Finite Group Databasebeta

← #2603×D73 #33256620

Subgroups — #2603×D73 #33256620

Order 18688.

3330 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D73C211yesmaximal, characteristic, complemented
2C2×C4×D4×D73C211yesmaximal, characteristic, complemented
3#22615561C211yesmaximal, characteristic, complemented
4#22615560C211yesmaximal, characteristic, complemented
5#22615559C211yesmaximal, characteristic, complemented
6#22615558C211yesmaximal, characteristic, complemented
7#22615557C212yesmaximal, complemented
8#22615556C212yesmaximal, complemented
9#22615555C212yesmaximal, complemented
10#22615554C212yesmaximal, complemented
11#22615553C211yesmaximal, characteristic, complemented
12#22615552C211yesmaximal, characteristic, complemented
13#22615551C211yesmaximal, characteristic, complemented
14#398×D73C211yesmaximal, characteristic, complemented
15#397×D73C211yesmaximal, characteristic, complemented
16#394×D73C211yesmaximal, characteristic, complemented
17#392×D73C211yesmaximal, characteristic
18#390×D73C212yesmaximal, complemented
19#388×D73C212yesmaximal, complemented
20#386×D73C212yesmaximal, complemented
21#385×D73C212yesmaximal, complemented
22#376×D73C211yesmaximal, characteristic, complemented
23C73×#2603C211yesmaximal, characteristic, complemented
24C22×D4×D73C2211yescharacteristic
25C22×D4×D73C2212yes—
26C23×C4×D73C2212yes—
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×C4×D292C2211yescharacteristic, complemented
36C2×D4×Dic73C2211yescharacteristic, complemented
37C2×#14556553C2211yescharacteristic, complemented
38C2×C4×C22⋊D73C2212yescomplemented
39C2×#14556551C2212yescomplemented
40C4×D4×D73—28no—
41C2×C4⋊C4×D73C2211yescharacteristic
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×D73C2212yes—
50C2×C22⋊C4×D73C2211yescharacteristic
51C2×C22⋊C4×D73C2211yescharacteristic
52C2×C22⋊C4×D73C2212yes—
53C2×C22⋊C4×D73C2212yes—
54C2×C42×D73C2212yes—
55C2×C42×D73C2211yescharacteristic
56#17988521C2212yescomplemented
57#17988520C2212yescomplemented
58#17988519C2211yescharacteristic, complemented
59#17988518C2211yescharacteristic, complemented
60#17988517C2211yescharacteristic, complemented
61#17988516C2212yescomplemented
62#17988515C2212yescomplemented
63#17988514C2211yescharacteristic, complemented
64#17988513C2211yescharacteristic, complemented
65#17988512C2211yescharacteristic, complemented
66#17988505C2211yescharacteristic, complemented
67#17988504C2211yescharacteristic, complemented
68#17988503C2212yescomplemented
69#17988502C2212yescomplemented
70#17988501C2211yescharacteristic, complemented
71#17988497C2211yescharacteristic
72#17988496C2212yes—
73#17988496C2211yescharacteristic
74#17988495C2211yescharacteristic
75#17988495C2212yes—
76#17988490C2212yescomplemented
77#17988489C2212yescomplemented
78#17988488C2212yescomplemented
79#17988487C2212yescomplemented
80#17988487C2212yescomplemented
81#17988487C2212yescomplemented
82#17988487C2212yescomplemented
83#17988481C2212yescomplemented
84#17988480C2212yescomplemented
85#17988479C2212yescomplemented
86#17988478C2212yescomplemented
87#17988477C2212yescomplemented
88#17988476C2212yescomplemented
89#17988475C2212yescomplemented
90#17988467C2212yescomplemented
91#17988466C2212yescomplemented
92#17988465C2212yescomplemented
93#17988465C2212yescomplemented
94#17988464C2212yescomplemented
95#17988463C2212yescomplemented
96#17988463C2212yescomplemented
97#17988462C2212yescomplemented
98#17988461C2212yescomplemented
99#17988461C2212yescomplemented
