Finite Group Databasebeta

← #13526744

Subgroups — #13526744

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×#90348C212yesmaximal, complemented
2C7×#2854C211yesmaximal, characteristic, complemented
3#11740312C212yesmaximal, complemented
4#11740093C211yesmaximal, characteristic, complemented
5#11740085C211yesmaximal, characteristic, complemented
6#11739526C211yesmaximal, characteristic, complemented
7C42×C22⋊D7C211yesmaximal, characteristic, complemented
8D7×#390C211yesmaximal, characteristic, complemented
9#11733869C211yesmaximal, characteristic, complemented
10#11733782C211yesmaximal, characteristic, complemented
11#11733759C211yesmaximal, characteristic, complemented
12#11733636C211yesmaximal, characteristic, complemented
13#11733449C211yesmaximal, characteristic, complemented
14#11733444C211yesmaximal, characteristic, complemented
15#11733409C211yesmaximal, characteristic, complemented
16#11733271C212yesmaximal, complemented
17#11733108C212yesmaximal, complemented
18#11733041C212yesmaximal, complemented
19#11732972C212yesmaximal, complemented
20#11732339C212yesmaximal, complemented
21#11732201C212yesmaximal, complemented
22#11731360C211yesmaximal, characteristic, complemented
23#11731332C211yesmaximal, characteristic, complemented
24C22×D4×D7C2211yescharacteristic
25C2×C7×#123C2212yescomplemented
26C2×C7×#121C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic, complemented
28C2×#6503C2211yescharacteristic
29C2×#6501C2212yescomplemented
30C2×#6500C2212yes—
31C2×#6493C2211yescharacteristic
32C2×#6493C2212yescomplemented
33C2×#6493C2212yescomplemented
34C2×#6493C2211yescharacteristic, complemented
35C2×C4×C22⋊D7C2211yescharacteristic
36C2×C4×C22⋊D7C2211yescharacteristic
37C2×C4×C22⋊D7C2211yescharacteristic
38#90348—216no—
39C2×#6461C2212yescomplemented
40C2×#6460C2212yes—
41C2×#6458C2211yescharacteristic
42C2×#6457C2212yescomplemented
43C2×#6456C2212yes—
44C2×#6456C2211yescharacteristic, complemented
45C2×D7×C4⋊C4C2211yescharacteristic
46C2×#6451C2211yescharacteristic, complemented
47C2×#6448C2212yescomplemented
48C2×#6448C2212yescomplemented
49C2×#6448C2212yescomplemented
50C2×#6447C2212yes—
51C2×#6445C2212yes—
52C2×#6445C2212yes—
53C2×D7×C22⋊C4C2212yes—
54C2×D7×C22⋊C4C2212yes—
55C2×#6442C2212yescomplemented
56C2×#6437C2211yescharacteristic
57C2×C42×D7C2211yescharacteristic
58C7×#390C2211yescharacteristic
59C7×#390C2211yescharacteristic
60C7×#389C2211yescharacteristic, complemented
61C7×#389C2211yescharacteristic, complemented
62C7×#388C2212yescomplemented
63C7×#388C2212yescomplemented
64C7×#386C2212yescomplemented
65C7×#380C2211yescharacteristic, complemented
66#89995C2212yes—
67#89995C2212yescomplemented
68#89993C2211yescharacteristic
69#89993C2211yescharacteristic
70C4×C22⋊Dic7C2211yescharacteristic, complemented
71C4×C22⋊Dic7C2211yescharacteristic, complemented
