Finite Group Databasebeta

← #33097083

Subgroups — #33097083

Order 18688.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988662C211yesmaximal, characteristic, complemented
2C2×#17988551C211yesmaximal, characteristic, complemented
3C4×#14556560C211yesmaximal, characteristic
4#22610727C211yesmaximal, characteristic, complemented
5#22610723C211yesmaximal, characteristic, complemented
6#22610541C211yesmaximal, characteristic, complemented
7#22610540C211yesmaximal, characteristic, complemented
8#22610540C211yesmaximal, characteristic, complemented
9#22610534C211yesmaximal, characteristic, complemented
10#22610226C211yesmaximal, characteristic, complemented
11#22610225C211yesmaximal, characteristic, complemented
12#22610225C211yesmaximal, characteristic, complemented
13#22610113C211yesmaximal, characteristic, complemented
14#22609717C211yesmaximal, characteristic, complemented
15C73×#1779C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C22×#11924011C2211yescharacteristic, complemented
19C2×#14556560C411yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×C4×C22⋊D73C2211yescharacteristic
22C2×C4×C22⋊D73C2211yescharacteristic
23#17988662—24no—
24C2×#14556520C2211yescharacteristic, complemented
25C2×#14556520C2211yescharacteristic, complemented
26C2×#14556520C2211yescharacteristic, complemented
27#17988551—24no—
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×#14556503C2211yescharacteristic, complemented
33C2×#14556503C2211yescharacteristic, complemented
34C2×#14556503C2211yescharacteristic, complemented
35C2×#14556501C2211yescharacteristic, complemented
36C2×C8×Dic73C2211yescharacteristic, complemented
37C2×C8×Dic73C2211yescharacteristic, complemented
38#17988466C411yescharacteristic
39#17988466C411yescharacteristic
40#17988466C411yescharacteristic
41#17988460C411yescharacteristic
42#17988460C411yescharacteristic
43#17988460C411yescharacteristic
44#17988443C411yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46C4×C22⋊Dic73C2211yescharacteristic
47C4×C22⋊Dic73C2211yescharacteristic
48#17988341C2211yescharacteristic, complemented
49#17988341C2211yescharacteristic, complemented
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52#17988341C2211yescharacteristic, complemented
53#17988341C2211yescharacteristic, complemented
54C24×C4×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C22⋊D73C2×C411yescharacteristic
63C22×C22⋊D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C2×#11924012—22no—
66C2×#11924012—41no—
67C2×#11924012—41no—
68C2×#11924012—41no—
69C2×#11924012—41no—
70C2×#11924012D414yescomplemented
71C2×#11924011—22no—
72C2×#11924011—41no—
73C2×#11924011—41no—
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78#14556560—24no—
79C4×C22⋊D73—22no—
80C4×C22⋊D73—22no—
81C4×C22⋊D73—41no—
82C4×C22⋊D73—41no—
83C4×C22⋊D73—41no—
84C4×C22⋊D73—41no—
85C2×#11924007C2×C411yescharacteristic
86C2×#11924007C2×C411yescharacteristic
87C2×#11924007C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C22⋊Dic73C2×C411yescharacteristic
90C2×C22⋊Dic73C2×C411yescharacteristic
91C2×C22⋊Dic73C2×C411yescharacteristic
92C2×C22⋊Dic73C2×C411yescharacteristic
93C2×C22⋊Dic73C2×C411yescharacteristic
94C2×C22⋊Dic73C2×C411yescharacteristic
95C2×C22⋊Dic73C2×C411yescharacteristic
96C2×C22⋊Dic73C2×C411yescharacteristic
