Finite Group Databasebeta

← #13321571

Subgroups — #13321571

Order 1792.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11743112C211yesmaximal, characteristic
2#11736077C211yesmaximal, characteristic, complemented
3#11730814C211yesmaximal, characteristic, complemented
4C7×#1504C211yesmaximal, characteristic, complemented
5#11729463C211yesmaximal, characteristic, complemented
6#11727733C211yesmaximal, characteristic, complemented
7#11727152C211yesmaximal, characteristic, complemented
8#11726093C211yesmaximal, characteristic, complemented
9D7×#328C211yesmaximal, characteristic, complemented
10#11726066C211yesmaximal, characteristic, complemented
11#11726065C211yesmaximal, characteristic, complemented
12#11726061C211yesmaximal, characteristic, complemented
13D7×#327C211yesmaximal, characteristic, complemented
14#11726034C211yesmaximal, characteristic, complemented
15#11726033C211yesmaximal, characteristic, complemented
16C7×#525C2211yescharacteristic
17#90522C411yescharacteristic, complemented
18#90520C411yescharacteristic, complemented
19#90482C2211yescharacteristic
20C2×C4×C22⋊D7—21no—
21C2×C4×C22⋊D7C2211yescharacteristic
22#90352—21no—
23#90350—21no—
24#90330C411yescharacteristic, complemented
25#90324C411yescharacteristic, complemented
26D7×C22⋊Q8C2211yescharacteristic
27#90315C2211yescharacteristic
28#90305C411yescharacteristic, complemented
29#90303C411yescharacteristic, complemented
30D7×#121C2211yescharacteristic
31#90291C2211yescharacteristic
32#90284—21no—
33#90280—21no—
34#90255—21no—
35#90249—21no—
36#90247—21no—
37#90236—21no—
38#90221C411yescharacteristic, complemented
39#90220C411yescharacteristic, complemented
40C7×#407C2211yescharacteristic, complemented
41C2×C7×#95C2211yescharacteristic, complemented
42#89984C2211yescharacteristic, complemented
43#89982—21no—
44#89979C2211yescharacteristic, complemented
45#89899—21no—
46#89899—21no—
47#89500—21no—
48#89500—21no—
49D7×C22⋊C8C2211yescharacteristic
50D7×C22⋊C8C2211yescharacteristic
51#89491C2211yescharacteristic, complemented
52#89491C2211yescharacteristic, complemented
53#89440—21no—
54#89439C2211yescharacteristic
55D7×#95C2211yescharacteristic
56#89422C2211yescharacteristic, complemented
57#89421C2211yescharacteristic, complemented
58#89419—21no—
59C7×#328C2211yescharacteristic, complemented
60C7×#328C2211yescharacteristic, complemented
61C7×#327C2211yescharacteristic
62C7×#327C2211yescharacteristic
63#89333C2211yescharacteristic, complemented
64#89333C2211yescharacteristic, complemented
65#89332C2211yescharacteristic
66#89332C2211yescharacteristic
67#89265C2211yescharacteristic
68#89265C2211yescharacteristic
69#89262C2211yescharacteristic, complemented
70#89262C2211yescharacteristic, complemented
71#89247C2211yescharacteristic, complemented
