Finite Group Databasebeta

← #2662×D73 #33252711

Subgroups — #2662×D73 #33252711

Order 18688.

3002 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D73C211yesmaximal, characteristic, complemented
2C2×#124×D73C211yesmaximal, characteristic, complemented
3#22616077C211yesmaximal, characteristic, complemented
4#22616076C211yesmaximal, characteristic, complemented
5#22616075C211yesmaximal, characteristic, complemented
6#22616074C212yesmaximal, complemented
7#22616073C211yesmaximal, characteristic, complemented
8#22616072C212yesmaximal, complemented
9#22616071C211yesmaximal, characteristic, complemented
10#22616070C211yesmaximal, characteristic, complemented
11#22616069C212yesmaximal, complemented
12#22616068C211yesmaximal, characteristic, complemented
13#22616067C212yesmaximal, complemented
14#396×D73C212yesmaximal, complemented
15#395×D73C211yesmaximal, characteristic, complemented
16#394×D73C212yesmaximal, complemented
17#394×D73C211yesmaximal, characteristic, complemented
18#393×D73C211yesmaximal, characteristic, complemented
19#392×D73C211yesmaximal, characteristic
20#390×D73C212yesmaximal, complemented
21#388×D73C212yesmaximal, complemented
22C4×C4⋊C4×D73C211yesmaximal, characteristic, complemented
23C73×#2662C211yesmaximal, characteristic, complemented
24C22×Q8×D73C2211yescharacteristic
25C22×D4×D73C2212yes—
26C22×D4×D73C2211yescharacteristic
27C2×#14556586C2211yescharacteristic, complemented
28C2×#14556586C2211yescharacteristic, complemented
29C2×#14556586C2211yescharacteristic, complemented
30C2×#14556585C2211yescharacteristic, complemented
31C2×#14556584C2211yescharacteristic, complemented
32C2×#14556584C2211yescharacteristic, complemented
33C2×#14556584C2211yescharacteristic, complemented
34#126×D73—28no—
35C2×#14556580C2211yescharacteristic, complemented
36C2×#14556579C2211yescharacteristic, complemented
37C2×#14556578C2211yescharacteristic, complemented
38C2×#14556577C2212yescomplemented
39C2×#14556577C2212yescomplemented
40#124×D73—28no—
41C2×C4⋊C4×D73C2212yes—
42C2×C4⋊C4×D73C2211yescharacteristic
43C2×C4⋊C4×D73C2211yescharacteristic
44C2×C4⋊C4×D73C2211yescharacteristic
45C2×C4⋊C4×D73C2212yes—
46C2×C22⋊C4×D73C2212yes—
47C2×C22⋊C4×D73C2211yescharacteristic
48C2×C22⋊C4×D73C2212yes—
49C2×C22⋊C4×D73C2211yescharacteristic
50C2×C22⋊C4×D73C2212yes—
51C2×C22⋊C4×D73C2211yescharacteristic
52C2×C22⋊C4×D73C2212yes—
53C2×C22⋊C4×D73C2212yes—
54C2×C22⋊C4×D73C2212yes—
55C2×C42×D73C2212yes—
56C2×C42×D73C2211yescharacteristic
57#17988511C2212yescomplemented
58#17988510C2212yescomplemented
59#17988510C2212yescomplemented
60#17988510C2212yescomplemented
61#17988509C2212yescomplemented
62#17988509C2212yescomplemented
63#17988509C2212yescomplemented
64#17988508C2212yescomplemented
65#17988508C2211yescharacteristic, complemented
66#17988507C2212yescomplemented
67#17988507C2211yescharacteristic, complemented
68#17988506C2211yescharacteristic, complemented
69#17988505C2211yescharacteristic, complemented
70#17988505C2212yescomplemented
71#17988504C2212yescomplemented
72#17988504C2211yescharacteristic, complemented
73#17988503C2212yescomplemented
74#17988503C2212yescomplemented
75#17988503C2212yescomplemented
76#17988502C2212yescomplemented
77#17988502C2212yescomplemented
78#17988502C2212yescomplemented
79#17988501C2211yescharacteristic, complemented
80#17988501C2212yescomplemented
81#17988500C2211yescharacteristic, complemented
82#17988500C2212yescomplemented
83#17988499C2212yescomplemented
84#17988499C2211yescharacteristic, complemented
85#17988498C2211yescharacteristic, complemented
86#17988497C2211yescharacteristic
