Finite Group Databasebeta

← #33097084

Subgroups — #33097084

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×#17988663C211yesmaximal, characteristic, complemented
2C2×#17988549C211yesmaximal, characteristic, complemented
3C4×#14556559C211yesmaximal, characteristic
4#22610730C211yesmaximal, characteristic, complemented
5#22610723C211yesmaximal, characteristic, complemented
6#22610542C211yesmaximal, characteristic, complemented
7#22610538C211yesmaximal, characteristic, complemented
8#22610534C211yesmaximal, characteristic, complemented
9#22610534C211yesmaximal, characteristic, complemented
10#22610228C211yesmaximal, characteristic, complemented
11#22610225C211yesmaximal, characteristic, complemented
12#22610115C211yesmaximal, characteristic, complemented
13#22609840C211yesmaximal, characteristic, complemented
14#22609713C211yesmaximal, characteristic, complemented
15C73×#1870C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C2×#14556559C411yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×C4×C22⋊D73C2211yescharacteristic
22#17988663—24no—
23C2×C4⋊#10596831C2211yescharacteristic, complemented
24C2×#14556520C2211yescharacteristic, complemented
25C2×#14556520C2211yescharacteristic, complemented
26#17988549—24no—
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic, complemented
30C2×C22⋊#10596831C2211yescharacteristic, complemented
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×#14556503C2211yescharacteristic
36C2×#14556503C2211yescharacteristic
37C2×#14556502C2211yescharacteristic, complemented
38C2×C8×Dic73C2211yescharacteristic, complemented
39C2×C8×Dic73C2211yescharacteristic, complemented
40#17988467C411yescharacteristic
41#17988463C411yescharacteristic
42#17988463C411yescharacteristic
43#17988459C411yescharacteristic
44#17988458C411yescharacteristic
45#17988458C411yescharacteristic
46#17988442C411yescharacteristic
47C4×#11924005C2211yescharacteristic
48C4×#11924005C2211yescharacteristic
49C4×C22⋊Dic73C2211yescharacteristic
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52#17988341C2211yescharacteristic, complemented
53#17988341C2211yescharacteristic, complemented
54C22×M16×C73C2211yescharacteristic, complemented
55C2×C4×D4×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic, complemented
59#336×C73C2211yescharacteristic, complemented
60#336×C73C2211yescharacteristic, complemented
61C24×D73C2×C411yescharacteristic
62C22×C22⋊D73C2×C411yescharacteristic
63C22×C22⋊D73C2×C411yescharacteristic
64C23×Dic73C2×C411yescharacteristic
65C22×C4×D73—22no—
66C22×C4×D73—22no—
67C22×C4×D73—41no—
68C22×C4×D73—41no—
69C22×C4×D73—41no—
70C22×C4×D73—41no—
71C22×C4×D73C2×C411yescharacteristic
72C22×C4×D73C2×C411yescharacteristic
73C22×C4×D73C2311yescharacteristic
74C22×C4×D73C2311yescharacteristic
75C2×#11924011—22no—
76C2×#11924011—41no—
77C2×#11924011—41no—
78C2×#11924011—41no—
79C2×#11924011—41no—
80C2×#11924011D414yescomplemented
81C22×#10596831C2311yescharacteristic
82C22×#10596831C2311yescharacteristic
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85#14556559—24no—
86C4×C22⋊D73—22no—
87C4×C22⋊D73—22no—
88C4×C22⋊D73—41no—
89C4×C22⋊D73—41no—
90C2×#11924007C2×C411yescharacteristic
91C2×#11924007C2×C411yescharacteristic
