Finite Group Databasebeta

← #1872×D73 #33087174

Subgroups — #1872×D73 #33087174

Order 18688.

2270 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D73C211yesmaximal, characteristic
2C22×C4⋊C4×D73C211yesmaximal, characteristic
3C2×#103×D73C212yesmaximal, complemented
4C2×C22⋊C8×D73C211yesmaximal, characteristic
5#22610239C211yesmaximal, characteristic, complemented
6#22610238C211yesmaximal, characteristic, complemented
7#22610237C212yesmaximal, complemented
8#22610236C211yesmaximal, characteristic, complemented
9#22610235C212yesmaximal, complemented
10#340×D73C212yesmaximal, complemented
11C73×#1872C211yesmaximal, characteristic, complemented
12C22×Q8×D73C2211yescharacteristic
13C23×C4×D73—21no—
14C23×C4×D73C2211yescharacteristic
15C22×C8×D73C2212yes—
16C2×#14556571C2211yescharacteristic
17C2×#14556570C2211yescharacteristic
18C2×#14556569—21no—
19C2×#14556568—21no—
20C2×#14556567C2211yescharacteristic
21C22⋊Q8×D73—24no—
22C22⋊Q8×D73C418yescomplemented
23C22×C4⋊Dic73C2211yescharacteristic
24C22×#11924007—21no—
25C2×C4⋊C4×D73—21no—
26C2×C4⋊C4×D73—21no—
27C2×C4⋊C4×D73—21no—
28C2×C4⋊C4×D73—28no—
29C2×C4⋊C4×D73C2212yes—
30C2×C4⋊C4×D73C2211yescharacteristic
31C2×C4⋊C4×D73C2212yes—
32C2×C22⋊C4×D73—21no—
33C2×#14556516C2212yescomplemented
34C2×#14556515C2212yescomplemented
35C2×#14556514C2212yescomplemented
36#103×D73—28no—
37C2×C22⋊#10596831C2211yescharacteristic
38C2×#14556503C2212yes—
39C22⋊C8×D73—24no—
40#17988350C2212yescomplemented
41#17988349C2212yescomplemented
42#17988349C2212yescomplemented
43C2×C22⋊Q8×C73C2211yescharacteristic
44C22×C4⋊C4×C73C2211yescharacteristic
45C2×#103×C73C2212yescomplemented
46C2×C22⋊C8×C73C2211yescharacteristic
47#340×C73C2212yescomplemented
48C24×D73D411yescharacteristic
49C22×Dic146—21no—
50C22×Dic146C2311yescharacteristic
51C2×Q8×D73—22no—
52C2×Q8×D73—24no—
53C2×Q8×D73—24no—
54C2×Q8×D73C2×C414yescomplemented
55C23×Dic73—21no—
56C23×Dic73D411yescharacteristic
57C22×C4×D73—24no—
58C22×C4×D73—24no—
59C22×C4×D73—28no—
60C22×C4×D73—22no—
61C22×C4×D73—22no—
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×C4×D73—44no—
65C22×C4×D73—44no—
66C22×C4×D73C2×C414yes—
67C22×C4×D73D411yescharacteristic
68C22×C4×D73D411yescharacteristic
69C22×C4×D73D414yes—
70C22×C4×D73C2311yescharacteristic
71C22×C4×D73C2311yescharacteristic
72C22×#10596831C2312yes—
73C2×C8×D73—24no—
74C2×C8×D73—24no—
75C2×C8×D73—24no—
76#14556571—22no—
77#14556571C2×C414yescomplemented
78#14556570—22no—
79#14556570C2×C414yescomplemented
80#14556569—28no—
81#14556568—28no—
82#14556567—22no—
83#14556567C2×C414yescomplemented
84C2×C4⋊Dic73—21no—
85C2×C4⋊Dic73—24no—
86C2×C4⋊Dic73—21no—
87C2×C4⋊Dic73C2311yescharacteristic
88C2×C4⋊Dic73C2312yes—
89C2×#11924007—28no—
90C2×#11924007—22no—
91C2×#11924007—22no—
92C2×#11924007—21no—
