Finite Group Databasebeta

← C89×#23335 #36401183

Subgroups — C89×#23335 #36401183

Order 22784.

776 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2392C211yesmaximal, characteristic
2C89×#1955C211yesmaximal, characteristic, complemented
3C89×#1955C211yesmaximal, characteristic, complemented
4C89×#1924C211yesmaximal, characteristic, complemented
5C89×#1924C211yesmaximal, characteristic, complemented
6C89×#1917C211yesmaximal, characteristic, complemented
7C89×#1917C211yesmaximal, characteristic, complemented
8C89×#1870C211yesmaximal, characteristic, complemented
9C89×#1870C211yesmaximal, characteristic, complemented
10C89×#1869C211yesmaximal, characteristic, complemented
11C89×#1869C211yesmaximal, characteristic, complemented
12C89×#1851C211yesmaximal, characteristic, complemented
13C89×#1850C211yesmaximal, characteristic, complemented
14C89×#1818C211yesmaximal, characteristic, complemented
15C89×#1798C211yesmaximal, characteristic, complemented
16C22×M16×C89C2211yescharacteristic
17C23×C8×C89C2211yescharacteristic
18C2×C4×D4×C89C2211yescharacteristic
19C2×C4×D4×C89C2211yescharacteristic
20C2×C4×D4×C89C2211yescharacteristic
21C2×#117×C89C2211yescharacteristic
22C2×C4⋊C8×C89C2211yescharacteristic
23C2×C4⋊C8×C89C2211yescharacteristic
24C2×C4⋊C8×C89C2211yescharacteristic
25C2×C4⋊C8×C89C2211yescharacteristic
26C2×C22⋊C8×C89C2211yescharacteristic
27C2×C22⋊C8×C89C2211yescharacteristic
28C2×C22⋊C8×C89C2211yescharacteristic
29C2×C22⋊C8×C89C2211yescharacteristic
30C2×C22⋊C8×C89C2211yescharacteristic
31C2×C22⋊C8×C89C2211yescharacteristic
32C2×C22⋊C8×C89C2211yescharacteristic
33C2×C22⋊C8×C89C2211yescharacteristic
34C2×C22⋊C8×C89C2211yescharacteristic
35C2×C22⋊C8×C89C2211yescharacteristic
36C2×#97×C89C2211yescharacteristic
37C2×#97×C89C2211yescharacteristic
38#398×C89C411yescharacteristic
39#397×C89C411yescharacteristic
40#396×C89C411yescharacteristic
41#396×C89C411yescharacteristic
42#394×C89C411yescharacteristic
43#394×C89C411yescharacteristic
44#394×C89C411yescharacteristic
45#392×C89C411yescharacteristic
46C4×C4⋊C4×C89C2211yescharacteristic
47C4×C22⋊C4×C89C2211yescharacteristic
48C4×C22⋊C4×C89C2211yescharacteristic
49#336×C89C2211yescharacteristic
50#336×C89C2211yescharacteristic
51#336×C89C2211yescharacteristic
52#336×C89C2211yescharacteristic
53#336×C89C2211yescharacteristic
54#336×C89C2211yescharacteristic
55#336×C89C2211yescharacteristic
56#336×C89C2211yescharacteristic
57#336×C89C2211yescharacteristic
58#336×C89C2211yescharacteristic
59C22×D4×C89C2×C411yescharacteristic
60C22×D4×C89C2×C411yescharacteristic
61C22×D4×C89C2×C411yescharacteristic
62C23×C4×C89C2311yescharacteristic
63C23×C4×C89C2311yescharacteristic
64C23×C4×C89C2311yescharacteristic
65C2×M16×C89—41no—
66C2×M16×C89—41no—
67C2×M16×C89—41no—
68C22×C8×C89—41no—
69C22×C8×C89—41no—
70C22×C8×C89—41no—