92C2×C22⋊Dic73C2×C411yescharacteristic
93C2×C22⋊Dic73C2×C411yescharacteristic
94C2×C22⋊Dic73C2×C411yescharacteristic
95C2×C22⋊Dic73C2×C411yescharacteristic
96C2×#11924005C2×C411yescharacteristic
97C2×#11924005C2×C411yescharacteristic
98C2×#11924005C2×C411yescharacteristic
99C2×#11924005C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×C4×Dic73C2311yescharacteristic
103C2×C4×Dic73C2311yescharacteristic
104C4⋊#10596831—41no—
105#14556520—22no—
106#14556520—41no—
107C22⋊#10596831—22no—
108C22⋊#10596831—22no—
109C22⋊#10596831—41no—
110C22⋊#10596831—41no—
111#14556503—22no—
112#14556503—22no—
113#14556503—22no—
114#14556503—22no—
115#14556503—41no—
116#14556503—41no—
117#14556502—41no—
118C8×Dic73—22no—
119C8×Dic73—41no—
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125#14556498C2×C411yescharacteristic
126C22×D4×C73C2×C411yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C2×M16×C73—22no—
130C2×M16×C73—41no—
131C2×M16×C73—41no—
132C22×C8×C73C2311yescharacteristic
133C22×C8×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136C4×D4×C73—41no—
137C4×D4×C73—41no—
138C2×C4⋊C4×C73C2×C411yescharacteristic
139C2×C22⋊C4×C73C2×C411yescharacteristic
140C2×C22⋊C4×C73C2×C411yescharacteristic
141C2×C42×C73C2311yescharacteristic
142C22⋊C8×C73—22no—
143C22⋊C8×C73—41no—
144C22⋊C8×C73—41no—
145C23×D73—22no—
146C23×D73—22no—
147C23×D73—22no—
148C23×D73—41no—
149C23×D73—41no—
150C23×D73—41no—
151C23×D73—41no—
152C23×D73C22×C411yescharacteristic
153C23×D73C22×C411yescharacteristic
154C2×C22⋊D73—22no—
155C2×C22⋊D73—22no—
156C2×C22⋊D73—22no—
157C2×C22⋊D73—22no—
158C2×C22⋊D73—41no—
159C2×C22⋊D73—41no—
160C22×Dic73—22no—
161C22×Dic73—41no—
162C22×Dic73—41no—
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—22no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×C4×D73—22no—
181C2×C4×D73—44no—
182C2×C4×D73—44no—
183C2×C4×D73—44no—
184C2×C4×D73—44no—
185C2×C4×D73—41no—
186C2×C4×D73—41no—
187C2×C4×D73—41no—
188C2×C4×D73—41no—
189C2×C4×D73C2×D412yes—
190C2×C4×D73#4112yes—
191#11924011—44no—
192#11924011—44no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198C2×#10596831—21no—
199C2×#10596831—21no—
200C2×#10596831—21no—
201C2×#10596831—21no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204C2×#10596831C2×D412yes—
205#11924007—22no—
206#11924007—41no—
207C22⋊Dic73—22no—
208C22⋊Dic73—41no—
209C22⋊Dic73—41no—
210C22⋊Dic73M1614yescomplemented
211#11924005—22no—
212#11924005—22no—
213#11924005—22no—
214#11924005—22no—
215#11924005—41no—
216#11924005—41no—
217C4×Dic73—21no—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C4×Dic73—21no—
221C24×C73C22×C411yescharacteristic
222C24×C73C22×C411yescharacteristic
223C2×D4×C73—22no—
224C2×D4×C73—41no—
225C2×D4×C73—41no—
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—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73C22×C411yescharacteristic
239C22×C4×C73C22×C411yescharacteristic
240C22×C4×C73C22×C411yescharacteristic
241C22×C4×C73C22×C411yescharacteristic
242C22×C4×C73C2411yescharacteristic
243M16×C73—44no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
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×C73C2×D412yes—
256C4⋊C4×C73—41no—
257C22⋊C4×C73—41no—
258C22⋊C4×C73—41no—