72#89247C2211yescharacteristic, complemented
73#89246C2211yescharacteristic
74#89246C2211yescharacteristic
75#17622—71nomaximal, Sylow
76C2×C7×#41C2×C411yescharacteristic, complemented
77C23×C4×C7—21no—
78C23×C4×C7C2311yescharacteristic
79C22×C22⋊D7D411yescharacteristic
80C2×Q8×D7C2×C411yescharacteristic, complemented
81C2×D4×D7—21no—
82C2×D4×D7C2×C411yescharacteristic, complemented
83C2×#1157C2×C411yescharacteristic, complemented
84C22×C4×D7—21no—
85C22×C4×D7C2311yescharacteristic
86C2×C7×M16—21no—
87C7×#123—21no—
88C7×C22⋊Q8C2×C411yescharacteristic, complemented
89C7×C22⋊Q8C2311yescharacteristic
90C7×#121C2×C411yescharacteristic, complemented
91C7×#121C2311yescharacteristic
92C7×#120—21no—
93C4×C7×D4—21no—
94C4×C7×D4—21no—
95C7×#117C2×C411yescharacteristic, complemented
96#6516—21no—
97C2×C22⋊Dic7—21no—
98C2×C22⋊Dic7D411yescharacteristic
99#6510C2×C411yescharacteristic, complemented
100#6509C2×C411yescharacteristic, complemented
101Q8×Dic7C2×C411yescharacteristic, complemented
102#6502—21no—
103#6502—21no—
104#6501—21no—
105#6501—21no—
106#6501—21no—
107#6501C2×C411yescharacteristic, complemented
108#6500—21no—
109#6500—21no—
110#6499—21no—
111#6499C2×C411yescharacteristic, complemented
112#6498—21no—
113#6498—21no—
114D4×Dic7—21no—
115D4×Dic7C2×C411yescharacteristic, complemented
116#6493C2×C411yescharacteristic, complemented
117#6493C2311yescharacteristic
118#6492—21no—
119#6492—21no—
120C4×C22⋊D7—21no—
121C4×C22⋊D7—21no—
122C4×C22⋊D7—21no—
123C4×C22⋊D7—44no—
124C4×C22⋊D7C2×C411yescharacteristic
125C4×C22⋊D7C2×C411yescharacteristic
126C4×C22⋊D7C2×C411yescharacteristic
127C4×C22⋊D7C2×C411yescharacteristic
128C4×C22⋊D7D411yescharacteristic
129C4×C22⋊D7D411yescharacteristic
130C4×C22⋊D7D411yescharacteristic
131C4×C22⋊D7D411yescharacteristic
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4D411yescharacteristic
135#6489C2×C411yescharacteristic, complemented
136C2×C4⋊Dic7—21no—
137#6487—21no—
138#6487C2×C411yescharacteristic, complemented
139#6487C2311yescharacteristic
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4D411yescharacteristic
144C2×C4×Dic7—21no—
145C2×C4×Dic7C2311yescharacteristic
146C2×#1136—21no—
147C2×C8×D7—21no—
148C2×C8×D7—21no—
149#6461—21no—
150#6460C2×C411yescharacteristic, complemented
151#6459—21no—
152#6459—21no—
153#6458C2×C411yescharacteristic, complemented
154#6456—21no—
155#6456C2×C411yescharacteristic, complemented
156#6455—21no—
157#6455—21no—
158D7×C4⋊C4—21no—
159D7×C4⋊C4C2×C411yescharacteristic, complemented
160D7×C4⋊C4C2×C411yescharacteristic, complemented
161#6453C2×C411yescharacteristic, complemented
162#6453C2×C411yescharacteristic, complemented
163#6452—21no—
164#6450C2×C411yescharacteristic, complemented
165#6449—21no—
166#6448—21no—
167#6447—21no—
168#6447—21no—
169#6447—21no—
170#6446—21no—