93C2×#11924007—21no—
94C2×#11924007—21no—
95C4⋊C4×D73—28no—
96C4⋊C4×D73—28no—
97C4⋊C4×D73—28no—
98C4⋊C4×D73—24no—
99C4⋊C4×D73—22no—
100C4⋊C4×D73—24no—
101C4⋊C4×D73—24no—
102C4⋊C4×D73C2×C414yescomplemented
103C4⋊C4×D73D418yes—
104C2×C22⋊Dic73—21no—
105C2×#11924005—21no—
106C2×#11924005—21no—
107C22⋊C4×D73—28no—
108#14556516—24no—
109#14556515—24no—
110#14556514—24no—
111C22⋊#10596831—22no—
112#14556503—24no—
113C22×Q8×C73C2311yescharacteristic
114C23×C4×C73—21no—
115C23×C4×C73C2311yescharacteristic
116C22×C8×C73C2312yes—
117C22⋊Q8×C73—22no—
118C22⋊Q8×C73C2×C414yescomplemented
119C2×C4⋊C4×C73—21no—
120C2×C4⋊C4×C73—21no—
121C2×C4⋊C4×C73—24no—
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2312yes—
124C2×C22⋊C4×C73—21no—
125#103×C73—24no—
126C22⋊C8×C73—22no—
127C23×D73—22no—
128C23×D73—22no—
129C23×D73—22no—
130C23×D73—22no—
131C23×D73C22⋊C414yes—
132C23×D73SD1614yes—
133C23×D73Q1614yes—
134C23×D73C2×D411yescharacteristic
135C23×D73C2×D411yescharacteristic
136C2×Dic146—22no—
137C2×Dic146—22no—
138C2×Dic146—21no—
139C2×Dic146—24no—
140C2×Dic146—42no—
141C2×Dic146—42no—
142C2×Dic146C22×C412yescomplemented
143Q8×D73—216no—
144Q8×D73—48no—
145C22×Dic73—22no—
146C22×Dic73—22no—
147C22×Dic73—24no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—22no—
151C22×Dic73—42no—
152C22×Dic73—42no—
153C22×Dic73C22⋊C414yes—
154C22×Dic73C2×D411yescharacteristic
155C22×Dic73C2×D411yescharacteristic
156C2×C4×D73—22no—
157C2×C4×D73—22no—
158C2×C4×D73—22no—
159C2×C4×D73—22no—
160C2×C4×D73—22no—
161C2×C4×D73—22no—
162C2×C4×D73—216no—
163C2×C4×D73—216no—
164C2×C4×D73—28no—
165C2×C4×D73—24no—
166C2×C4×D73—24no—
167C2×C4×D73—28no—
168C2×C4×D73—44no—
169C2×C4×D73—432no—
170C2×C4×D73—42no—
171C2×C4×D73—42no—
172C2×C4×D73—44no—
173C2×C4×D73—44no—
174C2×C4×D73—42no—
175C2×C4×D73—44no—
176C2×C4×D73—42no—
177C2×C4×D73C22⋊C414yes—
178C2×C4×D73C22⋊C414yes—
179C2×C4×D73C22×C412yes—
180C2×C4×D73C22×C412yes—
181C2×C4×D73C2×D412yes—
182C2×C4×D73C2×D414yes—
183C2×C4×D73C2×D412yes—
184C2×C4×D73#4114yes—
185C2×#10596831—22no—
186C2×#10596831—22no—
187C2×#10596831—22no—
188C8×D73—48no—
189C4⋊Dic73—24no—
190C4⋊Dic73—22no—
191C4⋊Dic73—21no—
192C4⋊Dic73—24no—
193C4⋊Dic73C22×C412yescomplemented
194C4⋊Dic73C2×D414yes—
195#11924007—28no—
196#11924007—24no—
197#11924007—24no—
198#11924007—24no—
199#11924007—28no—
200C22⋊Dic73—24no—
201#11924005—24no—
202#11924005—24no—
203C24×C73C2×D411yescharacteristic
204C2×Q8×C73—21no—
205C2×Q8×C73—22no—
206C2×Q8×C73—22no—
207C2×Q8×C73C22×C412yescomplemented
208C22×C4×C73—22no—
209C22×C4×C73—22no—
210C22×C4×C73—24no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—22no—
214C22×C4×C73—42no—
215C22×C4×C73—42no—
216C22×C4×C73C22×C412yes—
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D412yes—
219C22×C4×C73C2411yescharacteristic