100#17988460C2212yescomplemented
101#17988459C2212yescomplemented
102#17988458C2212yescomplemented
103#17988458C2212yescomplemented
104#17988433C2211yescharacteristic, complemented
105#17988433C2212yescomplemented
106#17988432C2211yescharacteristic, complemented
107#17988432C2212yescomplemented
108#17988432C2211yescharacteristic, complemented
109#95×D73C2212yes—
110#95×D73C2211yescharacteristic
111#95×D73C2211yescharacteristic
112#95×D73C2212yes—
113#95×D73C2212yes—
114C2×#126×C73C2211yescharacteristic, complemented
115C2×C4×D4×C73C2211yescharacteristic, complemented
116#398×C73C2211yescharacteristic, complemented
117#397×C73C2211yescharacteristic, complemented
118#394×C73C2211yescharacteristic, complemented
119#392×C73C2211yescharacteristic
120#390×C73C2212yescomplemented
121#388×C73C2212yescomplemented
122#386×C73C2212yescomplemented
123#385×C73C2212yescomplemented
124#376×C73C2211yescharacteristic, complemented
125C24×D73C2311yescharacteristic
126C24×D73C2312yes—
127C22×D292C2311yescharacteristic
128C22×D292C2312yes—
129C22×C22⋊D73C2312yes—
130C22×C22⋊D73C2312yes—
131C22×C22⋊D73C2312yes—
132C2×D4×D73—28no—
133C2×D4×D73—28no—
134C2×D4×D73—24no—
135C2×D4×D73—28no—
136C2×D4×D73—44no—
137C23×Dic73C2312yes—
138C22×C4×D73—28no—
139C22×C4×D73—44no—
140C22×C4×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—
150C22×C4×D73C2312yes—
151C22×C4×D73C2312yes—
152#14556586—24no—
153#14556586—24no—
154#14556586—24no—
155#14556585—24no—
156#14556584—24no—
157#14556584—24no—
158#14556584—24no—
159C4×D292—24no—
160D4×Dic73—24no—
161#14556553—24no—
162C4×C22⋊D73—28no—
163#14556551—28no—
164C2×C4⋊Dic73C2311yescharacteristic
165C2×C4⋊Dic73C2311yescharacteristic
166C2×C4⋊Dic73C2311yescharacteristic
167C2×C4⋊Dic73C2311yescharacteristic
168C2×C4⋊Dic73C2312yes—
169C2×#11924007C2311yescharacteristic
170C2×#11924007C2311yescharacteristic
171C2×#11924007C2311yescharacteristic
172C2×#11924007C2311yescharacteristic
173C2×#11924007C2311yescharacteristic
174C2×#11924007C2311yescharacteristic
175C2×#11924007C2312yes—
176C2×#11924007C2312yes—
177C2×#11924007C2312yes—
178C4⋊C4×D73—24no—
179C4⋊C4×D73—24no—
180C4⋊C4×D73—24no—
181C4⋊C4×D73—24no—
182C4⋊C4×D73—44no—
183C2×C22⋊Dic73C2312yes—
184C2×C22⋊Dic73C2311yescharacteristic
185C2×C22⋊Dic73C2312yes—
186C2×C22⋊Dic73C2312yes—
187C2×C22⋊Dic73C2311yescharacteristic
188C2×C22⋊Dic73C2311yescharacteristic
189C2×C22⋊Dic73C2312yes—
190C2×C22⋊Dic73C2312yes—
191C2×#11924005C2312yes—
192C2×#11924005C2312yes—
193C2×#11924005C2312yes—
194C2×#11924005C2312yes—
195C2×#11924005C2311yescharacteristic
196C2×#11924005C2311yescharacteristic
197C2×#11924005C2312yes—
198C2×#11924005C2312yes—
199C2×#11924005C2311yescharacteristic
200C2×#11924005C2311yescharacteristic
201C2×#11924005C2311yescharacteristic
202C2×#11924005C2311yescharacteristic
203C2×#11924005C2312yes—
204C2×#11924005C2312yes—
205C2×#11924005C2312yes—
206C2×#11924005C2312yes—
207C22⋊C4×D73—28no—
208C22⋊C4×D73—28no—
209C22⋊C4×D73—24no—
210C22⋊C4×D73—24no—
211C22⋊C4×D73—24no—
212C22⋊C4×D73—28no—
213C22⋊C4×D73—44no—
214C22⋊C4×D73—44no—
215C2×C4×Dic73C2312yes—
216C2×C4×Dic73C2312yes—
217C2×C4×Dic73C2312yes—
218C2×C4×Dic73C2311yescharacteristic
219C2×C4×Dic73C2311yescharacteristic
220C2×C4×Dic73C2311yescharacteristic
221C42×D73—28no—
222C42×D73D418yescomplemented
223#14556498C2312yes—
224#14556498C2312yes—
225#14556498C2312yes—
226#14556498C2311yescharacteristic
227#14556498C2312yes—
228#14556498C2311yescharacteristic
229#14556498C2312yes—
