Finite Group Databasebeta

← #13526752

Subgroups — #13526752

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×#90369C212yesmaximal, complemented
2C7×#2858C211yesmaximal, characteristic, complemented
3#11740702C211yesmaximal, characteristic, complemented
4#11740678C211yesmaximal, characteristic, complemented
5#11740631C211yesmaximal, characteristic, complemented
6#11740620C211yesmaximal, characteristic, complemented
7#11740426C212yesmaximal, complemented
8#11740420C212yesmaximal, complemented
9#11740410C212yesmaximal, complemented
10#11733921C211yesmaximal, characteristic, complemented
11#11733920C211yesmaximal, characteristic, complemented
12#11733905C212yesmaximal, complemented
13#11733887C212yesmaximal, complemented
14#11733884C211yesmaximal, characteristic, complemented
15#11733881C211yesmaximal, characteristic, complemented
16#11733874C212yesmaximal, complemented
17D7×#390C211yesmaximal, characteristic, complemented
18#11733799C212yesmaximal, complemented
19#11733784C211yesmaximal, characteristic, complemented
20#11733762C211yesmaximal, characteristic, complemented
21#11733736C211yesmaximal, characteristic, complemented
22#11730759C211yesmaximal, characteristic, complemented
23C42×D28C211yesmaximal, characteristic, complemented
24C22×D4×D7C2211yescharacteristic
25C2×C7×C4⋊Q8C2211yescharacteristic, complemented
26C2×C7×#127C2211yescharacteristic
27C2×C7×#124C2212yescomplemented
28C2×C7×#124C2212yescomplemented
29C2×#6510C2212yescomplemented
30C2×#6509C2212yes—
31C2×#6503C2211yescharacteristic
32C2×#6502C2212yescomplemented
33C2×#6501C2211yescharacteristic
34C2×#6501C2211yescharacteristic
35C2×#6501C2211yescharacteristic, complemented
36C2×#6500C2212yes—
37C2×#6500C2212yes—
38C2×D4×Dic7C2211yescharacteristic, complemented
39#90369—216no—
40C2×#6458C2211yescharacteristic
41C2×D7×C4⋊C4C2211yescharacteristic
42C2×#6449C2212yescomplemented
43C2×#6447C2212yes—
44C2×#6447C2212yescomplemented
45C2×#6447C2212yescomplemented
46C2×#6446C2212yescomplemented
47C2×#6445C2212yes—
48C2×(C22⋊D7)⋊C4C2212yes—
49C2×D7×C22⋊C4C2212yes—
50C2×D7×C22⋊C4C2212yes—
51C2×#6442C2212yescomplemented
52C2×#6439C2212yescomplemented
53C2×C4×D28C2211yescharacteristic
54C2×C4×D28C2211yescharacteristic
55C2×C4×D28C2211yescharacteristic
56C2×C42×D7C2211yescharacteristic
57C2×C42×D7C2211yescharacteristic, complemented
58C7×#390C2211yescharacteristic
59C7×#390C2211yescharacteristic
60C7×#390C2211yescharacteristic, complemented
61C7×#390C2212yescomplemented
62C7×#390C2212yescomplemented
63C7×#390C2211yescharacteristic, complemented
64C43×C7C2211yescharacteristic, complemented
65#90003C2212yescomplemented
66#90001C2212yescomplemented
67#89995C2212yes—
68#89995C2212yes—
69#89995C2212yescomplemented
70#89994C2212yescomplemented
71#89993C2211yescharacteristic
72#89993C2211yescharacteristic
73#89992C2212yescomplemented
74#89763C2212yescomplemented
75#89762C2212yescomplemented
76#89761C2212yes—
77#89760C2211yescharacteristic