97C2×#11924005C2×C411yescharacteristic
98C2×#11924005C2×C411yescharacteristic
99C2×#11924005C2×C411yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2311yescharacteristic
102C2×C4×Dic73C2311yescharacteristic
103#14556520—22no—
104#14556520—41no—
105#14556520—41no—
106C22⋊#10596831—22no—
107C22⋊#10596831—22no—
108C22⋊#10596831—22no—
109C22⋊#10596831—22no—
110#14556503—22no—
111#14556503—41no—
112#14556503—41no—
113#14556501—41no—
114C8×Dic73—22no—
115C8×Dic73—41no—
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122C25×C73C2×C411yescharacteristic
123C23×C4×C73—22no—
124C23×C4×C73—22no—
125C23×C4×C73—41no—
126C23×C4×C73—41no—
127C23×C4×C73—41no—
128C23×C4×C73—41no—
129C23×C4×C73C2×C411yescharacteristic
130C23×C4×C73C2×C411yescharacteristic
131C23×C4×C73C2×C411yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139C22⋊C8×C73—22no—
140C22⋊C8×C73—22no—
141C22⋊C8×C73—41no—
142C22⋊C8×C73—41no—
143C22⋊C8×C73—41no—
144C22⋊C8×C73—41no—
145C23×D73C22×C411yescharacteristic
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73—22no—
149C2×C22⋊D73—22no—
150C2×C22⋊D73—22no—
151C2×C22⋊D73—41no—
152C2×C22⋊D73—41no—
153C2×C22⋊D73—41no—
154C2×C22⋊D73—41no—
155C22×Dic73C22×C411yescharacteristic
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C22×Dic73C22×C411yescharacteristic
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168#11924012—44no—
169#11924012—44no—
170#11924011—44no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831C2×D412yes—
182C2×#10596831C2×D412yes—
183#11924007—22no—
184#11924007—41no—
185#11924007—41no—
186C22⋊Dic73—22no—
187C22⋊Dic73—22no—
188C22⋊Dic73—22no—
189C22⋊Dic73—22no—
190C22⋊Dic73—41no—
191C22⋊Dic73—41no—
192C22⋊Dic73—41no—
193C22⋊Dic73—41no—
194C22⋊Dic73M1614yescomplemented
195#11924005—22no—
196#11924005—41no—
197#11924005—41no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73—21no—
202C4×Dic73—21no—
203C4×Dic73—21no—
204C24×C73—22no—
205C24×C73—22no—
206C24×C73—22no—
207C24×C73—41no—
208C24×C73—41no—
209C24×C73—41no—
210C24×C73—41no—
211C24×C73C22×C411yescharacteristic
212C24×C73C22×C411yescharacteristic
213C24×C73C22×C411yescharacteristic
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73—22no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—41no—
234C22×C4×C73—41no—
235C22×C4×C73—41no—
236C22×C4×C73—41no—
237C22×C4×C73—41no—
238C22×C4×C73—41no—
239C22×C4×C73—44no—
240C22×C4×C73—44no—
241C22×C4×C73—44no—
242C22×C4×C73—44no—
243C22×C4×C73C22×C411yescharacteristic
244C22×C4×C73C22×C411yescharacteristic
245C22×C4×C73C22×C411yescharacteristic
246C22×C4×C73C2×D412yes—
247C22×C4×C73#4112yes—
248C22×C4×C73C2411yescharacteristic
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73—21no—
252C2×C8×C73—21no—
253C2×C8×C73—21no—
254C2×C8×C73—21no—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—44no—
280C23×C73—44no—
281C23×C73—44no—
282C23×C73—44no—
283C23×C73—44no—
284C23×C73—44no—
285C23×C73—44no—
286C23×C73C4×D412yes—
287C23×C73C2×M1612yes—
288C23×C73#13112yes—
289C23×C73C23×C411yescharacteristic
290C22×D73—21no—
291C22×D73—21no—
292C22×D73—21no—
293C22×D73—21no—
294C22×D73—21no—
295C22×D73—21no—
296C22×D73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—44no—
310C2×C4×C73—44no—
311C2×C4×C73—44no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73C4×D412yes—