230#14556498C2312yes—
231#14556498C2312yes—
232#14556498C2312yes—
233#14556498C2312yes—
234#14556498C2312yes—
235#14556498C2312yes—
236C22×D4×C73C2311yescharacteristic
237C22×D4×C73C2312yes—
238C23×C4×C73C2312yes—
239#126×C73—24no—
240C4×D4×C73—24no—
241C2×C4⋊C4×C73C2311yescharacteristic
242C2×C4⋊C4×C73C2311yescharacteristic
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2312yes—
246C2×C22⋊C4×C73C2312yes—
247C2×C22⋊C4×C73C2311yescharacteristic
248C2×C22⋊C4×C73C2312yes—
249C2×C22⋊C4×C73C2312yes—
250C2×C22⋊C4×C73C2311yescharacteristic
251C2×C22⋊C4×C73C2311yescharacteristic
252C2×C22⋊C4×C73C2312yes—
253C2×C22⋊C4×C73C2312yes—
254C2×C42×C73C2312yes—
255C2×C42×C73C2311yescharacteristic
256#95×C73C2312yes—
257#95×C73C2312yes—
258#95×C73C2312yes—
259#95×C73C2311yescharacteristic
260#95×C73C2311yescharacteristic
261C23×D73—24no—
262C23×D73—24no—
263C23×D73—24no—
264C23×D73—24no—
265C23×D73—24no—
266C23×D73—24no—
267C23×D73—22no—
268C23×D73—24no—
269C23×D73—24no—
270C23×D73—22no—
271C23×D73—22no—
272C23×D73#4118yes—
273C23×D73C2411yescharacteristic
274C23×D73C2412yes—
275C23×D73C2411yescharacteristic
276C2×D292—24no—
277C2×D292—22no—
278C2×D292—24no—
279C2×D292—24no—
280C2×D292—42no—
281C2×C22⋊D73—24no—
282C2×C22⋊D73—24no—
283C2×C22⋊D73—24no—
284C2×C22⋊D73—24no—
285C2×C22⋊D73—24no—
286C2×C22⋊D73—24no—
287C2×C22⋊D73—24no—
288C2×C22⋊D73—42no—
289C2×C22⋊D73—42no—
290D4×D73—232no—
291D4×D73—432no—
292C22×Dic73—24no—
293C22×Dic73—42no—
294C22×Dic73—42no—
295C22×Dic73C2412yes—
296C22×Dic73C2411yescharacteristic
297C22×Dic73C2411yescharacteristic
298C22×Dic73C2412yes—
299C22×Dic73C2411yescharacteristic
300C22×Dic73C2411yescharacteristic
301C22×Dic73C2411yescharacteristic
302C22×Dic73C2411yescharacteristic
303C22×Dic73C2412yes—
304C2×C4×D73—24no—
305C2×C4×D73—24no—
306C2×C4×D73—24no—
307C2×C4×D73—24no—
308C2×C4×D73—22no—
309C2×C4×D73—22no—
310C2×C4×D73—22no—
311C2×C4×D73—22no—
312C2×C4×D73—22no—
313C2×C4×D73—24no—
314C2×C4×D73—24no—
315C2×C4×D73—24no—
316C2×C4×D73—24no—
317C2×C4×D73—24no—
318C2×C4×D73—22no—
319C2×C4×D73—24no—
320C2×C4×D73—24no—
321C2×C4×D73—22no—
322C2×C4×D73—24no—
323C2×C4×D73—24no—
324C2×C4×D73—24no—
325C2×C4×D73—432no—
326C2×C4×D73—42no—
327C2×C4×D73—42no—
328C2×C4×D73—42no—
329C2×C4×D73—42no—
330C2×C4×D73C2×D414yes—
331C2×C4×D73C2×D414yes—
332C2×C4×D73C2×D414yes—
333C2×C4×D73#4118yes—
334C4⋊Dic73—22no—
335C4⋊Dic73—22no—
336C4⋊Dic73—22no—
337C4⋊Dic73—22no—
338C4⋊Dic73—42no—
339#11924007—22no—
340#11924007—22no—
341#11924007—22no—
342#11924007—24no—
343#11924007—22no—
344#11924007—22no—
345#11924007—22no—
346#11924007—42no—
347#11924007—42no—
348C22⋊Dic73—24no—
349C22⋊Dic73—24no—
350C22⋊Dic73—22no—
351C22⋊Dic73—22no—
352C22⋊Dic73—22no—
353C22⋊Dic73—24no—
354C22⋊Dic73—42no—
355C22⋊Dic73—42no—
356#11924005—24no—
357#11924005—24no—
358#11924005—24no—
359#11924005—22no—
360#11924005—22no—
361#11924005—22no—
362#11924005—24no—
363#11924005—24no—
364#11924005—22no—
365#11924005—22no—
366#11924005—22no—
367#11924005—24no—
368#11924005—42no—
369#11924005—42no—
370#11924005—42no—
371#11924005—42no—
372C4×Dic73—24no—
373C4×Dic73—24no—
374C4×Dic73—24no—
375C4×Dic73C2×D414yescomplemented
376C4×Dic73C2×D414yescomplemented
377C4×Dic73C2×D414yescomplemented
378C24×C73C2411yescharacteristic
379C24×C73C2412yes—
380C2×D4×C73—24no—
381C2×D4×C73—24no—
382C2×D4×C73—22no—
383C2×D4×C73—24no—
384C2×D4×C73—42no—
385C22×C4×C73—24no—
386C22×C4×C73—42no—
387C22×C4×C73—42no—
388C22×C4×C73C2412yes—
389C22×C4×C73C2411yescharacteristic
