×D4—72no—
673C22×D4—72no—
674C22×D4—71no—
675C22×D4—72no—
676C22×D4C22×D711yescharacteristic
677C22×D4C22×D711yescharacteristic
678C22×D4C22×D712yes—
679C23×C4—71no—
680C23×C4—71no—
681C23×C4—71no—
682C23×C4—72no—
683C23×C4C22×D711yescharacteristic
684C23×C4C22×D711yescharacteristic
685C23×C4C22×D712yes—
686C23×C4C22×D711yescharacteristic
687C4⋊Q8—282no—
688#127—282no—
689#127—282no—
690#126—148no—
691#126—148no—
692#124—148no—
693#124—148no—
694#124—284no—
695#123—148no—
696#123—148no—
697C22⋊Q8—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—78no—
710C4×D4—144no—
711C4×D4—144no—
712C4×D4—148no—
713C4×D4—282no—
714C2×C4⋊C4—42no—
715C2×C4⋊C4—71no—
716C2×C4⋊C4—71no—
717C2×C4⋊C4—72no—
718C2×C4⋊C4—71no—
719C2×C4⋊C4—71no—
720C2×C4⋊C4—72no—
721C2×C4⋊C4—72no—
722C2×C4⋊C4—72no—
723C2×C4⋊C4—71no—
724C2×C4⋊C4—71no—
725C2×C4⋊C4—72no—
726C2×C4⋊C4—72no—
727C2×C4⋊C4—72no—
728C2×C4⋊C4C22×D711yescharacteristic
729C2×C4⋊C4C22×D711yescharacteristic
730C2×C4⋊C4C22×D712yes—
731C2×C22⋊C4—28no—
732C2×C22⋊C4—44no—
733C2×C22⋊C4—71no—
734C2×C22⋊C4—71no—
735C2×C22⋊C4—71no—
736C2×C22⋊C4—72no—
737C2×C22⋊C4—71no—
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—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⋊C4C22×D712yes—
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—42no—
767C2×C42—71no—
768C2×C42—72no—
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×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#95—72no—
793#95—72no—
794#95—72no—
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—816no—
816C22×C7#53214yes—
817C22×C7C23×D411yescharacteristic
818C22×C7C22×#4111yescharacteristic
819C22×C7C22×#4111yescharacteristic
820C22×C7C2×H(5,𝔽2)11yescharacteristic
821C22×C7C2×H(5,𝔽2)11yescharacteristic
822C22×C7C2×H(5,𝔽2)11yescharacteristic
823C22×C7#58511yescharacteristic
824C2×D7—22no—
825C2×D7—22no—
826C2×D7—22no—
827C2×D7—41no—
828C2×D7—41no—
829C2×D7—41no—
830C2×D7—41no—
831C2×D7—42no—
832C2×D7—42no—
833C2×D7—42no—
834C2×D7—42no—
835C2×D7—42no—
836C2×D7—42no—
837C2×D7—42no—
838C4×C7—22no—
839C4×C7—22no—
840C4×C7—22no—
841C4×C7—22no—
842C4×C7—42no—
843C4×C7—42no—
844C4×C7—41no—
845C4×C7#53814yescomplemented
846Dic7—22no—
847Dic7—22no—
848Dic7—22no—
849Dic7—22no—
850Dic7—22no—
851Dic7—42no—
852Dic7—41no—
853Dic7—41no—
854Dic7—42no—
855Dic7—42no—
856C24—24no—
857C24—24no—
858C24—24no—
859C24—42no—
860C24—42no—
861C24—42no—
862C24—42no—
863C24—71no—
864C24—72no—
865C24C23×D712yes—
866C24C23×D712yes—
867C24C23×D711yescharacteristic
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—22no—
877C2×D4—22no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—416no—
881C2×D4—74no—
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—144no—
891C2×D4—144no—
892C2×D4—144no—
893C2×D4—144no—
894C2×D4—142no—
895C2×D4—142no—
896C2×D4—142no—
897C2×D4—282no—
898C2×D4—282no—
899C2×D4—282no—
900C2×D4—282no—
901C2×D4—282no—
902C2×D4—282no—
903C2×D4—282no—
904C2×D4—282no—
905C2×D4—282no—
906C2×D4—282no—
907C2×D4—282no—
908C2×D4—282no—
909C2×D4—282no—
910C2×D4—282no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—24no—
915C22×C4—22no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—71no—
922C22×C4—71no—
923C22×C4—71no—
924C22×C4—71no—
925C22×C4—71no—
926C22×C4—74no—
927C22×C4—71no—
928C22×C4—71no—
929C22×C4—72no—