321C2×C4×C73C22×D411yescharacteristic
322C2×C4×C73C2×#4111yescharacteristic
323C2×C4×C73H(5,𝔽2)11yescharacteristic
324C2×C4×C73H(5,𝔽2)11yescharacteristic
325C2×C4×C73H(5,𝔽2)11yescharacteristic
326C2×C4×C73H(5,𝔽2)11yescharacteristic
327C22⋊D73—44no—
328C22⋊D73—44no—
329C22⋊D73—44no—
330C2×Dic73—21no—
331C2×Dic73—21no—
332C2×Dic73—21no—
333C2×Dic73—21no—
334C2×Dic73—21no—
335C2×Dic73—21no—
336C2×Dic73—21no—
337C2×Dic73—21no—
338C2×Dic73—21no—
339C2×Dic73—21no—
340C2×Dic73—21no—
341C2×Dic73—21no—
342C2×Dic73—21no—
343C2×Dic73—21no—
344C2×Dic73—21no—
345C2×Dic73—21no—
346C2×Dic73—21no—
347C2×Dic73—21no—
348C2×Dic73—21no—
349C2×Dic73C2×M1612yes—
350C2×Dic73C2×M1612yes—
351C4×D73—41no—
352C4×D73—41no—
353C4×D73—41no—
354C4×D73—41no—
355C8×C73—41no—
356C8×C73—41no—
357C8×C73—41no—
358C8×C73—41no—
359#10596831—22no—
360#10596831—22no—
361#10596831—41no—
362#10596831—41no—
363C22×C73—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—22no—
372C22×C73—416no—
373C22×C73—41no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73—41no—
378C22×C73—41no—
379C22×C73—41no—
380C22×C73—41no—
381C22×C73—41no—
382C22×C73—41no—
383C22×C73—41no—
384C22×C73—41no—
385C22×C73C2×C4×D411yescharacteristic
386C22×C73#51811yescharacteristic
387C22×C73#51811yescharacteristic
388C22×C73C22×M1611yescharacteristic
389C22×C73C2×#13111yescharacteristic
390C22×C73#56811yescharacteristic
391C22×C73#56811yescharacteristic
392C2×D73—41no—
393C2×D73—41no—
394C2×D73—41no—
395C2×D73—41no—
396C2×D73—41no—
397C2×D73—41no—
398C2×D73—41no—
399C4×C73—22no—
400C4×C73—41no—
401C4×C73—41no—
402C4×C73#53411yescharacteristic
403C4×C73#53511yescharacteristic
404C4×C73#53811yescharacteristic
405C4×C73#53811yescharacteristic
406Dic73—22no—
407Dic73—22no—
408Dic73—41no—
409Dic73—41no—
410Dic73—41no—
411Dic73—41no—
412Dic73—41no—
413#22038—731nomaximal, Sylow
414C2×C73—42no—
415C2×C73—42no—
416C2×C73—42no—
417C2×C73#232111yescharacteristic
418C2×C73#293311yescharacteristic
419C2×C73D4×M1611yescharacteristic
420C2×C73#297411yescharacteristic
421C2×C73#297511yescharacteristic
422C2×C73#297611yescharacteristic
423C2×C73#297811yescharacteristic
424D73—81no—
425C2×#436—731no—
426C2×#407—731no—
427C4×#120—731no—
428#1955—731no—
429#1954—731no—
430#1924—731no—
431#1923—731no—
432#1923—731no—
433#1923—731no—
434#1870—731no—
435#1870—731no—
436#1870—731no—
437#1851—731no—
438#1779D7311yescharacteristic, complemented
439#1753—731no—
440C73#2203811yescharacteristic, complemented, Sylow
441C24×C4C2×D7311yescharacteristic
442C22×M16—731no—
443C22×M16—731no—
444C22×M16—731no—
445C2×#120—731no—
446C2×C4×D4—731no—
447C2×C4×D4—731no—
448C2×C4×D4—731no—
449#436—1464no—
450C2×C4⋊C8—731no—
451C2×C4⋊C8—731no—
452C2×C4⋊C8—731no—
453#407—1464no—
454C2×C22⋊C8—731no—
455C2×C22⋊C8—731no—
456C2×C22⋊C8—731no—
457C2×C22⋊C8—731no—
458C2×C22⋊C8—731no—
459C2×C22⋊C8—731no—
460C2×C22⋊C8—731no—
461C2×C22⋊C8C2×D7311yescharacteristic
462C2×C22⋊C8C2×D7311yescharacteristic
463C2×C22⋊C8C2×D7311yescharacteristic
464C2×C22⋊C8C2×D7311yescharacteristic
465C2×C22⋊C8C2×D7311yescharacteristic
466C2×C22⋊C8C2×D7311yescharacteristic
467C2×#97—731no—
468C2×C4×C8—731no—
469C2×C4×C8—731no—
470#386—731no—
471#386—731no—
472#386—731no—
473#385—731no—
474#385—731no—
475#385—731no—