171#6446—21no—
172#6446—21no—
173#6446—21no—
174(C22⋊D7)⋊C4—21no—
175(C22⋊D7)⋊C4—21no—
176D7×C22⋊C4—21no—
177D7×C22⋊C4—21no—
178D7×C22⋊C4—21no—
179#6442—21no—
180#6442—21no—
181#6442—21no—
182#6442—21no—
183#6441—21no—
184#6440—21no—
185#6439—21no—
186C4×D28—21no—
187#6435—21no—
188#6433—21no—
189C7×C22⋊C8—21no—
190C7×C22⋊C8C2311yescharacteristic
191C7×C22⋊C8C2311yescharacteristic
192C7×#95—21no—
193C7×#95C2311yescharacteristic
194C7×#95C2311yescharacteristic
195C7⋊#95—21no—
196C7⋊#95—21no—
197C7⋊#95C2311yescharacteristic
198C7⋊#95C2311yescharacteristic
199C22⋊(C7⋊C8)—21no—
200C22⋊(C7⋊C8)C2311yescharacteristic
201C22⋊(C7⋊C8)C2311yescharacteristic
202(C2×D7)⋊C8—21no—
203(C2×D7)⋊C8—21no—
204#6389—21no—
205#6389—21no—
206Dic7⋊C8—21no—
207Dic7⋊C8—21no—
208#3505—71no—
209#2973—71no—
210#2349—71no—
211#1520—71no—
212#1519—71no—
213#1513—71no—
214#1513—71no—
215#1512—71no—
216#1512—71no—
217#1509—71no—
218#1509—71no—
219#1504—71no—
220#1504D711yescharacteristic, complemented
221C2×#328—71no—
222C2×#327—71no—
223C24×C7C2×D411yescharacteristic
224C23×D7—21no—
225C23×D7C2×D411yescharacteristic
226C7×#41—81no—
227C2×C7×Q8C22×C411yescharacteristic
228C2×C7×D4—21no—
229C2×C7×D4—21no—
230C2×C7×D4—21no—
231C2×C7×D4C22×C411yescharacteristic
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—42no—
236C22×C4×C7—42no—
237C22×C4×C7—81no—
238C22×C4×C7—81no—
239C22×C4×C7C22×C411yescharacteristic
240C22×C4×C7C22×C411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2411yescharacteristic
245C2×C22⋊D7—22no—
246C2×C22⋊D7—22no—
247C2×C22⋊D7—21no—
248C2×C22⋊D7—21no—
249C2×C22⋊D7—21no—
250C2×C22⋊D7—21no—
251C2×C22⋊D7—21no—
252C2×C22⋊D7C22⋊C411yescharacteristic
253C2×C22⋊D7C22⋊C411yescharacteristic
254C2×C22⋊D7C22⋊C411yescharacteristic
255C2×C22⋊D7C22⋊C411yescharacteristic
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7C2×D411yescharacteristic
260C22×Dic7C2×D411yescharacteristic
261C22×Dic7C2×D411yescharacteristic
262Q8×D7—81no—
263D4×D7—42no—
264D4×D7—42no—
265D4×D7—81no—
266#1157—81no—
267C2×D28—21no—
268C2×D28C22×C411yescharacteristic
269C2×C4×D7—21no—
270C2×C4×D7—21no—
271C2×C4×D7—21no—
272C2×C4×D7—21no—
273C2×C4×D7—21no—
274C2×C4×D7—42no—
275C2×C4×D7—42no—
276C2×C4×D7—81no—
277C2×C4×D7—81no—
278C2×C4×D7C22×C411yescharacteristic
279C2×C4×D7C22×C411yescharacteristic
280C2×C4×D7C2×D411yescharacteristic
281C2×C4×D7C2×D411yescharacteristic
282C2×Dic14—21no—
283C2×Dic14C22×C411yescharacteristic
284C7×M16—81no—
285C2×C7×C8—21no—
286C2×C7×C8—21no—
287C7×C4⋊C4—21no—
288C7×C4⋊C4—21no—
289C7×C4⋊C4C22×C411yescharacteristic
290C7×C4⋊C4C22×C411yescharacteristic
291C7×C22⋊C4—21no—
292C7×C22⋊C4—21no—
293C7×C22⋊C4—21no—
294C7×C22⋊C4—21no—
295C7×C22⋊C4—21no—
296C42×C7—21no—
297C22⋊Dic7—21no—
298C22⋊Dic7—21no—
299C22⋊Dic7—21no—
300C22⋊Dic7—21no—