78#89759C2211yescharacteristic
79#89759C2211yescharacteristic, complemented
80#89757C2211yescharacteristic, complemented
81#89756C2212yescomplemented
82#89748C2211yescharacteristic, complemented
83C4⋊C4×Dic7C2211yescharacteristic, complemented
84#89733C2212yes—
85#89733C2212yescomplemented
86#89733C2212yescomplemented
87#89732C2212yes—
88#89731C2212yescomplemented
89#89730C2212yescomplemented
90#89729C2212yes—
91#89729C2212yes—
92#89729C2212yescomplemented
93#89729C2212yescomplemented
94#89728C2212yes—
95#89728C2212yes—
96#89728C2212yescomplemented
97#89727C2212yes—
98#89724C2212yescomplemented
99#89723C2212yescomplemented
100#89720C2212yescomplemented
101#89720C2212yescomplemented
102#89717C2212yescomplemented
103#89717C2212yescomplemented
104#89717C2212yescomplemented
105C22⋊C4×Dic7C2212yescomplemented
106#89712C2212yescomplemented
107#89712C2212yescomplemented
108#89712C2212yescomplemented
109#89711C2211yescharacteristic
110#89711C2211yescharacteristic
111#89711C2211yescharacteristic
112C4×(C2×D7)⋊C4C2211yescharacteristic
113C4×(C2×D7)⋊C4C2211yescharacteristic
114C4×(C2×D7)⋊C4C2211yescharacteristic
115C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
116C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
117C4×(C2×D7)⋊C4C2211yescharacteristic, complemented
118C4×C4⋊Dic7C2211yescharacteristic, complemented
119C4×C4⋊Dic7C2211yescharacteristic, complemented
120C4×C4⋊Dic7C2211yescharacteristic, complemented
121#89700C2211yescharacteristic, complemented
122#89700C2211yescharacteristic, complemented
123#89700C2211yescharacteristic, complemented
124#35007—71nomaximal, Sylow
125C24×D7C2312yes—
126C22×C7×Q8C2312yes—
127C22×C7×D4C2311yescharacteristic
128C22×C7×D4C2311yescharacteristic
129C22×C7×D4C2312yes—
130C22×C7×D4C2312yes—
131C22×C22⋊D7C2312yes—
132C22×C22⋊D7C2312yes—
133C22×C22⋊D7C2312yes—
134C22×C22⋊D7C2312yes—
135C22×C22⋊D7C2312yes—
136C22×C22⋊D7C2312yes—
137C23×Dic7C2312yes—
138C2×D4×D7—24no—
139C2×D4×D7—42no—
140C2×D4×D7—42no—
141C22×D28C2311yescharacteristic
142C22×D28C2311yescharacteristic
143C22×D28C2312yes—
144C22×C4×D7C2311yescharacteristic
145C22×C4×D7C2311yescharacteristic
146C22×C4×D7C2311yescharacteristic
147C22×C4×D7C2311yescharacteristic
148C22×C4×D7C2312yes—
149C22×C4×D7C2311yescharacteristic
150C22×C4×D7C2311yescharacteristic
151C7×C4⋊Q8—42no—
152C7×#127—42no—
153C7×#124—28no—
154C7×#124—44no—
155C2×C7×C4⋊C4C2311yescharacteristic
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×C7×C22⋊C4C2312yes—
165C2×C7×C22⋊C4C2312yes—
166C2×C42×C7C2311yescharacteristic
167C2×C42×C7C2311yescharacteristic
168C2×C42×C7C2311yescharacteristic
169C2×C42×C7C2311yescharacteristic
170C2×C42×C7C2311yescharacteristic
171C2×C42×C7C2311yescharacteristic
172C2×C42×C7C2311yescharacteristic
173C2×C22⋊Dic7C2312yes—
174C2×C22⋊Dic7C2312yes—
175C2×C22⋊Dic7C2312yes—
176C2×C22⋊Dic7C2312yes—
177C2×C22⋊Dic7C2312yes—
178C2×C22⋊Dic7C2312yes—
179C2×C22⋊Dic7C2312yes—
180C2×C22⋊Dic7C2312yes—