476#379—731no—
477C4×C22⋊C4—731no—
478C4×C22⋊C4—731no—
479C4×C22⋊C4—731no—
480#336—731no—
481#336—731no—
482#336—731no—
483#336—731no—
484#336—731no—
485#336—731no—
486C25C4×D7311yescharacteristic
487C22×D4—731no—
488C22×D4—731no—
489C22×D4—731no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4—731no—
497C23×C4C4×D7311yescharacteristic
498C23×C4C4×D7311yescharacteristic
499C23×C4C4×D7311yescharacteristic
500C23×C4C22×D7311yescharacteristic
501C23×C4C22×D7311yescharacteristic
502C23×C4C22×D7311yescharacteristic
503C2×M16—2921no—
504C2×M16—2921no—
505C2×M16—2921no—
506C2×M16—2921no—
507C2×M16—2921no—
508C2×M16—2921no—
509C2×M16—734no—
510C2×M16—1462no—
511C2×M16—1462no—
512C22×C8—731no—
513C22×C8—731no—
514C22×C8—731no—
515C22×C8—731no—
516C22×C8C22×D7311yescharacteristic
517C22×C8C22×D7311yescharacteristic
518C22×C8C22×D7311yescharacteristic
519C22×C8C22×D7311yescharacteristic
520#120—1464no—
521C4×D4—2921no—
522C4×D4—2921no—
523C4×D4—2921no—
524C4×D4—2921no—
525C4×D4—1462no—
526C4×D4—1462no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4—731no—
533C2×C22⋊C4—731no—
534C2×C22⋊C4—731no—
535C2×C22⋊C4—731no—
536C2×C22⋊C4—731no—
537C2×C22⋊C4—731no—
538C2×C22⋊C4—731no—
539C2×C22⋊C4—731no—
540C2×C22⋊C4—731no—
541C2×C22⋊C4—731no—
542C2×C42—731no—
543C2×C42—731no—
544C2×C42—731no—
545C4⋊C8—2921no—
546C4⋊C8—2921no—
547C4⋊C8—1462no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—41no—
551C22⋊C8—41no—
552C22⋊C8—41no—
553C22⋊C8—41no—
554C22⋊C8—2921no—
555C22⋊C8—2921no—
556C22⋊C8—1462no—
557C22⋊C8—1462no—
558C22⋊C8—1462no—
559C22⋊C8—1462no—
560C22⋊C8—1462no—
561#97—2921no—
562C4×C8—2921no—
563C4×C8—1462no—
564#95—731no—
565#95—731no—
566#95—731no—
567#95—731no—
568#95—731no—
569#95—731no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24—731no—
578C24C2×C4×D7311yescharacteristic
579C24C2×C4×D7311yescharacteristic
580C24C2×C4×D7311yescharacteristic
581C2×D4—2921no—
582C2×D4—2921no—
583C2×D4—2921no—
584C2×D4—2921no—
585C2×D4—1462no—
586C2×D4—1462no—
587C2×D4—1462no—
588C2×D4—1462no—
589C2×D4—1462no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—731no—
620C22×C4—731no—
621C22×C4—731no—
622C22×C4—731no—
623C22×C4—731no—
624C22×C4—731no—
625C22×C4—731no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4—1461no—
629C22×C4—1461no—
630C22×C4—1461no—
631C22×C4—1461no—
632C22×C4C2×C4×D7311yescharacteristic
633C22×C4C2×C4×D7311yescharacteristic
634C22×C4C2×C4×D7311yescharacteristic
635C22×C4D4×D7312yes—
636C22×C4#1192402712yes—
637C22×C4C23×D7311yescharacteristic
638M16—2924no—
639M16—2924no—
640M16—2924no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—732no—
654C2×C8—732no—
655C2×C8—1461no—
656C2×C8—1461no—
657C2×C8—1461no—
658C2×C8—1461no—
659C2×C8—1461no—
660C2×C8—1461no—
661C2×C8—1461no—
662C2×C8—1461no—
663C2×C8—1461no—
664C2×C8—1461no—
665C4⋊C4—2921no—
666C4⋊C4—2921no—
667C4⋊C4—1462no—
668C22⋊C4—2921no—
669C22⋊C4—2921no—
670C22⋊C4—2921no—
671C22⋊C4—2921no—
672C22⋊C4—2921no—
673C22⋊C4—2921no—
674C22⋊C4—734no—
675C22⋊C4—1462no—
676C22⋊C4—1462no—
677C22⋊C4—1462no—
678C22⋊C4—1462no—
679C22⋊C4—1462no—
680C42—1461no—
681C42—1461no—
682C42—1461no—
683C42—1461no—
684C42—1461no—
685C42—1461no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—1461no—
712C23—1461no—
713C23—1461no—