301C22⋊Dic7—21no—
302C22⋊Dic7—21no—
303C22⋊Dic7—21no—
304C22⋊Dic7—42no—
305C22⋊Dic7C22⋊C411yescharacteristic
306C22⋊Dic7C22⋊C411yescharacteristic
307C22⋊Dic7C22⋊C411yescharacteristic
308C22⋊Dic7C22⋊C411yescharacteristic
309(C2×D7)⋊C4—21no—
310(C2×D7)⋊C4—21no—
311(C2×D7)⋊C4—21no—
312(C2×D7)⋊C4—21no—
313(C2×D7)⋊C4—21no—
314(C2×D7)⋊C4—21no—
315(C2×D7)⋊C4—21no—
316(C2×D7)⋊C4—21no—
317(C2×D7)⋊C4—42no—
318(C2×D7)⋊C4C22⋊C411yescharacteristic
319(C2×D7)⋊C4C22⋊C411yescharacteristic
320(C2×D7)⋊C4C22⋊C411yescharacteristic
321(C2×D7)⋊C4C22⋊C411yescharacteristic
322C4⋊Dic7—21no—
323C4⋊Dic7—21no—
324C4⋊Dic7—21no—
325C4⋊Dic7—21no—
326C4⋊Dic7—81no—
327C4⋊Dic7C22×C411yescharacteristic
328C4⋊Dic7C22×C411yescharacteristic
329Dic7⋊C4—21no—
330Dic7⋊C4—21no—
331Dic7⋊C4—21no—
332Dic7⋊C4—21no—
333Dic7⋊C4—21no—
334Dic7⋊C4—21no—
335Dic7⋊C4—21no—
336Dic7⋊C4—21no—
337Dic7⋊C4—42no—
338Dic7⋊C4—42no—
339Dic7⋊C4—81no—
340Dic7⋊C4C22⋊C411yescharacteristic
341Dic7⋊C4C22⋊C411yescharacteristic
342Dic7⋊C4C22⋊C411yescharacteristic
343Dic7⋊C4C22⋊C411yescharacteristic
344C4×Dic7—21no—
345C4×Dic7—21no—
346C4×Dic7—21no—
347C4×Dic7—42no—
348C4×Dic7C22×C411yescharacteristic
349C4×Dic7C22×C411yescharacteristic
350C4×Dic7C2×D411yescharacteristic
351C4×Dic7C2×D411yescharacteristic
352#1136—81no—
353C2×C7⋊C8—21no—
354C2×C7⋊C8—21no—
355C8×D7—81no—
356C8×D7—81no—
357#553—71no—
358#553—71no—
359#553—141no—
360#553—141no—
361#552—71no—
362#552—71no—
363#551—141no—
364#551—141no—
365#548—71no—
366#548—71no—
367#546—71no—
368#546—71no—
369#539—141no—
370#538—141no—
371#534—141no—
372#529—71no—
373#529—71no—
374#525—71no—
375#525C2×D711yescharacteristic
376C2×C22⋊Q8—71no—
377C2×#121—71no—
378#518—141no—
379C2×C4×D4—71no—
380C2×C4×D4—141no—
381#435—141no—
382#435—141no—
383#435—141no—
384#435—141no—
385#432—71no—
386#432—71no—
387#407—71no—
388#407C2×D711yescharacteristic, complemented
389C2×C22⋊C8—71no—
390C2×C22⋊C8—71no—
391#389—141no—
392#385—141no—
393#385—141no—
394#382—71no—
395#380—71no—
396#380—71no—
397C4×C4⋊C4—71no—
398C2×#95—71no—
399C2×#95C2×D711yescharacteristic, complemented
400#328—71no—
401#328—71no—
402#328—71no—
403#328—71no—
404#328—71no—
405#328—71no—
406#328C2×D711yescharacteristic, complemented
407#328C2×D711yescharacteristic, complemented
408#327—71no—
409#327—71no—
410#327—71no—
411#327—71no—
412#327—71no—
413#327—71no—
414#327C2×D711yescharacteristic
415#327C2×D711yescharacteristic
416C23×C7—21no—
417C23×C7—21no—
418C23×C7—21no—
419C23×C7—41no—
420C23×C7—41no—
421C23×C7C2×C22⋊C411yescharacteristic
422C23×C7C2×C22⋊C411yescharacteristic
423C23×C7C22×D411yescharacteristic
424C22×D7—21no—
425C22×D7—41no—
426C22×D7—41no—
427C22×D7—42no—
428C22×D7—81no—
429C22×D7—81no—
430C22×D7C2×C22⋊C411yescharacteristic
431C22×D7C2×C22⋊C411yescharacteristic
432C22×D7AGL(1,ℤ/8)12yes—