259C42×C73—21no—
260C42×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×C73C2×M1612yes—
275C23×C73C23×C411yescharacteristic
276C22×D73—21no—
277C22×D73—21no—
278C22×D73—21no—
279C22×D73—21no—
280C22×D73—21no—
281C22×D73—21no—
282C22×D73—21no—
283C22×D73—21no—
284C22×D73—21no—
285C22×D73—21no—
286C22×D73—21no—
287C22×D73—21no—
288C22×D73—44no—
289C22×D73—44no—
290C22×D73—44no—
291C22×D73—44no—
292C22×D73—44no—
293C22×D73—44no—
294C22×D73—44no—
295C22×D73C4×D412yes—
296C22×D73#13112yes—
297D4×C73—44no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
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—21no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
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×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73H(5,𝔽2)11yescharacteristic
321C2×C4×C73H(5,𝔽2)11yescharacteristic
322C2×C4×C73H(5,𝔽2)11yescharacteristic
323C2×C4×C73H(5,𝔽2)11yescharacteristic
324C22⋊D73—44no—
325C22⋊D73—44no—
326C2×Dic73—21no—
327C2×Dic73—21no—
328C2×Dic73—21no—
329C2×Dic73—21no—
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—44no—
342C2×Dic73C4×D412yes—
343C2×Dic73C2×M1612yes—
344C2×Dic73C2×M1612yes—
345C4×D73—22no—
346C4×D73—22no—
347C4×D73—22no—
348C4×D73—22no—
349C4×D73—44no—
350C4×D73—44no—
351C4×D73—41no—
352C4×D73—41no—
353C4×D73—41no—
354C4×D73—41no—
355C8×C73—22no—
356C8×C73—41no—
357C8×C73—41no—
358C8×C73—41no—
359#10596831—22no—
360#10596831—41no—
361#10596831—41no—
362#10596831—41no—
363C22×C73—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—41no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73C2×C4×D411yescharacteristic
378C22×C73#51811yescharacteristic
379C22×C73#51811yescharacteristic
380C22×C73C22×M1611yescharacteristic
381C22×C73C2×#13111yescharacteristic
382C22×C73#56811yescharacteristic
383C22×C73#56811yescharacteristic
384C2×D73—22no—
385C2×D73—22no—
386C2×D73—22no—
387C2×D73—22no—
388C2×D73—22no—
389C2×D73—22no—
390C2×D73—416no—
391C2×D73—41no—
392C2×D73—41no—
393C2×D73—41no—
394C2×D73—41no—
395C2×D73—41no—
396C2×D73—41no—
397C2×D73—41no—
398C2×D73—41no—
399C4×C73—41no—
400C4×C73—41no—
401C4×C73—41no—
402C4×C73—41no—
403C4×C73#53411yescharacteristic
404C4×C73#53511yescharacteristic
405C4×C73#53811yescharacteristic
406C4×C73#53811yescharacteristic
407Dic73—22no—
408Dic73—22no—
409Dic73—22no—
410Dic73—41no—
411Dic73—41no—
412Dic73—41no—
413#22038—731nomaximal, Sylow
414C2×C73—42no—
415C2×C73—81no—
416C2×C73#232111yescharacteristic
417C2×C73#293311yescharacteristic
418C2×C73D4×M1611yescharacteristic
419C2×C73#297411yescharacteristic
420C2×C73#297511yescharacteristic
421C2×C73#297611yescharacteristic
422C2×C73#297811yescharacteristic
423D73—42no—
424D73—42no—
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#1870D7311yescharacteristic, complemented
437#1851—731no—
438#1779—731no—
439#1753—731no—
440C73#2203811yescharacteristic, complemented, Sylow
441C24×C4—731no—
442C22×M16—731no—
443C22×M16—731no—
444C22×M16C2×D7311yescharacteristic, complemented
445C2×#120—731no—
446C2×C4×D4—731no—
447C2×C4×D4—731no—
448C2×C4×D4C2×D7311yescharacteristic
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⋊C8—731no—
462C2×C22⋊C8—731no—
463C2×C22⋊C8—731no—
464C2×C22⋊C8C2×D7311yescharacteristic
