Finite Group Databasebeta

← #2974×D73 #33950713

Subgroups — #2974×D73 #33950713

Order 18688.

2654 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D73C211yesmaximal, characteristic
2#22618968C211yesmaximal, characteristic, complemented
3#22618967C212yesmaximal, complemented
4#22618966C211yesmaximal, characteristic, complemented
5#22618965C211yesmaximal, characteristic, complemented
6#22618964C212yesmaximal, complemented
7#22618963C212yesmaximal, complemented
8#22618962C212yesmaximal, complemented
9#22618961C214yesmaximal, complemented
10#436×D73C212yesmaximal, complemented
11#435×D73C214yesmaximal, complemented
12C8×D4×D73C212yesmaximal, complemented
13#432×D73C211yesmaximal, characteristic, complemented
14#431×D73C211yesmaximal, characteristic, complemented
15#407×D73C212yesmaximal, complemented
16C2×C22⋊C8×D73C212yesmaximal, complemented
17C73×#2974C211yesmaximal, characteristic, complemented
18C22×D4×D73C411yescharacteristic
19C23×C4×D73C2212yes—
20C2×M16×D73C2214yescomplemented
21C22×C8×D73C2214yescomplemented
22C2×C4×D292C2211yescharacteristic
23C2×D4×Dic73C411yescharacteristic
24C2×#14556553C411yescharacteristic
25C2×C4×C22⋊D73C2212yes—
26C2×#14556551C412yes—
27C4×D4×D73C412yes—
28C4×D4×D73C411yescharacteristic
29C4×D4×D73C412yes—
30C4×D4×D73C411yescharacteristic
31C4×D4×D73C411yescharacteristic
32C4×D4×D73C411yescharacteristic
33C4×D4×D73C2212yes—
34C4×D4×D73C2211yescharacteristic
35C4×D4×D73C2211yescharacteristic
36C4×D4×D73C2211yescharacteristic
37C4×D4×D73C2212yes—
38C4×D4×D73C2211yescharacteristic
39C2×C4⋊C4×D73C411yescharacteristic
40C2×C22⋊C4×D73C412yes—
41C2×C42×D73C2211yescharacteristic
42#17988666C2212yescomplemented
43#17988665C2212yescomplemented
44#17988664C2212yescomplemented
45#17988663C2214yescomplemented
46#17988662C2214yescomplemented
47#17988661C2214yescomplemented
48#17988660C2214yescomplemented
49#17988659C2214yescomplemented
50#17988658C2214yescomplemented
51#17988657C2214yescomplemented
52#17988656C2214yescomplemented
53#17988655C2214yescomplemented
54C8×D292C2212yescomplemented
55D4×#10596831C2212yescomplemented
56#17988652C2212yescomplemented
57C8×C22⋊D73C2214yescomplemented
58#17988650C2214yescomplemented
59#17988644C2211yescharacteristic, complemented
60#17988643C2212yescomplemented
61#17988642C2212yescomplemented
62#17988641C2212yescomplemented
63#17988640C2211yescharacteristic, complemented
64#17988639C2212yescomplemented
65#17988638C2212yescomplemented
66#17988637C2211yescharacteristic, complemented
67#17988637C2211yescharacteristic, complemented
68C4⋊C8×D73C2212yescomplemented
69C4⋊C8×D73C2212yescomplemented
70#17988551C2212yescomplemented
71#17988550C2214yescomplemented
72#17988549C2212yescomplemented
73#17988549C2212yescomplemented
74#17988549C2214yescomplemented
75C2×C22⋊#10596831C2212yescomplemented
76C2×#14556503C2214yescomplemented
77C22⋊C8×D73C2211yescharacteristic
78C22⋊C8×D73C2211yescharacteristic
79C22⋊C8×D73C2212yes—
80C22⋊C8×D73C2212yescomplemented
81C22⋊C8×D73C2212yescomplemented
82C22⋊C8×D73C2214yescomplemented
83C22⋊C8×D73C2214yescomplemented
84C22⋊C8×D73C2214yescomplemented
85#97×D73C2212yescomplemented
86C4×C8×D73C2212yescomplemented
87C2×C4×D4×C73C2211yescharacteristic
88#436×C73C2212yescomplemented
89#435×C73C2214yescomplemented
90C8×D4×C73C2212yescomplemented
91#432×C73C2211yescharacteristic, complemented
92#431×C73C2211yescharacteristic, complemented
93#407×C73C2212yescomplemented
94C2×C22⋊C8×C73C2212yescomplemented
95C24×D73C2×C412yes—
96C22×D292C2×C411yescharacteristic
97C22×C22⋊D73C2×C412yes—
98C2×D4×D73—28no—
99C2×D4×D73C2×C412yes—
