Finite Group Databasebeta

← #33254160

Subgroups — #33254160

Order 18688.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D73C211yesmaximal, characteristic, complemented
2#22614173C212yesmaximal, complemented
3#22613993C212yesmaximal, complemented
4#22613834C212yesmaximal, complemented
5#22613799C211yesmaximal, characteristic, complemented
6#22613714C211yesmaximal, characteristic, complemented
7#22613651C211yesmaximal, characteristic, complemented
8#22613579C211yesmaximal, characteristic, complemented
9#22613504C211yesmaximal, characteristic, complemented
10#22613419C211yesmaximal, characteristic, complemented
11#22613390C212yesmaximal, complemented
12#22613378C211yesmaximal, characteristic, complemented
13#22613283C211yesmaximal, characteristic
14#22613188C212yesmaximal, complemented
15#22613173C212yesmaximal, complemented
16C4×#14556580C211yesmaximal, characteristic, complemented
17C4×#14556567C211yesmaximal, characteristic, complemented
18C4×#14556565C211yesmaximal, characteristic, complemented
19C4×#14556559C212yesmaximal, complemented
20#22612396C211yesmaximal, characteristic, complemented
21#22612310C212yesmaximal, complemented
22C42×C22⋊D73C211yesmaximal, characteristic, complemented
23C2×#529×C73C211yesmaximal, characteristic, complemented
24C22×D4×D73C2211yescharacteristic
25C23×C4×D73C2212yes—
26C2×#14556580C2211yescharacteristic
27C2×#14556567C2211yescharacteristic
28C2×#14556565C2211yescharacteristic
29C2×#14556559C2212yes—
30C2×C4×D292C2211yescharacteristic
31C2×D4×Dic73C2211yescharacteristic
32C2×#14556553C2211yescharacteristic
33C2×C4×C22⋊D73C2211yescharacteristic
34C2×C4×C22⋊D73C2211yescharacteristic
35C2×C4×C22⋊D73C2211yescharacteristic
36C2×C4×C22⋊D73C2212yes—
37C2×C4×C22⋊D73C2212yescomplemented
38C2×#14556551C2212yes—
39C4×D4×D73—28no—
40C2×#14556550C2212yescomplemented
41C2×C4⋊C4×D73C2211yescharacteristic
42C2×C22⋊C4×D73C2212yes—
43C2×C42×D73C2211yescharacteristic
44#17988525C2212yescomplemented
45#17988522C2212yescomplemented
46#17988520C2212yescomplemented
47#17988518C2212yescomplemented
48#17988515C2212yescomplemented
49#17988515C2212yescomplemented
50#17988515C2212yescomplemented
51#17988513C2212yescomplemented
52#17988510C2212yescomplemented
53#17988509C2212yescomplemented
54#17988503C2212yescomplemented
55#17988502C2212yes—
56#17988502C2212yes—
57#17988502C2212yes—
58#17988501C2212yescomplemented
59#17988495C2212yes—
60#17988494C2211yescharacteristic, complemented
61#17988494C2211yescharacteristic, complemented
62#17988490C2211yescharacteristic
63#17988490C2211yescharacteristic
64#17988489C2211yescharacteristic
65#17988488C2211yescharacteristic
66#17988486C2211yescharacteristic, complemented
67#17988486C2211yescharacteristic, complemented
68#17988485C2211yescharacteristic, complemented
69#17988483C2211yescharacteristic, complemented
70#17988480C2212yescomplemented
71#17988480C2212yescomplemented
72#17988478C2212yescomplemented
73#17988477C2212yescomplemented
74#17988477C2212yescomplemented
75#17988468C2212yescomplemented
76#17988467C2212yescomplemented
77#17988466C2212yescomplemented
78#17988463C2212yes—
79#17988463C2212yescomplemented
80#17988459C2212yescomplemented
81#17988458C2212yes—
82#17988458C2212yes—
83#17988458C2212yescomplemented
84#17988452C2211yescharacteristic, complemented
85#17988448C2212yescomplemented
86#17988448C2212yescomplemented
87#17988447C2211yescharacteristic, complemented
88#17988444C2211yescharacteristic
89#17988444C2212yes—
90#17988444C2212yes—
91#17988444C2212yescomplemented
92#17988444C2212yescomplemented
93#17988442C2212yes—
