Finite Group Databasebeta

← #30609318

Subgroups — #30609318

Order 15616.

1310 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C2×#6923)⋊Q8C211yesmaximal, characteristic
2C2×#16840706C211yesmaximal, characteristic
3#21461009C211yesmaximal, characteristic
4#21461007C211yesmaximal, characteristic
5#21461006C211yesmaximal, characteristic
6#21461005C211yesmaximal, characteristic
7#21461005C211yesmaximal, characteristic
8#21461004C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic
11#21460999C211yesmaximal, characteristic
12#21460998C211yesmaximal, characteristic
13#21460995C211yesmaximal, characteristic
14#21460994C211yesmaximal, characteristic
15#391×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22(C2×#6923)⋊Q8—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
46C22×Q8×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839669C411yescharacteristic, complemented
50#16839668C411yescharacteristic, complemented
51#16839667C411yescharacteristic, complemented
52#16839666C411yescharacteristic, complemented
53#16839666C411yescharacteristic, complemented
54#16839666C411yescharacteristic, complemented
55#16839666C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#391C411yescharacteristic, 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—22no—
74C2×C4⋊#6923—22no—
75C2×C4⋊#6923—41no—
76C2×C4⋊#6923—41no—
77C2×C4⋊#6923—41no—
78C2×C4⋊#6923—41no—
79C2×C4⋊#6923—41no—
80C2×C4⋊#6923—41no—
81C2×C4×#6923—22no—
82C2×C4×#6923—22no—
83C2×C4×#6923—41no—
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—41no—
98(C2×#6923)⋊C4—41no—
99(C2×#6923)⋊C4—41no—
100(C2×#6923)⋊C4—41no—
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)⋊C4D414yes—
108(C2×#6923)⋊C4Q814yescomplemented
109C22×Dic122C2×C411yescharacteristic
110C22×Dic122C2×C411yescharacteristic
111C22×Dic122C2×C411yescharacteristic
112C2×Q8×D61—22no—
113C2×Q8×D61—22no—
114C2×Q8×D61—22no—
115C2×Q8×D61—22no—
116C2×Q8×D61—41no—
117C2×Q8×D61—41no—
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C2×C4⋊Dic61C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C4⋊C4×D61—41no—
129C4⋊C4×D61—41no—
130C2×C4×Dic61C2×C411yescharacteristic
131C2×C4×Dic61C2×C411yescharacteristic
132C2×C4×Dic61C2×C411yescharacteristic
133C42×D61—22no—
134C42×D61—22no—
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137#14519684C2×C411yescharacteristic
138#14519684C2×C411yescharacteristic
139#14519684C2×C411yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143#14519684C2×C411yescharacteristic
144#14519684C2×C411yescharacteristic
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147C22×Q8×C61C2×C411yescharacteristic
148C2×C4⋊C4×C61C2×C411yescharacteristic
149C2×C42×C61C2×C411yescharacteristic
150#95×C61C2×C411yescharacteristic
151#95×C61C2×C411yescharacteristic
152#95×C61C2×C411yescharacteristic
153#95×C61C2×C411yescharacteristic
154C23×D61C2411yescharacteristic
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×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923C2×D412yes—
208C22×#6923C2×D412yes—
209C22×#6923C2×Q812yes—
210C22×#6923C2×Q812yes—
211C2×Q8×C61—22no—
212C2×Q8×C61—22no—
213C2×Q8×C61—41no—
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228Q8×D61—44no—
229Q8×D61—44no—
230Q8×D61—44no—
231Q8×D61—44no—