72C4×C22⋊Dic7C2211yescharacteristic, complemented
73#89763C2212yescomplemented
74#89762C2212yescomplemented
75#89762C2212yescomplemented
76#89760C2211yescharacteristic
77#89760C2211yescharacteristic
78#89760C2211yescharacteristic
79#89760C2211yescharacteristic, complemented
80#89759C2211yescharacteristic
81#89757C2211yescharacteristic, complemented
82#89755C2212yescomplemented
83C4⋊C4×Dic7C2211yescharacteristic, complemented
84#89745C2211yescharacteristic, complemented
85#89733C2212yescomplemented
86#89732C2212yes—
87#89732C2212yes—
88#89731C2212yes—
89#89731C2212yescomplemented
90#89731C2212yescomplemented
91#89729C2212yes—
92#89729C2212yes—
93#89729C2212yescomplemented
94#89729C2212yescomplemented
95#89728C2212yescomplemented
96#89727C2212yes—
97#89725C2212yescomplemented
98#89723C2212yescomplemented
99#89720C2212yescomplemented
100#89711C2211yescharacteristic
101#89711C2212yescomplemented
102#89711C2212yescomplemented
103#89711C2211yescharacteristic, complemented
104C4×(C2×D7)⋊C4C2211yescharacteristic
105C4×(C2×D7)⋊C4C2211yescharacteristic
106C4×(C2×D7)⋊C4C2211yescharacteristic
107#89707C2211yescharacteristic, complemented
108C4×Dic7⋊C4C2211yescharacteristic, complemented
109C4×Dic7⋊C4C2211yescharacteristic, complemented
110C4×Dic7⋊C4C2211yescharacteristic, complemented
111C42×Dic7C2211yescharacteristic, complemented
112#89448C2212yescomplemented
113#89445C2212yescomplemented
114#89444C2212yescomplemented
115#89442C2212yescomplemented
116#89441C2212yescomplemented
117#89441C2212yescomplemented
118#89440C2212yes—
119#89438C2212yescomplemented
120#89437C2212yes—
121#89437C2212yes—
122#89437C2212yescomplemented
123#89428C2212yescomplemented
124#35007—71nomaximal, Sylow
125C24×D7C2312yes—
126C22×C7×D4C2311yescharacteristic
127C22×C7×D4C2312yes—
128C23×C4×C7C2311yescharacteristic
129C23×C4×C7C2311yescharacteristic
130C23×C4×C7C2311yescharacteristic
131C22×C22⋊D7C2311yescharacteristic
132C22×C22⋊D7C2312yes—
133C22×C22⋊D7C2312yes—
134C22×C22⋊D7C2312yes—
135C22×C22⋊D7C2312yes—
136C22×C22⋊D7C2312yes—
137C2×D4×D7—24no—
138C2×D4×D7—42no—
139C2×D4×D7—42no—
140C22×D28C2311yescharacteristic
141C22×D28C2311yescharacteristic
142C22×D28C2312yes—
143C22×D28C2312yes—
144C22×D28C2312yes—
145C22×C4×D7C2311yescharacteristic
146C22×C4×D7C2311yescharacteristic
147C22×C4×D7C2312yes—
148C22×C4×D7C2312yes—
149C22×C4×D7C2311yescharacteristic
150C22×Dic14C2312yes—
151C7×#123—28no—
152C7×#121—42no—
153C2×C7×C4⋊C4C2311yescharacteristic
154C2×C7×C4⋊C4C2312yes—
155C2×C7×C4⋊C4C2311yescharacteristic
156C2×C7×C4⋊C4C2312yes—
157C2×C7×C4⋊C4C2311yescharacteristic
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×C7—42no—
165C2×C42×C7C2311yescharacteristic
166C2×C42×C7C2311yescharacteristic
167C2×C42×C7C2311yescharacteristic
168C2×C42×C7C2311yescharacteristic
169C2×C22⋊Dic7C2312yes—
170C2×C22⋊Dic7C2312yes—
171C2×C22⋊Dic7C2311yescharacteristic