94#17988442C2212yes—
95#17988442C2212yes—
96C4×#11924007C2211yescharacteristic, complemented
97C4×#11924007C2211yescharacteristic, complemented
98C4×#11924007C2211yescharacteristic, complemented
99C4×#11924007C2212yescomplemented
100C4×C4⋊Dic73C2211yescharacteristic, complemented
101C4×#11924005C2211yescharacteristic
102C4×#11924005C2211yescharacteristic
103C4×#11924005C2211yescharacteristic
104C4×#11924005C2212yes—
105C4×#11924005C2212yescomplemented
106C4×#11924005C2212yescomplemented
107C4×#11924005C2212yescomplemented
108C4×C22⋊Dic73C2211yescharacteristic, complemented
109C4×C22⋊Dic73C2211yescharacteristic, complemented
110C4×C22⋊Dic73C2211yescharacteristic, complemented
111C4×C22⋊Dic73C2212yescomplemented
112C42×Dic73C2211yescharacteristic, complemented
113#529×C73—28no—
114C2×#126×C73C2212yescomplemented
115C2×#125×C73C2211yescharacteristic, complemented
116C2×#124×C73C2211yescharacteristic
117C2×#123×C73C2212yescomplemented
118C2×C22⋊Q8×C73C2211yescharacteristic, complemented
119C2×#121×C73C2211yescharacteristic
120C2×C4×Q8×C73C2211yescharacteristic, complemented
121C2×C4×D4×C73C2211yescharacteristic
122C2×C4×D4×C73C2212yescomplemented
123C2×#117×C73C2212yescomplemented
124C22×C42×C73C2211yescharacteristic, complemented
125C24×D73C2312yes—
126C22×D292C2311yescharacteristic
127C22×C22⋊D73C2312yes—
128C22×C22⋊D73C2312yes—
129C22×C22⋊D73C2311yescharacteristic
130C2×D4×D73—24no—
131C2×D4×D73—24no—
132C2×D4×D73—24no—
133C23×Dic73C2312yes—
134C22×C4×D73—28no—
135C22×C4×D73—28no—
136C22×C4×D73—44no—
137C22×C4×D73C2312yes—
138C22×C4×D73C2312yes—
139C22×C4×D73C2312yes—
140C22×C4×D73C2311yescharacteristic
141C22×C4×D73C2311yescharacteristic
142C22×C4×D73C2311yescharacteristic
143#14556580—24no—
144#14556567—24no—
145#14556565—24no—
146#14556559—28no—
147C4×D292—24no—
148D4×Dic73—24no—
149#14556553—24no—
150C4×C22⋊D73—24no—
151C4×C22⋊D73—24no—
152C4×C22⋊D73—24no—
153C4×C22⋊D73—28no—
154C4×C22⋊D73—44no—
155#14556551—28no—
156#14556550—44no—
157C2×C4⋊Dic73C2311yescharacteristic
158C2×C4⋊Dic73C2311yescharacteristic
159C2×C4⋊Dic73C2311yescharacteristic
160C2×C4⋊Dic73C2312yes—
161C2×C4⋊Dic73C2312yes—
162C2×#11924007C2311yescharacteristic
163C2×#11924007C2311yescharacteristic
164C2×#11924007C2311yescharacteristic
165C2×#11924007C2312yes—
166C2×#11924007C2312yes—
167C2×#11924007C2312yes—
168C2×#11924007C2312yes—
169C4⋊C4×D73—24no—
170C2×C22⋊Dic73C2311yescharacteristic
171C2×C22⋊Dic73C2311yescharacteristic
172C2×C22⋊Dic73C2311yescharacteristic
173C2×C22⋊Dic73C2312yes—
174C2×C22⋊Dic73C2312yes—
175C2×C22⋊Dic73C2312yes—
176C2×C22⋊Dic73C2312yes—
177C2×C22⋊Dic73C2312yes—
178C2×C22⋊Dic73C2312yes—
179C2×#11924005C2311yescharacteristic
180C2×#11924005C2311yescharacteristic
181C2×#11924005C2311yescharacteristic
182C2×#11924005C2312yes—
183C2×#11924005C2312yes—
184C2×#11924005C2312yes—
185C2×#11924005C2312yes—
186C2×#11924005C2312yes—
187C2×#11924005C2312yes—
188C2×#11924005C2312yes—
189C2×#11924005C2312yes—
190C2×#11924005C2312yes—
191C2×#11924005C2312yes—
192C2×#11924005C2312yes—
193C22⋊C4×D73—28no—
194C2×C4×Dic73C2311yescharacteristic
195C2×C4×Dic73C2311yescharacteristic
196C2×C4×Dic73C2311yescharacteristic
197C2×C4×Dic73C2311yescharacteristic
198C2×C4×Dic73C2311yescharacteristic
199C2×C4×Dic73C2312yes—
200C2×C4×Dic73C2311yescharacteristic
201C2×C4×Dic73C2311yescharacteristic
202C2×C4×Dic73C2311yescharacteristic
203C2×C4×Dic73C2311yescharacteristic
204C42×D73—24no—
205#14556498C2311yescharacteristic
206#14556498C2311yescharacteristic
207#14556498C2311yescharacteristic
208#14556498C2311yescharacteristic
209#14556498C2311yescharacteristic