465C2×C22⋊C8C2×D7311yescharacteristic
466C2×C22⋊C8C2×D7311yescharacteristic, complemented
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#336C2×D7311yescharacteristic, complemented
485#336C2×D7311yescharacteristic, complemented
486C25—731no—
487C22×D4—731no—
488C22×D4—731no—
489C22×D4C4×D7311yescharacteristic
490C23×C4—2921no—
491C23×C4—2921no—
492C23×C4—2921no—
493C23×C4—2921no—
494C23×C4—731no—
495C23×C4—731no—
496C23×C4—731no—
497C23×C4—731no—
498C23×C4—731no—
499C23×C4—1462no—
500C23×C4—1462no—
501C23×C4C22×D7311yescharacteristic
502C23×C4C22×D7311yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—2921no—
507C2×M16—2921no—
508C2×M16—2921no—
509C2×M16—2921no—
510C2×M16—734no—
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—41no—
522C4×D4—41no—
523C4×D4—2921no—
524C4×D4—2921no—
525C4×D4—1462no—
526C4×D4—1462no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4C4×D7311yescharacteristic
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⋊C4C4×D7311yescharacteristic
541C2×C22⋊C4C4×D7311yescharacteristic
542C2×C42—731no—
543C2×C42—731no—
544C2×C42C22×D7311yescharacteristic
545C4⋊C8—2921no—
546C4⋊C8—2921no—
547C4⋊C8—1462no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C22⋊C8—2921no—
552C22⋊C8—2921no—
553C22⋊C8—2921no—
554C22⋊C8—2921no—
555C22⋊C8—1462no—
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—2921no—
571C24—2921no—
572C24—2921no—
573C24—2921no—
574C24—731no—
575C24—731no—
576C24—1462no—
577C24—1462no—
578C24—1462no—
579C24C2×C4×D7311yescharacteristic
580C24C2×C4×D7311yescharacteristic
581C2×D4—22no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—2921no—
585C2×D4—2921no—
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—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—2921no—
603C22×C4—2921no—
604C22×C4—2921no—
605C22×C4—2921no—
606C22×C4—2924no—
607C22×C4—2924no—
608C22×C4—2924no—
609C22×C4—2924no—
610C22×C4—2921no—
611C22×C4—2921no—
612C22×C4—731no—
613C22×C4—731no—
614C22×C4—731no—
615C22×C4—732no—
616C22×C4—732no—
617C22×C4—731no—
618C22×C4—731no—
619C22×C4—731no—
620C22×C4—1462no—
621C22×C4—1462no—
622C22×C4—1462no—
623C22×C4—1461no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4—1461no—
629C22×C4—1461no—
630C22×C4—1461no—
631C22×C4—1461no—
632C22×C4—1461no—
633C22×C4C2×C4×D7311yescharacteristic
634C22×C4C2×C4×D7311yescharacteristic
635C22×C4C2×C4×D7311yescharacteristic
636C22×C4C2×C4×D7311yescharacteristic
637C22×C4C23×D7311yescharacteristic
638M16—44no—
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—732no—
653C2×C8—1461no—
654C2×C8—1461no—
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×C8D4×D7312yes—
665C4⋊C4—41no—
666C4⋊C4—2921no—
667C4⋊C4—1462no—
668C22⋊C4—41no—
669C22⋊C4—41no—
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—21no—
681C42—21no—
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—2924no—
700C23—2924no—
701C23—2924no—
702C23—2924no—
703C23—2924no—
704C23—2924no—
705C23—2924no—
706C23—732no—
707C23—732no—
708C23—1461no—
709C23—1461no—
710C23—1461no—
711C23—1461no—
712C23—1461no—
713C23—1461no—
714C23—1461no—
715C23—1461no—
716C23—1461no—
717C23—1461no—
718C23—1461no—
719C23—1461no—
720C23M16×D7312yes—
721C23C22×C4×D7311yescharacteristic