100C2×D4×D73C2×C412yes—
101C2×D4×D73C2×C411yescharacteristic
102C2×D4×D73C2×C411yescharacteristic
103C2×D4×D73C2×C411yescharacteristic
104C2×D4×D73C2×C411yescharacteristic
105C23×Dic73C2×C412yes—
106C22×C4×D73—48no—
107C22×C4×D73C2×C411yescharacteristic
108C22×C4×D73C2×C411yescharacteristic
109C22×C4×D73C2×C412yes—
110C22×C4×D73C2×C412yes—
111C22×C4×D73C2×C412yes—
112C22×C4×D73C2×C412yes—
113C22×C4×D73C2×C412yes—
114C22×C4×D73C2×C412yes—
115C22×C4×D73C2311yescharacteristic
116C22×C4×D73C2312yes—
117C22×C4×D73C2312yes—
118C22×C4×D73C2312yes—
119C22×C4×D73C2312yes—
120C22×C4×D73C2312yes—
121C2×#11924012C2314yescomplemented
122C2×#11924011C2314yescomplemented
123C2×#11924011C2314yescomplemented
124M16×D73—48no—
125C22×#10596831C2314yescomplemented
126C2×C8×D73—48no—
127C2×C8×D73C2312yes—
128C2×C8×D73C2312yes—
129C2×C8×D73C2314yes—
130C2×C8×D73C2314yescomplemented
131C2×C8×D73C2314yescomplemented
132C4×D292C2×C412yes—
133C4×D292C2×C411yescharacteristic
134C4×D292C2×C411yescharacteristic
135C4×D292C2311yescharacteristic
136C4×D292C2312yes—
137C4×D292C2311yescharacteristic
138D4×Dic73C2×C412yes—
139D4×Dic73C2×C411yescharacteristic
140D4×Dic73C2×C412yes—
141D4×Dic73C2×C411yescharacteristic
142D4×Dic73C2×C411yescharacteristic
143D4×Dic73C2×C411yescharacteristic
144#14556553C2×C412yes—
145#14556553C2×C411yescharacteristic
146#14556553C2×C411yescharacteristic
147#14556553C2×C412yes—
148#14556553C2×C411yescharacteristic
149#14556553C2×C411yescharacteristic
150C4×C22⋊D73C2×C412yes—
151C4×C22⋊D73C2×C412yes—
152C4×C22⋊D73C2×C412yes—
153C4×C22⋊D73C2×C412yes—
154C4×C22⋊D73C2312yes—
155C4×C22⋊D73C2312yes—
156C4×C22⋊D73C2312yes—
157C4×C22⋊D73C2312yes—
158#14556551C2×C412yes—
159#14556551C2×C412yes—
160#14556551C2×C412yes—
161#14556551C2×C412yes—
162#14556551C2×C412yes—
163#14556551C2×C412yes—
164#14556551C2×C412yes—
165#14556551C2×C412yes—
166C2×C4⋊Dic73C2×C411yescharacteristic
167C2×#11924007C2×C412yes—
168C4⋊C4×D73C2×C412yes—
169C4⋊C4×D73C2×C412yes—
170C4⋊C4×D73C2×C411yescharacteristic
171C4⋊C4×D73C2×C411yescharacteristic
172C4⋊C4×D73C2×C411yescharacteristic
173C4⋊C4×D73C2×C411yescharacteristic
174C2×C22⋊Dic73C2×C412yes—
175C2×#11924005C2×C412yes—
176C2×#11924005C2×C412yes—
177C22⋊C4×D73C2×C412yes—
178C22⋊C4×D73C2×C412yes—
179C22⋊C4×D73C2×C412yes—
180C22⋊C4×D73C2×C412yes—
181C22⋊C4×D73C2×C412yes—
182C22⋊C4×D73C2×C412yes—
183C22⋊C4×D73C2×C412yes—
184C22⋊C4×D73C2×C412yes—
185C2×C4×Dic73C2×C411yescharacteristic
186C2×C4×Dic73C2×C411yescharacteristic
187C2×C4×Dic73C2311yescharacteristic
188C42×D73C2×C411yescharacteristic
189C42×D73C2×C411yescharacteristic
190C42×D73C2×C411yescharacteristic
191C42×D73C2×C411yescharacteristic
192C42×D73C2311yescharacteristic
193C42×D73C2311yescharacteristic
194C42×D73C2311yescharacteristic
195C42×D73C2311yescharacteristic
196C4⋊#10596831C2312yescomplemented
197C4⋊#10596831C2312yescomplemented
198#14556520C2312yescomplemented
199#14556520C2312yescomplemented
200#14556520C2314yescomplemented
201C22⋊#10596831C2311yescharacteristic
202C22⋊#10596831C2311yescharacteristic
203C22⋊#10596831C2312yes—
204C22⋊#10596831C2314yescomplemented
205C22⋊#10596831C2314yescomplemented
206#14556503C2312yes—
207#14556503C2312yes—
208#14556503C2314yes—
209#14556503C2314yescomplemented
210#14556503C2314yescomplemented
211#14556503C2314yescomplemented
212#14556503C2314yescomplemented
213#14556502C2312yescomplemented
214#14556501C2314yescomplemented
215C4×#10596831C2312yescomplemented
216C8×Dic73C2312yescomplemented
217C8×Dic73C2312yescomplemented
218C22×D4×C73C2×C411yescharacteristic
219C23×C4×C73C2312yes—