210#14556498C2311yescharacteristic
211#14556498C2312yes—
212#14556498C2312yes—
213#14556498C2312yes—
214#14556498C2312yes—
215#14556498C2312yes—
216#14556498C2312yes—
217#14556498C2312yes—
218#14556498C2312yes—
219#14556498C2312yes—
220#14556498C2312yes—
221#14556498C2312yes—
222#14556498C2312yes—
223#14556498C2312yes—
224C22×Q8×C73C2311yescharacteristic
225C22×D4×C73C2312yes—
226C22×D4×C73C2311yescharacteristic
227C23×C4×C73C2311yescharacteristic
228C23×C4×C73C2311yescharacteristic
229C23×C4×C73C2311yescharacteristic
230C23×C4×C73C2312yes—
231#126×C73—28no—
232#125×C73—24no—
233#124×C73—24no—
234#123×C73—28no—
235C22⋊Q8×C73—24no—
236#121×C73—24no—
237C4×Q8×C73—24no—
238C4×D4×C73—28no—
239C4×D4×C73D418yescomplemented
240#117×C73—28no—
241C2×C4⋊C4×C73C2312yes—
242C2×C4⋊C4×C73C2312yes—
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2312yes—
245C2×C4⋊C4×C73C2312yes—
246C2×C4⋊C4×C73C2311yescharacteristic
247C2×C22⋊C4×C73C2312yes—
248C2×C22⋊C4×C73C2312yes—
249C2×C22⋊C4×C73C2312yes—
250C2×C22⋊C4×C73C2312yes—
251C2×C22⋊C4×C73C2312yes—
252C2×C42×C73—24no—
253C2×C42×C73C2311yescharacteristic
254C2×C42×C73C2312yes—
255C2×C42×C73C2311yescharacteristic
256C2×C42×C73C2311yescharacteristic
257C2×C42×C73C2311yescharacteristic
258C23×D73—24no—
259C23×D73—24no—
260C23×D73—24no—
261C23×D73—24no—
262C23×D73—24no—
263C23×D73—42no—
264C23×D73—42no—
265C23×D73C2412yes—
266C23×D73C2411yescharacteristic
267C2×D292—22no—
268C2×D292—22no—
269C2×D292#4114yes—
270C2×C22⋊D73—24no—
271C2×C22⋊D73—22no—
272C2×C22⋊D73—22no—
273C2×C22⋊D73—24no—
274C2×C22⋊D73—24no—
275C2×C22⋊D73—24no—
276C2×C22⋊D73—24no—
277C2×C22⋊D73—42no—
278C2×C22⋊D73#4114yes—
279D4×D73—232no—
280C22×Dic73—24no—
281C22×Dic73—24no—
282C22×Dic73—42no—
283C22×Dic73C2411yescharacteristic
284C22×Dic73C2412yes—
285C22×Dic73C2412yes—
286C22×Dic73C2411yescharacteristic
287C22×Dic73C2411yescharacteristic
288C22×Dic73C2411yescharacteristic
289C22×Dic73C2412yes—
290C22×Dic73C2411yescharacteristic
291C22×Dic73C2411yescharacteristic
292C22×Dic73C2411yescharacteristic
293C2×C4×D73—22no—
294C2×C4×D73—22no—
295C2×C4×D73—22no—
296C2×C4×D73—22no—
297C2×C4×D73—22no—
298C2×C4×D73—24no—
299C2×C4×D73—22no—
300C2×C4×D73—24no—
301C2×C4×D73—24no—
302C2×C4×D73—24no—
303C2×C4×D73—24no—
304C2×C4×D73—24no—
305C2×C4×D73—24no—
306C2×C4×D73—432no—
307C2×C4×D73—42no—
308C2×C4×D73—42no—
309C2×C4×D73—41no—
310C2×C4×D73#4114yes—
311C2×C4×D73#4114yes—
312C4⋊Dic73—22no—
313C4⋊Dic73—22no—
314C4⋊Dic73—22no—
315C4⋊Dic73—42no—
316C4⋊Dic73—42no—
317#11924007—24no—
318#11924007—22no—
319#11924007—22no—
320#11924007—22no—
321#11924007—24no—
322#11924007—42no—
323#11924007—42no—
324C22⋊Dic73—24no—
325C22⋊Dic73—22no—
326C22⋊Dic73—22no—
327C22⋊Dic73—22no—
328C22⋊Dic73—24no—
329C22⋊Dic73—42no—
330C22⋊Dic73—42no—
331C22⋊Dic73—42no—
332C22⋊Dic73—42no—
333#11924005—22no—
334#11924005—22no—
335#11924005—22no—
336#11924005—24no—
337#11924005—24no—
338#11924005—24no—
339#11924005—24no—
340#11924005—24no—
341#11924005—24no—
342#11924005—24no—
343#11924005—24no—
344#11924005—42no—
345#11924005—42no—
346#11924005—42no—
347C4×Dic73—22no—
348C4×Dic73—22no—
349C4×Dic73—22no—
350C4×Dic73—22no—
351C4×Dic73—22no—
352C4×Dic73—22no—
353C4×Dic73—22no—
354C4×Dic73—24no—
355C4×Dic73—22no—
356C4×Dic73—41no—
357C24×C73C2412yes—
358C24×C73C2411yescharacteristic
359C2×Q8×C73—22no—
360C2×Q8×C73—22no—
361C2×Q8×C73—22no—
362C2×D4×C73—24no—
363C2×D4×C73—24no—
364C2×D4×C73—22no—
365C2×D4×C73—22no—
366C2×D4×C73—42no—
367C2×D4×C73C2×D414yes—
368C22×C4×C73—24no—
369C22×C4×C73—24no—
370C22×C4×C73—22no—
371C22×C4×C73—22no—