172C2×C22⋊Dic7C2311yescharacteristic
173C2×C22⋊Dic7C2312yes—
174C2×C22⋊Dic7C2312yes—
175C2×C22⋊Dic7C2311yescharacteristic
176#6503—42no—
177#6501—28no—
178#6500—28no—
179#6493—28no—
180#6493—42no—
181#6493—42no—
182#6493—44no—
183C4×C22⋊D7—24no—
184C4×C22⋊D7—24no—
185C4×C22⋊D7D418yescomplemented
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)⋊C4C2312yes—
199C2×(C2×D7)⋊C4C2312yes—
200C2×(C2×D7)⋊C4C2312yes—
201C2×(C2×D7)⋊C4C2312yes—
202C2×(C2×D7)⋊C4C2312yes—
203C2×(C2×D7)⋊C4C2312yes—
204C2×(C2×D7)⋊C4C2311yescharacteristic
205C2×(C2×D7)⋊C4C2311yescharacteristic
206C2×C4⋊Dic7C2312yes—
207C2×C4⋊Dic7C2311yescharacteristic
208C2×C4⋊Dic7C2311yescharacteristic
209C2×C4⋊Dic7C2312yes—
210C2×C4⋊Dic7C2312yes—
211C2×Dic7⋊C4C2312yes—
212C2×Dic7⋊C4C2311yescharacteristic
213C2×Dic7⋊C4C2311yescharacteristic
214C2×Dic7⋊C4C2312yes—
215C2×Dic7⋊C4C2312yes—
216C2×Dic7⋊C4C2311yescharacteristic
217C2×C4×Dic7C2311yescharacteristic
218C2×C4×Dic7C2312yes—
219C2×C4×Dic7C2311yescharacteristic
220C2×C4×Dic7C2311yescharacteristic
221C2×C4×Dic7C2311yescharacteristic
222C2×C4×Dic7C2311yescharacteristic
223C2×C4×Dic7C2311yescharacteristic
224C2×C4×Dic7C2311yescharacteristic
225C2×C4×Dic7C2311yescharacteristic
226C2×C4×Dic7C2311yescharacteristic
227#6461—28no—
228#6460—28no—
229#6458—24no—
230#6457—28no—
231#6456—28no—
232#6456—42no—
233D7×C4⋊C4—42no—
234#6451—42no—
235#6448—28no—
236#6448—28no—
237#6448—44no—
238#6447—28no—
239#6445—28no—
240#6445—28no—
241D7×C22⋊C4—28no—
242D7×C22⋊C4—44no—
243#6442—28no—
244#6437—42no—
245C42×D7—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#2860—71no—
261#2858—71no—
262#2856—71no—
263#2854D711yescharacteristic, complemented
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×C7C2411yescharacteristic
284C23×D7—24no—
285C23×D7—24no—
286C23×D7—24no—
287C23×D7—42no—
288C23×D7—42no—
289C23×D7—42no—
290C23×D7—42no—
291C23×D7C2412yes—
292C23×D7C2412yes—
293C23×D7C2411yescharacteristic
294C2×C7×D4—24no—
295C2×C7×D4—22no—
296C2×C7×D4—22no—
297C2×C7×D4—22no—
298C2×C7×D4—42no—
299C2×C7×D4—42no—
300C22×C4×C7—22no—
301C22×C4×C7—22no—
302C22×C4×C7—22no—
303C22×C4×C7—22no—
304C22×C4×C7—22no—
305C22×C4×C7—41no—
306C22×C4×C7—41no—
307C22×C4×C7—41no—
308C22×C4×C7C2×D414yescomplemented
309C22×C4×C7C2412yes—
310C22×C4×C7C2411yescharacteristic
311C22×C4×C7C2412yes—
312C22×C4×C7C2412yes—
313C22×C4×C7C2411yescharacteristic
314C22×C4×C7C2411yescharacteristic
315C22×C4×C7C2411yescharacteristic
316C22×C4×C7C2411yescharacteristic
317C22×C4×C7C2411yescharacteristic
318C2×C22⋊D7—22no—
319C2×C22⋊D7—22no—
320C2×C22⋊D7—24no—
321C2×C22⋊D7—24no—
322C2×C22⋊D7—24no—
323C2×C22⋊D7—24no—
324C2×C22⋊D7—24no—
325C2×C22⋊D7—42no—
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⋊D7C2×D414yes—
336C22×Dic7C2411yescharacteristic
337C22×Dic7C2411yescharacteristic
338C22×Dic7C2412yes—
339C22×Dic7C2412yes—
340C22×Dic7C2411yescharacteristic