220C2×M16×C73C2314yescomplemented
221C22×C8×C73C2314yescomplemented
222C4×D4×C73C2×C412yes—
223C4×D4×C73C2×C411yescharacteristic
224C4×D4×C73C2×C411yescharacteristic
225C4×D4×C73C2311yescharacteristic
226C4×D4×C73C2312yes—
227C4×D4×C73C2311yescharacteristic
228C2×C4⋊C4×C73C2×C411yescharacteristic
229C2×C22⋊C4×C73C2×C412yes—
230C2×C42×C73C2311yescharacteristic
231C4⋊C8×C73C2312yescomplemented
232C4⋊C8×C73C2312yescomplemented
233C22⋊C8×C73C2311yescharacteristic
234C22⋊C8×C73C2312yes—
235C22⋊C8×C73C2311yescharacteristic
236C22⋊C8×C73C2314yescomplemented
237C22⋊C8×C73C2314yescomplemented
238#97×C73C2312yescomplemented
239C4×C8×C73C2312yescomplemented
240C23×D73—28no—
241C23×D73—28no—
242C23×D73—44no—
243C23×D73C22×C412yes—
244C23×D73C22×C412yes—
245C23×D73C22×C412yes—
246C23×D73C22×C412yes—
247C23×D73C22×C412yes—
248C23×D73C22×C411yescharacteristic
249C2×D292—24no—
250C2×D292C22×C412yes—
251C2×D292C22×C411yescharacteristic
252C2×D292C22×C411yescharacteristic
253C2×C22⋊D73—28no—
254C2×C22⋊D73C22×C412yes—
255C2×C22⋊D73C22×C412yes—
256C2×C22⋊D73C22×C412yes—
257C2×C22⋊D73C22×C412yes—
258D4×D73—28no—
259D4×D73—24no—
260D4×D73—28no—
261D4×D73—24no—
262D4×D73—24no—
263D4×D73M1618yescomplemented
264C22×Dic73—44no—
265C22×Dic73C22×C411yescharacteristic
266C22×Dic73C22×C411yescharacteristic
267C22×Dic73C22×C411yescharacteristic
268C22×Dic73C22×C412yes—
269C22×Dic73C22×C412yes—
270C22×Dic73C22×C412yes—
271C22×Dic73C22×C412yes—
272C22×Dic73C22×C412yes—
273C2×C4×D73—24no—
274C2×C4×D73—24no—
275C2×C4×D73—28no—
276C2×C4×D73—28no—
277C2×C4×D73—24no—
278C2×C4×D73—44no—
279C2×C4×D73—44no—
280C2×C4×D73—44no—
281C2×C4×D73—44no—
282C2×C4×D73—44no—
283C2×C4×D73—44no—
284C2×C4×D73—44no—
285C2×C4×D73—44no—
286C2×C4×D73—44no—
287C2×C4×D73C22×C411yescharacteristic
288C2×C4×D73C22×C411yescharacteristic
289C2×C4×D73C22×C411yescharacteristic
290C2×C4×D73C22×C411yescharacteristic
291C2×C4×D73C22×C411yescharacteristic
292C2×C4×D73C22×C411yescharacteristic
293C2×C4×D73C22×C411yescharacteristic
294C2×C4×D73C22×C411yescharacteristic
295C2×C4×D73C22×C411yescharacteristic
296C2×C4×D73C22×C412yes—
297C2×C4×D73C22×C412yes—
298C2×C4×D73C22×C412yes—
299C2×C4×D73C22×C412yes—
300C2×C4×D73C22×C412yes—
301C2×C4×D73C22×C412yes—
302C2×C4×D73C22×C412yes—
303C2×C4×D73C22×C412yes—
304C2×C4×D73C22×C412yes—
305C2×C4×D73C22×C412yes—
306C2×C4×D73C22×C411yescharacteristic
307C2×C4×D73C2411yescharacteristic
308C2×C4×D73C2412yes—
309C2×C4×D73C2412yes—
310C2×C4×D73C2411yescharacteristic
311#11924012—44no—
312#11924011—44no—
313#11924011—44no—
314C2×#10596831—44no—
315C2×#10596831C2412yes—
316C2×#10596831C2412yes—
317C2×#10596831C2414yes—
318C8×D73—24no—
319C8×D73—28no—
320C8×D73—24no—
321C8×D73—44no—
322C8×D73—44no—
323C4⋊Dic73C22×C412yes—
324C4⋊Dic73C22×C411yescharacteristic
325C4⋊Dic73C22×C411yescharacteristic
326#11924007C22×C412yes—
327#11924007C22×C412yes—
328#11924007C22×C412yes—
329#11924007C22×C412yes—
330C22⋊Dic73C22×C412yes—
331C22⋊Dic73C22×C412yes—
332C22⋊Dic73C22×C412yes—
333C22⋊Dic73C22×C412yes—
334#11924005C22×C412yes—
335#11924005C22×C412yes—
336#11924005C22×C412yes—
337#11924005C22×C412yes—
338#11924005C22×C412yes—
339#11924005C22×C412yes—
340#11924005C22×C412yes—
341#11924005C22×C412yes—
342C4×Dic73C22×C411yescharacteristic
343C4×Dic73C22×C411yescharacteristic
344C4×Dic73C22×C411yescharacteristic
345C4×Dic73C22×C411yescharacteristic
346C4×Dic73C22×C411yescharacteristic
347C4×Dic73C22×C411yescharacteristic
348C4×Dic73C22×C411yescharacteristic
349C4×Dic73C22×C411yescharacteristic
350C4×Dic73C22×C411yescharacteristic
351C4×Dic73C22×C411yescharacteristic