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×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61C2×D412yes—
269C2×C4×D61C2×Q812yes—
270C2×C4×D61#4112yes—
271C2×C4×D61#4112yes—
272C2×C4×D61#4112yes—
273C2×C4×D61#4112yes—
274C2×Dic122—22no—
275C2×Dic122—22no—
276C2×Dic122—22no—
277C2×Dic122—22no—
278C2×Dic122—22no—
279C2×Dic122—22no—
280C2×Dic122—41no—
281C2×Dic122—41no—
282C2×Dic122—41no—
283C4⋊#6923—44no—
284C4⋊#6923—44no—
285C4⋊#6923—44no—
286C4⋊#6923—44no—
287C4×#6923—44no—
288C4×#6923—44no—
289C4⋊C4×C61—41no—
290C42×C61—22no—
291C4⋊Dic61—41no—
292#11758196—41no—
293#11758196—41no—
294C4×Dic61—22no—
295C4×Dic61—22no—
296C4×Dic61—22no—
297C23×C61C23×C411yescharacteristic
298C22×D61C22×D411yescharacteristic
299C22×D61C22×Q811yescharacteristic
300C22×D61C2×#4111yescharacteristic
301C22×D61C2×#4111yescharacteristic
302C22×D61C2×#4111yescharacteristic
303C22×D61C2×#4111yescharacteristic
304C22×D61H(5,𝔽2)11yescharacteristic
305C22×D61H(5,𝔽2)11yescharacteristic
306C22×D61H(5,𝔽2)11yescharacteristic
307C22×D61H(5,𝔽2)11yescharacteristic
308C22×D612−1+411yescharacteristic
309C22×D612−1+411yescharacteristic
310C22×D612−1+411yescharacteristic
311C22×D612−1+411yescharacteristic
312C2×#6923—22no—
313C2×#6923—22no—
314C2×#6923—22no—
315C2×#6923—22no—
316C2×#6923—22no—
317C2×#6923—22no—
318C2×#6923—22no—
319C2×#6923—22no—
320C2×#6923—22no—
321C2×#6923—22no—
322C2×#6923—22no—
323C2×#6923—22no—
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×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366C2×#6923—41no—
367C2×#6923—41no—
368Q8×C61—44no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61#11712yes—
388C2×C4×C61C4×D412yes—
389C2×C4×C61C4×Q812yes—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61#11712yes—
409C2×Dic61C4×D412yes—
410C2×Dic61C4×Q812yes—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—41no—
438C4×D61—41no—
439Dic122—44no—
440Dic122—44no—
441Dic122—44no—
442#14378—611nomaximal, Sylow
443C22×C61C2×#11711yescharacteristic
444C22×C61C2×C4×D411yescharacteristic
445C22×C61C2×C4×Q811yescharacteristic
446C22×C61#51811yescharacteristic
447C22×C61#51911yescharacteristic
448C22×C61#52011yescharacteristic
449C22×C61#52011yescharacteristic
450C2×D61#53611yescharacteristic
451C2×D61#53711yescharacteristic
452C2×D61#54111yescharacteristic
453C2×D61#54111yescharacteristic
454C2×D61#54111yescharacteristic
455C2×D61#54211yescharacteristic
456C2×D61#54211yescharacteristic
457C2×D61#54211yescharacteristic
458C2×D61#54211yescharacteristic
459C2×D61#54211yescharacteristic
460C2×D61#54411yescharacteristic
461C2×D61#54411yescharacteristic
462C2×D61#54611yescharacteristic
463C2×D61#54611yescharacteristic
464C2×D61#54611yescharacteristic
465C2×D61D4×Q811yescharacteristic
466C2×D61#55111yescharacteristic
467C2×D61#55111yescharacteristic
468C2×D61#55211yescharacteristic
469C2×D61#55411yescharacteristic
470C2×D61#55411yescharacteristic
471C2×D61#55611yescharacteristic
472C2×D61#55711yescharacteristic
473C2×D61#55911yescharacteristic
474C2×D61H(3,𝔽4)11yescharacteristic
475C2×D61#56211yescharacteristic
476C2×D61#56211yescharacteristic
477C2×D61#56311yescharacteristic
478#6923—42no—
479#6923—42no—
480#6923—42no—
481#6923—42no—
482#6923—81no—
483#6923—81no—
484#6923—81no—
485#6923—81no—
486C4×C61—22no—
487C4×C61—22no—
488C4×C61—22no—