341C22×Dic7C2411yescharacteristic
342C22×Dic7C2411yescharacteristic
343C22×Dic7C2411yescharacteristic
344C22×Dic7C2411yescharacteristic
345D4×D7—416no—
346C2×D28—24no—
347C2×D28—24no—
348C2×D28—24no—
349C2×D28—22no—
350C2×D28—22no—
351C2×D28—22no—
352C2×D28—22no—
353C2×D28—22no—
354C2×D28—22no—
355C2×D28—24no—
356C2×D28—24no—
357C2×D28—42no—
358C2×D28—42no—
359C2×D28—42no—
360C2×D28—42no—
361C2×C4×D7—22no—
362C2×C4×D7—22no—
363C2×C4×D7—22no—
364C2×C4×D7—22no—
365C2×C4×D7—24no—
366C2×C4×D7—24no—
367C2×C4×D7—41no—
368C2×C4×D7—41no—
369C2×C4×D7—41no—
370C2×C4×D7—42no—
371C2×C4×D7—42no—
372C2×C4×D7—42no—
373C2×C4×D7—42no—
374C2×C4×D7C2×D414yes—
375C2×C4×D7#4114yes—
376C2×Dic14—24no—
377C2×Dic14—42no—
378C2×Dic14—42no—
379C7×C4⋊C4—24no—
380C7×C4⋊C4—24no—
381C7×C4⋊C4—22no—
382C7×C4⋊C4—22no—
383C7×C4⋊C4—22no—
384C7×C22⋊C4—24no—
385C7×C22⋊C4—24no—
386C7×C22⋊C4—24no—
387C7×C22⋊C4—24no—
388C7×C22⋊C4—24no—
389C7×C22⋊C4—42no—
390C42×C7—22no—
391C42×C7—22no—
392C42×C7—41no—
393C42×C7—41no—
394C22⋊Dic7—24no—
395C22⋊Dic7—24no—
396C22⋊Dic7—22no—
397C22⋊Dic7—22no—
398C22⋊Dic7—42no—
399C22⋊Dic7—42no—
400C22⋊Dic7C2×D414yescomplemented
401(C2×D7)⋊C4—24no—
402(C2×D7)⋊C4—22no—
403(C2×D7)⋊C4—24no—
404(C2×D7)⋊C4—24no—
405(C2×D7)⋊C4—24no—
406(C2×D7)⋊C4—24no—
407(C2×D7)⋊C4—24no—
408(C2×D7)⋊C4—24no—
409(C2×D7)⋊C4—24no—
410(C2×D7)⋊C4—24no—
411(C2×D7)⋊C4—24no—
412(C2×D7)⋊C4—24no—
413(C2×D7)⋊C4—42no—
414(C2×D7)⋊C4—42no—
415(C2×D7)⋊C4—42no—
416(C2×D7)⋊C4—42no—
417(C2×D7)⋊C4—42no—
418(C2×D7)⋊C4—42no—
419(C2×D7)⋊C4C2×D414yes—
420(C2×D7)⋊C4#4114yes—
421C4⋊Dic7—24no—
422C4⋊Dic7—22no—
423C4⋊Dic7—22no—
424C4⋊Dic7—24no—
425C4⋊Dic7—42no—
426Dic7⋊C4—22no—
427Dic7⋊C4—24no—
428Dic7⋊C4—22no—
429Dic7⋊C4—42no—
430Dic7⋊C4—42no—
431Dic7⋊C4C2×D414yescomplemented
432C4×Dic7—22no—
433C4×Dic7—22no—
434C4×Dic7—22no—
435C4×Dic7—22no—
436C4×Dic7—24no—
437C4×Dic7—22no—
438C4×Dic7—41no—
439C4×Dic7—41no—
440C4×Dic7—41no—
441C4×Dic7C2×D414yescomplemented
442C23×D4—71no—
443#538—1416no—
444C2×C4⋊Q8—71no—
445C2×#127—71no—
446C2×#127—71no—
447C2×#126—72no—
448C2×#126—72no—
449C2×#124—72no—
450C2×#124—72no—
451C2×#124—72no—
452C2×#123—72no—
453C2×#123C2×D712yescomplemented
454C2×C22⋊Q8—72no—
455C2×#121—72no—
456C2×#121—72no—
457C2×#121—71no—
458C2×#121—71no—
459C2×#121—72no—
460C2×#121—71no—
461C2×#121—72no—
462C2×#121C2×D711yescharacteristic
463C2×#120—72no—
464C2×#120—72no—
465C2×#120—72no—
466C2×C4×D4—71no—
467C2×C4×D4—71no—
468C2×C4×D4—71no—
469C2×C4×D4—72no—
470C2×C4×D4—71no—
471C22×C4⋊C4—71no—
472C22×C22⋊C4—72no—
473C22×C22⋊C4—72no—
474C22×C42—71no—
475C22×C42C2×D711yescharacteristic, complemented
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—71no—
498#390—72no—
499#390—72no—
500#390—72no—
501#390—72no—
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#389C2×D711yescharacteristic, complemented
511#389C2×D711yescharacteristic, complemented