181#6510—28no—
182#6509—28no—
183#6503—42no—
184#6502—28no—
185#6501—24no—
186#6501—42no—
187#6501—42no—
188#6500—28no—
189#6500—28no—
190D4×Dic7—42no—
191C2×(C2×D7)⋊C4C2311yescharacteristic
192C2×(C2×D7)⋊C4C2311yescharacteristic
193C2×(C2×D7)⋊C4C2311yescharacteristic
194C2×(C2×D7)⋊C4C2312yes—
195C2×(C2×D7)⋊C4C2312yes—
196C2×(C2×D7)⋊C4C2312yes—
197C2×(C2×D7)⋊C4C2312yes—
198C2×(C2×D7)⋊C4C2312yes—
199C2×(C2×D7)⋊C4C2312yes—
200C2×(C2×D7)⋊C4C2312yes—
201C2×(C2×D7)⋊C4C2312yes—
202C2×(C2×D7)⋊C4C2312yes—
203C2×(C2×D7)⋊C4C2312yes—
204C2×(C2×D7)⋊C4C2312yes—
205C2×(C2×D7)⋊C4C2311yescharacteristic
206C2×(C2×D7)⋊C4C2311yescharacteristic
207C2×(C2×D7)⋊C4C2311yescharacteristic
208C2×C4⋊Dic7C2311yescharacteristic
209C2×C4⋊Dic7C2311yescharacteristic
210C2×C4⋊Dic7C2312yes—
211C2×C4⋊Dic7C2311yescharacteristic
212C2×C4⋊Dic7C2311yescharacteristic
213C2×C4⋊Dic7C2311yescharacteristic
214C2×C4⋊Dic7C2311yescharacteristic
215C2×Dic7⋊C4C2312yes—
216C2×Dic7⋊C4C2312yes—
217C2×Dic7⋊C4C2312yes—
218C2×Dic7⋊C4C2312yes—
219C2×Dic7⋊C4C2312yes—
220C2×Dic7⋊C4C2312yes—
221C2×C4×Dic7C2311yescharacteristic
222C2×C4×Dic7C2311yescharacteristic
223C2×C4×Dic7C2312yes—
224C2×C4×Dic7C2311yescharacteristic
225C2×C4×Dic7C2311yescharacteristic
226C2×C4×Dic7C2311yescharacteristic
227C2×C4×Dic7C2311yescharacteristic
228#6458—42no—
229D7×C4⋊C4—42no—
230#6449—28no—
231#6447—28no—
232#6447—28no—
233#6447—44no—
234#6446—28no—
235#6445—28no—
236(C22⋊D7)⋊C4—28no—
237D7×C22⋊C4—28no—
238D7×C22⋊C4—44no—
239#6442—28no—
240#6439—28no—
241C4×D28—24no—
242C4×D28—24no—
243C4×D28D418yescomplemented
244C42×D7—42no—
245C42×D7—42no—
246C7⋊#95C2312yes—
247C7⋊#95C2312yes—
248C7⋊#95C2312yes—
249C7⋊#95C2311yescharacteristic
250C7⋊#95C2311yescharacteristic
251C7⋊#95C2311yescharacteristic
252C7⋊#95C2311yescharacteristic
253C7⋊#95C2311yescharacteristic
254C7⋊#95C2311yescharacteristic
255C7⋊#95C2312yes—
256C7⋊#95C2312yes—
257C7⋊#95C2312yes—
258C7⋊#95C2312yes—
259C2×#538—72no—
260#2860—71no—
261#2858D711yescharacteristic, complemented
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—
283C24×C7C2412yes—
284C23×D7—24no—
285C23×D7—24no—
286C23×D7—24no—
287C23×D7—42no—
288C23×D7—42no—
289C23×D7—42no—
290C23×D7—42no—
291C23×D7C2412yes—
292C23×D7C2411yescharacteristic
293C23×D7C2411yescharacteristic
294C2×C7×Q8—24no—
295C2×C7×Q8—42no—
296C2×C7×Q8—42no—
297C2×C7×D4—24no—
298C2×C7×D4—22no—
299C2×C7×D4—22no—
300C2×C7×D4—24no—
301C2×C7×D4—22no—
302C2×C7×D4—22no—
303C2×C7×D4—22no—
304C2×C7×D4—22no—
305C2×C7×D4—42no—
306C2×C7×D4—42no—
307C2×C7×D4—42no—
308C2×C7×D4—42no—
309C22×C4×C7C2411yescharacteristic
310C22×C4×C7C2412yes—
311C22×C4×C7C2412yes—
312C22×C4×C7C2411yescharacteristic
313C22×C4×C7C2411yescharacteristic
314C22×C4×C7C2411yescharacteristic
315C22×C4×C7C2411yescharacteristic
316C22×C4×C7C2411yescharacteristic
317C22×C4×C7C2411yescharacteristic
318C2×C22⋊D7—24no—
319C2×C22⋊D7—24no—
320C2×C22⋊D7—24no—
321C2×C22⋊D7—24no—
322C2×C22⋊D7—24no—
323C2×C22⋊D7—24no—