372C22×C4×C73—22no—
373C22×C4×C73—22no—
374C22×C4×C73—22no—
375C22×C4×C73—22no—
376C22×C4×C73—22no—
377C22×C4×C73—22no—
378C22×C4×C73—41no—
379C22×C4×C73C2×D418yes—
380C22×C4×C73C2411yescharacteristic
381C22×C4×C73C2411yescharacteristic
382C22×C4×C73C2411yescharacteristic
383C22×C4×C73C2412yes—
384C22×C4×C73C2412yes—
385C22×C4×C73C2411yescharacteristic
386C22×C4×C73C2412yes—
387C22×C4×C73C2411yescharacteristic
388C22×C4×C73C2411yescharacteristic
389C4⋊C4×C73—24no—
390C4⋊C4×C73—24no—
391C4⋊C4×C73—24no—
392C4⋊C4×C73—22no—
393C4⋊C4×C73—24no—
394C4⋊C4×C73C2×D414yes—
395C22⋊C4×C73—24no—
396C22⋊C4×C73—24no—
397C22⋊C4×C73—24no—
398C22⋊C4×C73—24no—
399C22⋊C4×C73C2×D418yes—
400C42×C73—22no—
401C42×C73—22no—
402C42×C73—22no—
403C42×C73—24no—
404C42×C73C2×D414yes—
405C23×C73—21no—
406C23×C73—21no—
407C23×C73—21no—
408C23×C73—22no—
409C23×C73—21no—
410C23×C73—22no—
411C23×C73—22no—
412C23×C73—22no—
413C23×C73—22no—
414C23×C73—21no—
415C23×C73—21no—
416C23×C73—22no—
417C23×C73C22×D414yes—
418C23×C73C2×#4112yes—
419C23×C73C2511yescharacteristic
420C22×D73—21no—
421C22×D73—21no—
422C22×D73—21no—
423C22×D73—21no—
424C22×D73—216no—
425C22×D73—22no—
426C22×D73—22no—
427C22×D73—22no—
428C22×D73—22no—
429C22×D73—22no—
430C22×D73—22no—
431C22×D73—48no—
432C22×D73—48no—
433C22×D73—48no—
434C22×D73—48no—
435C22×D73—48no—
436C22×D73—48no—
437C22×D73C2×#4114yes—
438C22×D73C2×#4112yes—
439C22×D73C2×#4112yes—
440C22×D73C2×#4112yes—
441Q8×C73—44no—
442D4×C73—28no—
443D4×C73—48no—
444C2×C4×C73—21no—
445C2×C4×C73—22no—
446C2×C4×C73—22no—
447C2×C4×C73—21no—
448C2×C4×C73—216no—
449C2×C4×C73—21no—
450C2×C4×C73—21no—
451C2×C4×C73—21no—
452C2×C4×C73—22no—
453C2×C4×C73—22no—
454C2×C4×C73—21no—
455C2×C4×C73—21no—
456C2×C4×C73—21no—
457C2×C4×C73—21no—
458C2×C4×C73—22no—
459C2×C4×C73—22no—
460C2×C4×C73—22no—
461C2×C4×C73—21no—
462C2×C4×C73—21no—
463C2×C4×C73—22no—
464C2×C4×C73—44no—
465C2×C4×C73—44no—
466C2×C4×C73—44no—
467C2×C4×C73C22×D412yes—
468C2×C4×C73C22×D414yes—
469C2×C4×C73C22×D412yes—
470C2×C4×C73C22×D412yes—
471C2×C4×C73C2×#4112yes—
472C2×C4×C73C2×#4112yes—
473C2×C4×C73C2×#4112yes—
474C2×C4×C73H(5,𝔽2)12yes—
475C22⋊D73—216no—
476C22⋊D73—28no—
477C22⋊D73—48no—
478C2×Dic73—21no—
479C2×Dic73—21no—
480C2×Dic73—21no—
481C2×Dic73—21no—
482C2×Dic73—21no—
483C2×Dic73—21no—
484C2×Dic73—21no—
485C2×Dic73—22no—
486C2×Dic73—21no—
487C2×Dic73—21no—
488C2×Dic73—21no—
489C2×Dic73—21no—
490C2×Dic73—21no—
491C2×Dic73—22no—
492C2×Dic73—22no—
493C2×Dic73—22no—
494C2×Dic73—21no—
495C2×Dic73—22no—
496C2×Dic73—22no—
497C2×Dic73—21no—
498C2×Dic73—21no—
499C2×Dic73—22no—
500C2×Dic73—22no—
501C2×Dic73—21no—
502C2×Dic73—21no—
503C2×Dic73—22no—
504C2×Dic73—21no—
505C2×Dic73—48no—
506C2×Dic73C2×#4112yes—
507C2×Dic73C2×#4112yes—
508C2×Dic73C2×#4112yes—
509D292—28no—
510C4×D73—28no—
511C4×D73—28no—
512C4×D73—48no—
513C4×D73—44no—
514C4×D73—48no—
515C4×D73—48no—
516C22×C73—24no—
517C22×C73—22no—
518C22×C73—24no—
519C22×C73—22no—
520C22×C73—24no—
521C22×C73—22no—
522C22×C73—41no—
523C22×C73—42no—
524C22×C73—42no—
525C22×C73—41no—
526C22×C73—41no—
527C22×C73—42no—
528C22×C73—41no—
529C22×C73—42no—
530C22×C73C23×D411yescharacteristic
531C22×C73C22×#4111yescharacteristic
532C22×C73C22×#4111yescharacteristic
533C22×C73C22×#4111yescharacteristic
534C22×C73C22×#4111yescharacteristic
535C22×C73C2×H(5,𝔽2)11yescharacteristic
536C22×C73#58511yescharacteristic
537C2×D73—22no—
538C2×D73—22no—
539C2×D73—22no—
540C2×D73—22no—
541C2×D73—22no—
542C2×D73—22no—
543C2×D73—24no—
544C2×D73—24no—
545C2×D73—24no—
546C2×D73—432no—
547C2×D73—42no—
548C2×D73—42no—
549C2×D73—42no—