87#17988496C2212yes—
88#17988496C2211yescharacteristic
89#17988495C2212yes—
90#17988495C2211yescharacteristic
91#17988490C2212yescomplemented
92#17988489C2212yescomplemented
93#17988488C2212yescomplemented
94#17988487C2212yescomplemented
95#17988487C2212yescomplemented
96#17988487C2212yescomplemented
97#17988487C2212yescomplemented
98#17988481C2212yescomplemented
99#17988480C2212yescomplemented
100#17988479C2212yescomplemented
101#17988478C2212yescomplemented
102#17988477C2212yescomplemented
103#17988476C2212yescomplemented
104#17988475C2212yescomplemented
105C4⋊C4×Dic73C2212yescomplemented
106C4×#11924007C2212yescomplemented
107C4×C4⋊Dic73C2211yescharacteristic, complemented
108#17988438C2211yescharacteristic, complemented
109#17988438C2211yescharacteristic, complemented
110#95×D73C2211yescharacteristic
111#95×D73C2211yescharacteristic
112#95×D73C2212yes—
113#95×D73C2212yes—
114C2×#126×C73C2211yescharacteristic, complemented
115C2×#124×C73C2211yescharacteristic, complemented
116#396×C73C2212yescomplemented
117#395×C73C2211yescharacteristic, complemented
118#394×C73C2212yescomplemented
119#394×C73C2211yescharacteristic, complemented
120#393×C73C2211yescharacteristic, complemented
121#392×C73C2211yescharacteristic
122#390×C73C2212yescomplemented
123#388×C73C2212yescomplemented
124C4×C4⋊C4×C73C2211yescharacteristic, complemented
125C24×D73C2311yescharacteristic
126C24×D73C2312yes—
127C22×Dic146C2312yes—
128C22×Dic146C2311yescharacteristic
129C2×Q8×D73—24no—
130C2×Q8×D73—44no—
131C22×D292C2312yes—
132C22×D292C2311yescharacteristic
133C22×C22⋊D73C2312yes—
134C22×C22⋊D73C2312yes—
135C22×C22⋊D73C2312yes—
136C2×D4×D73—24no—
137C2×D4×D73—28no—
138C2×D4×D73—44no—
139C2×D4×D73—44no—
140C2×D4×D73—44no—
141C22×C4×D73C2312yes—
142C22×C4×D73C2312yes—
143C22×C4×D73C2311yescharacteristic
144C22×C4×D73C2311yescharacteristic
145C22×C4×D73C2311yescharacteristic
146C22×C4×D73C2311yescharacteristic
147C22×C4×D73C2311yescharacteristic
148C22×C4×D73C2311yescharacteristic
149C22×C4×D73C2312yes—
150#14556586—24no—
151#14556586—24no—
152#14556586—24no—
153#14556585—24no—
154#14556584—24no—
155#14556584—24no—
156#14556584—24no—
157#14556580—24no—
158#14556579—24no—
159#14556578—24no—
160#14556577—28no—
161#14556577—28no—
162C2×C4⋊Dic73C2312yes—
163C2×C4⋊Dic73C2311yescharacteristic
164C2×C4⋊Dic73C2311yescharacteristic
165C2×C4⋊Dic73C2311yescharacteristic
166C2×C4⋊Dic73C2312yes—
167C2×#11924007C2312yes—
168C2×#11924007C2312yes—
169C2×#11924007C2311yescharacteristic
170C2×#11924007C2311yescharacteristic
171C2×#11924007C2311yescharacteristic
172C2×#11924007C2311yescharacteristic
173C2×#11924007C2311yescharacteristic
174C2×#11924007C2311yescharacteristic
175C2×#11924007C2312yes—
176C2×#11924007C2312yes—
177C4⋊C4×D73—24no—
178C4⋊C4×D73—24no—
179C4⋊C4×D73—24no—
180C4⋊C4×D73—28no—
181C4⋊C4×D73—44no—
182C2×C22⋊Dic73C2312yes—
183C2×C22⋊Dic73C2312yes—
184C2×C22⋊Dic73C2311yescharacteristic
185C2×C22⋊Dic73C2311yescharacteristic
186C2×C22⋊Dic73C2311yescharacteristic
187C2×C22⋊Dic73C2312yes—
188C2×C22⋊Dic73C2312yes—
189C2×C22⋊Dic73C2312yes—
190C2×C22⋊Dic73C2312yes—
191C2×#11924005C2312yes—
192C2×#11924005C2312yes—
193C2×#11924005C2312yes—
194C2×#11924005C2312yes—
195C2×#11924005C2311yescharacteristic
196C2×#11924005C2311yescharacteristic
197C2×#11924005C2311yescharacteristic
198C2×#11924005C2311yescharacteristic
199C2×#11924005C2311yescharacteristic
200C2×#11924005C2312yes—
201C2×#11924005C2311yescharacteristic
202C2×#11924005C2312yes—
203C2×#11924005C2312yes—
204C2×#11924005C2312yes—
205C2×#11924005C2312yes—
206C2×#11924005C2312yes—
207C2×#11924005C2312yes—