71C22×C8×C89C2311yescharacteristic
72C22×C8×C89C2311yescharacteristic
73C22×C8×C89C2311yescharacteristic
74C22×C8×C89C2311yescharacteristic
75C22×C8×C89C2311yescharacteristic
76C22×C8×C89C2311yescharacteristic
77C22×C8×C89C2311yescharacteristic
78C22×C8×C89C2311yescharacteristic
79C4×D4×C89—41no—
80C4×D4×C89—41no—
81C4×D4×C89—41no—
82C4×D4×C89—41no—
83C4×D4×C89—41no—
84C4×D4×C89—41no—
85#117×C89—41no—
86#117×C89—41no—
87C2×C4⋊C4×C89C2×C411yescharacteristic
88C2×C4⋊C4×C89C2×C411yescharacteristic
89C2×C4⋊C4×C89C2×C411yescharacteristic
90C2×C4⋊C4×C89C2×C411yescharacteristic
91C2×C4⋊C4×C89C2×C411yescharacteristic
92C2×C4⋊C4×C89C2×C411yescharacteristic
93C2×C4⋊C4×C89C2×C411yescharacteristic
94C2×C22⋊C4×C89C2×C411yescharacteristic
95C2×C22⋊C4×C89C2×C411yescharacteristic
96C2×C22⋊C4×C89C2×C411yescharacteristic
97C2×C22⋊C4×C89C2×C411yescharacteristic
98C2×C22⋊C4×C89C2×C411yescharacteristic
99C2×C22⋊C4×C89C2×C411yescharacteristic
100C2×C22⋊C4×C89C2×C411yescharacteristic
101C2×C22⋊C4×C89C2×C411yescharacteristic
102C2×C22⋊C4×C89C2×C411yescharacteristic
103C2×C22⋊C4×C89C2×C411yescharacteristic
104C2×C22⋊C4×C89C2×C411yescharacteristic
105C2×C22⋊C4×C89C2×C411yescharacteristic
106C2×C42×C89C2311yescharacteristic
107C2×C42×C89C2311yescharacteristic
108C2×C42×C89C2311yescharacteristic
109C2×C42×C89C2311yescharacteristic
110C4⋊C8×C89—41no—
111C4⋊C8×C89—41no—
112C4⋊C8×C89—41no—
113C4⋊C8×C89—41no—
114C22⋊C8×C89—41no—
115C22⋊C8×C89—41no—
116C22⋊C8×C89—41no—
117C22⋊C8×C89—41no—
118C22⋊C8×C89—41no—
119C22⋊C8×C89—41no—
120C22⋊C8×C89—41no—
121C22⋊C8×C89—41no—
122C22⋊C8×C89—41no—
123C22⋊C8×C89—41no—
124#97×C89—41no—
125#97×C89—41no—
126#95×C89C2×C411yescharacteristic
127#95×C89C2×C411yescharacteristic
128#95×C89C2×C411yescharacteristic
129#95×C89C2×C411yescharacteristic
130#95×C89C2×C411yescharacteristic
131#95×C89C2×C411yescharacteristic
132C24×C89C22×C411yescharacteristic
133C24×C89C22×C411yescharacteristic
134C24×C89C22×C411yescharacteristic
135C2×D4×C89—22no—
136C2×D4×C89—22no—
137C2×D4×C89—41no—
138C2×D4×C89—41no—
139C2×D4×C89—41no—
140C2×D4×C89—41no—
141C2×D4×C89—41no—
142C2×D4×C89—41no—
143C2×D4×C89—41no—
144C22×C4×C89—21no—
145C22×C4×C89—21no—
146C22×C4×C89—21no—
147C22×C4×C89—21no—
148C22×C4×C89—21no—
149C22×C4×C89—21no—
150C22×C4×C89—21no—
151C22×C4×C89—21no—
152C22×C4×C89—21no—
153C22×C4×C89—21no—
154C22×C4×C89—21no—
155C22×C4×C89—21no—
156C22×C4×C89—21no—
157C22×C4×C89—21no—
158C22×C4×C89—21no—
159C22×C4×C89—21no—
160C22×C4×C89—21no—
161C22×C4×C89—21no—
162C22×C4×C89C22×C411yescharacteristic
163C22×C4×C89C22×C411yescharacteristic
164C22×C4×C89C22×C411yescharacteristic
165C22×C4×C89C22×C411yescharacteristic
166C22×C4×C89C22×C411yescharacteristic
167C22×C4×C89C22×C411yescharacteristic
168C22×C4×C89C22×C411yescharacteristic
169C22×C4×C89C22×C411yescharacteristic