714C23—1461no—
715C23—1461no—
716C23—1461no—
717C23—1461no—
718C23#1455655112yes—
719C23M16×D7312yes—
720C23#1455659712yes—
721C23C22×C4×D7311yescharacteristic
722D4—2924no—
723D4—2924no—
724D4—2924no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—2921no—
749C2×C4—2921no—
750C2×C4—2921no—
751C2×C4—2921no—
752C2×C4—732no—
753C2×C4—732no—
754C2×C4—1461no—
755C2×C4—1461no—
756C2×C4—1461no—
757C2×C4—1461no—
758C2×C4—1461no—
759C2×C4—1461no—
760C2×C4—1461no—
761C2×C4—1461no—
762C2×C4—1461no—
763C2×C4—1461no—
764C2×C4—1461no—
765C2×C4—1461no—
766C2×C4—1461no—
767C2×C4—1461no—
768C2×C4—1461no—
769C2×C4—1461no—
770C2×C4—1461no—
771C2×C4—1461no—
772C2×C4—1461no—
773C2×C4#1455655112yes—
774C2×C4C2×D4×D7311yescharacteristic
775C2×C4C2×#1192402711yescharacteristic
776C2×C4#1455663611yescharacteristic
777C2×C4#1455663611yescharacteristic
778C2×C4#1455663611yescharacteristic
779C2×C4#1455663611yescharacteristic
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—2921no—
785C8—2921no—
786C8—1462no—
787C8—1462no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—2921no—
811C22—2921no—
812C22—2921no—
813C22—2921no—
814C22—2921no—
815C22—2921no—
816C22—2921no—
817C22C2×#1455655111yescharacteristic
818C22#1798906011yescharacteristic
819C22#1798906011yescharacteristic
820C22C2×M16×D7311yescharacteristic
821C22C2×#1455659711yescharacteristic
822C22#1798935311yescharacteristic
823C22#1798935311yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—2921no—
828C4—2921no—
829C4—2921no—
830C4—2921no—
831C4—2921no—
832C4—1462no—
833C4—1462no—
834C4#1798914711yescharacteristic
835C4#1798915211yescharacteristic
836C4#1798917211yescharacteristic
837C4#1798917211yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—5841no—
842C2#2261258611yescharacteristic
843C2#2261865211yescharacteristic
844C2#2261866311yescharacteristic
845C2#2261896211yescharacteristic
846C2#2261897011yescharacteristic
847C2#2261897611yescharacteristic
848C2#2261899111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1779C2
prime radicalC2×#14556560C4
cosocleC22×C4×C73C24
hypercenter#1779D73
hypocenterC73#22038
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
1. C2×#17988662C2semidirect
2. C2×#17988551C2semidirect
4. #22610727C2semidirect
5. #22610723C2semidirect
6. #22610541C2semidirect
7. #22610540C2semidirect
8. #22610540C2semidirect
9. #22610534C2semidirect
10. #22610226C2semidirect
11. #22610225C2semidirect
12. #22610225C2semidirect
13. #22610113C2semidirect
14. #22609717C2semidirect
15. C73×#1779C2semidirect
18. C22×#11924011C22semidirect
24. C2×#14556520C22semidirect
25. C2×#14556520C22semidirect
26. C2×#14556520C22semidirect
32. C2×#14556503C22semidirect
33. C2×#14556503C22semidirect
34. C2×#14556503C22semidirect
35. C2×#14556501C22semidirect
36. C2×C8×Dic73C22semidirect
37. C2×C8×Dic73C22semidirect
48. #17988341C22semidirect
49. #17988341C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
52. #17988341C22semidirect
53. #17988341C22semidirect
70. C2×#11924012D4semidirect
194. C22⋊Dic73M16semidirect
438. #1779D73semidirect
440. C73#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#179886622
C2×#179885512
C4×#145565602
#226107272
#226107232
#226105412
#226105402
#226105342
#226102262
#226102252
#226101132
#226097172
C73×#17792
#2203873