324C2×C22⋊D7—24no—
325C2×C22⋊D7—24no—
326C2×C22⋊D7—42no—
327C2×C22⋊D7—42no—
328C2×C22⋊D7—42no—
329C2×C22⋊D7—42no—
330C2×C22⋊D7—42no—
331C2×C22⋊D7—42no—
332C2×C22⋊D7—42no—
333C2×C22⋊D7—42no—
334C2×C22⋊D7—42no—
335C2×C22⋊D7—42no—
336C22×Dic7—24no—
337C22×Dic7—42no—
338C22×Dic7—42no—
339C22×Dic7C2411yescharacteristic
340C22×Dic7C2411yescharacteristic
341C22×Dic7C2412yes—
342C22×Dic7C2412yes—
343C22×Dic7C2412yes—
344C22×Dic7C2411yescharacteristic
345C22×Dic7C2411yescharacteristic
346C22×Dic7C2411yescharacteristic
347C22×Dic7C2411yescharacteristic
348D4×D7—416no—
349C2×D28—22no—
350C2×D28—22no—
351C2×D28—22no—
352C2×D28—22no—
353C2×D28—22no—
354C2×D28—24no—
355C2×D28—42no—
356C2×D28—42no—
357C2×D28C2×D414yes—
358C2×C4×D7—22no—
359C2×C4×D7—22no—
360C2×C4×D7—22no—
361C2×C4×D7—22no—
362C2×C4×D7—22no—
363C2×C4×D7—22no—
364C2×C4×D7—22no—
365C2×C4×D7—22no—
366C2×C4×D7—22no—
367C2×C4×D7—24no—
368C2×C4×D7—41no—
369C2×C4×D7—41no—
370C2×C4×D7—41no—
371C2×C4×D7—41no—
372C2×C4×D7—41no—
373C2×C4×D7—41no—
374C2×C4×D7—42no—
375C2×C4×D7—42no—
376C2×C4×D7C2×D414yes—
377C2×C4×D7C2×D414yescomplemented
378C2×C4×D7#4114yes—
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—22no—
393C42×C7—22no—
394C42×C7—22no—
395C42×C7—41no—
396C42×C7C2×D414yescomplemented
397C22⋊Dic7—24no—
398C22⋊Dic7—24no—
399C22⋊Dic7—24no—
400C22⋊Dic7—24no—
401C22⋊Dic7—42no—
402C22⋊Dic7—42no—
403C22⋊Dic7—42no—
404C22⋊Dic7—42no—
405(C2×D7)⋊C4—24no—
406(C2×D7)⋊C4—24no—
407(C2×D7)⋊C4—22no—
408(C2×D7)⋊C4—24no—
409(C2×D7)⋊C4—24no—
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—22no—
416(C2×D7)⋊C4—42no—
417(C2×D7)⋊C4—42no—
418(C2×D7)⋊C4—42no—
419(C2×D7)⋊C4C2×D414yes—
420(C2×D7)⋊C4C2×D414yescomplemented
421(C2×D7)⋊C4#4114yes—
422C4⋊Dic7—22no—
423C4⋊Dic7—22no—
424C4⋊Dic7—22no—
425C4⋊Dic7—24no—
426C4⋊Dic7—22no—
427C4⋊Dic7—22no—
428C4⋊Dic7C2×D414yescomplemented
429Dic7⋊C4—24no—
430Dic7⋊C4—24no—
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⋊Q8C2×D711yescharacteristic, complemented
445C2×#127—71no—
446C2×#127C2×D711yescharacteristic
447C2×#126—72no—
448C2×#126—72no—
449C2×#124—72no—
450C2×#124C2×D712yescomplemented
451C2×#124C2×D712yescomplemented
452C2×#123—72no—
453C2×#123—72no—
454C2×C22⋊Q8—72no—
455C2×#121—71no—
456C2×#121—72no—
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⋊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—71no—
500#390—71no—
501#390—71no—
502#390C2×D711yescharacteristic
503#390C2×D711yescharacteristic
504#390C2×D712yescomplemented
505#390C2×D711yescharacteristic, complemented
506#390C2×D711yescharacteristic, complemented
507#390C2×D712yescomplemented
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—72no—
535C4×C22⋊C4—71no—
536C4×C22⋊C4—71no—
537C4×C22⋊C4—71no—
538C4×C22⋊C4—71no—
539C4×C22⋊C4—71no—
540C4×C22⋊C4—71no—
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×C7—22no—
550C23×C7—22no—
551C23×C7—22no—
552C23×C7—22no—
553C23×C7—22no—
554C23×C7—22no—
555C23×C7—22no—
556C23×C7C2511yescharacteristic