170C22×C4×C89C22×C411yescharacteristic
171C22×C4×C89C22×C411yescharacteristic
172C22×C4×C89C22×C411yescharacteristic
173C22×C4×C89C2411yescharacteristic
174M16×C89—44no—
175C2×C8×C89—21no—
176C2×C8×C89—21no—
177C2×C8×C89—21no—
178C2×C8×C89—21no—
179C2×C8×C89—21no—
180C2×C8×C89—21no—
181C2×C8×C89—21no—
182C2×C8×C89—21no—
183C2×C8×C89—21no—
184C2×C8×C89—21no—
185C2×C8×C89—21no—
186C2×C8×C89—21no—
187C2×C8×C89—21no—
188C2×C8×C89—21no—
189C2×C8×C89—21no—
190C2×C8×C89—21no—
191C2×C8×C89—21no—
192C2×C8×C89—21no—
193C2×C8×C89—21no—
194C2×C8×C89—21no—
195C2×C8×C89—21no—
196C2×C8×C89—21no—
197C2×C8×C89—21no—
198C2×C8×C89—21no—
199C2×C8×C89—44no—
200C4⋊C4×C89—41no—
201C4⋊C4×C89—41no—
202C4⋊C4×C89—41no—
203C4⋊C4×C89—41no—
204C4⋊C4×C89—41no—
205C4⋊C4×C89—41no—
206C4⋊C4×C89—41no—
207C22⋊C4×C89—22no—
208C22⋊C4×C89—41no—
209C22⋊C4×C89—41no—
210C22⋊C4×C89—41no—
211C22⋊C4×C89—41no—
212C22⋊C4×C89—41no—
213C22⋊C4×C89—41no—
214C22⋊C4×C89—41no—
215C22⋊C4×C89—41no—
216C22⋊C4×C89—41no—
217C22⋊C4×C89—41no—
218C22⋊C4×C89—41no—
219C42×C89—21no—
220C42×C89—21no—
221C42×C89—21no—
222C42×C89—21no—
223C42×C89—21no—
224C42×C89—21no—
225C42×C89—21no—
226C42×C89—21no—
227C23×C89—21no—
228C23×C89—21no—
229C23×C89—21no—
230C23×C89—21no—
231C23×C89—21no—
232C23×C89—21no—
233C23×C89—21no—
234C23×C89—21no—
235C23×C89—21no—
236C23×C89—21no—
237C23×C89—21no—
238C23×C89—21no—
239C23×C89—21no—
240C23×C89—21no—
241C23×C89—21no—
242C23×C89—21no—
243C23×C89—21no—
244C23×C89—21no—
245C23×C89—21no—
246C23×C89—21no—
247C23×C89#13112yes—
248C23×C89C23×C411yescharacteristic
249D4×C89—44no—
250D4×C89—44no—
251D4×C89—44no—
252C2×C4×C89—21no—
253C2×C4×C89—21no—
254C2×C4×C89—21no—
255C2×C4×C89—21no—
256C2×C4×C89—21no—
257C2×C4×C89—21no—
258C2×C4×C89—21no—
259C2×C4×C89—21no—
260C2×C4×C89—21no—
261C2×C4×C89—21no—
262C2×C4×C89—21no—
263C2×C4×C89—21no—
264C2×C4×C89—21no—
265C2×C4×C89—21no—
266C2×C4×C89—21no—
267C2×C4×C89—21no—
268C2×C4×C89—21no—
269C2×C4×C89—21no—
270C2×C4×C89—21no—
271C2×C4×C89—21no—
272C2×C4×C89—21no—
273C2×C4×C89—21no—
274C2×C4×C89—21no—
275C2×C4×C89—21no—
276C2×C4×C89—21no—
277C2×C4×C89—21no—
278C2×C4×C89—21no—
279C2×C4×C89—21no—
280C2×C4×C89—21no—
281C2×C4×C89—21no—
282C2×C4×C89—21no—
283C2×C4×C89—21no—
284C2×C4×C89—21no—
285C2×C4×C89—41no—
286C2×C4×C89—41no—
287C2×C4×C89—41no—
288C2×C4×C89—41no—
289C2×C4×C89—41no—
290C2×C4×C89—41no—
291C2×C4×C89—41no—
292C2×C4×C89—41no—
293C2×C4×C89—41no—
294C2×C4×C89—41no—
295C2×C4×C89—41no—
296C2×C4×C89—41no—
297C2×C4×C89H(5,𝔽2)11yescharacteristic
298C2×C4×C89H(5,𝔽2)11yescharacteristic
299C2×C4×C89H(5,𝔽2)11yescharacteristic
300C2×C4×C89H(5,𝔽2)11yescharacteristic
301C2×C4×C89H(5,𝔽2)11yescharacteristic
302C2×C4×C892−1+411yescharacteristic
303C8×C89—41no—
304C8×C89—41no—
305C8×C89—41no—
306C8×C89—41no—
307C8×C89—41no—
308C8×C89—41no—
309C8×C89—41no—
310C8×C89—41no—