512#388—72no—
513#388—72no—
514#388—72no—
515#388—72no—
516#388—72no—
517#388—72no—
518#388C2×D712yescomplemented
519#388C2×D712yescomplemented
520#386—72no—
521#386—72no—
522#386—72no—
523#386—72no—
524#386C2×D712yescomplemented
525#385—72no—
526#384—71no—
527#380—71no—
528#380C2×D711yescharacteristic, complemented
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—21no—
547C23×C7—21no—
548C23×C7—22no—
549C23×C7—22no—
550C23×C7—22no—
551C23×C7—22no—
552C23×C7—22no—
553C23×C7—22no—
554C23×C7—22no—
555C23×C7C22×D412yes—
556C23×C7C2511yescharacteristic
557C22×D7—21no—
558C22×D7—21no—
559C22×D7—21no—
560C22×D7—21no—
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—22no—
575C22×D7—48no—
576C22×D7—48no—
577C22×D7—48no—
578C22×D7—84no—
579C22×D7—84no—
580C22×D7—84no—
581C22×D7—84no—
582C22×D7C22×D412yes—
583C22×D7C2×#4112yes—
584C22×D7C2×#4112yes—
585C7×D4—44no—
586C7×D4—84no—
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—22no—
596C2×C4×C7—22no—
597C2×C4×C7—22no—
598C2×C4×C7—21no—
599C2×C4×C7—22no—
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—22no—
607C2×C4×C7—44no—
608C2×C4×C7—44no—
609C2×C4×C7—44no—
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—28no—
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—21no—
632C2×Dic7—21no—
633C2×Dic7—22no—
634C2×Dic7—22no—
635C2×Dic7—21no—
636C2×Dic7—21no—
637C2×Dic7—21no—
638C2×Dic7—21no—
639C2×Dic7—22no—
640C2×Dic7—22no—
641C2×Dic7—22no—
642C2×Dic7—22no—
643C2×Dic7—21no—
644C2×Dic7—21no—
645C2×Dic7C22×D412yes—
646C2×Dic7C22×D412yes—
647C2×Dic7C22×D412yes—
648C2×Dic7C2×#4112yes—
649C2×Dic7C2×#4112yes—
650D28—48no—
651D28—44no—
652D28—44no—
653D28—84no—
654D28—84no—
655C4×D7—28no—
656C4×D7—44no—
657C4×D7—44no—
658C4×D7—84no—
659C4×D7—84no—
660Dic14—84no—
661C25—72no—
662C22×Q8—72no—
663C22×D4—71no—
664C22×D4—72no—
665C22×D4—72no—
666C22×D4—72no—
667C22×D4—72no—
668C22×D4—72no—
669C22×D4—72no—
670C22×D4—71no—
671C22×D4—71no—
672C22×D4—72no—
673C22×D4—72no—
674C22×D4—144no—
675C22×D4—282no—
676C22×D4—282no—
677C22×D4C22×D711yescharacteristic
678C22×D4C22×D712yes—
679C23×C4—71no—
680C23×C4—71no—
681C23×C4—71no—
682C23×C4—72no—
683C23×C4—72no—
684C23×C4C22×D711yescharacteristic
685C23×C4C22×D711yescharacteristic
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—28no—
696#123—148no—
697C22⋊Q8—148no—
698#121—42no—
699#121—148no—
700#121—148no—
701#121—144no—
702#121—148no—
703#121—284no—
704#121—282no—
705#121—282no—
706#120—148no—
707#120—148no—
708#120—148no—
709C4×D4—78no—
710C4×D4—144no—
711C4×D4—148no—
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—72no—
720C2×C4⋊C4—72no—
721C2×C4⋊C4—71no—
722C2×C4⋊C4—72no—
723C2×C4⋊C4—72no—
724C2×C4⋊C4—72no—
725C2×C4⋊C4—282no—
726C2×C4⋊C4C22×D711yescharacteristic
727C2×C4⋊C4C22×D711yescharacteristic
728C2×C4⋊C4C22×D712yes—
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—71no—