550C2×D73—42no—
551C2×D73#52914yescomplemented
552C4×C73—24no—
553C4×C73—22no—
554C4×C73—41no—
555C4×C73—42no—
556C4×C73—41no—
557C4×C73—41no—
558C4×C73—42no—
559C4×C73#52514yes—
560C4×C73#54614yes—
561Dic73—22no—
562Dic73—22no—
563Dic73—22no—
564Dic73—41no—
565Dic73—42no—
566Dic73—42no—
567Dic73—41no—
568Dic73—41no—
569Dic73—41no—
570Dic73—42no—
571#34700—731nomaximal, Sylow
572C2×C73—44no—
573C2×C73—42no—
574C2×C73C2×#52511yescharacteristic
575C2×C73C2×#52911yescharacteristic
576C2×C73#346011yescharacteristic
577C2×C73C2×#54611yescharacteristic
578C2×C73D4×#4111yescharacteristic
579C2×C73#347511yescharacteristic
580C2×C73#348111yescharacteristic
581D73—24no—
582D73—44no—
583C2×#529D7311yescharacteristic, complemented
584C22×C4×D4—731no—
585#2480—732no—
586#2468—732no—
587#2457—732no—
588#2454—731no—
589#2447—731no—
590#2442—731no—
591#2435—731no—
592#2427—731no—
593#2420—731no—
594#2418—732no—
595#2417—731no—
596#2408—731no—
597#2395—732no—
598#2392—732no—
599C4×#124—731no—
600C4×C22⋊Q8—731no—
601C4×#121—731no—
602C4×#120—732no—
603#2293—731no—
604#2280—732no—
605C42×D4—731no—
606C73#3470011yescharacteristic, complemented, Sylow
607C23×D4—731no—
608C24×C4—732no—
609#529—28no—
610C2×#126C2×D7312yescomplemented
611C2×#125C2×D7311yescharacteristic, complemented
612C2×#124—731no—
613C2×#124C2×D7311yescharacteristic
614C2×#123C2×D7312yescomplemented
615C2×C22⋊Q8—731no—
616C2×C22⋊Q8C2×D7311yescharacteristic, complemented
617C2×#121—731no—
618C2×#121C2×D7311yescharacteristic
619C2×#120—732no—
620C2×C4×Q8C2×D7311yescharacteristic, complemented
621C2×C4×D4—732no—
622C2×C4×D4—731no—
623C2×C4×D4—732no—
624C2×C4×D4—731no—
625C2×C4×D4—731no—
626C2×C4×D4—731no—
627C2×C4×D4—731no—
628C2×C4×D4—732no—
629C2×C4×D4—731no—
630C2×C4×D4—1468no—
631C2×C4×D4C2×D7311yescharacteristic
632C2×C4×D4C2×D7312yescomplemented
633C2×#117—732no—
634C2×#117C2×D7312yescomplemented
635C22×C4⋊C4—731no—
636C22×C22⋊C4—732no—
637C22×C42—731no—
638C22×C42C2×D7311yescharacteristic, complemented
639#400—732no—
640#399—732no—
641#398—732no—
642#398—732no—
643#397—732no—
644#397—732no—
645#397—732no—
646#397—732no—
647#396—732no—
648#396—732no—
649#394—732no—
650#394—732no—
651#394—732no—
652#394—732no—
653#394—732no—
654#392—732no—
655#391—731no—
656#391—731no—
657#390—731no—
658#390—731no—
659#390—731no—
660#390—731no—
661#389—731no—
662#389—731no—
663#389—731no—
664#389—731no—
665#388—732no—
666#388—732no—
667#388—732no—
668#388—732no—
669#388—732no—
670#387—732no—
671#386—732no—
672#386—732no—
673#386—732no—
674#386—732no—
675#385—732no—
676#385—732no—
677#385—732no—
678#385—732no—
679#382—731no—
680#381—732no—
681#381—732no—
682#380—731no—
683#380—731no—
684#380—732no—
685#380—732no—
686#380—732no—
687#380—732no—
688#379—732no—
689#379—732no—
690#379—732no—
691C4×C4⋊C4—731no—
692C4×C4⋊C4—732no—
693C4×C4⋊C4—731no—
694C4×C4⋊C4—731no—
695C4×C4⋊C4—731no—
696C4×C22⋊C4—731no—
697C4×C22⋊C4—732no—
698C4×C22⋊C4—731no—
699C4×C22⋊C4—731no—
700C4×C22⋊C4—731no—
701C4×C22⋊C4—731no—
702C4×C22⋊C4—731no—
703C4×C22⋊C4—732no—
704C4×C22⋊C4—732no—
705C4×C22⋊C4—732no—
706C4×C22⋊C4—732no—
707C43—731no—
708C25—732no—
709C22×Q8C22×D7311yescharacteristic
710C22×D4—732no—
711C22×D4—731no—
712C22×D4—732no—
713C22×D4—731no—
714C22×D4—1464no—
715C22×D4—1464no—
716C22×D4—1464no—
717C22×D4C22×D7312yes—
718C22×D4C22×D7311yescharacteristic
719C23×C4—2924no—
720C23×C4—732no—
721C23×C4—731no—
722C23×C4—732no—
723C23×C4—732no—
724C23×C4—731no—
725C23×C4—731no—
726C23×C4—732no—
727C23×C4—1468no—
728C23×C4—1468no—
729C23×C4C22×D7311yescharacteristic