311C22×C89—22no—
312C22×C89—22no—
313C22×C89—22no—
314C22×C89—41no—
315C22×C89—41no—
316C22×C89—41no—
317C22×C89—41no—
318C22×C89—41no—
319C22×C89—41no—
320C22×C89—41no—
321C22×C89—41no—
322C22×C89—41no—
323C22×C89—41no—
324C22×C89—41no—
325C22×C89—41no—
326C22×C89—41no—
327C22×C89—41no—
328C22×C89—41no—
329C22×C89—41no—
330C22×C89—41no—
331C22×C89—41no—
332C22×C89#51811yescharacteristic
333C22×C89#51811yescharacteristic
334C22×C89#52011yescharacteristic
335C22×C89C2×#13111yescharacteristic
336C22×C89#56811yescharacteristic
337C22×C89#56811yescharacteristic
338C22×C89#56811yescharacteristic
339C4×C89—41no—
340C4×C89—41no—
341C4×C89—41no—
342C4×C89—41no—
343C4×C89—41no—
344C4×C89—41no—
345C4×C89—41no—
346C4×C89—41no—
347C4×C89—41no—
348C4×C89—41no—
349C4×C89—41no—
350C4×C89#56011yescharacteristic
351C4×C89#56011yescharacteristic
352C4×C89#56211yescharacteristic
353C4×C89#56211yescharacteristic
354#23335C8911yesmaximal, characteristic, direct product factor, Sylow
355C2×C89—42no—
356C2×C89—81no—
357C2×C89—81no—
358C2×C89#237711yescharacteristic
359C2×C89#297611yescharacteristic
360C2×C89#297611yescharacteristic
361C2×C89#297811yescharacteristic
362C2×C89#298011yescharacteristic
363C2×C89#299211yescharacteristic
364C2×C89#299511yescharacteristic
365#2392C2×C8911yescharacteristic
366#1955C2×C8911yescharacteristic, complemented
367#1955C2×C8911yescharacteristic, complemented
368#1924C2×C8911yescharacteristic, complemented
369#1924C2×C8911yescharacteristic, complemented
370#1917C2×C8911yescharacteristic, complemented
371#1917C2×C8911yescharacteristic, complemented
372#1870C2×C8911yescharacteristic, complemented
373#1870C2×C8911yescharacteristic, complemented
374#1869C2×C8911yescharacteristic, complemented
375#1869C2×C8911yescharacteristic, complemented
376#1851C2×C8911yescharacteristic, complemented
377#1850C2×C8911yescharacteristic, complemented
378#1818C2×C8911yescharacteristic, complemented
379#1798C2×C8911yescharacteristic, complemented
380C89#2333511yescharacteristic, direct product factor, Sylow
381C22×M16C22×C8911yescharacteristic
382C23×C8C22×C8911yescharacteristic
383C2×C4×D4C22×C8911yescharacteristic
384C2×C4×D4C22×C8911yescharacteristic
385C2×C4×D4C22×C8911yescharacteristic
386C2×#117C22×C8911yescharacteristic
387C2×C4⋊C8C22×C8911yescharacteristic
388C2×C4⋊C8C22×C8911yescharacteristic
389C2×C4⋊C8C22×C8911yescharacteristic
390C2×C4⋊C8C22×C8911yescharacteristic
391C2×C22⋊C8C22×C8911yescharacteristic
392C2×C22⋊C8C22×C8911yescharacteristic
393C2×C22⋊C8C22×C8911yescharacteristic
394C2×C22⋊C8C22×C8911yescharacteristic
395C2×C22⋊C8C22×C8911yescharacteristic
396C2×C22⋊C8C22×C8911yescharacteristic
397C2×C22⋊C8C22×C8911yescharacteristic
398C2×C22⋊C8C22×C8911yescharacteristic
399C2×C22⋊C8C22×C8911yescharacteristic
400C2×C22⋊C8C22×C8911yescharacteristic