390C22×C4×C73C2411yescharacteristic
391C22×C4×C73C2412yes—
392C22×C4×C73C2411yescharacteristic
393C22×C4×C73C2411yescharacteristic
394C22×C4×C73C2411yescharacteristic
395C22×C4×C73C2411yescharacteristic
396C22×C4×C73C2412yes—
397C4⋊C4×C73—22no—
398C4⋊C4×C73—22no—
399C4⋊C4×C73—22no—
400C4⋊C4×C73—22no—
401C4⋊C4×C73—42no—
402C22⋊C4×C73—24no—
403C22⋊C4×C73—24no—
404C22⋊C4×C73—22no—
405C22⋊C4×C73—22no—
406C22⋊C4×C73—22no—
407C22⋊C4×C73—24no—
408C22⋊C4×C73—42no—
409C22⋊C4×C73—42no—
410C42×C73—24no—
411C42×C73C2×D414yescomplemented
412C23×C73—22no—
413C23×C73—22no—
414C23×C73—22no—
415C23×C73—22no—
416C23×C73—22no—
417C23×C73—22no—
418C23×C73—21no—
419C23×C73—22no—
420C23×C73—22no—
421C23×C73—21no—
422C23×C73—21no—
423C23×C73C2×#4114yes—
424C23×C73C2511yescharacteristic
425C22×D73—22no—
426C22×D73—22no—
427C22×D73—22no—
428C22×D73—22no—
429C22×D73—22no—
430C22×D73—22no—
431C22×D73—216no—
432C22×D73—216no—
433C22×D73—216no—
434C22×D73—21no—
435C22×D73—22no—
436C22×D73—22no—
437C22×D73—21no—
438C22×D73—21no—
439C22×D73—48no—
440C22×D73—48no—
441C22×D73—48no—
442C22×D73—48no—
443C22×D73—44no—
444C22×D73—44no—
445C22×D73—44no—
446C22×D73—48no—
447C22×D73—48no—
448C22×D73C22×D412yes—
449C22×D73C2×#4114yes—
450C22×D73C2×#4114yes—
451C22×D73C2×#4114yes—
452C22×D73H(5,𝔽2)12yes—
453C22×D73H(5,𝔽2)12yes—
454D4×C73—28no—
455D4×C73—48no—
456C2×C4×C73—22no—
457C2×C4×C73—22no—
458C2×C4×C73—22no—
459C2×C4×C73—22no—
460C2×C4×C73—21no—
461C2×C4×C73—21no—
462C2×C4×C73—21no—
463C2×C4×C73—21no—
464C2×C4×C73—21no—
465C2×C4×C73—22no—
466C2×C4×C73—22no—
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—21no—
474C2×C4×C73—22no—
475C2×C4×C73—48no—
476C2×C4×C73C22×D412yes—
477C2×C4×C73C22×D412yes—
478C2×C4×C73C22×D412yes—
479C2×C4×C73C2×#4114yes—
480C22⋊D73—216no—
481C22⋊D73—48no—
482C22⋊D73—48no—
483C2×Dic73—22no—
484C2×Dic73—22no—
485C2×Dic73—22no—
486C2×Dic73—22no—
487C2×Dic73—21no—
488C2×Dic73—21no—
489C2×Dic73—21no—
490C2×Dic73—21no—
491C2×Dic73—21no—
492C2×Dic73—22no—
493C2×Dic73—22no—
494C2×Dic73—22no—
495C2×Dic73—22no—
496C2×Dic73—22no—
497C2×Dic73—21no—
498C2×Dic73—22no—
499C2×Dic73—22no—
500C2×Dic73—21no—
501C2×Dic73—22no—
502C2×Dic73—48no—
503C2×Dic73C22×D412yes—
504C2×Dic73C22×D412yes—
505C2×Dic73C22×D412yes—
506C2×Dic73C2×#4114yes—
507D292—28no—
508D292—48no—
509C4×D73—28no—
510C4×D73—28no—
511C4×D73—28no—
512C4×D73—216no—
513C4×D73—48no—
514C4×D73—48no—
515C4×D73—44no—
516C4×D73—44no—
517C4×D73—44no—
518C4×D73—48no—
519C4×D73—48no—
520C22×C73—24no—
521C22×C73—24no—
522C22×C73—24no—
523C22×C73—42no—
524C22×C73—42no—
525C22×C73—42no—
526C22×C73—42no—
527C22×C73—41no—
528C22×C73—41no—
529C22×C73—41no—
530C22×C73—42no—
531C22×C73—42no—
532C22×C73C23×D411yescharacteristic
533C22×C73C22×#4112yes—
534C22×C73C22×#4112yes—
535C22×C73C2×H(5,𝔽2)11yescharacteristic
536C22×C73C2×H(5,𝔽2)11yescharacteristic
537C2×D73—24no—
538C2×D73—24no—
539C2×D73—24no—
540C2×D73—42no—
541C2×D73—42no—
542C2×D73—42no—
543C2×D73—42no—
544C2×D73—432no—
545C2×D73—41no—
546C2×D73—41no—
547C2×D73—41no—
548C2×D73—42no—
549C2×D73—42no—
550C2×D73—88no—
551C2×D73#52514yes—
552C2×D73#53214yes—
553C2×D73#53514yes—
554C2×D73#55118yes—
555C2×D73#55318yes—
556C4×C73—22no—
557C4×C73—22no—
558C4×C73—22no—
559C4×C73—24no—
560C4×C73—41no—
561C4×C73—41no—
562C4×C73—42no—
563C4×C73—41no—
564C4×C73—42no—
565Dic73—22no—
566Dic73—22no—
567Dic73—22no—
568Dic73—24no—
569Dic73—41no—
570Dic73—41no—
571Dic73—42no—
572Dic73—41no—
573Dic73—42no—
574C2×#2603—731nomaximal, Sylow