220C2×C8×C73—22no—
221C2×C8×C73—22no—
222C2×C8×C73—22no—
223C4⋊C4×C73—24no—
224C4⋊C4×C73—24no—
225C4⋊C4×C73—22no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73C22×C412yescomplemented
228C4⋊C4×C73C2×D414yes—
229C22⋊C4×C73—24no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73C2×C22⋊C412yes—
235C23×C73C2×SD1612yes—
236C23×C73C2×Q1612yes—
237C23×C73C22×D411yescharacteristic
238C22×D73—21no—
239C22×D73—21no—
240C22×D73—21no—
241C22×D73—21no—
242C22×D73—28no—
243C22×D73—28no—
244C22×D73—28no—
245C22×D73—28no—
246C22×D73—28no—
247C22×D73—28no—
248C22×D73#103116yescomplemented
249C22×D73C2×C22⋊C412yes—
250C22×D73C2×C22⋊C412yes—
251C22×D73#12012yes—
252C22×D73#12312yes—
253C22×D73C2×SD1612yes—
254C22×D73C2×SD1612yes—
255C22×D73C2×Q1612yes—
256C22×D73C2×Q1612yes—
257C22×D73AGL(1,ℤ/8)12yes—
258C22×D73#13712yes—
259Q8×C73—24no—
260Q8×C73—42no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—24no—
264C2×C4×C73—24no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—24no—
268C2×C4×C73—48no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—42no—
272C2×C4×C73—42no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73C2×C22⋊C412yes—
276C2×C4×C73C23×C411yescharacteristic
277C2×C4×C73C22×D412yes—
278C2×C4×C73C22×D411yescharacteristic
279C2×C4×C73C2×#4112yes—
280C2×Dic73—21no—
281C2×Dic73—21no—
282C2×Dic73—28no—
283C2×Dic73—22no—
284C2×Dic73—22no—
285C2×Dic73—24no—
286C2×Dic73—48no—
287C2×Dic73—41no—
288C2×Dic73—41no—
289C2×Dic73—42no—
290C2×Dic73—42no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73C2×C22⋊C412yes—
294C2×Dic73C2×C22⋊C412yes—
295C2×Dic73#12012yes—
296C2×Dic73#12312yes—
297C4×D73—28no—
298C4×D73—24no—
299C4×D73—24no—
300C4×D73—28no—
301C4×D73—416no—
302C4×D73—48no—
303C4×D73—48no—
304C4×D73—416no—
305C4×D73C4×D418yes—
306C4×D73#12118yes—
307Dic146—24no—
308Dic146—42no—
309Dic146—48no—
310C8×C73—42no—
311#10596831—42no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—22no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—22no—
318C22×C73C2×#10314yescomplemented
319C22×C73C22×C22⋊C411yescharacteristic
320C22×C73C2×#12011yescharacteristic
321C22×C73C2×#12311yescharacteristic
322C22×C73C22×SD1611yescharacteristic
323C22×C73C22×Q1611yescharacteristic
324C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C73C2×#13711yescharacteristic
326C2×D73—22no—
327C2×D73—22no—
328C2×D73—22no—
329C2×D73—22no—
330C2×D73—22no—
331C2×D73—22no—
332C2×D73—232no—
333C2×D73#38614yes—
334C2×D73C2×#10314yes—
335C2×D73C2×#10314yescomplemented
336C2×D73#41714yes—
337C2×D73#45014yes—
338C2×D73#45114yes—
339C2×D73#48314yes—
340C2×D73#48414yes—
341C4×C73—22no—
342C4×C73—42no—
343C4×C73—44no—
344C4×C73—42no—
345C4×C73C2×C4×D412yes—
346C4×C73C2×#12112yes—
347Dic73—22no—
348Dic73—42no—
349Dic73—44no—
350Dic73—42no—