352C4×Dic73C2411yescharacteristic
353C4×Dic73C2411yescharacteristic
354C24×C73C22×C412yes—
355C2×D4×C73—24no—
356C2×D4×C73C22×C412yes—
357C2×D4×C73C22×C411yescharacteristic
358C2×D4×C73C22×C411yescharacteristic
359C22×C4×C73—44no—
360C22×C4×C73C22×C411yescharacteristic
361C22×C4×C73C22×C411yescharacteristic
362C22×C4×C73C22×C412yes—
363C22×C4×C73C22×C412yes—
364C22×C4×C73C22×C412yes—
365C22×C4×C73C2411yescharacteristic
366C22×C4×C73C2412yes—
367C22×C4×C73C2412yes—
368M16×C73—44no—
369C2×C8×C73—44no—
370C2×C8×C73C2412yes—
371C2×C8×C73C2412yes—
372C2×C8×C73C2414yes—
373C4⋊C4×C73C22×C412yes—
374C4⋊C4×C73C22×C411yescharacteristic
375C4⋊C4×C73C22×C411yescharacteristic
376C22⋊C4×C73C22×C412yes—
377C22⋊C4×C73C22×C412yes—
378C22⋊C4×C73C22×C412yes—
379C22⋊C4×C73C22×C412yes—
380C42×C73C22×C411yescharacteristic
381C42×C73C22×C411yescharacteristic
382C42×C73C2411yescharacteristic
383C42×C73C2411yescharacteristic
384C23×C73—24no—
385C23×C73—24no—
386C23×C73—42no—
387C23×C73C23×C412yes—
388C23×C73C23×C412yes—
389C23×C73C23×C411yescharacteristic
390C22×D73—22no—
391C22×D73—24no—
392C22×D73—22no—
393C22×D73—24no—
394C22×D73—24no—
395C22×D73—24no—
396C22×D73—24no—
397C22×D73—24no—
398C22×D73—24no—
399C22×D73—24no—
400C22×D73—24no—
401C22×D73—24no—
402C22×D73—24no—
403C22×D73—42no—
404C22×D73—42no—
405C22×D73—42no—
406C22×D73—432no—
407C22×D73C2×M1618yes—
408C22×D73#13114yes—
409C22×D73C23×C412yes—
410C22×D73C23×C412yes—
411C22×D73C23×C411yescharacteristic
412C22×D73C23×C411yescharacteristic
413D4×C73—24no—
414D4×C73—22no—
415D4×C73C2×M1614yescomplemented
416C2×C4×C73—22no—
417C2×C4×C73—22no—
418C2×C4×C73—24no—
419C2×C4×C73—24no—
420C2×C4×C73—22no—
421C2×C4×C73—42no—
422C2×C4×C73—42no—
423C2×C4×C73—42no—
424C2×C4×C73C23×C411yescharacteristic
425C2×C4×C73C23×C411yescharacteristic
426C2×C4×C73C23×C411yescharacteristic
427C2×C4×C73C23×C411yescharacteristic
428C2×C4×C73C23×C412yes—
429C2×C4×C73C23×C412yes—
430C2×C4×C73C23×C411yescharacteristic
431C2×C4×C73C2511yescharacteristic
432C22⋊D73—24no—
433C22⋊D73—24no—
434C22⋊D73—24no—
435C22⋊D73C2×M1618yescomplemented
436C2×Dic73—22no—
437C2×Dic73—22no—
438C2×Dic73—24no—
439C2×Dic73—24no—
440C2×Dic73—22no—
441C2×Dic73—42no—
442C2×Dic73—42no—
443C2×Dic73—42no—
444C2×Dic73C23×C411yescharacteristic
445C2×Dic73C23×C411yescharacteristic
446C2×Dic73C23×C411yescharacteristic
447C2×Dic73C23×C411yescharacteristic
448C2×Dic73C23×C412yes—
449C2×Dic73C23×C412yes—
450C2×Dic73C23×C411yescharacteristic
451C2×Dic73C23×C411yescharacteristic
452D292—24no—
453D292—22no—
454D292C2×M1614yescomplemented
455C4×D73—22no—
456C4×D73—24no—
457C4×D73—24no—
458C4×D73—22no—
459C4×D73—22no—
460C4×D73—22no—
461C4×D73—22no—
462C4×D73—22no—
463C4×D73—22no—
464C4×D73—24no—
465C4×D73—24no—
466C4×D73—22no—
467C4×D73—22no—
468C4×D73—24no—
469C4×D73—24no—
470C4×D73—22no—
471C4×D73—42no—
472C4×D73—42no—
473C4×D73—42no—
474C4×D73—42no—
475C4×D73—42no—
476C4×D73—42no—
477C4×D73C2×M1614yes—
478C4×D73H(5,𝔽2)14yes—
479C8×C73—22no—
480C8×C73—24no—
481C8×C73—22no—
482#10596831—22no—
483#10596831—24no—
484#10596831—22no—
485C22×C73—21no—
486C22×C73—22no—
487C22×C73—21no—
488C22×C73—22no—
489C22×C73—22no—
490C22×C73—22no—
491C22×C73—22no—
492C22×C73—48no—
493C22×C73C22×M1614yes—
494C22×C73C2×#13112yes—
495C22×C73C24×C411yescharacteristic
496C2×D73—21no—
497C2×D73—22no—
498C2×D73—21no—
499C2×D73—22no—
500C2×D73—28no—
501C2×D73—216no—
502C2×D73—22no—
503C2×D73—22no—
504C2×D73—22no—
505C2×D73—48no—
506C2×D73—48no—
507C2×D73—48no—
508C2×D73—48no—
509C2×D73#51812yes—
510C2×D73C22×M1614yes—
511C2×D73C22×M1612yes—