575C2×C73—44no—
576C2×C73—81no—
577C2×C73C2×#52511yescharacteristic
578C2×C73C2×#53211yescharacteristic
579C2×C73C2×#53511yescharacteristic
580C2×C73C2×#55112yes—
581C2×C73C2×#55312yes—
582D73—44no—
583D73—81no—
584D73#260318yesdirect product factor
585C22×#126—731no—
586C22×C4×D4—731no—
587#2603—731no—
588#2603—731no—
589#2603—731no—
590#2603—731no—
591#2603—732no—
592#2603—732no—
593#2603—732no—
594#2603—732no—
595#2603—731no—
596#2603—731no—
597#2603—731no—
598#2603D7311yescharacteristic, direct product factor
599C2×#398—731no—
600C2×#397—731no—
601C2×#394—731no—
602C2×#392—731no—
603C2×#390—732no—
604C2×#388—732no—
605C2×#386—732no—
606C2×#385—732no—
607C2×#376—731no—
608C73C2×#260311yescharacteristic, complemented, Sylow
609C23×D4—732no—
610C23×D4—731no—
611C24×C4—732no—
612C2×#126—731no—
613C2×#126—731no—
614C2×#126—731no—
615C2×#126—731no—
616C2×#126—731no—
617C2×#126—731no—
618C2×#126—731no—
619C2×#126—1468no—
620C2×#126C2×D7311yescharacteristic, complemented
621C2×C4×D4—731no—
622C2×C4×D4—732no—
623C2×C4×D4—731no—
624C2×C4×D4—732no—
625C2×C4×D4—731no—
626C2×C4×D4—1468no—
627C2×C4×D4C2×D7311yescharacteristic, complemented
628C22×C4⋊C4—732no—
629C22×C4⋊C4—731no—
630C22×C4⋊C4—731no—
631C22×C4⋊C4—731no—
632C22×C4⋊C4—731no—
633C22×C22⋊C4—732no—
634C22×C22⋊C4—732no—
635C22×C22⋊C4—731no—
636C22×C22⋊C4—732no—
637C22×C22⋊C4—732no—
638C22×C22⋊C4—732no—
639C22×C22⋊C4—731no—
640C22×C22⋊C4—731no—
641C22×C42—731no—
642C22×C42—732no—
643#398—731no—
644#398—731no—
645#398—732no—
646#398—731no—
647#398—732no—
648#398C2×D7311yescharacteristic, complemented
649#397—731no—
650#397—731no—
651#397—732no—
652#397—731no—
653#397—732no—
654#397C2×D7311yescharacteristic, complemented
655#394—731no—
656#394—731no—
657#394—732no—
658#394—732no—
659#394—731no—
660#394C2×D7311yescharacteristic, complemented
661#392—732no—
662#392—731no—
663#392—732no—
664#392—731no—
665#392—731no—
666#392C2×D7311yescharacteristic
667#390—732no—
668#390—732no—
669#390—732no—
670#390—732no—
671#390—732no—
672#390—732no—
673#390—732no—
674#390C2×D7312yescomplemented
675#388—732no—
676#388—732no—
677#388—732no—
678#388—732no—
679#388—732no—
680#388—732no—
681#388—732no—
682#388C2×D7312yescomplemented
683#386—732no—
684#386—732no—
685#386—732no—
686#386—732no—
687#386—732no—
688#386—732no—
689#386—732no—
690#386C2×D7312yescomplemented
691#385—732no—
692#385—732no—
693#385—732no—
694#385—732no—
695#385—732no—
696#385—732no—
697#385—732no—
698#385C2×D7312yescomplemented
699#376—732no—
700#376—731no—
701#376—731no—
702#376—731no—
703#376—732no—
704#376C2×D7311yescharacteristic, complemented
705C2×#95—731no—
706C2×#95—731no—
707C2×#95—732no—
708C2×#95—732no—
709C2×#95—732no—
710C25—732no—
711C25—731no—
712C22×D4—2924no—
713C22×D4—732no—
714C22×D4—732no—
715C22×D4—732no—
716C22×D4—732no—
717C22×D4—731no—
718C22×D4—1468no—
719C22×D4—1464no—
720C22×D4—1468no—
721C22×D4—1468no—
722C22×D4C22×D7311yescharacteristic
723C22×D4C22×D7312yes—
724C23×C4—2924no—
725C23×C4—2924no—
726C23×C4—732no—
727C23×C4—732no—
728C23×C4—732no—
729C23×C4—731no—
730C23×C4—731no—
731C23×C4—731no—
732C23×C4—732no—
733C23×C4—731no—
734C23×C4—731no—
735C23×C4—731no—
736C23×C4—732no—
737C23×C4—732no—
738C23×C4—1468no—
739C23×C4C22×D7312yes—
740#126—24no—
741#126—1464no—
742#126—1464no—
743#126—1464no—
744#126—1464no—
745#126—1464no—
746#126—1464no—
747#126—1464no—
748C4×D4—24no—
749C4×D4—1468no—
750C4×D4—1464no—
751C4×D4—1468no—
752C4×D4—1464no—
753C4×D4—1464no—
754C2×C4⋊C4—2924no—