730C23×C4C22×D7311yescharacteristic
731C23×C4C22×D7311yescharacteristic
732C23×C4C22×D7312yes—
733#126—28no—
734#125—24no—
735#124—24no—
736#124—1464no—
737#123—28no—
738C22⋊Q8—24no—
739C22⋊Q8—1464no—
740#121—24no—
741#121—1464no—
742#120—1468no—
743C4×Q8—24no—
744C4×D4—28no—
745C4×D4—2924no—
746C4×D4—1464no—
747C4×D4—1464no—
748C4×D4—1464no—
749C4×D4—1464no—
750C4×D4—1468no—
751C4×D4—1464no—
752C4×D4—1468no—
753C4×D4—1464no—
754C4×D4C22⋊D7318yescomplemented
755#117—28no—
756#117—2924no—
757C2×C4⋊C4—732no—
758C2×C4⋊C4—732no—
759C2×C4⋊C4—732no—
760C2×C4⋊C4—732no—
761C2×C4⋊C4—731no—
762C2×C4⋊C4—732no—
763C2×C4⋊C4—731no—
764C2×C4⋊C4—731no—
765C2×C4⋊C4—731no—
766C2×C4⋊C4—731no—
767C2×C4⋊C4—731no—
768C2×C4⋊C4—732no—
769C2×C4⋊C4—1464no—
770C2×C4⋊C4C22×D7312yes—
771C2×C4⋊C4C22×D7312yes—
772C2×C4⋊C4C22×D7312yes—
773C2×C4⋊C4C22×D7311yescharacteristic
774C2×C4⋊C4C22×D7312yes—
775C2×C4⋊C4C22×D7311yescharacteristic
776C2×C22⋊C4—732no—
777C2×C22⋊C4—732no—
778C2×C22⋊C4—732no—
779C2×C22⋊C4—732no—
780C2×C22⋊C4—732no—
781C2×C22⋊C4—732no—
782C2×C22⋊C4—732no—
783C2×C22⋊C4—732no—
784C2×C22⋊C4—731no—
785C2×C22⋊C4—731no—
786C2×C22⋊C4—731no—
787C2×C22⋊C4—732no—
788C2×C22⋊C4—732no—
789C2×C22⋊C4—732no—
790C2×C22⋊C4—731no—
791C2×C22⋊C4—731no—
792C2×C22⋊C4—731no—
793C2×C22⋊C4—732no—
794C2×C22⋊C4—732no—
795C2×C22⋊C4—732no—
796C2×C22⋊C4—732no—
797C2×C22⋊C4—732no—
798C2×C22⋊C4—732no—
799C2×C22⋊C4—1468no—
800C2×C22⋊C4C22×D7312yes—
801C2×C22⋊C4C22×D7312yes—
802C2×C22⋊C4C22×D7312yes—
803C2×C22⋊C4C22×D7312yes—
804C2×C22⋊C4C22×D7312yes—
805C2×C42—24no—
806C2×C42—731no—
807C2×C42—731no—
808C2×C42—731no—
809C2×C42—731no—
810C2×C42—731no—
811C2×C42—731no—
812C2×C42—731no—
813C2×C42—732no—
814C2×C42—731no—
815C2×C42—731no—
816C2×C42—1464no—
817C2×C42C22×D7311yescharacteristic
818C2×C42C22×D7311yescharacteristic
819C2×C42C22×D7311yescharacteristic
820C2×C42C22×D7312yes—
821C2×C42C22×D7311yescharacteristic
822#95—731no—
823#95—731no—
824#95—731no—
825#95—731no—
826#95—731no—
827#95—731no—
828#95—732no—
829#95—732no—
830#95—732no—
831#95—732no—
832#95—732no—
833#95—732no—
834#95—732no—
835#95—732no—
836#95—732no—
837#95—732no—
838#95—732no—
839#95—732no—
840#95—732no—
841C24—2922no—
842C24—2922no—
843C24—731no—
844C24—732no—
845C24—1464no—
846C24—1464no—
847C24—1464no—
848C24—1464no—
849C24—1464no—
850C24C23×D7312yes—
851C24C23×D7311yescharacteristic
852C2×Q8—22no—
853C2×Q8—22no—
854C2×Q8—22no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—42no—
860C2×D4—2922no—
861C2×D4—734no—
862C2×D4—734no—
863C2×D4—1464no—
864C2×D4—14632no—
865C2×D4—1464no—
866C2×D4—1464no—
867C2×D4—1462no—
868C2×D4—1462no—
869C2×D4—1464no—
870C2×D4—1464no—
871C2×D4—1462no—
872C2×D4—1462no—
873C2×D4C2×C22⋊D7314yes—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—41no—
885C22×C4—29232no—
886C22×C4—2922no—
887C22×C4—2922no—
888C22×C4—2921no—
889C22×C4—2922no—
890C22×C4—731no—
891C22×C4—731no—
892C22×C4—731no—
893C22×C4—734no—
894C22×C4—734no—
895C22×C4—731no—
896C22×C4—732no—
897C22×C4—732no—
898C22×C4—731no—
899C22×C4—731no—
900C22×C4—731no—
901C22×C4—732no—
902C22×C4—1464no—
903C22×C4—1462no—
904C22×C4—1464no—
905C22×C4—1464no—
906C22×C4—1464no—
907C22×C4—1462no—
908C22×C4—1464no—
909C22×C4—1464no—
910C22×C4—1464no—
911C22×C4—1464no—
912C22×C4—1464no—
913C22×C4—1462no—
914C22×C4—1462no—
915C22×C4—1462no—
916C22×C4—1462no—
917C22×C4C2×C22⋊D7318yes—
918C22×C4C23×D7311yescharacteristic
919C22×C4C23×D7311yescharacteristic
920C22×C4C23×D7312yes—
921C22×C4C23×D7312yes—
922C22×C4C23×D7311yescharacteristic
923C22×C4C23×D7311yescharacteristic
924C22×C4C23×D7312yes—