208C2×#11924005C2312yes—
209C22⋊C4×D73—28no—
210C22⋊C4×D73—28no—
211C22⋊C4×D73—24no—
212C22⋊C4×D73—24no—
213C22⋊C4×D73—24no—
214C22⋊C4×D73—28no—
215C22⋊C4×D73—44no—
216C22⋊C4×D73—44no—
217C22⋊C4×D73—44no—
218C2×C4×Dic73C2312yes—
219C2×C4×Dic73C2312yes—
220C2×C4×Dic73C2312yes—
221C2×C4×Dic73C2311yescharacteristic
222C2×C4×Dic73C2311yescharacteristic
223C2×C4×Dic73C2311yescharacteristic
224C42×D73—44no—
225C42×D73D418yescomplemented
226#14556498C2311yescharacteristic
227#14556498C2311yescharacteristic
228#14556498C2312yes—
229#14556498C2312yes—
230#14556498C2312yes—
231#14556498C2312yes—
232#14556498C2312yes—
233#14556498C2312yes—
234#14556498C2312yes—
235#14556498C2312yes—
236C22×Q8×C73C2311yescharacteristic
237C22×D4×C73C2312yes—
238C22×D4×C73C2311yescharacteristic
239#126×C73—24no—
240#124×C73—24no—
241C2×C4⋊C4×C73C2312yes—
242C2×C4⋊C4×C73C2311yescharacteristic
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2312yes—
246C2×C22⋊C4×C73C2312yes—
247C2×C22⋊C4×C73C2312yes—
248C2×C22⋊C4×C73C2311yescharacteristic
249C2×C22⋊C4×C73C2311yescharacteristic
250C2×C22⋊C4×C73C2311yescharacteristic
251C2×C22⋊C4×C73C2312yes—
252C2×C22⋊C4×C73C2312yes—
253C2×C22⋊C4×C73C2312yes—
254C2×C22⋊C4×C73C2312yes—
255C2×C42×C73C2312yes—
256C2×C42×C73C2311yescharacteristic
257#95×C73C2311yescharacteristic
258#95×C73C2311yescharacteristic
259#95×C73C2312yes—
260#95×C73C2312yes—
261C23×D73—22no—
262C23×D73—24no—
263C23×D73—24no—
264C23×D73—24no—
265C23×D73—24no—
266C23×D73—24no—
267C23×D73—24no—
268C23×D73—24no—
269C23×D73—24no—
270C23×D73—22no—
271C23×D73—22no—
272C23×D73—24no—
273C23×D73C2411yescharacteristic
274C23×D73C2412yes—
275C23×D73C2411yescharacteristic
276C2×Dic146—22no—
277C2×Dic146—24no—
278C2×Dic146—42no—
279C2×Dic146—42no—
280C2×Dic146—42no—
281Q8×D73—416no—
282C2×D292—22no—
283C2×D292—24no—
284C2×D292—42no—
285C2×D292—42no—
286C2×D292—42no—
287C2×C22⋊D73—24no—
288C2×C22⋊D73—24no—
289C2×C22⋊D73—24no—
290C2×C22⋊D73—42no—
291C2×C22⋊D73—42no—
292C2×C22⋊D73—42no—
293C2×C22⋊D73—42no—
294C2×C22⋊D73—42no—
295C2×C22⋊D73—42no—
296D4×D73—416no—
297D4×D73—432no—
298C22×Dic73C2412yes—
299C22×Dic73C2411yescharacteristic
300C22×Dic73C2411yescharacteristic
301C22×Dic73C2412yes—
302C22×Dic73C2411yescharacteristic
303C22×Dic73C2411yescharacteristic
304C22×Dic73C2411yescharacteristic
305C22×Dic73C2411yescharacteristic
306C22×Dic73C2412yes—
307C2×C4×D73—24no—
308C2×C4×D73—22no—
309C2×C4×D73—24no—
310C2×C4×D73—24no—
311C2×C4×D73—24no—
312C2×C4×D73—22no—
313C2×C4×D73—24no—
314C2×C4×D73—22no—
315C2×C4×D73—22no—
316C2×C4×D73—22no—
317C2×C4×D73—24no—
318C2×C4×D73—24no—
319C2×C4×D73—24no—
320C2×C4×D73—22no—
321C2×C4×D73—24no—
322C2×C4×D73—24no—
323C2×C4×D73—24no—
324C2×C4×D73—24no—
325C2×C4×D73—22no—
326C2×C4×D73C2×D414yes—
327C2×C4×D73C2×D414yes—
328C2×C4×D73C2×D414yes—
329C2×C4×D73#4118yes—
330C4⋊Dic73—22no—
331C4⋊Dic73—22no—
332C4⋊Dic73—22no—
333C4⋊Dic73—24no—
334C4⋊Dic73—42no—
335#11924007—22no—
336#11924007—22no—
337#11924007—22no—
338#11924007—24no—
339#11924007—22no—
340#11924007—22no—
341#11924007—22no—
342#11924007—24no—
343#11924007—42no—
344#11924007—42no—
345C22⋊Dic73—24no—
346C22⋊Dic73—24no—
347C22⋊Dic73—22no—
348C22⋊Dic73—22no—
349C22⋊Dic73—22no—
350C22⋊Dic73—24no—
351C22⋊Dic73—42no—
352C22⋊Dic73—42no—
353C22⋊Dic73—42no—
354#11924005—24no—
355#11924005—24no—
356#11924005—22no—
357#11924005—22no—
358#11924005—22no—
359#11924005—24no—
360#11924005—24no—
361#11924005—24no—
362#11924005—22no—
363#11924005—22no—
364#11924005—22no—
365#11924005—24no—
366#11924005—42no—
367#11924005—42no—
368#11924005—42no—
369#11924005—42no—