755C2×C4⋊C4—732no—
756C2×C4⋊C4—732no—
757C2×C4⋊C4—732no—
758C2×C4⋊C4—732no—
759C2×C4⋊C4—731no—
760C2×C4⋊C4—731no—
761C2×C4⋊C4—731no—
762C2×C4⋊C4—731no—
763C2×C4⋊C4—731no—
764C2×C4⋊C4—731no—
765C2×C4⋊C4—731no—
766C2×C4⋊C4—731no—
767C2×C4⋊C4—731no—
768C2×C4⋊C4—731no—
769C2×C4⋊C4—1464no—
770C2×C4⋊C4—1464no—
771C2×C4⋊C4—1464no—
772C2×C4⋊C4—1464no—
773C2×C4⋊C4C22×D7311yescharacteristic
774C2×C4⋊C4C22×D7311yescharacteristic
775C2×C4⋊C4C22×D7311yescharacteristic
776C2×C4⋊C4C22×D7311yescharacteristic
777C2×C4⋊C4C22×D7312yes—
778C2×C22⋊C4—2924no—
779C2×C22⋊C4—2924no—
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—731no—
788C2×C22⋊C4—731no—
789C2×C22⋊C4—731no—
790C2×C22⋊C4—732no—
791C2×C22⋊C4—732no—
792C2×C22⋊C4—732no—
793C2×C22⋊C4—732no—
794C2×C22⋊C4—731no—
795C2×C22⋊C4—731no—
796C2×C22⋊C4—731no—
797C2×C22⋊C4—731no—
798C2×C22⋊C4—731no—
799C2×C22⋊C4—731no—
800C2×C22⋊C4—732no—
801C2×C22⋊C4—732no—
802C2×C22⋊C4—732no—
803C2×C22⋊C4—732no—
804C2×C22⋊C4—1468no—
805C2×C22⋊C4—1464no—
806C2×C22⋊C4—1464no—
807C2×C22⋊C4—1464no—
808C2×C22⋊C4—1468no—
809C2×C22⋊C4—1468no—
810C2×C22⋊C4C22×D7312yes—
811C2×C22⋊C4C22×D7311yescharacteristic
812C2×C22⋊C4C22×D7311yescharacteristic
813C2×C22⋊C4C22×D7311yescharacteristic
814C2×C22⋊C4C22×D7312yes—
815C2×C22⋊C4C22×D7312yes—
816C2×C22⋊C4C22×D7312yes—
817C2×C22⋊C4C22×D7312yes—
818C2×C42—731no—
819C2×C42—731no—
820C2×C42—731no—
821C2×C42—738no—
822C2×C42—732no—
823C2×C42—732no—
824C2×C42—732no—
825C2×C42—1468no—
826C2×C42C22×D7312yes—
827C2×C42C22×D7311yescharacteristic
828#95—732no—
829#95—732no—
830#95—732no—
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×D7312yes—
842#95C22×D7311yescharacteristic
843#95C22×D7311yescharacteristic
844#95C22×D7312yes—
845#95C22×D7312yes—
846C24—731no—
847C24—738no—
848C24—732no—
849C24—731no—
850C24—1462no—
851C24—1462no—
852C24—1462no—
853C24—1464no—
854C24—1464no—
855C24—1464no—
856C24—1464no—
857C24—1464no—
858C24—1464no—
859C24—1464no—
860C24—1464no—
861C24C23×D7311yescharacteristic
862C24C23×D7312yes—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—22no—
866C2×D4—24no—
867C2×D4—42no—
868C2×D4—2922no—
869C2×D4—29232no—
870C2×D4—2922no—
871C2×D4—2922no—
872C2×D4—1464no—
873C2×D4—1464no—
874C2×D4—1464no—
875C2×D4—1464no—
876C2×D4—1464no—
877C2×D4—14632no—
878C2×D4—1464no—
879C2×D4—1464no—
880C2×D4—1464no—
881C2×D4—1464no—
882C2×D4—1462no—
883C2×D4—1464no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—2922no—
888C22×C4—2922no—
889C22×C4—2922no—
890C22×C4—2922no—
891C22×C4—29232no—
892C22×C4—2922no—
893C22×C4—2922no—
894C22×C4—732no—
895C22×C4—731no—
896C22×C4—731no—
897C22×C4—731no—
898C22×C4—734no—
899C22×C4—734no—
900C22×C4—734no—
901C22×C4—738no—
902C22×C4—732no—
903C22×C4—731no—
904C22×C4—731no—
905C22×C4—732no—
906C22×C4—731no—
907C22×C4—1464no—
908C22×C4—1464no—
909C22×C4—1462no—
910C22×C4—1464no—
911C22×C4—1464no—
912C22×C4—1462no—
913C22×C4—1462no—
914C22×C4—1462no—
915C22×C4—1464no—
916C22×C4—1464no—
917C22×C4—1464no—
918C22×C4—1464no—
919C22×C4—1462no—
920C22×C4—1464no—
921C22×C4—1464no—
922C22×C4—1464no—
923C22×C4—1462no—
924C22×C4—1462no—
925C22×C4—1464no—
926C22×C4—1464no—
927C22×C4—1464no—
928C22×C4—1464no—
929C22×C4C23×D7312yes—
930C22×C4C23×D7311yescharacteristic
931C22×C4C23×D7311yescharacteristic
932C22×C4C23×D7312yes—
933C22×C4C23×D7311yescharacteristic
934C22×C4C23×D7311yescharacteristic
935C22×C4C23×D7311yescharacteristic
936C22×C4C23×D7311yescharacteristic
937C22×C4C23×D7312yes—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—2922no—