557C22×D7—21no—
558C22×D7—21no—
559C22×D7—21no—
560C22×D7—21no—
561C22×D7—21no—
562C22×D7—21no—
563C22×D7—21no—
564C22×D7—21no—
565C22×D7—21no—
566C22×D7—21no—
567C22×D7—22no—
568C22×D7—22no—
569C22×D7—22no—
570C22×D7—22no—
571C22×D7—22no—
572C22×D7—22no—
573C22×D7—22no—
574C22×D7—48no—
575C22×D7—48no—
576C22×D7—48no—
577C22×D7—84no—
578C22×D7—84no—
579C22×D7—84no—
580C22×D7—84no—
581C22×D7C22×D412yes—
582C22×D7C22×D412yes—
583C22×D7C2×#4112yes—
584C22×D7C2×#4112yes—
585C7×Q8—84no—
586C7×D4—44no—
587C7×D4—44no—
588C7×D4—84no—
589C7×D4—84no—
590C2×C4×C7—21no—
591C2×C4×C7—21no—
592C2×C4×C7—21no—
593C2×C4×C7—21no—
594C2×C4×C7—21no—
595C2×C4×C7—21no—
596C2×C4×C7—21no—
597C2×C4×C7—21no—
598C2×C4×C7—21no—
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—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—
616C2×C4×C7H(5,𝔽2)12yes—
617C22⋊D7—48no—
618C22⋊D7—48no—
619C22⋊D7—84no—
620C22⋊D7—84no—
621C22⋊D7—84no—
622C22⋊D7—84no—
623C2×Dic7—21no—
624C2×Dic7—21no—
625C2×Dic7—21no—
626C2×Dic7—21no—
627C2×Dic7—21no—
628C2×Dic7—21no—
629C2×Dic7—21no—
630C2×Dic7—21no—
631C2×Dic7—22no—
632C2×Dic7—22no—
633C2×Dic7—22no—
634C2×Dic7—21no—
635C2×Dic7—21no—
636C2×Dic7—22no—
637C2×Dic7—22no—
638C2×Dic7—21no—
639C2×Dic7—21no—
640C2×Dic7—22no—
641C2×Dic7—22no—
642C2×Dic7—22no—
643C2×Dic7—21no—
644C2×Dic7—21no—
645C2×Dic7—22no—
646C2×Dic7—84no—
647C2×Dic7C22×D412yes—
648C2×Dic7C22×D412yes—
649C2×Dic7C2×#4112yes—
650C2×Dic7C2×#4112yes—
651D28—28no—
652D28—44no—
653D28—84no—
654C4×D7—28no—
655C4×D7—44no—
656C4×D7—44no—
657C4×D7—44no—
658C4×D7—44no—
659C4×D7—44no—
660C4×D7—84no—
661C25—72no—
662C22×Q8C22×D712yes—
663C22×D4—72no—
664C22×D4—72no—
665C22×D4—72no—
666C22×D4—72no—
667C22×D4—72no—
668C22×D4—72no—
669C22×D4—71no—
670C22×D4—71no—
671C22×D4—72no—
672C22×D4—144no—
673C22×D4—282no—
674C22×D4—282no—
675C22×D4C22×D711yescharacteristic
676C22×D4C22×D711yescharacteristic
677C22×D4C22×D712yes—
678C22×D4C22×D712yes—
679C23×C4—71no—
680C23×C4—71no—
681C23×C4—71no—
682C23×C4—72no—
683C23×C4—71no—
684C23×C4—71no—
685C23×C4—71no—
686C23×C4—72no—
687C4⋊Q8—42no—
688#127—42no—
689#127—282no—
690#126—148no—
691#126—148no—
692#124—28no—
693#124—44no—
694#124—148no—
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—71no—
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—72no—
725C2×C4⋊C4—72no—
726C2×C4⋊C4—72no—
727C2×C4⋊C4—282no—
728C2×C4⋊C4C22×D711yescharacteristic
729C2×C4⋊C4C22×D711yescharacteristic
730C2×C4⋊C4C22×D712yes—
731C2×C22⋊C4—71no—
732C2×C22⋊C4—71no—
733C2×C22⋊C4—71no—
734C2×C22⋊C4—72no—
735C2×C22⋊C4—72no—
736C2×C22⋊C4—72no—
737C2×C22⋊C4—72no—
738C2×C22⋊C4—72no—
739C2×C22⋊C4—72no—
740C2×C22⋊C4—72no—
741C2×C22⋊C4—72no—
742C2×C22⋊C4—71no—
743C2×C22⋊C4—71no—
744C2×C22⋊C4—71no—
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—148no—
757C2×C22⋊C4—284no—
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—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#95—72no—
793#95—72no—
794#95—72no—