370#11924005—42no—
371#11924005—42no—
372C4×Dic73—42no—
373C4×Dic73—42no—
374C4×Dic73—42no—
375C4×Dic73C2×D414yescomplemented
376C4×Dic73C2×D414yescomplemented
377C4×Dic73C2×D414yescomplemented
378C24×C73C2411yescharacteristic
379C24×C73C2412yes—
380C2×Q8×C73—22no—
381C2×Q8×C73—42no—
382C2×D4×C73—22no—
383C2×D4×C73—24no—
384C2×D4×C73—42no—
385C2×D4×C73—42no—
386C2×D4×C73—42no—
387C22×C4×C73C2412yes—
388C22×C4×C73C2411yescharacteristic
389C22×C4×C73C2411yescharacteristic
390C22×C4×C73C2412yes—
391C22×C4×C73C2411yescharacteristic
392C22×C4×C73C2411yescharacteristic
393C22×C4×C73C2411yescharacteristic
394C22×C4×C73C2411yescharacteristic
395C22×C4×C73C2412yes—
396C4⋊C4×C73—22no—
397C4⋊C4×C73—22no—
398C4⋊C4×C73—22no—
399C4⋊C4×C73—24no—
400C4⋊C4×C73—42no—
401C22⋊C4×C73—24no—
402C22⋊C4×C73—24no—
403C22⋊C4×C73—22no—
404C22⋊C4×C73—22no—
405C22⋊C4×C73—22no—
406C22⋊C4×C73—24no—
407C22⋊C4×C73—42no—
408C22⋊C4×C73—42no—
409C22⋊C4×C73—42no—
410C42×C73—42no—
411C42×C73C2×D414yescomplemented
412C23×C73—21no—
413C23×C73—22no—
414C23×C73—22no—
415C23×C73—22no—
416C23×C73—22no—
417C23×C73—22no—
418C23×C73—22no—
419C23×C73—22no—
420C23×C73—22no—
421C23×C73—21no—
422C23×C73—21no—
423C23×C73—22no—
424C23×C73C2511yescharacteristic
425C22×D73—21no—
426C22×D73—22no—
427C22×D73—22no—
428C22×D73—22no—
429C22×D73—22no—
430C22×D73—22no—
431C22×D73—22no—
432C22×D73—22no—
433C22×D73—22no—
434C22×D73—21no—
435C22×D73—21no—
436C22×D73—22no—
437C22×D73—44no—
438C22×D73—48no—
439C22×D73—48no—
440C22×D73—44no—
441C22×D73—44no—
442C22×D73—48no—
443C22×D73—48no—
444C22×D73—48no—
445C22×D73—48no—
446C22×D73—48no—
447C22×D73—48no—
448C22×D73—48no—
449C22×D73C22×D412yes—
450C22×D73C2×#4114yes—
451C22×D73H(5,𝔽2)14yes—
452C22×D73H(5,𝔽2)12yes—
453C22×D732−1+412yes—
454Q8×C73—44no—
455D4×C73—44no—
456D4×C73—48no—
457C2×C4×C73—22no—
458C2×C4×C73—21no—
459C2×C4×C73—22no—
460C2×C4×C73—22no—
461C2×C4×C73—22no—
462C2×C4×C73—21no—
463C2×C4×C73—22no—
464C2×C4×C73—21no—
465C2×C4×C73—21no—
466C2×C4×C73—21no—
467C2×C4×C73—22no—
468C2×C4×C73—22no—
469C2×C4×C73—22no—
470C2×C4×C73—21no—
471C2×C4×C73—22no—
472C2×C4×C73—22no—
473C2×C4×C73—22no—
474C2×C4×C73—22no—
475C2×C4×C73—21no—
476C2×C4×C73C22×D412yes—
477C2×C4×C73C22×D412yes—
478C2×C4×C73C22×D412yes—
479C2×C4×C73C2×#4114yes—
480C22⋊D73—48no—
481C22⋊D73—48no—
482C22⋊D73—48no—
483C2×Dic73—22no—
484C2×Dic73—21no—
485C2×Dic73—22no—
486C2×Dic73—22no—
487C2×Dic73—22no—
488C2×Dic73—21no—
489C2×Dic73—22no—
490C2×Dic73—21no—
491C2×Dic73—21no—
492C2×Dic73—21no—
493C2×Dic73—22no—
494C2×Dic73—22no—
495C2×Dic73—22no—
496C2×Dic73—21no—
497C2×Dic73—22no—
498C2×Dic73—22no—
499C2×Dic73—22no—
500C2×Dic73—22no—
501C2×Dic73—21no—
502C2×Dic73C22×D412yes—
503C2×Dic73C22×D412yes—
504C2×Dic73C22×D412yes—
505C2×Dic73C2×#4114yes—
506D292—44no—
507D292—48no—
508C4×D73—28no—
509C4×D73—28no—
510C4×D73—28no—
511C4×D73—216no—
512C4×D73—44no—
513C4×D73—44no—
514C4×D73—48no—
515C4×D73—44no—
516C4×D73—48no—
517Dic146—48no—
518Dic146—44no—
519C22×C73—41no—
520C22×C73—42no—
521C22×C73—42no—
522C22×C73—41no—
523C22×C73—41no—
524C22×C73—42no—
525C22×C73—42no—
526C22×C73—42no—
527C22×C73—42no—
528C22×C73—42no—
529C22×C73—42no—
530C22×C73—42no—
531C22×C73C23×D411yescharacteristic
532C22×C73C22×#4112yes—
533C22×C73C2×H(5,𝔽2)12yes—
534C22×C73C2×H(5,𝔽2)11yescharacteristic
535C22×C73C2×2−1+411yescharacteristic
536C2×D73—41no—
537C2×D73—42no—
538C2×D73—42no—
539C2×D73—41no—
540C2×D73—41no—
541C2×D73—42no—
542C2×D73—42no—
543C2×D73—42no—
544C2×D73—42no—
545C2×D73—42no—
546C2×D73—42no—
547C2×D73—42no—
548C2×D73—816no—
549C2×D73—88no—
550C2×D73#53214yes—
551C2×D73#53514yes—