512C2×D73C2×#13112yes—
513C2×D73C2×#13112yes—
514C4×C73—21no—
515C4×C73—22no—
516C4×C73—22no—
517C4×C73—21no—
518C4×C73—21no—
519C4×C73—21no—
520C4×C73C22×M1612yes—
521C4×C73C2×H(5,𝔽2)12yes—
522Dic73—21no—
523Dic73—22no—
524Dic73—22no—
525Dic73—21no—
526Dic73—21no—
527Dic73—21no—
528Dic73#51812yes—
529Dic73C22×M1612yes—
530C2×#2974—731nomaximal, Sylow
531C2×C73—22no—
532C2×C73—24no—
533C2×C73—42no—
534C2×C73C2×#51811yescharacteristic
535C2×C73C23×M1611yescharacteristic
536C2×C73C22×#13111yescharacteristic
537D73—22no—
538D73—24no—
539D73—42no—
540D73#297414yesdirect product factor
541C22×C4×D4—731no—
542#2974—732no—
543#2974—734no—
544#2974—732no—
545#2974—731no—
546#2974—731no—
547#2974—732no—
548#2974—732no—
549#2974—731no—
550#2974D7311yescharacteristic, direct product factor
551C2×#436—732no—
552C2×#435—734no—
553C2×C8×D4—732no—
554C2×#432—731no—
555C2×#431—731no—
556C2×#407—732no—
557C22×C22⋊C8—732no—
558C73C2×#297411yescharacteristic, complemented, Sylow
559C23×D4—731no—
560C24×C4—732no—
561C22×M16—734no—
562C23×C8—734no—
563C2×C4×D4—731no—
564C2×C4×D4—732no—
565C2×C4×D4—731no—
566C2×C4×D4—731no—
567C2×C4×D4—732no—
568C2×C4×D4—731no—
569C2×C4×D4—731no—
570C2×C4×D4—732no—
571C2×C4×D4—731no—
572C2×C4×D4—732no—
573C2×C4×D4—731no—
574C2×C4×D4—732no—
575C2×C4×D4—731no—
576C2×C4×D4—731no—
577C2×C4×D4—731no—
578C2×C4×D4—732no—
579C2×C4×D4—731no—
580C2×C4×D4C2×D7311yescharacteristic
581C22×C4⋊C4—731no—
582C22×C22⋊C4—732no—
583C22×C42—731no—
584#436—734no—
585#436—732no—
586#436—732no—
587#436—734no—
588#436—732no—
589#436C2×D7312yescomplemented
590#435—734no—
591#435—734no—
592#435—734no—
593#435—734no—
594#435—734no—
595#435—734no—
596#435—734no—
597#435C2×D7314yescomplemented
598C8×D4—734no—
599C8×D4—732no—
600C8×D4—732no—
601C8×D4—734no—
602C8×D4—732no—
603C8×D4C2×D7312yescomplemented
604#432—731no—
605#432—732no—
606#432—732no—
607#432—732no—
608#432C2×D7311yescharacteristic, complemented
609#431—731no—
610#431—732no—
611#431—731no—
612#431—731no—
613#431—732no—
614#431C2×D7311yescharacteristic, complemented
615C2×C4⋊C8—732no—
616C2×C4⋊C8—732no—
617#407—732no—
618#407—734no—
619#407—732no—
620#407—732no—
621#407—734no—
622#407C2×D7312yescomplemented
623C2×C22⋊C8—732no—
624C2×C22⋊C8—734no—
625C2×C22⋊C8—731no—
626C2×C22⋊C8—732no—
627C2×C22⋊C8—732no—
628C2×C22⋊C8—732no—
629C2×C22⋊C8—731no—
630C2×C22⋊C8—734no—
631C2×C22⋊C8—734no—
632C2×C22⋊C8—734no—
633C2×C22⋊C8C2×D7312yescomplemented
634C2×#97—732no—
635C2×C4×C8—732no—
636C25—732no—
637C22×D4—731no—
638C22×D4—732no—
639C22×D4—731no—
640C22×D4—732no—
641C22×D4—731no—
642C22×D4—732no—
643C22×D4—731no—
644C22×D4—731no—
645C22×D4—1468no—
646C22×D4C4×D7311yescharacteristic
647C23×C4—2928no—
648C23×C4—732no—
649C23×C4—732no—
650C23×C4—732no—
651C23×C4—732no—
652C23×C4—732no—
653C23×C4—732no—
654C23×C4—732no—
655C23×C4—732no—
656C23×C4—732no—
657C23×C4—732no—
658C23×C4—731no—
659C23×C4—731no—
660C23×C4—732no—
661C23×C4—732no—
662C23×C4—731no—
663C23×C4C22×D7312yes—
664C2×M16—2928no—
665C2×M16—734no—
666C2×M16—734no—
667C2×M16—734no—
668C2×M16C22×D7314yescomplemented
669C22×C8—2928no—
670C22×C8—734no—
671C22×C8—734no—
672C22×C8—734no—
673C22×C8—732no—
674C22×C8—734no—
675C22×C8—732no—
676C22×C8C22×D7314yescomplemented
677C4×D4—732no—
678C4×D4—731no—
679C4×D4—731no—
680C4×D4—732no—
681C4×D4—731no—
682C4×D4—731no—
683C4×D4—732no—
684C4×D4—732no—
685C4×D4—732no—
686C4×D4—732no—
687C4×D4—732no—
688C4×D4—732no—
689C4×D4—732no—
690C4×D4—732no—
691C4×D4—731no—
692C4×D4—732no—
693C4×D4—731no—
694C4×D4—731no—
695C4×D4—732no—
696C4×D4—731no—
697C4×D4—732no—
698C4×D4—732no—