795C22×C7—42no—
796C22×C7—42no—
797C22×C7—42no—
798C22×C7—42no—
799C22×C7—42no—
800C22×C7—42no—
801C22×C7—42no—
802C22×C7—42no—
803C22×C7—42no—
804C22×C7—42no—
805C22×C7—42no—
806C22×C7—42no—
807C22×C7—42no—
808C22×C7—42no—
809C22×C7C23×D411yescharacteristic
810C22×C7C22×#4111yescharacteristic
811C22×C7C22×#4111yescharacteristic
812C22×C7C2×H(5,𝔽2)11yescharacteristic
813C22×C7C2×H(5,𝔽2)11yescharacteristic
814C22×C7C2×H(5,𝔽2)11yescharacteristic
815C22×C7#58511yescharacteristic
816C2×D7—22no—
817C2×D7—22no—
818C2×D7—22no—
819C2×D7—22no—
820C2×D7—22no—
821C2×D7—22no—
822C2×D7—22no—
823C2×D7—22no—
824C2×D7—22no—
825C2×D7—41no—
826C2×D7—41no—
827C2×D7—41no—
828C2×D7—41no—
829C2×D7—42no—
830C2×D7—42no—
831C2×D7—42no—
832C2×D7—42no—
833C2×D7—42no—
834C2×D7—42no—
835C2×D7—42no—
836C2×D7—816no—
837C2×D7#53214yes—
838C4×C7—22no—
839C4×C7—22no—
840C4×C7—22no—
841C4×C7—22no—
842C4×C7—22no—
843C4×C7—41no—
844C4×C7—42no—
845C4×C7—42no—
846C4×C7#53814yescomplemented
847Dic7—22no—
848Dic7—22no—
849Dic7—22no—
850Dic7—22no—
851Dic7—42no—
852Dic7—41no—
853Dic7—42no—
854Dic7—42no—
855Dic7—41no—
856C24—71no—
857C24—71no—
858C24—72no—
859C24—144no—
860C24—144no—
861C24—144no—
862C24—282no—
863C24—282no—
864C24—282no—
865C24—282no—
866C24C23×D712yes—
867C24C23×D712yes—
868C2×Q8—24no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×D4—24no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—24no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—74no—
884C2×D4—142no—
885C2×D4—142no—
886C2×D4—144no—
887C2×D4—144no—
888C2×D4—144no—
889C2×D4—144no—
890C2×D4—144no—
891C2×D4—144no—
892C2×D4—144no—
893C2×D4—144no—
894C2×D4—144no—
895C2×D4—142no—
896C2×D4—142no—
897C2×D4—142no—
898C2×D4—282no—
899C2×D4—282no—
900C2×D4—2816no—
901C2×D4—282no—
902C2×D4—282no—
903C2×D4—282no—
904C2×D4—282no—
905C2×D4—282no—
906C2×D4—282no—
907C2×D4—282no—
908C2×D4—282no—
909C2×D4—282no—
910C2×D4—282no—
911C22×C4—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—72no—
923C22×C4—142no—
924C22×C4—142no—
925C22×C4—144no—
926C22×C4—144no—
927C22×C4—142no—
928C22×C4—142no—
929C22×C4—142no—
930C22×C4—142no—
931C22×C4—142no—
932C22×C4—142no—
933C22×C4—142no—
934C22×C4—281no—
935C22×C4—281no—
936C22×C4—281no—
937C22×C4—281no—
938C22×C4—281no—
939C22×C4—281no—
940C22×C4—282no—
941C22×C4—282no—
942C22×C4—282no—
943C22×C4—282no—
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—22no—
954C4⋊C4—22no—
955C4⋊C4—42no—
956C4⋊C4—74no—
957C4⋊C4—144no—
958C4⋊C4—142no—
959C4⋊C4—142no—
960C4⋊C4—144no—
961C4⋊C4—144no—
962C4⋊C4—144no—
963C4⋊C4—144no—
964C4⋊C4—142no—
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—144no—
981C22⋊C4—142no—
982C22⋊C4—142no—
983C22⋊C4—144no—
984C22⋊C4—144no—
985C22⋊C4—144no—
986C22⋊C4—144no—
987C22⋊C4—144no—
988C22⋊C4—144no—
989C22⋊C4—144no—
990C22⋊C4—144no—
991C22⋊C4—144no—
992C22⋊C4—144no—
993C22⋊C4—142no—
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—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×C7—82no—