489C4×C61—41no—
490C4×C61—41no—
491C4×C61—41no—
492C4×C61—41no—
493Dic61—22no—
494Dic61—22no—
495Dic61—22no—
496Dic61—41no—
497Dic61—41no—
498Dic61—41no—
499Dic61—41no—
500C2×#391—611no—
501C2×#391—611no—
502C2×#382—611no—
503#1446—611no—
504#1444—611no—
505#1443—611no—
506#1442—611no—
507#1442—611no—
508#1441—611no—
509#1436—611no—
510#1436—611no—
511#1436—611no—
512#1436—611no—
513#1434—611no—
514#1434—611no—
515C2×C61#232011yescharacteristic
516C2×C61#232311yescharacteristic
517C2×C61#233111yescharacteristic
518C2×C61#234211yescharacteristic
519C2×C61#235511yescharacteristic
520C2×C61#236011yescharacteristic
521C2×C61#237911yescharacteristic
522D61#270011yescharacteristic
523D61#270411yescharacteristic
524D61#271211yescharacteristic
525D61#271311yescharacteristic
526D61#275411yescharacteristic
527D61#275511yescharacteristic
528D61#276211yescharacteristic
529D61#276311yescharacteristic
530C23×Q8—611no—
531C22×C4⋊C4—611no—
532C22×C4⋊C4—611no—
533C22×C4⋊C4—611no—
534C22×C4⋊C4—611no—
535C22×C4⋊C4—611no—
536C22×C42—611no—
537C22×C42—611no—
538C22×C42—611no—
539#391—611no—
540#391—611no—
541#391—611no—
542#391—611no—
543#391—611no—
544#391—611no—
545#391—611no—
546#391—1224no—
547#391#692311yescharacteristic, complemented
548#382—1224no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C2×#95—611no—
568C2×#95—611no—
569C2×#95—611no—
570C2×#95—611no—
571C2×#95—611no—
572C2×#95—611no—
573C2×#95—611no—
574C2×#95—611no—
575C61#1437811yescharacteristic, complemented, Sylow
576C22×Q8—611no—
577C22×Q8—611no—
578C22×Q8—611no—
579C22×Q8—1222no—
580C22×Q8—1222no—
581C22×Q8—1222no—
582C22×Q8—1222no—
583C22×Q8—2441no—
584C22×Q8—2441no—
585C22×Q8C2×#692311yescharacteristic
586C23×C4—611no—
587C23×C4—611no—
588C23×C4—611no—
589C23×C4—611no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—2441no—
611C2×C4⋊C4—2441no—
612C2×C4⋊C4—2441no—
613C2×C4⋊C4—2441no—
614C2×C4⋊C4—2441no—
615C2×C4⋊C4—2441no—
616C2×C4⋊C4—2441no—
617C2×C4⋊C4—2441no—
618C2×C4⋊C4C2×#692311yescharacteristic
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—611no—
622C2×C42—1222no—
623C2×C42—1222no—
624C2×C42—1222no—
625C2×C42—1222no—
626C2×C42—2441no—
627C2×C42—2441no—
628C2×C42—2441no—
629C2×C42—2441no—
630C2×C42C2×#692311yescharacteristic
631#95—614no—
632#95—614no—
633#95—611no—
634#95—611no—
635#95—611no—
636#95—611no—
637#95—611no—
638#95—611no—
639#95—611no—
640#95—611no—
641#95—611no—
642#95—611no—
643#95—611no—
644#95—611no—
645#95—1222no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95—1222no—
652#95—1222no—
653#95—1222no—
654#95—1222no—
655#95—2441no—
656#95—2441no—
657#95—2441no—
658#95—2441no—
659#95—2441no—
660#95—2441no—
661#95—2441no—
662#95—2441no—
663#95—2441no—
664#95—2441no—
665#95C2×#692311yescharacteristic
666#95C2×#692311yescharacteristic
667#95C2×#692311yescharacteristic
668#95C2×#692311yescharacteristic
669C24—611no—
670C2×Q8—22no—
671C2×Q8—22no—
672C2×Q8—41no—
673C2×Q8—1222no—
674C2×Q8—1222no—
675C2×Q8—1222no—
676C2×Q8—1222no—
677C2×Q8—1222no—
678C2×Q8—1222no—
679C2×Q8—2441no—
680C2×Q8—2441no—
681C2×Q8—2441no—
682C2×Q8—2444no—
683C2×Q8—2444no—
684C2×Q8—2444no—
685C2×Q8—2444no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—612no—
696C22×C4—612no—
697C22×C4—612no—
698C22×C4—612no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