930C22×C4—72no—
931C22×C4—72no—
932C22×C4—142no—
933C22×C4—142no—
934C22×C4—142no—
935C22×C4—142no—
936C22×C4—142no—
937C22×C4—144no—
938C22×C4—281no—
939C22×C4—281no—
940C22×C4—281no—
941C22×C4—282no—
942C22×C4—282no—
943C22×C4#115714yes—
944C22×C4D4×D714yes—
945C22×C4C23×D711yescharacteristic
946C22×C4C23×D712yes—
947C22×C4C23×D712yes—
948C22×C4C23×D711yescharacteristic
949C22×C4C23×D711yescharacteristic
950C22×C4C23×D711yescharacteristic
951C22×C4C23×D711yescharacteristic
952C22×C4C23×D711yescharacteristic
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—42no—
956C4⋊C4—74no—
957C4⋊C4—142no—
958C4⋊C4—144no—
959C4⋊C4—144no—
960C4⋊C4—144no—
961C4⋊C4—144no—
962C4⋊C4—142no—
963C4⋊C4—142no—
964C4⋊C4—144no—
965C4⋊C4—142no—
966C4⋊C4—142no—
967C4⋊C4—282no—
968C4⋊C4—282no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—74no—
978C22⋊C4—74no—
979C22⋊C4—74no—
980C22⋊C4—142no—
981C22⋊C4—144no—
982C22⋊C4—144no—
983C22⋊C4—144no—
984C22⋊C4—144no—
985C22⋊C4—144no—
986C22⋊C4—144no—
987C22⋊C4—144no—
988C22⋊C4—144no—
989C22⋊C4—142no—
990C22⋊C4—144no—
991C22⋊C4—142no—
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—22no—
1003C42—22no—
1004C42—41no—
1005C42—41no—
1006C42—74no—
1007C42—142no—
1008C42—142no—
1009C42—144no—
1010C42—142no—
1011C42—142no—
1012C42—142no—
1013C42—281no—
1014C42—281no—
1015C42—281no—
1016C2×C7—24no—
1017C2×C7—82no—
1018C2×C7—82no—
1019C2×C7C2×#53211yescharacteristic
1020C2×C7C2×#53811yescharacteristic
1021C2×C7#346011yescharacteristic
1022C2×C7#349611yescharacteristic
1023C2×C7#349811yescharacteristic
1024C2×C7#351411yescharacteristic
1025C2×C7#351911yescharacteristic
1026D7—42no—
1027D7—82no—
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—48no—
1047C23—48no—
1048C23—48no—
1049C23—72no—
1050C23—84no—
1051C23—84no—
1052C23—84no—
1053C23—84no—
1054C23—141no—
1055C23—141no—
1056C23—141no—
1057C23—141no—
1058C23—141no—
1059C23—141no—
1060C23—142no—
1061C23—142no—
1062C23—142no—
1063C23—142no—
1064C23—142no—
1065C23—142no—
1066C23—142no—
1067C23C2×#115712yes—
1068C23C2×D4×D712yes—
1069C23D7×#4112yes—
1070C23C24×D711yescharacteristic
1071Q8—564no—
1072D4—48no—
1073D4—44no—
1074D4—44no—
1075D4—148no—
1076D4—288no—
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—28no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—44no—
1104C2×C4—44no—
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—141no—
1122C2×C4—141no—
1123C2×C4—142no—
1124C2×C4—142no—
1125C2×C4—142no—
1126C2×C4—142no—
1127C2×C4—141no—
1128C2×C4—141no—
1129C2×C4—142no—
1130C2×C4—141no—
1131C2×C4—142no—
1132C2×C4—142no—
1133C2×C4—142no—
1134C2×C4—141no—
1135C2×C4—142no—
1136C2×C4—284no—
1137C2×C4—284no—
1138C2×C4—284no—
1139C2×C4—564no—
1140C2×C4C2×#115712yes—
1141C2×C4C2×#115712yes—
1142C2×C4C2×D4×D712yes—
1143C2×C4C2×D4×D712yes—
1144C2×C4#654812yes—
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—816no—
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#9023914yes—
1184C22C22×#115711yescharacteristic
1185C22C22×D4×D711yescharacteristic
1186C22C2×#654811yescharacteristic
1187C22C2×#654811yescharacteristic
1188C22C2×#654811yescharacteristic
1189C22C2×D7×#4111yescharacteristic
1190C22#9061611yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—42no—
1196C4—42no—
1197C4—41no—
1198C4—142no—
1199C4—142no—