351Dic73#38614yes—
352C2×#1872—731nomaximal, Sylow
353C2×C73—24no—
354C2×C73C2×#38611yescharacteristic
355C2×C73C22×#10311yescharacteristic
356C2×C73C2×#41711yescharacteristic
357C2×C73C2×#45011yescharacteristic
358C2×C73C2×#45111yescharacteristic
359C2×C73C2×#48311yescharacteristic
360C2×C73C2×#48411yescharacteristic
361D73—24no—
362D73#187218yesdirect product factor
363C22×C22⋊Q8—731no—
364C23×C4⋊C4—731no—
365C22×#103—732no—
366C22×C22⋊C8—731no—
367#1872—732no—
368#1872—731no—
369#1872—732no—
370#1872—731no—
371#1872—731no—
372#1872D7311yescharacteristic, direct product factor
373C2×#340—732no—
374C73C2×#187211yescharacteristic, complemented, Sylow
375C23×Q8—731no—
376C24×C4—731no—
377C24×C4—1461no—
378C23×C8—732no—
379C2×C22⋊Q8—731no—
380C2×C22⋊Q8—731no—
381C2×C22⋊Q8—738no—
382C2×C22⋊Q8—731no—
383C2×C22⋊Q8—1461no—
384C2×C22⋊Q8—1461no—
385C2×C22⋊Q8—1464no—
386C2×C22⋊Q8C2×D7311yescharacteristic
387C22×C4⋊C4—732no—
388C22×C4⋊C4—731no—
389C22×C4⋊C4—731no—
390C22×C4⋊C4—732no—
391C22×C4⋊C4—1468no—
392C22×C4⋊C4—1461no—
393C22×C4⋊C4—1461no—
394C22×C4⋊C4—1461no—
395C22×C4⋊C4—1461no—
396C22×C4⋊C4C2×D7311yescharacteristic
397C22×C22⋊C4—1461no—
398C2×#103—732no—
399C2×#103—732no—
400C2×#103—732no—
401C2×#103—1468no—
402C2×#103C2×D7312yescomplemented
403C2×C22⋊C8—731no—
404C2×C22⋊C8—732no—
405C2×C22⋊C8—1464no—
406C2×C22⋊C8C2×D7311yescharacteristic
407#340—732no—
408#340—732no—
409#340—732no—
410#340C2×D7312yescomplemented
411C25—731no—
412C22×Q8—734no—
413C22×Q8—731no—
414C22×Q8—1461no—
415C22×Q8—1464no—
416C22×Q8—1464no—
417C22×Q8—1462no—
418C22×Q8C22×D7311yescharacteristic
419C23×C4—21no—
420C23×C4—2924no—
421C23×C4—2924no—
422C23×C4—731no—
423C23×C4—731no—
424C23×C4—734no—
425C23×C4—731no—
426C23×C4—731no—
427C23×C4—734no—
428C23×C4—731no—
429C23×C4—1461no—
430C23×C4—1461no—
431C23×C4—1462no—
432C23×C4—1462no—
433C23×C4—1468no—
434C23×C4—1464no—
435C23×C4—1464no—
436C23×C4—1461no—
437C23×C4C22×D7311yescharacteristic
438C22×C8—732no—
439C22×C8—1464no—
440C22×C8—1464no—
441C22×C8—1464no—
442C22×C8C22×D7312yes—
443C22⋊Q8—22no—
444C22⋊Q8—734no—
445C22⋊Q8—734no—
446C22⋊Q8—734no—
447C22⋊Q8—1468no—
448C22⋊Q8—1468no—
449C22⋊Q8—1462no—
450C22⋊Q8—1462no—
451C22⋊Q8—1462no—
452C22⋊Q8C4×D7314yescomplemented
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—732no—
457C2×C4⋊C4—731no—
458C2×C4⋊C4—734no—
459C2×C4⋊C4—738no—
460C2×C4⋊C4—1464no—
461C2×C4⋊C4—1464no—
462C2×C4⋊C4—1462no—
463C2×C4⋊C4—1468no—
464C2×C4⋊C4—1468no—
465C2×C4⋊C4—1468no—
466C2×C4⋊C4—1464no—
467C2×C4⋊C4—1462no—
468C2×C4⋊C4—1462no—
469C2×C4⋊C4—1461no—
470C2×C4⋊C4—1461no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1468no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1464no—
476C2×C4⋊C4C22×D7311yescharacteristic
477C2×C4⋊C4C22×D7312yes—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1468no—
