Finite Group Databasebeta

← #30609334

Subgroups — #30609334

Order 15616.

1202 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840713C211yesmaximal, characteristic
2C2×#16840706C211yesmaximal, characteristic
3#21461006C211yesmaximal, characteristic
4#21461005C211yesmaximal, characteristic
5#21461005C211yesmaximal, characteristic
6#21461005C211yesmaximal, characteristic
7#21461004C211yesmaximal, characteristic
8#21461004C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic
11#21460998C211yesmaximal, characteristic
12#21460995C211yesmaximal, characteristic
13#21460994C211yesmaximal, characteristic
14#21460994C211yesmaximal, characteristic
15#387×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22#16840713—24no—
23#16840706—24no—
24C2×(C2×#6923)⋊C4C2211yescharacteristic
25C2×(C2×#6923)⋊C4C2211yescharacteristic
26C2×(C2×#6923)⋊C4C2211yescharacteristic
27C2×(C2×#6923)⋊C4C2211yescharacteristic
28C2×(C2×#6923)⋊C4C2211yescharacteristic
29C2×(C2×#6923)⋊C4C2211yescharacteristic
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839649C411yescharacteristic, complemented
50#16839648C411yescharacteristic, complemented
51#16839647C411yescharacteristic, complemented
52#16839646C411yescharacteristic, complemented
53#16839645C411yescharacteristic, complemented
54#16839644C411yescharacteristic, complemented
55#16839643C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#387C411yescharacteristic, complemented
61C23×#6923C2311yescharacteristic
62C23×#6923C2311yescharacteristic
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C2×C4⋊#6923—22no—
70C2×C4⋊#6923—22no—
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923—22no—
73C2×C4⋊#6923—41no—
74C2×C4⋊#6923—41no—
75C2×C4⋊#6923—41no—
76C2×C4⋊#6923—41no—
77C2×C4⋊#6923—41no—
78C2×C4⋊#6923—41no—
79C2×C4⋊#6923—41no—
80C2×C4⋊#6923D414yes—
81C2×C4×#6923—22no—
82C2×C4×#6923—22no—
83C2×C4×#6923—22no—
84C2×C4×#6923—41no—
85C2×C4×#6923—41no—
86C2×C4×#6923—41no—
87(C2×#6923)⋊C4—22no—
88(C2×#6923)⋊C4—22no—
89(C2×#6923)⋊C4—22no—
90(C2×#6923)⋊C4—22no—
91(C2×#6923)⋊C4—22no—
92(C2×#6923)⋊C4—22no—
93(C2×#6923)⋊C4—22no—
94(C2×#6923)⋊C4—22no—
95(C2×#6923)⋊C4—22no—
96(C2×#6923)⋊C4—22no—
97(C2×#6923)⋊C4—22no—
98(C2×#6923)⋊C4—22no—
99(C2×#6923)⋊C4—22no—
100(C2×#6923)⋊C4—22no—
101(C2×#6923)⋊C4—41no—
102(C2×#6923)⋊C4—41no—
103(C2×#6923)⋊C4—41no—
104(C2×#6923)⋊C4—41no—
105(C2×#6923)⋊C4—41no—
106(C2×#6923)⋊C4—41no—
107(C2×#6923)⋊C4—41no—
108(C2×#6923)⋊C4—41no—
109C22×C4×D61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×C4⋊Dic61C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C4⋊C4×D61—22no—
123C4⋊C4×D61—22no—
124C4⋊C4×D61—22no—
125C4⋊C4×D61—22no—
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2×C411yescharacteristic
129C42×D61—22no—
130C42×D61—22no—
131#14519684C2×C411yescharacteristic
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137#14519684C2×C411yescharacteristic
138#14519684C2×C411yescharacteristic
139#14519684C2×C411yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143C2×C4⋊C4×C61C2×C411yescharacteristic
144C2×C4⋊C4×C61C2×C411yescharacteristic
145C2×C42×C61C2×C411yescharacteristic