1018C2×C7C2×#53211yescharacteristic
1019C2×C7C2×#53811yescharacteristic
1020C2×C7#346011yescharacteristic
1021C2×C7#349611yescharacteristic
1022C2×C7#349811yescharacteristic
1023C2×C7#351411yescharacteristic
1024C2×C7#351911yescharacteristic
1025D7—24no—
1026D7—42no—
1027D7—82no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—72no—
1043C23—72no—
1044C23—72no—
1045C23—72no—
1046C23—141no—
1047C23—141no—
1048C23—141no—
1049C23—141no—
1050C23—141no—
1051C23—141no—
1052C23—141no—
1053C23—141no—
1054C23—141no—
1055C23—141no—
1056C23—142no—
1057C23—142no—
1058C23—142no—
1059C23—142no—
1060C23—142no—
1061C23—142no—
1062C23—142no—
1063C23—288no—
1064C23—288no—
1065C23—288no—
1066C23—564no—
1067C23—564no—
1068C23—564no—
1069C23—564no—
1070C23C24×D711yescharacteristic
1071Q8—84no—
1072D4—44no—
1073D4—44no—
1074D4—84no—
1075D4—84no—
1076D4—148no—
1077D4—288no—
1078D4—288no—
1079D4—284no—
1080D4—564no—
1081D4—564no—
1082D4—564no—
1083D4—564no—
1084D4—564no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—72no—
1105C2×C4—72no—
1106C2×C4—72no—
1107C2×C4—72no—
1108C2×C4—141no—
1109C2×C4—141no—
1110C2×C4—141no—
1111C2×C4—141no—
1112C2×C4—141no—
1113C2×C4—141no—
1114C2×C4—141no—
1115C2×C4—141no—
1116C2×C4—148no—
1117C2×C4—142no—
1118C2×C4—142no—
1119C2×C4—142no—
1120C2×C4—142no—
1121C2×C4—141no—
1122C2×C4—141no—
1123C2×C4—142no—
1124C2×C4—142no—
1125C2×C4—141no—
1126C2×C4—141no—
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×C4#654812yes—
1143C2×C4#654812yes—
1144C2×C4D7×#4112yes—
1145C2×C4D7×#4112yes—
1146C2×C4#655312yes—
1147C7#3500711yescharacteristic, complemented, Sylow
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—74no—
1163C22—142no—
1164C22—142no—
1165C22—142no—
1166C22—142no—
1167C22—142no—
1168C22—142no—
1169C22—142no—
1170C22—142no—
1171C22—142no—
1172C22—281no—
1173C22—281no—
1174C22—281no—
1175C22—281no—
1176C22—282no—
1177C22—282no—
1178C22—282no—
1179C22—282no—
1180C22—282no—
1181C22—282no—
1182C22—282no—
1183C22—5616no—
1184C22C22×D4×D711yescharacteristic
1185C22C2×#654811yescharacteristic
1186C22C2×#654811yescharacteristic
1187C22C2×D7×#4111yescharacteristic
1188C22C2×D7×#4111yescharacteristic
1189C22C2×#655311yescharacteristic
1190C22#9061611yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—42no—
1198C4—41no—
1199C4—142no—
1200C4—142no—
1201C4—142no—
1202C4—142no—
1203C4—282no—
1204C4—282no—
1205C4—282no—
1206C4—281no—
1207C4—281no—
1208C4#9036914yescomplemented
1209C2—82no—
1210C2—82no—
1211C2—144no—
1212C2—282no—
1213C2—562no—
1214C2C2×#9036911yescharacteristic
1215C2#1174314511yescharacteristic
1216C2#1174326311yescharacteristic
1217C2D7×#53211yescharacteristic
1218C2#1174330511yescharacteristic
1219C2#1174330911yescharacteristic
1220C2#1174331511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2858C2
hypercenter#2858D7
hypocenterC7#35007
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2858

Complements