944C4⋊C4—2922no—
945C4⋊C4—2922no—
946C4⋊C4—1464no—
947C4⋊C4—1462no—
948C4⋊C4—1462no—
949C4⋊C4—1462no—
950C4⋊C4—1462no—
951C4⋊C4—1462no—
952C4⋊C4—1462no—
953C4⋊C4—1462no—
954C4⋊C4—1462no—
955C4⋊C4—1462no—
956C4⋊C4—1462no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—22no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—24no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—2922no—
966C22⋊C4—2922no—
967C22⋊C4—2922no—
968C22⋊C4—2922no—
969C22⋊C4—2922no—
970C22⋊C4—2922no—
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—1464no—
980C22⋊C4—1462no—
981C22⋊C4—1462no—
982C22⋊C4—1462no—
983C22⋊C4—1464no—
984C22⋊C4—1464no—
985C22⋊C4—1462no—
986C22⋊C4—1462no—
987C22⋊C4—1462no—
988C22⋊C4—1464no—
989C42—24no—
990C42—734no—
991C42—734no—
992C42—734no—
993C42—1464no—
994C42—1464no—
995C42—1464no—
996C42D4×D7314yescomplemented
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—21no—
1008C23—2928no—
1009C23—2928no—
1010C23—2928no—
1011C23—2928no—
1012C23—2928no—
1013C23—2924no—
1014C23—2924no—
1015C23—2928no—
1016C23—2924no—
1017C23—732no—
1018C23—734no—
1019C23—734no—
1020C23—732no—
1021C23—732no—
1022C23—734no—
1023C23—14616no—
1024C23—14616no—
1025C23—14616no—
1026C23—1461no—
1027C23—1462no—
1028C23—1462no—
1029C23—1461no—
1030C23—1461no—
1031C23—1462no—
1032C23—1462no—
1033C23—1462no—
1034C23—1462no—
1035C23—1462no—
1036C23—1462no—
1037C23#41×D7314yes—
1038C23C24×D7311yescharacteristic
1039D4—28no—
1040D4—48no—
1041D4—2928no—
1042D4—2928no—
1043D4—2928no—
1044D4—1468no—
1045D4—14616no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—48no—
1066C2×C4—2928no—
1067C2×C4—2928no—
1068C2×C4—2924no—
1069C2×C4—2924no—
1070C2×C4—2928no—
1071C2×C4—2924no—
1072C2×C4—2928no—
1073C2×C4—2928no—
1074C2×C4—732no—
1075C2×C4—732no—
1076C2×C4—732no—
1077C2×C4—734no—
1078C2×C4—1468no—
1079C2×C4—14616no—
1080C2×C4—1468no—
1081C2×C4—1468no—
1082C2×C4—1461no—
1083C2×C4—1461no—
1084C2×C4—1461no—
1085C2×C4—1462no—
1086C2×C4—1462no—
1087C2×C4—1462no—
1088C2×C4—1462no—
1089C2×C4—1462no—
1090C2×C4—1461no—
1091C2×C4—1462no—
1092C2×C4—1462no—
1093C2×C4—1461no—
1094C2×C4—1462no—
1095C2×C4—1462no—
1096C2×C4—1462no—
1097C2×C4—1462no—
1098C2×C4—1462no—
1099C2×C4—1461no—
1100C2×C4—1461no—
1101C2×C4C2×D4×D7312yes—
1102C2×C4C2×D4×D7312yes—
1103C2×C4C2×D4×D7312yes—
1104C2×C4#41×D7314yes—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—41no—
1113C22—41no—
1114C22—42no—
1115C22—42no—
1116C22—41no—
1117C22—29232no—
1118C22—2922no—
1119C22—2922no—
1120C22—2922no—
1121C22—2922no—
1122C22—2921no—
1123C22—2921no—
1124C22—2922no—
1125C22—2922no—
1126C22—2921no—
1127C22—5848no—
1128C22—734no—
1129C22—734no—
1130C22—738no—
1131C22—738no—
1132C22—734no—
1133C22—1464no—
1134C22—1464no—
1135C22—1464no—
1136C22C22×D4×D7311yescharacteristic
1137C22C2×#41×D7312yes—
1138C22C2×#41×D7312yes—
1139C22H(5,𝔽2)×D7311yescharacteristic
1140C22H(5,𝔽2)×D7311yescharacteristic
1141C4—22no—
1142C4—22no—
1143C4—24no—
1144C4—22no—
1145C4—42no—
1146C4—41no—
1147C4—41no—
1148C4—42no—
1149C4—41no—
1150C4—2922no—
1151C4—2921no—
1152C4—2921no—
1153C4—2922no—
1154C4—2921no—
1155C4—1462no—
1156C4—1462no—
1157C4—1464no—
1158C4—1462no—
1159C2—44no—
1160C2—81no—
1161C2—2924no—
1162C2—5841no—
1163C2—738no—
1164C2#525×D7311yescharacteristic
1165C2#532×D7311yescharacteristic
1166C2#535×D7311yescharacteristic
1167C2#551×D7312yes—
1168C2#553×D7312yes—
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2603C2
prime radical#392×D73C2