401C2×#97C22×C8911yescharacteristic
402C2×#97C22×C8911yescharacteristic
403#398C4×C8911yescharacteristic
404#397C4×C8911yescharacteristic
405#396C4×C8911yescharacteristic
406#396C4×C8911yescharacteristic
407#394C4×C8911yescharacteristic
408#394C4×C8911yescharacteristic
409#394C4×C8911yescharacteristic
410#392C4×C8911yescharacteristic
411C4×C4⋊C4C22×C8911yescharacteristic
412C4×C22⋊C4C22×C8911yescharacteristic
413C4×C22⋊C4C22×C8911yescharacteristic
414#336C22×C8911yescharacteristic
415#336C22×C8911yescharacteristic
416#336C22×C8911yescharacteristic
417#336C22×C8911yescharacteristic
418#336C22×C8911yescharacteristic
419#336C22×C8911yescharacteristic
420#336C22×C8911yescharacteristic
421#336C22×C8911yescharacteristic
422#336C22×C8911yescharacteristic
423#336C22×C8911yescharacteristic
424C22×D4C2×C4×C8911yescharacteristic
425C22×D4C2×C4×C8911yescharacteristic
426C22×D4C2×C4×C8911yescharacteristic
427C23×C4C23×C8911yescharacteristic
428C23×C4C23×C8911yescharacteristic
429C23×C4C23×C8911yescharacteristic
430C2×M16—41no—
431C2×M16—41no—
432C2×M16—41no—
433C22×C8—41no—
434C22×C8—41no—
435C22×C8—41no—
436C22×C8C23×C8911yescharacteristic
437C22×C8C23×C8911yescharacteristic
438C22×C8C23×C8911yescharacteristic
439C22×C8C23×C8911yescharacteristic
440C22×C8C23×C8911yescharacteristic
441C22×C8C23×C8911yescharacteristic
442C22×C8C23×C8911yescharacteristic
443C22×C8C23×C8911yescharacteristic
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C4×D4—41no—
450#117—41no—
451#117—41no—
452C2×C4⋊C4C2×C4×C8911yescharacteristic
453C2×C4⋊C4C2×C4×C8911yescharacteristic
454C2×C4⋊C4C2×C4×C8911yescharacteristic
455C2×C4⋊C4C2×C4×C8911yescharacteristic
456C2×C4⋊C4C2×C4×C8911yescharacteristic
457C2×C4⋊C4C2×C4×C8911yescharacteristic
458C2×C4⋊C4C2×C4×C8911yescharacteristic
459C2×C22⋊C4C2×C4×C8911yescharacteristic
460C2×C22⋊C4C2×C4×C8911yescharacteristic
461C2×C22⋊C4C2×C4×C8911yescharacteristic
462C2×C22⋊C4C2×C4×C8911yescharacteristic
463C2×C22⋊C4C2×C4×C8911yescharacteristic
464C2×C22⋊C4C2×C4×C8911yescharacteristic
465C2×C22⋊C4C2×C4×C8911yescharacteristic
466C2×C22⋊C4C2×C4×C8911yescharacteristic
467C2×C22⋊C4C2×C4×C8911yescharacteristic
468C2×C22⋊C4C2×C4×C8911yescharacteristic
469C2×C22⋊C4C2×C4×C8911yescharacteristic
470C2×C22⋊C4C2×C4×C8911yescharacteristic
471C2×C42C23×C8911yescharacteristic
472C2×C42C23×C8911yescharacteristic
473C2×C42C23×C8911yescharacteristic
474C2×C42C23×C8911yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C4⋊C8—41no—
478C4⋊C8—41no—
479C22⋊C8—41no—
480C22⋊C8—41no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489#97—41no—
490#97—41no—
491#95C2×C4×C8911yescharacteristic
492#95C2×C4×C8911yescharacteristic
493#95C2×C4×C8911yescharacteristic
494#95C2×C4×C8911yescharacteristic
495#95C2×C4×C8911yescharacteristic
496#95C2×C4×C8911yescharacteristic
497C24C22×C4×C8911yescharacteristic