433C22×D7#13712yes—
434C7×Q8—41no—
435C7×D4—41no—
436C7×D4—41no—
437C7×D4—41no—
438C7×D4—81no—
439C7×D4—81no—
440C2×C4×C7—22no—
441C2×C4×C7—21no—
442C2×C4×C7—21no—
443C2×C4×C7—21no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—81no—
456C2×C4×C7—84no—
457C2×C4×C7C2×C22⋊C411yescharacteristic
458C2×C4×C7C2×C22⋊C411yescharacteristic
459C2×C4×C7C23×C411yescharacteristic
460C2×C4×C7C22×D411yescharacteristic
461C22⋊D7—22no—
462C22⋊D7—22no—
463C22⋊D7—22no—
464C22⋊D7—22no—
465C22⋊D7—41no—
466C22⋊D7—41no—
467C22⋊D7—42no—
468C22⋊D7—81no—
469C22⋊D7—81no—
470C22⋊D7—81no—
471C2×Dic7—21no—
472C2×Dic7—21no—
473C2×Dic7—21no—
474C2×Dic7—21no—
475C2×Dic7—21no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—81no—
485C2×Dic7C2×C22⋊C411yescharacteristic
486C2×Dic7C2×C22⋊C411yescharacteristic
487C2×Dic7C2×C22⋊C411yescharacteristic
488C2×Dic7C2×C22⋊C411yescharacteristic
489C2×Dic7C2×C22⋊C411yescharacteristic
490C2×Dic7C2×C22⋊C411yescharacteristic
491D28—41no—
492D28—42no—
493C4×D7—41no—
494C4×D7—41no—
495C4×D7—41no—
496C4×D7—41no—
497C4×D7—42no—
498C4×D7—81no—
499C4×D7—81no—
500C4×D7—81no—
501C4×D7—81no—
502C4×D7—84no—
503Dic14—41no—
504Dic14—81no—
505C7×C8—41no—
506C7×C8—41no—
507C7⋊C8—41no—
508C7⋊C8—41no—
509C2×#41—71no—
510C2×#41C4×D711yescharacteristic, complemented
511C22×Q8—71no—
512C22×D4—71no—
513C22×D4—71no—
514C22×D4—141no—
515C23×C4—21no—
516C23×C4—71no—
517C23×C4—141no—
518C23×C4C22×D711yescharacteristic
519C2×M16—21no—
520C2×M16—141no—
521C22×C8—141no—
522C22×C8—141no—
523#126—141no—
524#126—141no—
525#126—141no—
526#126—141no—
527#126—141no—
528#126—141no—
529#125—71no—
530#125—71no—
531#125—141no—
532#125—141no—
533#124—71no—
534#124—71no—
535#124—141no—
536#124—141no—
537#123—21no—
538#123—141no—
539#123—141no—
540#123—141no—
541#123—141no—
542#123—141no—
543#123—141no—
544#123—141no—
545#123—141no—
546#123—141no—
547C22⋊Q8—71no—
548C22⋊Q8—71no—
549C22⋊Q8—71no—
550C22⋊Q8—71no—
551C22⋊Q8—141no—
552C22⋊Q8—141no—
553C22⋊Q8—141no—
554C22⋊Q8—141no—
555C22⋊Q8C4×D711yescharacteristic, complemented
556C22⋊Q8C22×D711yescharacteristic
557#121—71no—
558#121—71no—
559#121—71no—
560#121—71no—
561#121—141no—
562#121—141no—
563#121—141no—
564#121—141no—
565#121—141no—
566#121—141no—
567#121—141no—
568#121—141no—
569#121C4×D711yescharacteristic, complemented
570#121C22×D711yescharacteristic
571#120—21no—
572#120—141no—
573#120—141no—
574#120—141no—
575C4×Q8—71no—
576C4×Q8—71no—
577C4×D4—21no—
578C4×D4—21no—
579C4×D4—71no—
580C4×D4—71no—
581C4×D4—71no—
582C4×D4—71no—
583C4×D4—71no—
584C4×D4—71no—
585C4×D4—71no—
586C4×D4—71no—
587C4×D4—71no—
588C4×D4—71no—
589C4×D4—141no—
590C4×D4—141no—
591C4×D4—141no—
592C4×D4—141no—
593C4×D4—141no—
594C4×D4—141no—
595C4×D4—141no—
596C4×D4—141no—
597C4×D4—284no—
598#117—71no—
599#117—141no—
600#117—141no—