hypercenter#2603D73
hypocenterC73C2×#2603
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2603

Complements

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

NH ≅ G/Ntype
1. C2×#126×D73C2semidirect
2. C2×C4×D4×D73C2semidirect
3. #22615561C2semidirect
4. #22615560C2semidirect
5. #22615559C2semidirect
6. #22615558C2semidirect
7. #22615557C2semidirect
8. #22615556C2semidirect
9. #22615555C2semidirect
10. #22615554C2semidirect
11. #22615553C2semidirect
12. #22615552C2semidirect
13. #22615551C2semidirect
14. #398×D73C2semidirect
15. #397×D73C2semidirect
16. #394×D73C2semidirect
18. #390×D73C2semidirect
19. #388×D73C2semidirect
20. #386×D73C2semidirect
21. #385×D73C2semidirect
22. #376×D73C2semidirect
23. C73×#2603C2semidirect
27. C2×#14556586C22semidirect
28. C2×#14556586C22semidirect
29. C2×#14556586C22semidirect
30. C2×#14556585C22semidirect
31. C2×#14556584C22semidirect
32. C2×#14556584C22semidirect
33. C2×#14556584C22semidirect
35. C2×C4×D292C22semidirect
36. C2×D4×Dic73C22semidirect
37. C2×#14556553C22semidirect
38. C2×C4×C22⋊D73C22semidirect
39. C2×#14556551C22semidirect
56. #17988521C22semidirect
57. #17988520C22semidirect
58. #17988519C22semidirect
59. #17988518C22semidirect
60. #17988517C22semidirect
61. #17988516C22semidirect
62. #17988515C22semidirect
63. #17988514C22semidirect
64. #17988513C22semidirect
65. #17988512C22semidirect
66. #17988505C22semidirect
67. #17988504C22semidirect
68. #17988503C22semidirect
69. #17988502C22semidirect
70. #17988501C22semidirect
76. #17988490C22semidirect
77. #17988489C22semidirect
78. #17988488C22semidirect
79. #17988487C22semidirect
80. #17988487C22semidirect
81. #17988487C22semidirect
82. #17988487C22semidirect
83. #17988481C22semidirect
84. #17988480C22semidirect
85. #17988479C22semidirect
86. #17988478C22semidirect
87. #17988477C22semidirect
88. #17988476C22semidirect
89. #17988475C22semidirect
90. #17988467C22semidirect
91. #17988466C22semidirect
92. #17988465C22semidirect
93. #17988465C22semidirect
94. #17988464C22semidirect
95. #17988463C22semidirect
96. #17988463C22semidirect
97. #17988462C22semidirect
98. #17988461C22semidirect
99. #17988461C22semidirect
100. #17988460C22semidirect
101. #17988459C22semidirect
102. #17988458C22semidirect
103. #17988458C22semidirect
104. #17988433C22semidirect
105. #17988433C22semidirect
106. #17988432C22semidirect
107. #17988432C22semidirect
108. #17988432C22semidirect
114. C2×#126×C73C22semidirect
115. C2×C4×D4×C73C22semidirect
116. #398×C73C22semidirect
117. #397×C73C22semidirect
118. #394×C73C22semidirect
120. #390×C73C22semidirect
121. #388×C73C22semidirect
122. #386×C73C22semidirect
123. #385×C73C22semidirect
124. #376×C73C22semidirect
222. C42×D73D4semidirect
375. C4×Dic73C2×D4semidirect
376. C4×Dic73C2×D4semidirect
377. C4×Dic73C2×D4semidirect
411. C42×C73C2×D4semidirect
584. D73#2603direct (N × H)
598. #2603D73direct (N × H)
608. C73C2×#2603semidirect
620. C2×#126C2×D73semidirect
627. C2×C4×D4C2×D73semidirect
648. #398C2×D73semidirect
654. #397C2×D73semidirect
660. #394C2×D73semidirect
674. #390C2×D73semidirect
682. #388C2×D73semidirect
690. #386C2×D73semidirect
698. #385C2×D73semidirect
704. #376C2×D73semidirect
996. 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×C4×D4×D732
#226155612
#226155602
#226155592
#226155582
#226155572
#226155562
#226155552
#226155542
#226155532
#226155522
#226155512
#398×D732
#397×D732
#394×D732
#392×D732
#390×D732
#388×D732
#386×D732
#385×D732
#376×D732
C73×#26032
C2×#260373