736C2×C22⋊C4—71no—
737C2×C22⋊C4—72no—
738C2×C22⋊C4—72no—
739C2×C22⋊C4—72no—
740C2×C22⋊C4—72no—
741C2×C22⋊C4—72no—
742C2×C22⋊C4—72no—
743C2×C22⋊C4—71no—
744C2×C22⋊C4—72no—
745C2×C22⋊C4—72no—
746C2×C22⋊C4—72no—
747C2×C22⋊C4—72no—
748C2×C22⋊C4—72no—
749C2×C22⋊C4—72no—
750C2×C22⋊C4—72no—
751C2×C22⋊C4—72no—
752C2×C22⋊C4—72no—
753C2×C22⋊C4—72no—
754C2×C22⋊C4—72no—
755C2×C22⋊C4—72no—
756C2×C22⋊C4—72no—
757C2×C22⋊C4—72no—
758C2×C22⋊C4—148no—
759C2×C22⋊C4—284no—
760C2×C22⋊C4C22×D712yes—
761C2×C22⋊C4C22×D712yes—
762C2×C22⋊C4C22×D712yes—
763C2×C22⋊C4C22×D712yes—
764C2×C22⋊C4C22×D712yes—
765C2×C22⋊C4C22×D712yes—
766C2×C42—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#95C22×D712yes—
793#95C22×D712yes—
794#95C22×D712yes—
795C22×C7—22no—
796C22×C7—22no—
797C22×C7—22no—
798C22×C7—41no—
799C22×C7—41no—
800C22×C7—41no—
801C22×C7—41no—
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—42no—
823C2×D7—42no—
824C2×D7—42no—
825C2×D7—42no—
826C2×D7—42no—
827C2×D7—42no—
828C2×D7—42no—
829C2×D7—42no—
830C2×D7—42no—
831C2×D7—42no—
832C2×D7—42no—
833C2×D7—42no—
834C2×D7—42no—
835C2×D7—42no—
836C2×D7—816no—
837C2×D7#53214yes—
838C4×C7—22no—
839C4×C7—22no—
840C4×C7—22no—
841C4×C7—22no—
842C4×C7—42no—
843C4×C7—41no—
844C4×C7—42no—
845C4×C7—42no—
846C4×C7#53814yescomplemented
847Dic7—22no—
848Dic7—22no—
849Dic7—22no—
850Dic7—22no—
851Dic7—22no—
852Dic7—41no—
853Dic7—42no—
854Dic7—42no—
855Dic7—41no—
856C24—71no—
857C24—72no—
858C24—72no—
859C24—144no—
860C24—144no—
861C24—144no—
862C24—282no—
863C24—282no—
864C24—282no—
865C24—282no—
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—42no—
876C2×D4—42no—
877C2×D4—74no—
878C2×D4—144no—
879C2×D4—144no—
880C2×D4—144no—
881C2×D4—144no—
882C2×D4—144no—
883C2×D4—144no—
884C2×D4—142no—
885C2×D4—142no—
886C2×D4—144no—
887C2×D4—144no—
888C2×D4—144no—
889C2×D4—142no—
890C2×D4—142no—
891C2×D4—142no—
892C2×D4—142no—
893C2×D4—144no—
894C2×D4—142no—
895C2×D4—142no—
896C2×D4—282no—
897C2×D4—282no—
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—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—71no—
920C22×C4—71no—
921C22×C4—71no—
922C22×C4—71no—
923C22×C4—71no—
924C22×C4—74no—
925C22×C4—74no—
926C22×C4—71no—
927C22×C4—71no—
928C22×C4—72no—
929C22×C4—72no—
930C22×C4—144no—
931C22×C4—142no—
932C22×C4—144no—
933C22×C4—142no—
934C22×C4—142no—
935C22×C4—142no—
936C22×C4—281no—
937C22×C4—281no—
938C22×C4—281no—
939C22×C4—282no—
940C22×C4—282no—
941C22×C4—282no—
942C22×C4—282no—
943C22×C4D4×D714yescomplemented
944C22×C4C23×D712yes—
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—24no—
954C4⋊C4—24no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—74no—
959C4⋊C4—142no—
960C4⋊C4—144no—
961C4⋊C4—144no—
962C4⋊C4—144no—
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—144no—
980C22⋊C4—144no—
981C22⋊C4—144no—
982C22⋊C4—144no—
983C22⋊C4—144no—