601#117—141no—
602#117—141no—
603#117C4×D711yescharacteristic, complemented
604C2×C4⋊C4—71no—
605C2×C4⋊C4—71no—
606C2×C4⋊C4—71no—
607C2×C4⋊C4—141no—
608C2×C4⋊C4—141no—
609C2×C4⋊C4—141no—
610C2×C4⋊C4—141no—
611C2×C4⋊C4—141no—
612C2×C22⋊C4—71no—
613C2×C22⋊C4—71no—
614C2×C22⋊C4—141no—
615C2×C22⋊C4—141no—
616C2×C22⋊C4—141no—
617C2×C22⋊C4—141no—
618C2×C22⋊C4—141no—
619C2×C22⋊C4—141no—
620C2×C42—71no—
621C2×C42—141no—
622C4⋊C8—141no—
623C4⋊C8—141no—
624C22⋊C8—21no—
625C22⋊C8—71no—
626C22⋊C8—71no—
627C22⋊C8—141no—
628C22⋊C8—141no—
629C22⋊C8—141no—
630C22⋊C8C22×D711yescharacteristic
631C22⋊C8C22×D711yescharacteristic
632#97—141no—
633#97—141no—
634#95—21no—
635#95—71no—
636#95—71no—
637#95—141no—
638#95—141no—
639#95C22×D711yescharacteristic
640#95C22×D711yescharacteristic
641C22×C7—21no—
642C22×C7—21no—
643C22×C7—21no—
644C22×C7—21no—
645C22×C7—21no—
646C22×C7—21no—
647C22×C7—21no—
648C22×C7—21no—
649C22×C7—42no—
650C22×C7—42no—
651C22×C7—41no—
652C22×C7—41no—
653C22×C7—41no—
654C22×C7C22×C22⋊C411yescharacteristic
655C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
656C22×C7C2×#13711yescharacteristic
657C2×D7—21no—
658C2×D7—21no—
659C2×D7—21no—
660C2×D7—21no—
661C2×D7—42no—
662C2×D7—42no—
663C2×D7—41no—
664C2×D7—41no—
665C2×D7—41no—
666C2×D7—162no—
667C2×D7#41712yes—
668C2×D7#41712yes—
669C4×C7—21no—
670C4×C7—21no—
671C4×C7—21no—
672C4×C7—21no—
673C4×C7—42no—
674C4×C7—41no—
675C4×C7—41no—
676C4×C7—41no—
677C4×C7—81no—
678Dic7—21no—
679Dic7—21no—
680Dic7—21no—
681Dic7—21no—
682Dic7—21no—
683Dic7—21no—
684Dic7—41no—
685Dic7—41no—
686Dic7—41no—
687Dic7—81no—
688Dic7—81no—
689C24—71no—
690C24—141no—
691C24D4×D711yescharacteristic
692#41—81no—
693#41—561no—
694C2×Q8—71no—
695C2×Q8—141no—
696C2×Q8—561no—
697C2×Q8C2×C4×D711yescharacteristic
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—71no—
702C2×D4—71no—
703C2×D4—71no—
704C2×D4—71no—
705C2×D4—71no—
706C2×D4—141no—
707C2×D4—141no—
708C2×D4—142no—
709C2×D4—142no—
710C2×D4—141no—
711C2×D4—141no—
712C2×D4—141no—
713C2×D4—141no—
714C2×D4—282no—
715C2×D4—282no—
716C2×D4—561no—
717C2×D4C2×C4×D711yescharacteristic
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—71no—
724C22×C4—71no—
725C22×C4—71no—
726C22×C4—71no—
727C22×C4—71no—
728C22×C4—71no—
729C22×C4—71no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—282no—
741C22×C4—282no—
742C22×C4—561no—
743C22×C4—561no—
744C22×C4C2×C4×D711yescharacteristic
745C22×C4C2×C4×D711yescharacteristic
746C22×C4D4×D711yescharacteristic
747C22×C4D4×D711yescharacteristic
748C22×C4D4×D711yescharacteristic
749C22×C4C23×D711yescharacteristic
750M16—81no—
751M16—561no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—141no—
755C2×C8—141no—
756C2×C8—561no—
757C2×C8—561no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—71no—
761C4⋊C4—71no—