552C2×D73#53714yes—
553C2×D73#53818yes—
554C2×D73#54218yes—
555C4×C73—22no—
556C4×C73—22no—
557C4×C73—22no—
558C4×C73—24no—
559C4×C73—41no—
560C4×C73—42no—
561C4×C73—41no—
562C4×C73—41no—
563C4×C73—42no—
564Dic73—22no—
565Dic73—22no—
566Dic73—22no—
567Dic73—24no—
568Dic73—41no—
569Dic73—42no—
570Dic73—41no—
571Dic73—41no—
572Dic73—42no—
573C2×#2662—731nomaximal, Sylow
574C2×C73—82no—
575C2×C73—81no—
576C2×C73C2×#53211yescharacteristic
577C2×C73C2×#53511yescharacteristic
578C2×C73C2×#53711yescharacteristic
579C2×C73C2×#53812yes—
580C2×C73C2×#54212yes—
581D73—82no—
582D73—81no—
583D73#266218yesdirect product factor
584C22×#126—731no—
585C22×#124—731no—
586#2662—732no—
587#2662—731no—
588#2662—732no—
589#2662—731no—
590#2662—731no—
591#2662—731no—
592#2662—732no—
593#2662—732no—
594#2662—731no—
595#2662—731no—
596#2662—731no—
597#2662D7311yescharacteristic, direct product factor
598C2×#396—732no—
599C2×#395—731no—
600C2×#394—732no—
601C2×#394—731no—
602C2×#393—731no—
603C2×#392—731no—
604C2×#390—732no—
605C2×#388—732no—
606C2×C4×C4⋊C4—731no—
607C73C2×#266211yescharacteristic, complemented, Sylow
608C23×Q8—731no—
609C23×D4—731no—
610C23×D4—732no—
611C2×#126—731no—
612C2×#126—731no—
613C2×#126—731no—
614C2×#126—731no—
615C2×#126—731no—
616C2×#126—731no—
617C2×#126—731no—
618C2×#126—1468no—
619C2×#126C2×D7311yescharacteristic, complemented
620C2×#124—731no—
621C2×#124—731no—
622C2×#124—732no—
623C2×#124—732no—
624C2×#124—731no—
625C2×#124—1468no—
626C2×#124C2×D7311yescharacteristic, complemented
627C22×C4⋊C4—732no—
628C22×C4⋊C4—731no—
629C22×C4⋊C4—732no—
630C22×C4⋊C4—731no—
631C22×C4⋊C4—731no—
632C22×C22⋊C4—732no—
633C22×C22⋊C4—732no—
634C22×C22⋊C4—732no—
635C22×C22⋊C4—731no—
636C22×C22⋊C4—732no—
637C22×C22⋊C4—731no—
638C22×C22⋊C4—732no—
639C22×C22⋊C4—732no—
640C22×C22⋊C4—731no—
641C22×C42—732no—
642C22×C42—731no—
643#396—732no—
644#396—732no—
645#396—732no—
646#396—732no—
647#396—732no—
648#396—732no—
649#396—732no—
650#396C2×D7312yescomplemented
651#395—731no—
652#395—731no—
653#395—732no—
654#395—732no—
655#395—731no—
656#395C2×D7311yescharacteristic, complemented
657#394—731no—
658#394—732no—
659#394—731no—
660#394—732no—
661#394—732no—
662#394—732no—
663#394—732no—
664#394—732no—
665#394—732no—
666#394—732no—
667#394—731no—
668#394—732no—
669#394C2×D7311yescharacteristic, complemented
670#394C2×D7312yescomplemented
671#393—731no—
672#393—731no—
673#393—732no—
674#393—732no—
675#393—731no—
676#393C2×D7311yescharacteristic, complemented
677#392—732no—
678#392—731no—
679#392—732no—
680#392—731no—
681#392—731no—
682#392C2×D7311yescharacteristic
683#390—732no—
684#390—732no—
685#390—732no—
686#390—732no—
687#390—732no—
688#390—732no—
689#390—732no—
690#390C2×D7312yescomplemented
691#388—732no—
692#388—732no—
693#388—732no—
694#388—732no—
695#388—732no—
696#388—732no—
697#388—732no—
698#388C2×D7312yescomplemented
699C4×C4⋊C4—732no—
700C4×C4⋊C4—731no—
701C4×C4⋊C4—732no—
702C4×C4⋊C4—731no—
703C4×C4⋊C4—731no—
704C4×C4⋊C4C2×D7311yescharacteristic, complemented
705C2×#95—731no—
706C2×#95—731no—
707C2×#95—732no—
708C2×#95—732no—
709C25—731no—
710C25—732no—
711C22×Q8—2924no—
712C22×Q8—732no—
713C22×Q8—731no—
714C22×Q8—1464no—
715C22×Q8C22×D7311yescharacteristic
716C22×D4—2924no—
717C22×D4—2924no—
718C22×D4—2924no—
719C22×D4—732no—
720C22×D4—732no—
721C22×D4—732no—
722C22×D4—731no—
723C22×D4—732no—
724C22×D4—1464no—
725C22×D4—1468no—
726C22×D4C22×D7311yescharacteristic
727C22×D4C22×D7312yes—
728C23×C4—731no—
729C23×C4—731no—
730C23×C4—732no—
731C23×C4—731no—
732C23×C4—731no—
733C23×C4—731no—
734C23×C4—731no—
735C23×C4—732no—