925C22×C4C23×D7311yescharacteristic
926C22×C4C23×D7311yescharacteristic
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—22no—
931C4⋊C4—24no—
932C4⋊C4—2922no—
933C4⋊C4—2922no—
934C4⋊C4—2922no—
935C4⋊C4—2922no—
936C4⋊C4—1462no—
937C4⋊C4—1462no—
938C4⋊C4—1462no—
939C4⋊C4—1464no—
940C4⋊C4—1464no—
941C4⋊C4—1462no—
942C4⋊C4—1462no—
943C4⋊C4—1462no—
944C4⋊C4C2×C22⋊D7314yes—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—2922no—
950C22⋊C4—2922no—
951C22⋊C4—2922no—
952C22⋊C4—2922no—
953C22⋊C4—2922no—
954C22⋊C4—2922no—
955C22⋊C4—2922no—
956C22⋊C4—1464no—
957C22⋊C4—1462no—
958C22⋊C4—1462no—
959C22⋊C4—1462no—
960C22⋊C4—1464no—
961C22⋊C4—1464no—
962C22⋊C4—1464no—
963C22⋊C4—1464no—
964C22⋊C4—1464no—
965C22⋊C4—1462no—
966C22⋊C4—1462no—
967C22⋊C4—1464no—
968C22⋊C4—1464no—
969C22⋊C4—1462no—
970C22⋊C4—1464no—
971C22⋊C4—1464no—
972C22⋊C4C2×C22⋊D7318yes—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—24no—
977C42—2921no—
978C42—1462no—
979C42—1462no—
980C42—1462no—
981C42—1462no—
982C42—1462no—
983C42—1462no—
984C42—1462no—
985C42—1462no—
986C42—1464no—
987C42C2×C22⋊D7314yes—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—21no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—21no—
998C23—22no—
999C23—21no—
1000C23—2928no—
1001C23—2928no—
1002C23—2928no—
1003C23—2928no—
1004C23—2928no—
1005C23—2928no—
1006C23—732no—
1007C23—732no—
1008C23—732no—
1009C23—734no—
1010C23—14616no—
1011C23—1462no—
1012C23—1462no—
1013C23—1462no—
1014C23—1462no—
1015C23—1462no—
1016C23—1462no—
1017C23—1461no—
1018C23—1461no—
1019C23—1461no—
1020C23—1461no—
1021C23C22×C22⋊D7314yes—
1022C23#41×D7312yes—
1023C23C24×D7311yescharacteristic
1024Q8—44no—
1025D4—28no—
1026D4—48no—
1027D4—2928no—
1028D4—1468no—
1029D4—14616no—
1030D4—1468no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—216no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—2928no—
1055C2×C4—2924no—
1056C2×C4—2928no—
1057C2×C4—2928no—
1058C2×C4—2928no—
1059C2×C4—732no—
1060C2×C4—732no—
1061C2×C4—732no—
1062C2×C4—1461no—
1063C2×C4—1462no—
1064C2×C4—1461no—
1065C2×C4—1461no—
1066C2×C4—1461no—
1067C2×C4—1461no—
1068C2×C4—1461no—
1069C2×C4—1462no—
1070C2×C4—1462no—
1071C2×C4—1461no—
1072C2×C4—1462no—
1073C2×C4—1462no—
1074C2×C4—1462no—
1075C2×C4—1461no—
1076C2×C4—1461no—
1077C2×C4—1462no—
1078C2×C4—1462no—
1079C2×C4—1461no—
1080C2×C4—1461no—
1081C2×C4—1462no—
1082C2×C4—1461no—
1083C2×C4—1461no—
1084C2×C4—1461no—
1085C2×C4—1461no—
1086C2×C4—1461no—
1087C2×C4—1461no—
1088C2×C4—1461no—
1089C2×C4—1468no—
1090C2×C4—1468no—
1091C2×C4C22×C22⋊D7312yes—
1092C2×C4C22×C22⋊D7314yes—
1093C2×C4C22×C22⋊D7312yes—
1094C2×C4C22×C22⋊D7312yes—
1095C2×C4#41×D7312yes—
1096C2×C4#41×D7312yes—
1097C2×C4#41×D7312yes—
1098C2×C4#1455663712yes—
1099C22—22no—
1100C22—24no—
1101C22—22no—
1102C22—24no—
1103C22—24no—
1104C22—22no—
1105C22—42no—
1106C22—42no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—42no—
1111C22—42no—
1112C22—41no—
1113C22—29232no—
1114C22—2922no—
1115C22—2922no—
1116C22—2922no—
1117C22—2922no—
1118C22—734no—
1119C22—1464no—
1120C22—1464no—
1121C22—1464no—
1122C22—1462no—
1123C22—1462no—
1124C22—1462no—
1125C22—1462no—
1126C22—1462no—
1127C22—1462no—
1128C22C23×C22⋊D7311yescharacteristic
1129C22C2×#41×D7311yescharacteristic
1130C22C2×#41×D7311yescharacteristic
1131C22C2×#41×D7311yescharacteristic
1132C22C2×#41×D7311yescharacteristic
1133C22C2×#1455663711yescharacteristic
1134C22#1798942311yescharacteristic
1135C4—24no—
1136C4—22no—
1137C4—41no—
1138C4—41no—
1139C4—42no—
1140C4—41no—
1141C4—42no—
1142C4—2922no—
1143C4—2921no—
1144C4—2921no—
1145C4—2922no—
1146C4—2922no—