146#95×C61C2×C411yescharacteristic
147#95×C61C2×C411yescharacteristic
148#95×C61C2×C411yescharacteristic
149#95×C61C2×C411yescharacteristic
150C23×D61C2411yescharacteristic
151C22×#6923—21no—
152C22×#6923—21no—
153C22×#6923—21no—
154C22×#6923—21no—
155C22×#6923—21no—
156C22×#6923—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—21no—
183C22×#6923—21no—
184C22×#6923—21no—
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—21no—
201C22×#6923—21no—
202C22×#6923—21no—
203C22×#6923C2×D412yes—
204C22×#6923C2×D412yes—
205C22×#6923#4112yes—
206C22×#6923#4112yes—
207C22×C4×C61C22×C411yescharacteristic
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61C2×D412yes—
260C2×C4×D61#4112yes—
261C2×C4×D61#4112yes—
262C2×C4×D61#4112yes—
263C4⋊#6923—44no—
264C4⋊#6923—44no—
265C4⋊#6923—44no—
266C4⋊#6923—44no—
267C4×#6923—44no—
268C4×#6923—44no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61—22no—
271C42×C61—22no—
272C4⋊Dic61—22no—
273C4⋊Dic61—22no—
274#11758196—22no—
275#11758196—22no—
276#11758196—22no—
277#11758196—22no—
278C4×Dic61—22no—
279C4×Dic61—22no—
280C4×Dic61—22no—
281C23×C61C23×C411yescharacteristic
282C22×D61C22×D411yescharacteristic
283C22×D61C2×#4111yescharacteristic
284C22×D61C2×#4111yescharacteristic
285C22×D61C2×#4111yescharacteristic
286C22×D61C2×#4111yescharacteristic
287C22×D61C2×#4111yescharacteristic
288C22×D61H(5,𝔽2)11yescharacteristic
289C22×D61H(5,𝔽2)11yescharacteristic
290C22×D61H(5,𝔽2)11yescharacteristic
291C22×D612−1+411yescharacteristic
292C22×D612−1+411yescharacteristic
293C22×D612−1+411yescharacteristic
294C22×D612−1+411yescharacteristic
295C22×D612−1+411yescharacteristic
296C2×#6923—22no—
297C2×#6923—22no—
298C2×#6923—22no—
299C2×#6923—22no—
300C2×#6923—22no—
301C2×#6923—22no—
302C2×#6923—22no—
303C2×#6923—22no—
304C2×#6923—22no—
305C2×#6923—22no—
306C2×#6923—22no—
307C2×#6923—22no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61#11712yes—
372C2×C4×C61C4×D412yes—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61#11712yes—
393C2×Dic61C4×D412yes—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422#14394—611nomaximal, Sylow
423C22×C61C2×#11711yescharacteristic
424C22×C61C2×C4×D411yescharacteristic
425C22×C61C4×#4111yescharacteristic
426C22×C61#51911yescharacteristic
427C22×C61#52011yescharacteristic
428C22×C61#52011yescharacteristic
429C22×C61#52011yescharacteristic
430C2×D61#53411yescharacteristic
431C2×D61#53611yescharacteristic
432C2×D61#53811yescharacteristic
433C2×D61#53911yescharacteristic
434C2×D61#53911yescharacteristic
435C2×D61#53911yescharacteristic
436C2×D61#54111yescharacteristic
437C2×D61#54111yescharacteristic
438C2×D61#54111yescharacteristic
439C2×D61#54211yescharacteristic
440C2×D61#54211yescharacteristic
441C2×D61#54211yescharacteristic
442C2×D61#54611yescharacteristic
443C2×D61#54711yescharacteristic
444C2×D61#54811yescharacteristic
445C2×D61#54811yescharacteristic
446C2×D61#55211yescharacteristic
447C2×D61#55211yescharacteristic
448C2×D61#55211yescharacteristic
449C2×D61#55211yescharacteristic
450C2×D61#55311yescharacteristic
451C2×D61#55511yescharacteristic