722D4—44no—
723D4—2924no—
724D4—2924no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—2924no—
746C2×C4—2924no—
747C2×C4—2924no—
748C2×C4—2921no—
749C2×C4—2921no—
750C2×C4—2921no—
751C2×C4—2921no—
752C2×C4—732no—
753C2×C4—732no—
754C2×C4—732no—
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—1462no—
771C2×C4—1462no—
772C2×C4—1462no—
773C2×C4—1462no—
774C2×C4C2×D4×D7311yescharacteristic
775C2×C4#41×D7311yescharacteristic
776C2×C4#1455663611yescharacteristic
777C2×C4#1455663611yescharacteristic
778C2×C4#1455663611yescharacteristic
779C2×C4#1455663711yescharacteristic
780C8—22no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—2921no—
785C8—2921no—
786C8—2921no—
787C8—1462no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—29216no—
803C22—2921no—
804C22—2921no—
805C22—2921no—
806C22—2921no—
807C22—2921no—
808C22—2921no—
809C22—2921no—
810C22—2921no—
811C22—1462no—
812C22—1462no—
813C22—1462no—
814C22—1462no—
815C22—1462no—
816C22—1462no—
817C22C4×D4×D7311yescharacteristic
818C22#1798905911yescharacteristic
819C22#1798906011yescharacteristic
820C22C2×M16×D7311yescharacteristic
821C22#131×D7311yescharacteristic
822C22#1798935211yescharacteristic
823C22#1798935311yescharacteristic
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—2921no—
829C4—2921no—
830C4—2921no—
831C4—1462no—
832C4—1462no—
833C4—1462no—
834C4#1798914711yescharacteristic
835C4#1798915311yescharacteristic
836C4#1798916911yescharacteristic
837C4#1798917311yescharacteristic
838C2—42no—
839C2—81no—
840C2—2922no—
841C2—2922no—
842C2#2261258711yescharacteristic
843C2#2261866011yescharacteristic
844C2#2261866411yescharacteristic
845C2#2261896111yescharacteristic
846C2#2261897011yescharacteristic
847C2#2261897411yescharacteristic
848C2#2261898811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1870C2
prime radicalC2×#14556559C4
cosocleC22×C4×C73C24
hypercenter#1870D73
hypocenterC73#22038
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#17988663C2semidirect
2. C2×#17988549C2semidirect
4. #22610730C2semidirect
5. #22610723C2semidirect
6. #22610542C2semidirect
7. #22610538C2semidirect
8. #22610534C2semidirect
9. #22610534C2semidirect
10. #22610228C2semidirect
11. #22610225C2semidirect
12. #22610115C2semidirect
13. #22609840C2semidirect
14. #22609713C2semidirect
15. C73×#1870C2semidirect
23. C2×C4⋊#10596831C22semidirect
24. C2×#14556520C22semidirect
25. C2×#14556520C22semidirect
29. C2×C22⋊#10596831C22semidirect
30. C2×C22⋊#10596831C22semidirect
37. C2×#14556502C22semidirect
38. C2×C8×Dic73C22semidirect
39. C2×C8×Dic73C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
52. #17988341C22semidirect
53. #17988341C22semidirect
54. C22×M16×C73C22semidirect
58. C2×C22⋊C8×C73C22semidirect
59. #336×C73C22semidirect
60. #336×C73C22semidirect
80. C2×#11924011D4semidirect
210. C22⋊Dic73M16semidirect
436. #1870D73semidirect
440. C73#22038semidirect
444. C22×M16C2×D73semidirect
466. C2×C22⋊C8C2×D73semidirect
484. #336C2×D73semidirect
485. #336C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886632
C2×#179885492
C4×#145565592
#226107302
#226107232
#226105422
#226105382
#226105342
#226102282
#226102252
#226101152
#226098402
#226097132
C73×#18702
#2203873