1147C4—2921no—
1148C4—2921no—
1149C4—1462no—
1150C4—1462no—
1151C4—1462no—
1152C4#1798909414yes—
1153C4#1798922514yes—
1154C2—44no—
1155C2—42no—
1156C2—2924no—
1157C2—1464no—
1158C2C2×#1798909411yescharacteristic
1159C2#529×D7311yescharacteristic
1160C2#2262335211yescharacteristic
1161C2C2×#1798922511yescharacteristic
1162C2#41×C22⋊D7311yescharacteristic
1163C2#2262348711yescharacteristic
1164C2#2262353711yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutator, socle, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#529×C73C2
prime radical#22613283C2
hypercenterC2×#529D73
hypocenterC73#34700
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×D73C2semidirect
2. #22614173C2semidirect
3. #22613993C2semidirect
4. #22613834C2semidirect
5. #22613799C2semidirect
6. #22613714C2semidirect
7. #22613651C2semidirect
8. #22613579C2semidirect
9. #22613504C2semidirect
10. #22613419C2semidirect
11. #22613390C2semidirect
12. #22613378C2semidirect
14. #22613188C2semidirect
15. #22613173C2semidirect
16. C4×#14556580C2semidirect
17. C4×#14556567C2semidirect
18. C4×#14556565C2semidirect
19. C4×#14556559C2semidirect
20. #22612396C2semidirect
21. #22612310C2semidirect
22. C42×C22⋊D73C2semidirect
23. C2×#529×C73C2semidirect
37. C2×C4×C22⋊D73C22semidirect
40. C2×#14556550C22semidirect
44. #17988525C22semidirect
45. #17988522C22semidirect
46. #17988520C22semidirect
47. #17988518C22semidirect
48. #17988515C22semidirect
49. #17988515C22semidirect
50. #17988515C22semidirect
51. #17988513C22semidirect
52. #17988510C22semidirect
53. #17988509C22semidirect
54. #17988503C22semidirect
58. #17988501C22semidirect
60. #17988494C22semidirect
61. #17988494C22semidirect
66. #17988486C22semidirect
67. #17988486C22semidirect
68. #17988485C22semidirect
69. #17988483C22semidirect
70. #17988480C22semidirect
71. #17988480C22semidirect
72. #17988478C22semidirect
73. #17988477C22semidirect
74. #17988477C22semidirect
75. #17988468C22semidirect
76. #17988467C22semidirect
77. #17988466C22semidirect
79. #17988463C22semidirect
80. #17988459C22semidirect
83. #17988458C22semidirect
84. #17988452C22semidirect
85. #17988448C22semidirect
86. #17988448C22semidirect
87. #17988447C22semidirect
91. #17988444C22semidirect
92. #17988444C22semidirect
96. C4×#11924007C22semidirect
97. C4×#11924007C22semidirect
98. C4×#11924007C22semidirect
99. C4×#11924007C22semidirect
100. C4×C4⋊Dic73C22semidirect
105. C4×#11924005C22semidirect
106. C4×#11924005C22semidirect
107. C4×#11924005C22semidirect
108. C4×C22⋊Dic73C22semidirect
109. C4×C22⋊Dic73C22semidirect
110. C4×C22⋊Dic73C22semidirect
111. C4×C22⋊Dic73C22semidirect
112. C42×Dic73C22semidirect
114. C2×#126×C73C22semidirect
115. C2×#125×C73C22semidirect
117. C2×#123×C73C22semidirect
118. C2×C22⋊Q8×C73C22semidirect
120. C2×C4×Q8×C73C22semidirect
122. C2×C4×D4×C73C22semidirect
123. C2×#117×C73C22semidirect
124. C22×C42×C73C22semidirect
239. C4×D4×C73D4semidirect
551. C2×D73#529semidirect
583. C2×#529D73semidirect
606. C73#34700semidirect
610. C2×#126C2×D73semidirect
611. C2×#125C2×D73semidirect
614. C2×#123C2×D73semidirect
616. C2×C22⋊Q8C2×D73semidirect
620. C2×C4×Q8C2×D73semidirect
632. C2×C4×D4C2×D73semidirect
634. C2×#117C2×D73semidirect
638. C22×C42C2×D73semidirect
754. C4×D4C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D732
#226141732
#226139932
#226138342
#226137992
#226137142
#226136512
#226135792
#226135042
#226134192
#226133902
#226133782
#226132832
#226131882
#226131732
C4×#145565802
C4×#145565672
C4×#145565652
C4×#145565592
#226123962
#226123102
C42×C22⋊D732
C2×#529×C732
#3470073