480C2×C22⋊C4—1461no—
481C2×C22⋊C4—1461no—
482C2×C22⋊C4—1461no—
483#103—24no—
484#103—1464no—
485#103—1464no—
486#103—1464no—
487C22⋊C8—22no—
488C22⋊C8—1464no—
489C22⋊C8—1462no—
490C24—731no—
491C24—734no—
492C24—734no—
493C24—734no—
494C24—731no—
495C24—1462no—
496C24—1462no—
497C24—1462no—
498C24—1462no—
499C24D4×D7311yescharacteristic
500C2×Q8—21no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—2922no—
504C2×Q8—2922no—
505C2×Q8—2928no—
506C2×Q8—732no—
507C2×Q8—1464no—
508C2×Q8—14616no—
509C2×Q8—1462no—
510C2×Q8—1462no—
511C2×Q8—1461no—
512C2×Q8C2×C4×D7312yescomplemented
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—2924no—
522C22×C4—2924no—
523C22×C4—2924no—
524C22×C4—2922no—
525C22×C4—2922no—
526C22×C4—2922no—
527C22×C4—2922no—
528C22×C4—29232no—
529C22×C4—2924no—
530C22×C4—2922no—
531C22×C4—2922no—
532C22×C4—731no—
533C22×C4—732no—
534C22×C4—734no—
535C22×C4—732no—
536C22×C4—734no—
537C22×C4—734no—
538C22×C4—731no—
539C22×C4—734no—
540C22×C4—734no—
541C22×C4—732no—
542C22×C4—732no—
543C22×C4—1464no—
544C22×C4—1464no—
545C22×C4—1468no—
546C22×C4—1468no—
547C22×C4—1462no—
548C22×C4—1462no—
549C22×C4—14616no—
550C22×C4—14616no—
551C22×C4—1462no—
552C22×C4—1462no—
553C22×C4—1464no—
554C22×C4—1461no—
555C22×C4—1461no—
556C22×C4—1462no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4C2×C4×D7312yes—
562C22×C4D4×D7311yescharacteristic
563C22×C4D4×D7312yes—
564C22×C4C23×D7311yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—2928no—
569C2×C8—1462no—
570C2×C8—1462no—
571C2×C8—1462no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—732no—
577C4⋊C4—734no—
578C4⋊C4—1468no—
579C4⋊C4—1464no—
580C4⋊C4—1464no—
581C4⋊C4—1464no—
582C4⋊C4—1468no—
583C4⋊C4—1464no—
584C4⋊C4—1464no—
585C4⋊C4—1462no—
586C4⋊C4—1461no—
587C4⋊C4C2×C4×D7312yescomplemented
588C4⋊C4D4×D7314yes—
589C22⋊C4—24no—
590C22⋊C4—1464no—
591C22⋊C4—1464no—
592C22⋊C4—1464no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—732no—
598C23—732no—
599C23—732no—
600C23—732no—
601C23—732no—
602C23—732no—
603C23—732no—
604C23—732no—
605C23—7316no—
606C23—732no—
607C23—732no—
608C23—1468no—
609C23—1468no—
610C23—1468no—
611C23—1468no—
612C23—1468no—
613C23—1468no—
614C23—1461no—
615C23—1461no—
616C23—1461no—
617C23—1461no—
618C23C22⋊C4×D7312yes—
619C23SD16×D7312yes—
620C23Q16×D7312yes—
621C23C2×D4×D7311yescharacteristic
622Q8—24no—
623Q8—42no—
624Q8—2928no—
625Q8—2922no—
626Q8—1464no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—29216no—
642C2×C4—2928no—
643C2×C4—2928no—
644C2×C4—29216no—
645C2×C4—2928no—
646C2×C4—2921no—
647C2×C4—2921no—
648C2×C4—2921no—
649C2×C4—2922no—
650C2×C4—2922no—
651C2×C4—2921no—
652C2×C4—732no—
653C2×C4—732no—
654C2×C4—732no—
655C2×C4—738no—
656C2×C4—738no—
657C2×C4—732no—
658C2×C4—1468no—