498C24C22×C4×C8911yescharacteristic
499C24C22×C4×C8911yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C22×C4×C8911yescharacteristic
528C22×C4C22×C4×C8911yescharacteristic
529C22×C4C22×C4×C8911yescharacteristic
530C22×C4C22×C4×C8911yescharacteristic
531C22×C4C22×C4×C8911yescharacteristic
532C22×C4C22×C4×C8911yescharacteristic
533C22×C4C22×C4×C8911yescharacteristic
534C22×C4C22×C4×C8911yescharacteristic
535C22×C4C22×C4×C8911yescharacteristic
536C22×C4C22×C4×C8911yescharacteristic
537C22×C4C22×C4×C8911yescharacteristic
538C22×C4C24×C8911yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—44no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23#131×C8912yes—
613C23C23×C4×C8911yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4H(5,𝔽2)×C8911yescharacteristic
663C2×C4H(5,𝔽2)×C8911yescharacteristic
664C2×C4H(5,𝔽2)×C8911yescharacteristic
665C2×C4H(5,𝔽2)×C8911yescharacteristic
666C2×C4H(5,𝔽2)×C8911yescharacteristic
667C2×C42−1+4×C8911yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22#518×C8911yescharacteristic
698C22#518×C8911yescharacteristic
699C22#520×C8911yescharacteristic
700C22C2×#131×C8911yescharacteristic
701C22#568×C8911yescharacteristic
702C22#568×C8911yescharacteristic
703C22#568×C8911yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4#560×C8911yescharacteristic
716C4#560×C8911yescharacteristic
717C4#562×C8911yescharacteristic
718C4#562×C8911yescharacteristic
719C2—42no—
720C2—81no—
721C2—81no—
722C2C89×#237711yescharacteristic
723C2C89×#297611yescharacteristic
724C2C89×#297611yescharacteristic
725C2C89×#297811yescharacteristic
726C2C89×#298011yescharacteristic
727C2C89×#299211yescharacteristic
728C2C89×#299511yescharacteristic
subgroupG/H
centerC22×C4×C89C24
commutatorC23C23×C4×C89
Frattini, cosocleC22×C4C24×C89
socleC23×C89C23×C4
prime radical#392×C89C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C89×#1955C2semidirect
3. C89×#1955C2semidirect
4. C89×#1924C2semidirect
5. C89×#1924C2semidirect
6. C89×#1917C2semidirect
7. C89×#1917C2semidirect
8. C89×#1870C2semidirect
9. C89×#1870C2semidirect
10. C89×#1869C2semidirect
11. C89×#1869C2semidirect
12. C89×#1851C2semidirect
13. C89×#1850C2semidirect
14. C89×#1818C2semidirect
15. C89×#1798C2semidirect
354. #23335C89direct (N × H)
366. #1955C2×C89semidirect
367. #1955C2×C89semidirect
368. #1924C2×C89semidirect
369. #1924C2×C89semidirect
370. #1917C2×C89semidirect
371. #1917C2×C89semidirect
372. #1870C2×C89semidirect
373. #1870C2×C89semidirect
374. #1869C2×C89semidirect
375. #1869C2×C89semidirect
376. #1851C2×C89semidirect
377. #1850C2×C89semidirect
378. #1818C2×C89semidirect
379. #1798C2×C89semidirect
380. C89#23335direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#23922
C89×#19552
C89×#19242
C89×#19172
C89×#18702
C89×#18692
C89×#18512
C89×#18502
C89×#18182
C89×#17982
#2333589