452C2×D61#55511yescharacteristic
453C2×D61#55611yescharacteristic
454C2×D61#56211yescharacteristic
455C2×D61#56311yescharacteristic
456C2×D61#56311yescharacteristic
457C2×D61#56411yescharacteristic
458#6923—42no—
459#6923—42no—
460#6923—42no—
461#6923—42no—
462#6923—81no—
463#6923—81no—
464#6923—81no—
465#6923—81no—
466C4×C61—22no—
467C4×C61—22no—
468C4×C61—41no—
469C4×C61—41no—
470C4×C61—41no—
471C4×C61—41no—
472C4×C61—41no—
473Dic61—22no—
474Dic61—22no—
475Dic61—41no—
476Dic61—41no—
477Dic61—41no—
478Dic61—41no—
479Dic61—41no—
480C2×#389—611no—
481C2×#387—611no—
482C2×#382—611no—
483#1443—611no—
484#1442—611no—
485#1442—611no—
486#1442—611no—
487#1441—611no—
488#1441—611no—
489#1436—611no—
490#1436—611no—
491#1436—611no—
492#1434—611no—
493#1434—611no—
494#1434—611no—
495C2×C61#232011yescharacteristic
496C2×C61#232211yescharacteristic
497C2×C61#233411yescharacteristic
498C2×C61#234611yescharacteristic
499C2×C61#235211yescharacteristic
500C2×C61#236211yescharacteristic
501C2×C61#238211yescharacteristic
502D61#268611yescharacteristic
503D61#269011yescharacteristic
504D61#271911yescharacteristic
505D61#273111yescharacteristic
506D61#276511yescharacteristic
507D61#276711yescharacteristic
508D61#276911yescharacteristic
509D61#278311yescharacteristic
510C22×C4⋊C4—611no—
511C22×C4⋊C4—611no—
512C22×C4⋊C4—611no—
513C22×C4⋊C4—611no—
514C22×C4⋊C4—611no—
515C22×C4⋊C4—611no—
516C22×C42—611no—
517C22×C42—611no—
518C22×C42—611no—
519#389—1224no—
520#387—611no—
521#387—611no—
522#387—611no—
523#387—611no—
524#387—611no—
525#387—611no—
526#387—611no—
527#387#692311yescharacteristic, complemented
528#382—1224no—
529C2×#95—611no—
530C2×#95—611no—
531C2×#95—611no—
532C2×#95—611no—
533C2×#95—611no—
534C2×#95—611no—
535C2×#95—611no—
536C2×#95—611no—
537C2×#95—611no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C61#1439411yescharacteristic, complemented, Sylow
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—611no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—614no—
578C2×C4⋊C4—1222no—
579C2×C4⋊C4—1222no—
580C2×C4⋊C4—1222no—
581C2×C4⋊C4—1222no—
582C2×C4⋊C4—1222no—
583C2×C4⋊C4—1222no—
584C2×C4⋊C4—1222no—
585C2×C4⋊C4—1222no—
586C2×C4⋊C4—2441no—
587C2×C4⋊C4—2441no—
588C2×C4⋊C4—2441no—
589C2×C4⋊C4—2441no—
590C2×C4⋊C4—2441no—
591C2×C4⋊C4—2441no—
592C2×C4⋊C4—2441no—
593C2×C4⋊C4C2×#692311yescharacteristic
594C2×C4⋊C4C2×#692311yescharacteristic
595C2×C42—611no—
596C2×C42—611no—
597C2×C42—611no—
598C2×C42—1222no—
599C2×C42—1222no—
600C2×C42—1222no—
601C2×C42—1222no—
602C2×C42—1222no—
603C2×C42—2441no—
604C2×C42—2441no—
605C2×C42—2441no—
606C2×C42C2×#692311yescharacteristic
607#95—611no—
608#95—611no—
609#95—611no—
610#95—611no—
611#95—611no—
612#95—611no—
613#95—611no—
614#95—611no—
615#95—611no—
616#95—611no—
617#95—611no—
618#95—611no—
619#95—1222no—
620#95—1222no—
621#95—1222no—
622#95—1222no—
623#95—1222no—
624#95—1222no—
625#95—1222no—
626#95—1222no—
627#95—1222no—
628#95—1222no—
629#95—1222no—
630#95—1222no—
631#95—1222no—
632#95—1222no—
633#95—2441no—
634#95—2441no—
635#95—2441no—
636#95—2441no—
637#95—2441no—
638#95—2441no—