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×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4C22×#692311yescharacteristic
792C22×C4C22×#692311yescharacteristic
793C22×C4C22×#692311yescharacteristic
794C22×C4C22×#692311yescharacteristic
795C22×C4C22×#692311yescharacteristic
796C22×C4C22×#692311yescharacteristic
797C22×C4C22×#692311yescharacteristic
798C4⋊C4—41no—
799C4⋊C4—2441no—
800C4⋊C4—2441no—
801C4⋊C4—2441no—
802C4⋊C4—2444no—
803C4⋊C4—2444no—
804C4⋊C4—2444no—
805C4⋊C4—2444no—
806C42—22no—
807C42—1222no—
808C42—1222no—
809C42—1222no—
810C42—2444no—
811C42—2444no—
812C23—611no—
813C23—611no—
814C23—611no—
815C23—611no—
816C23—611no—
817C23—611no—
818C23—611no—
819C23—611no—
820C23—611no—
821C23—611no—
822C23—611no—
823C23—611no—
824C23—611no—
825C23—611no—
826C23C23×#692311yescharacteristic
827Q8—44no—
828Q8—2444no—
829Q8—2444no—
830Q8—2444no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—612no—
850C2×C4—612no—
851C2×C4—612no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
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—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4—2441no—
953C2×C4—2441no—
954C2×C4#1451985612yes—
955C2×C4D4×#692312yes—
956C2×C4Q8×#692312yes—
957C22—611no—
958C22—611no—
959C22—611no—
960C22—611no—
961C22—611no—
962C22—611no—
963C22—611no—
964C22—611no—
965C22—611no—
966C22—611no—
967C22—611no—
968C22—611no—
969C22—611no—
970C22—611no—
971C22—611no—
972C22—611no—
973C22—611no—
974C22—611no—
975C22—611no—
976C22—611no—
977C22—611no—
978C22—611no—
979C22—611no—
980C22—611no—
981C22—611no—
982C22—611no—
983C22—611no—
984C22—611no—
985C22C2×#1451985611yescharacteristic
986C22C2×D4×#692311yescharacteristic
987C22C2×Q8×#692311yescharacteristic
988C22#1684082911yescharacteristic
989C22#1684083011yescharacteristic
990C22#1684083111yescharacteristic
991C22#1684083111yescharacteristic
992C4—22no—
993C4—22no—
994C4—22no—
995C4—41no—
996C4—41no—
997C4—41no—
998C4—41no—
999C4—1222no—
1000C4—1222no—
1001C4—1222no—
1002C4—4881no—
1003C4—4881no—
1004C4—4881no—
1005C4—4881no—
1006C4—2442no—
1007C4—2442no—
1008C4—2442no—
1009C4—2442no—
1010C4—2441no—
1011C4—2441no—
1012C4—2441no—
1013C4—2441no—
1014C2—611no—
1015C2—611no—
1016C2—611no—
1017C2—611no—
1018C2—611no—
1019C2—611no—
1020C2—611no—
1021C2—611no—
1022C2#2146230311yescharacteristic
1023C2#2146230611yescharacteristic
1024C2#2146231411yescharacteristic
1025C2#2146232511yescharacteristic
1026C2#2146233811yescharacteristic
1027C2#2146234311yescharacteristic
1028C2#2146236211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#391C4
prime radical, cosocleC23×D61C24
hypercenter#391#6923
hypocenterC61#14378
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
49. #16839669C4semidirect
50. #16839668C4semidirect
51. #16839667C4semidirect
52. #16839666C4semidirect
53. #16839666C4semidirect
54. #16839666C4semidirect
55. #16839666C4semidirect
60. C61×#391C4semidirect
108. (C2×#6923)⋊C4Q8semidirect
547. #391#6923semidirect
575. C61#14378semidirect

Maximal subgroups

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

subgroupindex
C2×(C2×#6923)⋊Q82
C2×#168407062
#214610092
#214610072
#214610062
#214610052
#214610042
#214609992
#214609982
#214609952
#214609942
#391×D612
#1437861