699C4×D4—732no—
700C4×D4—732no—
701C4×D4—732no—
702C4×D4—732no—
703C4×D4—732no—
704C4×D4—732no—
705C4×D4—731no—
706C4×D4—732no—
707C4×D4—731no—
708C4×D4—731no—
709C4×D4—732no—
710C4×D4—731no—
711C4×D4C4×D7312yes—
712C4×D4C4×D7311yescharacteristic
713C4×D4C4×D7311yescharacteristic
714C4×D4C22×D7311yescharacteristic
715C4×D4C22×D7312yes—
716C4×D4C22×D7311yescharacteristic
717C2×C4⋊C4—732no—
718C2×C4⋊C4—731no—
719C2×C4⋊C4—732no—
720C2×C4⋊C4—731no—
721C2×C4⋊C4—731no—
722C2×C4⋊C4—731no—
723C2×C4⋊C4—731no—
724C2×C4⋊C4—732no—
725C2×C4⋊C4C4×D7311yescharacteristic
726C2×C22⋊C4—732no—
727C2×C22⋊C4—732no—
728C2×C22⋊C4—732no—
729C2×C22⋊C4—732no—
730C2×C22⋊C4—732no—
731C2×C22⋊C4—732no—
732C2×C22⋊C4—732no—
733C2×C22⋊C4—732no—
734C2×C22⋊C4—732no—
735C2×C22⋊C4—732no—
736C2×C22⋊C4—732no—
737C2×C22⋊C4C4×D7312yes—
738C2×C42—731no—
739C2×C42—731no—
740C2×C42—731no—
741C2×C42—731no—
742C2×C42—731no—
743C2×C42—731no—
744C2×C42—731no—
745C2×C42—731no—
746C2×C42—731no—
747C2×C42—731no—
748C2×C42—731no—
749C2×C42C22×D7311yescharacteristic
750C4⋊C8—732no—
751C4⋊C8—732no—
752C4⋊C8—734no—
753C4⋊C8—732no—
754C4⋊C8—732no—
755C4⋊C8C22×D7312yescomplemented
756C4⋊C8C22×D7312yescomplemented
757C22⋊C8—731no—
758C22⋊C8—732no—
759C22⋊C8—731no—
760C22⋊C8—734no—
761C22⋊C8—734no—
762C22⋊C8—732no—
763C22⋊C8—734no—
764C22⋊C8—732no—
765C22⋊C8—734no—
766C22⋊C8—734no—
767C22⋊C8—734no—
768C22⋊C8—734no—
769C22⋊C8C22×D7311yescharacteristic
770C22⋊C8C22×D7312yes—
771C22⋊C8C22×D7311yescharacteristic
772C22⋊C8C22×D7314yescomplemented
773C22⋊C8C22×D7314yescomplemented
774#97—734no—
775#97—732no—
776#97C22×D7312yescomplemented
777C4×C8—732no—
778C4×C8—732no—
779C4×C8—732no—
780C4×C8C22×D7312yescomplemented
781C24—2924no—
782C24—732no—
783C24—732no—
784C24—732no—
785C24—732no—
786C24—731no—
787C24—732no—
788C24—1468no—
789C24—1468no—
790C24C2×C4×D7312yes—
791C2×D4—24no—
792C2×D4—732no—
793C2×D4—738no—
794C2×D4—732no—
795C2×D4—732no—
796C2×D4—732no—
797C2×D4—731no—
798C2×D4—732no—
799C2×D4—731no—
800C2×D4—1464no—
801C2×D4—1464no—
802C2×D4—1468no—
803C2×D4—1464no—
804C2×D4—1468no—
805C2×D4—1468no—
806C2×D4—1464no—
807C2×D4C2×C4×D7312yes—
808C2×D4C2×C4×D7311yescharacteristic
809C2×D4C2×C4×D7311yescharacteristic
810C22×C4—44no—
811C22×C4—2924no—
812C22×C4—2924no—
813C22×C4—2924no—
814C22×C4—2924no—
815C22×C4—2924no—
816C22×C4—2924no—
817C22×C4—2924no—
818C22×C4—2924no—
819C22×C4—2924no—
820C22×C4—2924no—
821C22×C4—732no—
822C22×C4—732no—
823C22×C4—732no—
824C22×C4—732no—
825C22×C4—732no—
826C22×C4—732no—
827C22×C4—732no—
828C22×C4—732no—
829C22×C4—732no—
830C22×C4—731no—
831C22×C4—731no—
832C22×C4—731no—
833C22×C4—731no—
834C22×C4—731no—
835C22×C4—732no—
836C22×C4—732no—
837C22×C4—731no—
838C22×C4—731no—
839C22×C4—731no—
840C22×C4—731no—
841C22×C4—731no—
842C22×C4—731no—
843C22×C4—731no—
844C22×C4—731no—
845C22×C4—731no—
846C22×C4—732no—
847C22×C4—732no—
848C22×C4—732no—
849C22×C4—732no—
850C22×C4—731no—
851C22×C4—732no—
852C22×C4—732no—
853C22×C4—1468no—
854C22×C4—1468no—
855C22×C4—1464no—
856C22×C4—1464no—
857C22×C4—1464no—
858C22×C4C2×C4×D7311yescharacteristic
859C22×C4C2×C4×D7311yescharacteristic
860C22×C4C2×C4×D7312yes—
861C22×C4C2×C4×D7312yes—
862C22×C4C2×C4×D7312yes—
863C22×C4C23×D7311yescharacteristic
864C22×C4C23×D7312yes—
865C22×C4C23×D7312yes—
866M16—44no—
867M16—2924no—
868M16—2924no—
869M16—2924no—
870C2×C8—44no—
871C2×C8—2924no—
872C2×C8—2924no—
873C2×C8—2924no—
874C2×C8—732no—
875C2×C8—732no—
876C2×C8—734no—
877C2×C8—1464no—
878C2×C8—1468no—
879C2×C8—1464no—
880C2×C8C23×D7312yes—
881C2×C8C23×D7312yes—
882C2×C8C23×D7314yes—
883C4⋊C4—732no—