736C23×C4—732no—
737#126—24no—
738#126—1464no—
739#126—1464no—
740#126—1464no—
741#126—1464no—
742#126—1464no—
743#126—1464no—
744#126—1464no—
745#124—24no—
746#124—1468no—
747#124—1468no—
748#124—1464no—
749#124—1464no—
750#124—1464no—
751C2×C4⋊C4—2924no—
752C2×C4⋊C4—732no—
753C2×C4⋊C4—732no—
754C2×C4⋊C4—732no—
755C2×C4⋊C4—731no—
756C2×C4⋊C4—731no—
757C2×C4⋊C4—731no—
758C2×C4⋊C4—731no—
759C2×C4⋊C4—731no—
760C2×C4⋊C4—731no—
761C2×C4⋊C4—731no—
762C2×C4⋊C4—731no—
763C2×C4⋊C4—731no—
764C2×C4⋊C4—732no—
765C2×C4⋊C4—732no—
766C2×C4⋊C4—732no—
767C2×C4⋊C4—1464no—
768C2×C4⋊C4—1464no—
769C2×C4⋊C4—1464no—
770C2×C4⋊C4—1468no—
771C2×C4⋊C4C22×D7311yescharacteristic
772C2×C4⋊C4C22×D7311yescharacteristic
773C2×C4⋊C4C22×D7311yescharacteristic
774C2×C4⋊C4C22×D7312yes—
775C2×C4⋊C4C22×D7312yes—
776C2×C22⋊C4—2924no—
777C2×C22⋊C4—2924no—
778C2×C22⋊C4—2924no—
779C2×C22⋊C4—732no—
780C2×C22⋊C4—732no—
781C2×C22⋊C4—732no—
782C2×C22⋊C4—732no—
783C2×C22⋊C4—732no—
784C2×C22⋊C4—732no—
785C2×C22⋊C4—732no—
786C2×C22⋊C4—732no—
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—731no—
799C2×C22⋊C4—731no—
800C2×C22⋊C4—731no—
801C2×C22⋊C4—731no—
802C2×C22⋊C4—731no—
803C2×C22⋊C4—731no—
804C2×C22⋊C4—732no—
805C2×C22⋊C4—732no—
806C2×C22⋊C4—1468no—
807C2×C22⋊C4—1468no—
808C2×C22⋊C4—1464no—
809C2×C22⋊C4—1464no—
810C2×C22⋊C4—1464no—
811C2×C22⋊C4—1468no—
812C2×C22⋊C4C22×D7312yes—
813C2×C22⋊C4C22×D7312yes—
814C2×C22⋊C4C22×D7311yescharacteristic
815C2×C22⋊C4C22×D7311yescharacteristic
816C2×C22⋊C4C22×D7311yescharacteristic
817C2×C22⋊C4C22×D7312yes—
818C2×C22⋊C4C22×D7312yes—
819C2×C22⋊C4C22×D7312yes—
820C2×C22⋊C4C22×D7312yes—
821C2×C42—2924no—
822C2×C42—732no—
823C2×C42—732no—
824C2×C42—732no—
825C2×C42—731no—
826C2×C42—731no—
827C2×C42—731no—
828C2×C42—738no—
829C2×C42C22×D7312yes—
830C2×C42C22×D7311yescharacteristic
831#95—731no—
832#95—732no—
833#95—732no—
834#95—731no—
835#95—732no—
836#95—732no—
837#95—732no—
838#95—732no—
839#95—732no—
840#95—732no—
841#95C22×D7311yescharacteristic
842#95C22×D7311yescharacteristic
843#95C22×D7312yes—
844#95C22×D7312yes—
845C24—731no—
846C24—731no—
847C24—732no—
848C24—1464no—
849C24—1464no—
850C24—1464no—
851C24—1462no—
852C24—1464no—
853C24—1464no—
854C24—1464no—
855C24—1462no—
856C24—1464no—
857C24—1464no—
858C24—1464no—
859C24—1462no—
860C24C23×D7311yescharacteristic
861C24C23×D7312yes—
862C2×Q8—22no—
863C2×Q8—42no—
864C2×Q8—2922no—
865C2×Q8—2922no—
866C2×Q8—2922no—
867C2×Q8—29216no—
868C2×Q8—1464no—
869C2×Q8—1462no—
870C2×D4—22no—
871C2×D4—24no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—2922no—
876C2×D4—2922no—
877C2×D4—2922no—
878C2×D4—29216no—
879C2×D4—29232no—
880C2×D4—2922no—
881C2×D4—2922no—
882C2×D4—2922no—
883C2×D4—2922no—
884C2×D4—2922no—
885C2×D4—2922no—
886C2×D4—1464no—
887C2×D4—1464no—
888C2×D4—1464no—
889C2×D4—1462no—
890C2×D4—1464no—
891C22×C4—732no—
892C22×C4—731no—
893C22×C4—731no—
894C22×C4—731no—
895C22×C4—734no—
896C22×C4—734no—
897C22×C4—734no—
898C22×C4—738no—
899C22×C4—732no—
900C22×C4—731no—
901C22×C4—731no—
902C22×C4—732no—
903C22×C4—731no—
904C22×C4—1464no—
905C22×C4—1462no—
906C22×C4—1464no—
907C22×C4—1464no—
908C22×C4—1464no—
909C22×C4—1464no—
910C22×C4—1462no—
911C22×C4—1462no—
912C22×C4—1462no—
913C22×C4—1464no—
914C22×C4—1464no—
915C22×C4—1464no—
916C22×C4—1462no—
917C22×C4—1462no—
918C22×C4—1464no—
919C22×C4—1464no—
920C22×C4—1464no—
921C22×C4—1462no—
922C22×C4—1464no—
923C22×C4C23×D7312yes—
924C22×C4C23×D7311yescharacteristic
925C22×C4C23×D7311yescharacteristic
926C22×C4C23×D7312yes—
927C22×C4C23×D7311yescharacteristic
928C22×C4C23×D7311yescharacteristic