1200C4—142no—
1201C4—142no—
1202C4—142no—
1203C4—282no—
1204C4—282no—
1205C4—281no—
1206C4—282no—
1207C4—281no—
1208C4#9018514yescomplemented
1209C2—24no—
1210C2—82no—
1211C2—82no—
1212C2—282no—
1213C2—562no—
1214C2C2×#9018511yescharacteristic
1215C2C2×#9023911yescharacteristic
1216C2#1174284511yescharacteristic
1217C2#1174301811yescharacteristic
1218C2#1174301911yescharacteristic
1219C2#1174314511yescharacteristic
1220C2#1174326311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC2×C7×#390C2
hypercenterC2×#390D7
hypocenterC7#35007
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#90185C2semidirect
2. C2×C7×#390C2semidirect
3. #11741498C2semidirect
4. #11741494C2semidirect
5. #11739638C2semidirect
6. #11739616C2semidirect
7. #11739556C2semidirect
8. #11739554C2semidirect
9. #11739541C2semidirect
10. C4×#6493C2semidirect
11. C42×C22⋊D7C2semidirect
12. #11733921C2semidirect
13. #11733920C2semidirect
14. #11733905C2semidirect
15. #11733900C2semidirect
16. #11733896C2semidirect
17. #11733889C2semidirect
18. #11733870C2semidirect
19. #11733869C2semidirect
20. #11733822C2semidirect
21. #11733801C2semidirect
22. #11733783C2semidirect
23. #11733761C2semidirect
43. C2×#6458C22semidirect
44. C2×#6451C22semidirect
46. C2×#6448C22semidirect
47. C2×#6448C22semidirect
48. C2×#6448C22semidirect
49. C2×#6447C22semidirect
50. C2×#6447C22semidirect
51. C2×#6447C22semidirect
52. C2×#6446C22semidirect
53. C2×#6446C22semidirect
54. C2×#6442C22semidirect
55. C2×#6442C22semidirect
56. C2×C4×D28C22semidirect
57. C2×C42×D7C22semidirect
80. #89766C22semidirect
81. #89763C22semidirect
82. #89760C22semidirect
83. #89759C22semidirect
84. #89757C22semidirect
85. #89757C22semidirect
86. #89756C22semidirect
87. #89751C22semidirect
88. #89748C22semidirect
89. #89745C22semidirect
90. #89733C22semidirect
91. #89732C22semidirect
92. #89731C22semidirect
93. #89731C22semidirect
94. #89731C22semidirect
95. #89729C22semidirect
96. #89729C22semidirect
97. #89729C22semidirect
98. #89729C22semidirect
99. #89728C22semidirect
100. #89728C22semidirect
101. #89728C22semidirect
102. #89724C22semidirect
103. #89723C22semidirect
104. #89723C22semidirect
105. #89720C22semidirect
106. #89719C22semidirect
107. #89717C22semidirect
108. #89717C22semidirect
109. #89716C22semidirect
110. #89716C22semidirect
111. #89716C22semidirect
112. #89712C22semidirect
113. #89711C22semidirect
114. C4×(C2×D7)⋊C4C22semidirect
115. C4×(C2×D7)⋊C4C22semidirect
116. C4×(C2×D7)⋊C4C22semidirect
117. C4×(C2×D7)⋊C4C22semidirect
118. C4×C4⋊Dic7C22semidirect
119. C4×Dic7⋊C4C22semidirect
120. C4×Dic7⋊C4C22semidirect
121. C4×Dic7⋊C4C22semidirect
122. C42×Dic7C22semidirect
123. #89700C22semidirect
196. C4×C22⋊D7D4semidirect
280. C2×#390D7semidirect
375. C2×C4×D7C2×D4semidirect
418. (C2×D7)⋊C4C2×D4semidirect
431. Dic7⋊C4C2×D4semidirect
441. C4×Dic7C2×D4semidirect
845. C4×C7#538semidirect
1147. C7#35007semidirect
1208. C4#90185semidirect

Maximal subgroups

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

subgroupindex
C2×#901852
C2×C7×#3902
#117414982
#117414942
#117396382
#117396162
#117395562
#117395542
#117395412
C4×#64932
C42×C22⋊D72
#117339212
#117339202
#117339052
#117339002
#117338962
#117338892
#117338702
#117338692
#117338222
#117338012
#117337832
#117337612
#350077