762C4⋊C4—71no—
763C4⋊C4—71no—
764C4⋊C4—71no—
765C4⋊C4—71no—
766C4⋊C4—141no—
767C4⋊C4—141no—
768C4⋊C4—141no—
769C4⋊C4—141no—
770C4⋊C4—141no—
771C4⋊C4—141no—
772C4⋊C4—141no—
773C4⋊C4—141no—
774C4⋊C4—141no—
775C4⋊C4—141no—
776C4⋊C4—141no—
777C4⋊C4—141no—
778C4⋊C4—282no—
779C4⋊C4—282no—
780C4⋊C4—561no—
781C4⋊C4—561no—
782C4⋊C4C2×C4×D711yescharacteristic
783C4⋊C4C2×C4×D711yescharacteristic
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—71no—
790C22⋊C4—71no—
791C22⋊C4—71no—
792C22⋊C4—71no—
793C22⋊C4—71no—
794C22⋊C4—71no—
795C22⋊C4—71no—
796C22⋊C4—71no—
797C22⋊C4—141no—
798C22⋊C4—141no—
799C22⋊C4—141no—
800C22⋊C4—141no—
801C22⋊C4—141no—
802C22⋊C4—141no—
803C22⋊C4—141no—
804C22⋊C4—141no—
805C22⋊C4—141no—
806C22⋊C4—141no—
807C22⋊C4—141no—
808C22⋊C4—141no—
809C22⋊C4—141no—
810C22⋊C4—141no—
811C22⋊C4—141no—
812C22⋊C4—282no—
813C22⋊C4—282no—
814C42—21no—
815C42—71no—
816C42—71no—
817C42—71no—
818C42—71no—
819C42—141no—
820C42—141no—
821C42—141no—
822C42—282no—
823C2×C7—21no—
824C2×C7—21no—
825C2×C7—41no—
826C2×C7—41no—
827C2×C7—81no—
828C2×C7#288311yescharacteristic
829C2×C7C2×#41711yescharacteristic
830C2×C7#290111yescharacteristic
831D7—22no—
832D7—22no—
833D7—81no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—41no—
838C23—41no—
839C23—71no—
840C23—71no—
841C23—72no—
842C23—72no—
843C23—141no—
844C23—281no—
845C23—281no—
846C23—282no—
847C23—561no—
848C23—561no—
849C23D7×C22⋊C411yescharacteristic
850C23D7×C22⋊C411yescharacteristic
851C23C2×D4×D711yescharacteristic
852Q8—41no—
853Q8—281no—
854Q8—561no—
855D4—41no—
856D4—41no—
857D4—41no—
858D4—81no—
859D4—81no—
860D4—142no—
861D4—142no—
862D4—142no—
863D4—142no—
864D4—281no—
865D4—282no—
866D4—282no—
867D4—281no—
868D4—281no—
869D4—561no—
870D4—561no—
871D4—561no—
872C2×C4—22no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—71no—
888C2×C4—71no—
889C2×C4—71no—
890C2×C4—71no—
891C2×C4—71no—
892C2×C4—71no—
893C2×C4—81no—
894C2×C4—84no—
895C2×C4—141no—
896C2×C4—141no—
897C2×C4—141no—
898C2×C4—141no—
899C2×C4—141no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—282no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—561no—
914C2×C4—561no—
915C2×C4—561no—
916C2×C4—561no—
917C2×C4—564no—
918C2×C4—561no—
919C2×C4D7×C22⋊C411yescharacteristic
920C2×C4D7×C22⋊C411yescharacteristic
921C2×C4C22×C4×D711yescharacteristic
922C2×C4C2×D4×D711yescharacteristic
923C8—41no—
924C8—41no—
925C8—281no—
926C8—281no—
927C7#1762211yescharacteristic, complemented, Sylow
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—42no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—72no—
942C22—72no—
943C22—141no—
944C22—141no—
945C22—141no—
946C22—141no—
947C22—282no—
948C22—282no—
949C22—281no—
950C22—281no—
951C22—281no—
952C22—1122no—
953C22C2×D7×C22⋊C411yescharacteristic