984C22⋊C4—142no—
985C22⋊C4—144no—
986C22⋊C4—144no—
987C22⋊C4—142no—
988C22⋊C4—142no—
989C22⋊C4—144no—
990C22⋊C4—144no—
991C22⋊C4—144no—
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—41no—
1005C42—41no—
1006C42—74no—
1007C42—142no—
1008C42—144no—
1009C42—142no—
1010C42—142no—
1011C42—142no—
1012C42—142no—
1013C42—281no—
1014C42—281no—
1015C42—281no—
1016C2×C7—42no—
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—82no—
1027D7—82no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—72no—
1042C23—72no—
1043C23—72no—
1044C23—141no—
1045C23—141no—
1046C23—141no—
1047C23—141no—
1048C23—142no—
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—288no—
1063C23—288no—
1064C23—288no—
1065C23—564no—
1066C23—564no—
1067C23—564no—
1068C23—564no—
1069C23C2×D4×D712yes—
1070C23C24×D711yescharacteristic
1071Q8—564no—
1072D4—44no—
1073D4—84no—
1074D4—148no—
1075D4—288no—
1076D4—288no—
1077D4—284no—
1078D4—284no—
1079D4—564no—
1080D4—564no—
1081D4—564no—
1082D4—564no—
1083D4—564no—
1084D4—564no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—44no—
1108C2×C4—72no—
1109C2×C4—72no—
1110C2×C4—72no—
1111C2×C4—72no—
1112C2×C4—72no—
1113C2×C4—141no—
1114C2×C4—141no—
1115C2×C4—141no—
1116C2×C4—141no—
1117C2×C4—141no—
1118C2×C4—141no—
1119C2×C4—141no—
1120C2×C4—141no—
1121C2×C4—141no—
1122C2×C4—141no—
1123C2×C4—148no—
1124C2×C4—142no—
1125C2×C4—142no—
1126C2×C4—141no—
1127C2×C4—141no—
1128C2×C4—141no—
1129C2×C4—141no—
1130C2×C4—142no—
1131C2×C4—142no—
1132C2×C4—141no—
1133C2×C4—142no—
1134C2×C4—142no—
1135C2×C4—141no—
1136C2×C4—284no—
1137C2×C4—284no—
1138C2×C4—564no—
1139C2×C4—564no—
1140C2×C4C2×D4×D712yes—
1141C2×C4C2×D4×D712yes—
1142C2×C4#654812yes—
1143C2×C4D7×#4112yes—
1144C2×C4D7×#4112yes—
1145C2×C4#655312yes—
1146C2×C4#655312yes—
1147C7#3500711yescharacteristic, complemented, Sylow
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
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—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×#654811yescharacteristic
1186C22C2×D7×#4111yescharacteristic
1187C22C2×D7×#4111yescharacteristic
1188C22C2×#655311yescharacteristic
1189C22C2×#655311yescharacteristic
1190C22#9061611yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—41no—
1199C4—142no—
1200C4—142no—
1201C4—142no—
1202C4—142no—
1203C4—142no—
1204C4—282no—
1205C4—282no—
1206C4—281no—
1207C4—281no—
1208C4#9034814yescomplemented
1209C2—42no—
1210C2—82no—
1211C2—144no—
1212C2—562no—
1213C2—562no—
1214C2#1174301811yescharacteristic
1215C2C2×#9034811yescharacteristic
1216C2#1174311411yescharacteristic
1217C2#1174321611yescharacteristic
1218C2#1174323111yescharacteristic
1219C2D7×#53211yescharacteristic
1220C2#1174331011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2854C2
hypercenter#2854D7
hypocenterC7#35007
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#90348C2semidirect
2. C7×#2854C2semidirect