639#95—2441no—
640#95—2441no—
641#95C2×#692311yescharacteristic
642#95C2×#692311yescharacteristic
643#95C2×#692311yescharacteristic
644#95C2×#692311yescharacteristic
645C24—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—612no—
655C22×C4—612no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4C22×#692311yescharacteristic
752C22×C4C22×#692311yescharacteristic
753C22×C4C22×#692311yescharacteristic
754C22×C4C22×#692311yescharacteristic
755C22×C4C22×#692311yescharacteristic
756C22×C4C22×#692311yescharacteristic
757C22×C4C22×#692311yescharacteristic
758C4⋊C4—22no—
759C4⋊C4—22no—
760C4⋊C4—1222no—
761C4⋊C4—1222no—
762C4⋊C4—1222no—
763C4⋊C4—1222no—
764C4⋊C4—1222no—
765C4⋊C4—1222no—
766C4⋊C4—2444no—
767C4⋊C4—2444no—
768C4⋊C4—2444no—
769C4⋊C4—2444no—
770C42—22no—
771C42—1222no—
772C42—1222no—
773C42—1222no—
774C42—2444no—
775C42—2444no—
776C23—611no—
777C23—611no—
778C23—611no—
779C23—611no—
780C23—611no—
781C23—611no—
782C23—611no—
783C23—611no—
784C23—611no—
785C23—611no—
786C23—611no—
787C23—611no—
788C23—611no—
789C23—611no—
790C23C23×#692311yescharacteristic
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—612no—
811C2×C4—612no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4#1451985612yes—
916C2×C4D4×#692312yes—
917C22—611no—
918C22—611no—
919C22—611no—
920C22—611no—
921C22—611no—
922C22—611no—
923C22—611no—
924C22—611no—
925C22—611no—
926C22—611no—
927C22—611no—
928C22—611no—
929C22—611no—
930C22—611no—
931C22—611no—
932C22—611no—
933C22—611no—
934C22—611no—
935C22—611no—
936C22—611no—
937C22—611no—
938C22—611no—
939C22—611no—
940C22—611no—
941C22—611no—
942C22—611no—
943C22—611no—
944C22—611no—
945C22C2×#1451985611yescharacteristic
946C22C2×D4×#692311yescharacteristic
947C22#41×#692311yescharacteristic
948C22#1684083011yescharacteristic
949C22#1684083111yescharacteristic
950C22#1684083111yescharacteristic
951C22#1684083111yescharacteristic
952C4—22no—
953C4—22no—
954C4—41no—
955C4—41no—
956C4—41no—
957C4—41no—
958C4—41no—
959C4—1222no—
960C4—1222no—
961C4—4881no—
962C4—4881no—
963C4—4881no—
964C4—4881no—
965C4—2442no—
966C4—2442no—
967C4—2442no—
968C4—2442no—
969C4—2441no—
970C4—2441no—
971C4—2441no—
972C4—2441no—
973C4—2441no—
974C2—611no—
975C2—611no—
976C2—611no—
977C2—611no—
978C2—611no—
979C2—611no—
980C2—611no—
981C2—611no—
982C2#2146230311yescharacteristic
983C2#2146230511yescharacteristic
984C2#2146231711yescharacteristic
985C2#2146232911yescharacteristic
986C2#2146233511yescharacteristic
987C2#2146234511yescharacteristic
988C2#2146236511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#14394
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
49. #16839649C4semidirect
50. #16839648C4semidirect
51. #16839647C4semidirect
52. #16839646C4semidirect
53. #16839645C4semidirect
54. #16839644C4semidirect
55. #16839643C4semidirect
60. C61×#387C4semidirect
527. #387#6923semidirect
555. C61#14394semidirect

Maximal subgroups

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

subgroupindex
C2×#168407132
C2×#168407062
#214610062
#214610052
#214610042
#214609992
#214609982
#214609952
#214609942
#387×D612
#1439461