659C2×C4—1468no—
660C2×C4—1462no—
661C2×C4—1462no—
662C2×C4—1464no—
663C2×C4—1468no—
664C2×C4—1461no—
665C2×C4—1461no—
666C2×C4—1464no—
667C2×C4—1464no—
668C2×C4C22⋊C4×D7312yes—
669C2×C4C22×C4×D7311yescharacteristic
670C2×C4C2×D4×D7312yes—
671C2×C4C2×D4×D7311yescharacteristic
672C2×C4#41×D7312yes—
673C8—42no—
674C8—2922no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—734no—
682C22—734no—
683C22—734no—
684C22—734no—
685C22—734no—
686C22—734no—
687C22—734no—
688C22—734no—
689C22—14632no—
690C22—1462no—
691C22—1462no—
692C22—1462no—
693C22—1462no—
694C22—1462no—
695C22—1462no—
696C22#103×D7314yescomplemented
697C22C2×C22⋊C4×D7311yescharacteristic
698C22#120×D7311yescharacteristic
699C22#123×D7311yescharacteristic
700C22C2×SD16×D7311yescharacteristic
701C22C2×Q16×D7311yescharacteristic
702C22AGL(1,ℤ/8)×D7311yescharacteristic
703C22#137×D7311yescharacteristic
704C4—22no—
705C4—42no—
706C4—42no—
707C4—44no—
708C4—2922no—
709C4—2922no—
710C4—2924no—
711C4—734no—
712C4—1462no—
713C4C4×D4×D7312yes—
714C4#121×D7312yes—
715C2—24no—
716C2—738no—
717C2—1464no—
718C2#386×D7311yescharacteristic
719C2C2×#103×D7311yescharacteristic
720C2#417×D7311yescharacteristic
721C2#450×D7311yescharacteristic
722C2#451×D7311yescharacteristic
723C2#483×D7311yescharacteristic
724C2#484×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1872C2
socleC23×C73C22×D4
prime radicalC24×D73D4
cosocleC22×C4×C73C24
hypercenter#1872D73
hypocenterC73C2×#1872
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#103×D73C2semidirect
5. #22610239C2semidirect
6. #22610238C2semidirect
7. #22610237C2semidirect
8. #22610236C2semidirect
9. #22610235C2semidirect
10. #340×D73C2semidirect
11. C73×#1872C2semidirect
22. C22⋊Q8×D73C4semidirect
33. C2×#14556516C22semidirect
34. C2×#14556515C22semidirect
35. C2×#14556514C22semidirect
40. #17988350C22semidirect
41. #17988349C22semidirect
42. #17988349C22semidirect
45. C2×#103×C73C22semidirect
47. #340×C73C22semidirect
54. C2×Q8×D73C2×C4semidirect
77. #14556571C2×C4semidirect
79. #14556570C2×C4semidirect
83. #14556567C2×C4semidirect
102. C4⋊C4×D73C2×C4semidirect
118. C22⋊Q8×C73C2×C4semidirect
142. C2×Dic146C22×C4semidirect
193. C4⋊Dic73C22×C4semidirect
207. C2×Q8×C73C22×C4semidirect
227. C4⋊C4×C73C22×C4semidirect
248. C22×D73#103semidirect
318. C22×C73C2×#103semidirect
335. C2×D73C2×#103semidirect
362. D73#1872direct (N × H)
372. #1872D73direct (N × H)
374. C73C2×#1872semidirect
402. C2×#103C2×D73semidirect
410. #340C2×D73semidirect
452. C22⋊Q8C4×D73semidirect
512. C2×Q8C2×C4×D73semidirect
587. C4⋊C4C2×C4×D73semidirect
696. C22#103×D73semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D732
C22×C4⋊C4×D732
C2×#103×D732
C2×C22⋊C8×D732
#226102392
#226102382
#226102372
#226102362
#226102352
#340×D732
C73×#18722
C2×#187273