3. #11740312C2semidirect
4. #11740093C2semidirect
5. #11740085C2semidirect
6. #11739526C2semidirect
7. C42×C22⋊D7C2semidirect
8. D7×#390C2semidirect
9. #11733869C2semidirect
10. #11733782C2semidirect
11. #11733759C2semidirect
12. #11733636C2semidirect
13. #11733449C2semidirect
14. #11733444C2semidirect
15. #11733409C2semidirect
16. #11733271C2semidirect
17. #11733108C2semidirect
18. #11733041C2semidirect
19. #11732972C2semidirect
20. #11732339C2semidirect
21. #11732201C2semidirect
22. #11731360C2semidirect
23. #11731332C2semidirect
25. C2×C7×#123C22semidirect
27. C22×C42×C7C22semidirect
29. C2×#6501C22semidirect
32. C2×#6493C22semidirect
33. C2×#6493C22semidirect
34. C2×#6493C22semidirect
39. C2×#6461C22semidirect
42. C2×#6457C22semidirect
44. C2×#6456C22semidirect
46. C2×#6451C22semidirect
47. C2×#6448C22semidirect
48. C2×#6448C22semidirect
49. C2×#6448C22semidirect
55. C2×#6442C22semidirect
60. C7×#389C22semidirect
61. C7×#389C22semidirect
62. C7×#388C22semidirect
63. C7×#388C22semidirect
64. C7×#386C22semidirect
65. C7×#380C22semidirect
67. #89995C22semidirect
70. C4×C22⋊Dic7C22semidirect
71. C4×C22⋊Dic7C22semidirect
72. C4×C22⋊Dic7C22semidirect
73. #89763C22semidirect
74. #89762C22semidirect
75. #89762C22semidirect
79. #89760C22semidirect
81. #89757C22semidirect
82. #89755C22semidirect
83. C4⋊C4×Dic7C22semidirect
84. #89745C22semidirect
85. #89733C22semidirect
89. #89731C22semidirect
90. #89731C22semidirect
93. #89729C22semidirect
94. #89729C22semidirect
95. #89728C22semidirect
97. #89725C22semidirect
98. #89723C22semidirect
99. #89720C22semidirect
101. #89711C22semidirect
102. #89711C22semidirect
103. #89711C22semidirect
107. #89707C22semidirect
108. C4×Dic7⋊C4C22semidirect
109. C4×Dic7⋊C4C22semidirect
110. C4×Dic7⋊C4C22semidirect
111. C42×Dic7C22semidirect
112. #89448C22semidirect
113. #89445C22semidirect
114. #89444C22semidirect
115. #89442C22semidirect
116. #89441C22semidirect
117. #89441C22semidirect
119. #89438C22semidirect
122. #89437C22semidirect
123. #89428C22semidirect
185. C4×C22⋊D7D4semidirect
263. #2854D7semidirect
308. C22×C4×C7C2×D4semidirect
400. C22⋊Dic7C2×D4semidirect
431. Dic7⋊C4C2×D4semidirect
441. C4×Dic7C2×D4semidirect
453. C2×#123C2×D7semidirect
475. C22×C42C2×D7semidirect
510. #389C2×D7semidirect
511. #389C2×D7semidirect
518. #388C2×D7semidirect
519. #388C2×D7semidirect
524. #386C2×D7semidirect
528. #380C2×D7semidirect
846. C4×C7#538semidirect
943. C22×C4D4×D7semidirect
1147. C7#35007semidirect
1208. C4#90348semidirect

Maximal subgroups

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

subgroupindex
C2×#903482
C7×#28542
#117403122
#117400932
#117400852
#117395262
C42×C22⋊D72
D7×#3902
#117338692
#117337822
#117337592
#117336362
#117334492
#117334442
#117334092
#117332712
#117331082
#117330412
#117329722
#117323392
#117322012
#117313602
#117313322
#350077