929C22×C4C23×D7311yescharacteristic
930C22×C4C23×D7311yescharacteristic
931C22×C4C23×D7312yes—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—24no—
936C4⋊C4—42no—
937C4⋊C4—2922no—
938C4⋊C4—2922no—
939C4⋊C4—2922no—
940C4⋊C4—1464no—
941C4⋊C4—1462no—
942C4⋊C4—1462no—
943C4⋊C4—1462no—
944C4⋊C4—1464no—
945C4⋊C4—1462no—
946C4⋊C4—1462no—
947C4⋊C4—1462no—
948C4⋊C4—1462no—
949C4⋊C4—1462no—
950C4⋊C4—1462no—
951C4⋊C4—1464no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—24no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—2922no—
962C22⋊C4—2922no—
963C22⋊C4—2922no—
964C22⋊C4—2922no—
965C22⋊C4—2922no—
966C22⋊C4—2922no—
967C22⋊C4—2922no—
968C22⋊C4—2922no—
969C22⋊C4—2922no—
970C22⋊C4—1464no—
971C22⋊C4—1464no—
972C22⋊C4—1464no—
973C22⋊C4—1462no—
974C22⋊C4—1462no—
975C22⋊C4—1462no—
976C22⋊C4—1464no—
977C22⋊C4—1464no—
978C22⋊C4—1464no—
979C22⋊C4—1462no—
980C22⋊C4—1462no—
981C22⋊C4—1462no—
982C22⋊C4—1464no—
983C22⋊C4—1464no—
984C22⋊C4—1462no—
985C22⋊C4—1462no—
986C22⋊C4—1462no—
987C22⋊C4—1464no—
988C42—42no—
989C42—2922no—
990C42—2922no—
991C42—2922no—
992C42—734no—
993C42—734no—
994C42—734no—
995C42D4×D7314yescomplemented
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—2928no—
1009C23—2928no—
1010C23—2928no—
1011C23—2924no—
1012C23—2928no—
1013C23—2924no—
1014C23—2928no—
1015C23—2928no—
1016C23—2928no—
1017C23—2928no—
1018C23—2924no—
1019C23—2928no—
1020C23—732no—
1021C23—734no—
1022C23—734no—
1023C23—732no—
1024C23—732no—
1025C23—1461no—
1026C23—1462no—
1027C23—1462no—
1028C23—1462no—
1029C23—1462no—
1030C23—1462no—
1031C23—1462no—
1032C23—1462no—
1033C23—1462no—
1034C23—1461no—
1035C23—1461no—
1036C23—1462no—
1037C23C24×D7311yescharacteristic
1038Q8—44no—
1039Q8—2924no—
1040Q8—2928no—
1041D4—44no—
1042D4—48no—
1043D4—2924no—
1044D4—2928no—
1045D4—2928no—
1046D4—2928no—
1047D4—2928no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—2928no—
1068C2×C4—2924no—
1069C2×C4—2924no—
1070C2×C4—2928no—
1071C2×C4—2924no—
1072C2×C4—732no—
1073C2×C4—732no—
1074C2×C4—732no—
1075C2×C4—734no—
1076C2×C4—1468no—
1077C2×C4—14616no—
1078C2×C4—1468no—
1079C2×C4—1468no—
1080C2×C4—1462no—
1081C2×C4—1461no—
1082C2×C4—1461no—
1083C2×C4—1461no—
1084C2×C4—1462no—
1085C2×C4—1462no—
1086C2×C4—1462no—
1087C2×C4—1461no—
1088C2×C4—1462no—
1089C2×C4—1462no—
1090C2×C4—1462no—
1091C2×C4—1462no—
1092C2×C4—1461no—
1093C2×C4—1462no—
1094C2×C4—1461no—
1095C2×C4—1462no—
1096C2×C4—1462no—
1097C2×C4—1462no—
1098C2×C4—1461no—
1099C2×C4C2×D4×D7312yes—
1100C2×C4C2×D4×D7312yes—
1101C2×C4C2×D4×D7312yes—
1102C2×C4#41×D7314yes—
1103C22—42no—
1104C22—41no—
1105C22—41no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—41no—
1114C22—42no—
1115C22—2922no—
1116C22—2921no—
1117C22—2921no—
1118C22—2922no—
1119C22—2922no—
1120C22—2922no—
1121C22—2922no—
1122C22—2922no—
1123C22—2922no—
1124C22—2922no—
1125C22—2921no—
1126C22—2922no—
1127C22—58416no—
1128C22—5848no—
1129C22—734no—
1130C22—734no—
1131C22—738no—
1132C22—738no—
1133C22—734no—
1134C22C22×D4×D7311yescharacteristic
1135C22C2×#41×D7312yes—
1136C22H(5,𝔽2)×D7312yes—
1137C22H(5,𝔽2)×D7311yescharacteristic
1138C222−1+4×D7311yescharacteristic
1139C4—22no—
1140C4—22no—
1141C4—24no—
1142C4—22no—
1143C4—42no—
1144C4—41no—
1145C4—41no—
1146C4—42no—
1147C4—41no—
1148C4—2922no—
1149C4—2921no—
1150C4—2921no—
1151C4—2922no—
1152C4—2921no—
1153C4—1462no—
1154C4—1462no—
1155C4—1464no—
1156C4—1462no—
1157C2—82no—
1158C2—81no—
1159C2—5842no—
1160C2—5841no—
1161C2—738no—
1162C2#532×D7311yescharacteristic
1163C2#535×D7311yescharacteristic
1164C2#537×D7311yescharacteristic
1165C2#538×D7312yes—
1166C2#542×D7312yes—