884C4⋊C4—732no—
885C4⋊C4—732no—
886C4⋊C4—732no—
887C4⋊C4—732no—
888C4⋊C4—731no—
889C4⋊C4—731no—
890C4⋊C4C2×C4×D7312yes—
891C4⋊C4C2×C4×D7311yescharacteristic
892C4⋊C4C2×C4×D7311yescharacteristic
893C22⋊C4—732no—
894C22⋊C4—732no—
895C22⋊C4—732no—
896C22⋊C4—732no—
897C22⋊C4—732no—
898C22⋊C4—732no—
899C22⋊C4—732no—
900C22⋊C4—732no—
901C22⋊C4—732no—
902C22⋊C4—732no—
903C22⋊C4—732no—
904C22⋊C4—732no—
905C22⋊C4C2×C4×D7312yes—
906C22⋊C4C2×C4×D7312yes—
907C22⋊C4C2×C4×D7312yes—
908C22⋊C4C2×C4×D7312yes—
909C42—731no—
910C42—731no—
911C42—731no—
912C42—731no—
913C42—731no—
914C42—731no—
915C42—731no—
916C42—731no—
917C42—731no—
918C42—731no—
919C42—731no—
920C42—731no—
921C42C2×C4×D7311yescharacteristic
922C42C2×C4×D7311yescharacteristic
923C42C23×D7311yescharacteristic
924C42C23×D7311yescharacteristic
925C23—24no—
926C23—24no—
927C23—42no—
928C23—2922no—
929C23—2922no—
930C23—2922no—
931C23—29232no—
932C23—731no—
933C23—732no—
934C23—731no—
935C23—738no—
936C23—734no—
937C23—732no—
938C23—1464no—
939C23—1464no—
940C23—1464no—
941C23—1464no—
942C23—1464no—
943C23—1464no—
944C23—1464no—
945C23—1462no—
946C23—1464no—
947C23—1462no—
948C23—1464no—
949C23—1464no—
950C23—1464no—
951C23C22×C4×D7312yes—
952C23C22×C4×D7312yes—
953C23C22×C4×D7311yescharacteristic
954D4—24no—
955D4—22no—
956D4—738no—
957D4—734no—
958D4—1464no—
959D4—1464no—
960D4—1464no—
961D4—1464no—
962D4—1462no—
963D4M16×D7314yescomplemented
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—2922no—
973C2×C4—2922no—
974C2×C4—2922no—
975C2×C4—2922no—
976C2×C4—2922no—
977C2×C4—2922no—
978C2×C4—2922no—
979C2×C4—2922no—
980C2×C4—2922no—
981C2×C4—731no—
982C2×C4—731no—
983C2×C4—734no—
984C2×C4—734no—
985C2×C4—731no—
986C2×C4—731no—
987C2×C4—731no—
988C2×C4—731no—
989C2×C4—732no—
990C2×C4—732no—
991C2×C4—1462no—
992C2×C4—1464no—
993C2×C4—1464no—
994C2×C4—1462no—
995C2×C4—1462no—
996C2×C4—1464no—
997C2×C4—1464no—
998C2×C4—1462no—
999C2×C4—1462no—
1000C2×C4—1462no—
1001C2×C4—1462no—
1002C2×C4—1462no—
1003C2×C4—1462no—
1004C2×C4—1464no—
1005C2×C4—1464no—
1006C2×C4—1462no—
1007C2×C4—1462no—
1008C2×C4—1464no—
1009C2×C4—1464no—
1010C2×C4—1462no—
1011C2×C4—1462no—
1012C2×C4C22×C4×D7311yescharacteristic
1013C2×C4C22×C4×D7311yescharacteristic
1014C2×C4C22×C4×D7311yescharacteristic
1015C2×C4C22×C4×D7311yescharacteristic
1016C2×C4C22×C4×D7312yes—
1017C2×C4C22×C4×D7312yes—
1018C2×C4C22×C4×D7311yescharacteristic
1019C2×C4C24×D7311yescharacteristic
1020C8—22no—
1021C8—24no—
1022C8—22no—
1023C8—1462no—
1024C8—1464no—
1025C8—1462no—
1026C22—21no—
1027C22—22no—
1028C22—21no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—48no—
1034C22—2928no—
1035C22—2928no—
1036C22—2928no—
1037C22—2928no—
1038C22—732no—
1039C22—732no—
1040C22—732no—
1041C22—734no—
1042C22—732no—
1043C22—1468no—
1044C22—14616no—
1045C22—1462no—
1046C22—1462no—
1047C22—1462no—
1048C22—1461no—
1049C22—1462no—
1050C22—1461no—
1051C22—1462no—
1052C22C2×M16×D7314yes—
1053C22#131×D7312yes—
1054C22C23×C4×D7311yescharacteristic
1055C4—21no—
1056C4—21no—
1057C4—21no—
1058C4—21no—
1059C4—22no—
1060C4—22no—
1061C4—732no—
1062C4—732no—
1063C4—1461no—
1064C4—1461no—
1065C4—1461no—
1066C4—1461no—
1067C4—1462no—
1068C4—1462no—
1069C4C2×M16×D7312yes—
1070C4H(5,𝔽2)×D7312yes—
1071C2—22no—
1072C2—24no—
1073C2—42no—
1074C2—2922no—
1075C2—734no—
1076C2—1462no—
1077C2—1464no—
1078C2#518×D7311yescharacteristic
1079C2C22×M16×D7311yescharacteristic
1080C2C2×#131×D7311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2974C2
prime radicalC22×D4×D73C4
cosocleC2×C4×C73C25
hypercenter#2974D73
hypocenterC73C2×#2974