954C22D7×AGL(1,ℤ/8)11yescharacteristic
955C22D7×#13711yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—42no—
961C4—41no—
962C4—41no—
963C4—41no—
964C4—81no—
965C4—141no—
966C4—141no—
967C4—141no—
968C4—141no—
969C4—141no—
970C4—141no—
971C4—281no—
972C4—281no—
973C4—281no—
974C4—561no—
975C4—561no—
976C2—21no—
977C2—21no—
978C2—41no—
979C2—41no—
980C2—81no—
981C2—142no—
982C2—142no—
983C2—561no—
984C2#1173613311yescharacteristic
985C2D7×#41711yescharacteristic
986C2#1173642811yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1504C2
socleC22×C7C22×C22⋊C4
prime radical#11743112C2
cosocleC22×C4×C7C24
hypercenter#1504D7
hypocenterC7#17622
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #11736077C2semidirect
3. #11730814C2semidirect
4. C7×#1504C2semidirect
5. #11729463C2semidirect
6. #11727733C2semidirect
7. #11727152C2semidirect
8. #11726093C2semidirect
9. D7×#328C2semidirect
10. #11726066C2semidirect
11. #11726065C2semidirect
12. #11726061C2semidirect
13. D7×#327C2semidirect
14. #11726034C2semidirect
15. #11726033C2semidirect
17. #90522C4semidirect
18. #90520C4semidirect
24. #90330C4semidirect
25. #90324C4semidirect
28. #90305C4semidirect
29. #90303C4semidirect
38. #90221C4semidirect
39. #90220C4semidirect
40. C7×#407C22semidirect
41. C2×C7×#95C22semidirect
42. #89984C22semidirect
44. #89979C22semidirect
51. #89491C22semidirect
52. #89491C22semidirect
56. #89422C22semidirect
57. #89421C22semidirect
59. C7×#328C22semidirect
60. C7×#328C22semidirect
63. #89333C22semidirect
64. #89333C22semidirect
69. #89262C22semidirect
70. #89262C22semidirect
71. #89247C22semidirect
72. #89247C22semidirect
76. C2×C7×#41C2×C4semidirect
80. C2×Q8×D7C2×C4semidirect
82. C2×D4×D7C2×C4semidirect
83. C2×#1157C2×C4semidirect
88. C7×C22⋊Q8C2×C4semidirect
90. C7×#121C2×C4semidirect
95. C7×#117C2×C4semidirect
99. #6510C2×C4semidirect
100. #6509C2×C4semidirect
101. Q8×Dic7C2×C4semidirect
107. #6501C2×C4semidirect
111. #6499C2×C4semidirect
115. D4×Dic7C2×C4semidirect
116. #6493C2×C4semidirect
135. #6489C2×C4semidirect
138. #6487C2×C4semidirect
150. #6460C2×C4semidirect
153. #6458C2×C4semidirect
155. #6456C2×C4semidirect
159. D7×C4⋊C4C2×C4semidirect
160. D7×C4⋊C4C2×C4semidirect
161. #6453C2×C4semidirect
162. #6453C2×C4semidirect
164. #6450C2×C4semidirect
220. #1504D7semidirect
388. #407C2×D7semidirect
399. C2×#95C2×D7semidirect
406. #328C2×D7semidirect
407. #328C2×D7semidirect
510. C2×#41C4×D7semidirect
555. C22⋊Q8C4×D7semidirect
569. #121C4×D7semidirect
603. #117C4×D7semidirect
927. C7#17622semidirect

Maximal subgroups

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

subgroupindex
#117431122
#117360772
#117308142
C7×#15042
#117294632
#117277332
#117271522
#117260932
D7×#3282
#117260662
#117260652
#117260612
D7×#3272
#117260342
#117260332
#176227