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2662C2
prime radical#392×D73C2
hypercenter#2662D73
hypocenterC73C2×#2662
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2662

Complements

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

NH ≅ G/Ntype
1. C2×#126×D73C2semidirect
2. C2×#124×D73C2semidirect
3. #22616077C2semidirect
4. #22616076C2semidirect
5. #22616075C2semidirect
6. #22616074C2semidirect
7. #22616073C2semidirect
8. #22616072C2semidirect
9. #22616071C2semidirect
10. #22616070C2semidirect
11. #22616069C2semidirect
12. #22616068C2semidirect
13. #22616067C2semidirect
14. #396×D73C2semidirect
15. #395×D73C2semidirect
16. #394×D73C2semidirect
17. #394×D73C2semidirect
18. #393×D73C2semidirect
20. #390×D73C2semidirect
21. #388×D73C2semidirect
22. C4×C4⋊C4×D73C2semidirect
23. C73×#2662C2semidirect
27. C2×#14556586C22semidirect
28. C2×#14556586C22semidirect
29. C2×#14556586C22semidirect
30. C2×#14556585C22semidirect
31. C2×#14556584C22semidirect
32. C2×#14556584C22semidirect
33. C2×#14556584C22semidirect
35. C2×#14556580C22semidirect
36. C2×#14556579C22semidirect
37. C2×#14556578C22semidirect
38. C2×#14556577C22semidirect
39. C2×#14556577C22semidirect
57. #17988511C22semidirect
58. #17988510C22semidirect
59. #17988510C22semidirect
60. #17988510C22semidirect
61. #17988509C22semidirect
62. #17988509C22semidirect
63. #17988509C22semidirect
64. #17988508C22semidirect
65. #17988508C22semidirect
66. #17988507C22semidirect
67. #17988507C22semidirect
68. #17988506C22semidirect
69. #17988505C22semidirect
70. #17988505C22semidirect
71. #17988504C22semidirect
72. #17988504C22semidirect
73. #17988503C22semidirect
74. #17988503C22semidirect
75. #17988503C22semidirect
76. #17988502C22semidirect
77. #17988502C22semidirect
78. #17988502C22semidirect
79. #17988501C22semidirect
80. #17988501C22semidirect
81. #17988500C22semidirect
82. #17988500C22semidirect
83. #17988499C22semidirect
84. #17988499C22semidirect
85. #17988498C22semidirect
91. #17988490C22semidirect
92. #17988489C22semidirect
93. #17988488C22semidirect
94. #17988487C22semidirect
95. #17988487C22semidirect
96. #17988487C22semidirect
97. #17988487C22semidirect
98. #17988481C22semidirect
99. #17988480C22semidirect
100. #17988479C22semidirect
101. #17988478C22semidirect
102. #17988477C22semidirect
103. #17988476C22semidirect
104. #17988475C22semidirect
105. C4⋊C4×Dic73C22semidirect
106. C4×#11924007C22semidirect
107. C4×C4⋊Dic73C22semidirect
108. #17988438C22semidirect
109. #17988438C22semidirect
114. C2×#126×C73C22semidirect
115. C2×#124×C73C22semidirect
116. #396×C73C22semidirect
117. #395×C73C22semidirect
118. #394×C73C22semidirect
119. #394×C73C22semidirect
120. #393×C73C22semidirect
122. #390×C73C22semidirect
123. #388×C73C22semidirect
124. C4×C4⋊C4×C73C22semidirect
225. C42×D73D4semidirect
375. C4×Dic73C2×D4semidirect
376. C4×Dic73C2×D4semidirect
377. C4×Dic73C2×D4semidirect
411. C42×C73C2×D4semidirect
583. D73#2662direct (N × H)
597. #2662D73direct (N × H)
607. C73C2×#2662semidirect
619. C2×#126C2×D73semidirect
626. C2×#124C2×D73semidirect
650. #396C2×D73semidirect
656. #395C2×D73semidirect
669. #394C2×D73semidirect
670. #394C2×D73semidirect
676. #393C2×D73semidirect
690. #390C2×D73semidirect
698. #388C2×D73semidirect
704. C4×C4⋊C4C2×D73semidirect
995. C42D4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D732
C2×#124×D732
#226160772
#226160762
#226160752
#226160742
#226160732
#226160722
#226160712
#226160702
#226160692
#226160682
#226160672
#396×D732
#395×D732
#394×D732
#393×D732
#392×D732
#390×D732
#388×D732
C4×C4⋊C4×D732
C73×#26622
C2×#266273