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #22618968C2semidirect
3. #22618967C2semidirect
4. #22618966C2semidirect
5. #22618965C2semidirect
6. #22618964C2semidirect
7. #22618963C2semidirect
8. #22618962C2semidirect
9. #22618961C2semidirect
10. #436×D73C2semidirect
11. #435×D73C2semidirect
12. C8×D4×D73C2semidirect
13. #432×D73C2semidirect
14. #431×D73C2semidirect
15. #407×D73C2semidirect
16. C2×C22⋊C8×D73C2semidirect
17. C73×#2974C2semidirect
20. C2×M16×D73C22semidirect
21. C22×C8×D73C22semidirect
42. #17988666C22semidirect
43. #17988665C22semidirect
44. #17988664C22semidirect
45. #17988663C22semidirect
46. #17988662C22semidirect
47. #17988661C22semidirect
48. #17988660C22semidirect
49. #17988659C22semidirect
50. #17988658C22semidirect
51. #17988657C22semidirect
52. #17988656C22semidirect
53. #17988655C22semidirect
54. C8×D292C22semidirect
55. D4×#10596831C22semidirect
56. #17988652C22semidirect
57. C8×C22⋊D73C22semidirect
58. #17988650C22semidirect
59. #17988644C22semidirect
60. #17988643C22semidirect
61. #17988642C22semidirect
62. #17988641C22semidirect
63. #17988640C22semidirect
64. #17988639C22semidirect
65. #17988638C22semidirect
66. #17988637C22semidirect
67. #17988637C22semidirect
68. C4⋊C8×D73C22semidirect
69. C4⋊C8×D73C22semidirect
70. #17988551C22semidirect
71. #17988550C22semidirect
72. #17988549C22semidirect
73. #17988549C22semidirect
74. #17988549C22semidirect
75. C2×C22⋊#10596831C22semidirect
76. C2×#14556503C22semidirect
80. C22⋊C8×D73C22semidirect
81. C22⋊C8×D73C22semidirect
82. C22⋊C8×D73C22semidirect
83. C22⋊C8×D73C22semidirect
84. C22⋊C8×D73C22semidirect
85. #97×D73C22semidirect
86. C4×C8×D73C22semidirect
88. #436×C73C22semidirect
89. #435×C73C22semidirect
90. C8×D4×C73C22semidirect
91. #432×C73C22semidirect
92. #431×C73C22semidirect
93. #407×C73C22semidirect
94. C2×C22⋊C8×C73C22semidirect
121. C2×#11924012C23semidirect
122. C2×#11924011C23semidirect
123. C2×#11924011C23semidirect
125. C22×#10596831C23semidirect
130. C2×C8×D73C23semidirect
131. C2×C8×D73C23semidirect
196. C4⋊#10596831C23semidirect
197. C4⋊#10596831C23semidirect
198. #14556520C23semidirect
199. #14556520C23semidirect
200. #14556520C23semidirect
204. C22⋊#10596831C23semidirect
205. C22⋊#10596831C23semidirect
209. #14556503C23semidirect
210. #14556503C23semidirect
211. #14556503C23semidirect
212. #14556503C23semidirect
213. #14556502C23semidirect
214. #14556501C23semidirect
215. C4×#10596831C23semidirect
216. C8×Dic73C23semidirect
217. C8×Dic73C23semidirect
220. C2×M16×C73C23semidirect
221. C22×C8×C73C23semidirect
231. C4⋊C8×C73C23semidirect
232. C4⋊C8×C73C23semidirect
236. C22⋊C8×C73C23semidirect
237. C22⋊C8×C73C23semidirect
238. #97×C73C23semidirect
239. C4×C8×C73C23semidirect
263. D4×D73M16semidirect
415. D4×C73C2×M16semidirect
435. C22⋊D73C2×M16semidirect
454. D292C2×M16semidirect
540. D73#2974direct (N × H)
550. #2974D73direct (N × H)
558. C73C2×#2974semidirect
589. #436C2×D73semidirect
597. #435C2×D73semidirect
603. C8×D4C2×D73semidirect
608. #432C2×D73semidirect
614. #431C2×D73semidirect
622. #407C2×D73semidirect
633. C2×C22⋊C8C2×D73semidirect
668. C2×M16C22×D73semidirect
676. C22×C8C22×D73semidirect
755. C4⋊C8C22×D73semidirect
756. C4⋊C8C22×D73semidirect
772. C22⋊C8C22×D73semidirect
773. C22⋊C8C22×D73semidirect
776. #97C22×D73semidirect
780. C4×C8C22×D73semidirect
963. D4M16×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
#226189682
#226189672
#226189662
#226189652
#226189642
#226189632
#226189622
#226189612
#436×D732
#435×D732
C8×D4×D732
#432×D732
#431×D732
#407×D732
C2×C22⋊C8×D732
C73×#29742
C2×#297473