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

NH ≅ G/Ntype
1. C2×#90369C2semidirect
2. C7×#2858C2semidirect
3. #11740702C2semidirect
4. #11740678C2semidirect
5. #11740631C2semidirect
6. #11740620C2semidirect
7. #11740426C2semidirect
8. #11740420C2semidirect
9. #11740410C2semidirect
10. #11733921C2semidirect
11. #11733920C2semidirect
12. #11733905C2semidirect
13. #11733887C2semidirect
14. #11733884C2semidirect
15. #11733881C2semidirect
16. #11733874C2semidirect
17. D7×#390C2semidirect
18. #11733799C2semidirect
19. #11733784C2semidirect
20. #11733762C2semidirect
21. #11733736C2semidirect
22. #11730759C2semidirect
23. C42×D28C2semidirect
25. C2×C7×C4⋊Q8C22semidirect
27. C2×C7×#124C22semidirect
28. C2×C7×#124C22semidirect
29. C2×#6510C22semidirect
32. C2×#6502C22semidirect
35. C2×#6501C22semidirect
38. C2×D4×Dic7C22semidirect
42. C2×#6449C22semidirect
44. C2×#6447C22semidirect
45. C2×#6447C22semidirect
46. C2×#6446C22semidirect
51. C2×#6442C22semidirect
52. C2×#6439C22semidirect
57. C2×C42×D7C22semidirect
60. C7×#390C22semidirect
61. C7×#390C22semidirect
62. C7×#390C22semidirect
63. C7×#390C22semidirect
64. C43×C7C22semidirect
65. #90003C22semidirect
66. #90001C22semidirect
69. #89995C22semidirect
70. #89994C22semidirect
73. #89992C22semidirect
74. #89763C22semidirect
75. #89762C22semidirect
79. #89759C22semidirect
80. #89757C22semidirect
81. #89756C22semidirect
82. #89748C22semidirect
83. C4⋊C4×Dic7C22semidirect
85. #89733C22semidirect
86. #89733C22semidirect
88. #89731C22semidirect
89. #89730C22semidirect
92. #89729C22semidirect
93. #89729C22semidirect
96. #89728C22semidirect
98. #89724C22semidirect
99. #89723C22semidirect
100. #89720C22semidirect
101. #89720C22semidirect
102. #89717C22semidirect
103. #89717C22semidirect
104. #89717C22semidirect
105. C22⋊C4×Dic7C22semidirect
106. #89712C22semidirect
107. #89712C22semidirect
108. #89712C22semidirect
115. C4×(C2×D7)⋊C4C22semidirect
116. C4×(C2×D7)⋊C4C22semidirect
117. C4×(C2×D7)⋊C4C22semidirect
118. C4×C4⋊Dic7C22semidirect
119. C4×C4⋊Dic7C22semidirect
120. C4×C4⋊Dic7C22semidirect
121. #89700C22semidirect
122. #89700C22semidirect
123. #89700C22semidirect
243. C4×D28D4semidirect
261. #2858D7semidirect
377. C2×C4×D7C2×D4semidirect
396. C42×C7C2×D4semidirect
420. (C2×D7)⋊C4C2×D4semidirect
428. C4⋊Dic7C2×D4semidirect
444. C2×C4⋊Q8C2×D7semidirect
450. C2×#124C2×D7semidirect
451. C2×#124C2×D7semidirect
504. #390C2×D7semidirect
505. #390C2×D7semidirect
506. #390C2×D7semidirect
507. #390C2×D7semidirect
541. C43C2×D7semidirect
846. C4×C7#538semidirect
1015. C42D4×D7semidirect
1147. C7#35007semidirect
1208. C4#90369semidirect

Maximal subgroups

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

subgroupindex
C2×#903692
C7×#28582
#117407022
#117406782
#117406312
#117406202
#117404262
#117404202
#117404102
#117339212
#117339202
#117339052
#117338872
#117338842
#117338812
#117338742
D7×#3902
#117337992
#117337842
#117337622
#117337362
#117307592
C42×D282
#350077