Finite Group Databasebeta

← C2×#21456669 #30550664

Subgroups — C2×#21456669 #30550664

Order 15616.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840341C211yesmaximal, characteristic, complemented
2C2×#16840331C211yesmaximal, characteristic, complemented
3#21456669C2116yesmaximal, direct product factor
4C2×#16840082C211yesmaximal, characteristic, complemented
5C2×#16840103C211yesmaximal, characteristic, complemented
6C2×#16840077C211yesmaximal, characteristic, complemented
7C2×#16840014C211yesmaximal, characteristic, complemented
8C2×#16840009C211yesmaximal, characteristic, complemented
9C2×#16839997C211yesmaximal, characteristic, complemented
10C2×#16839992C211yesmaximal, characteristic, complemented
11C2×#16839908C211yesmaximal, characteristic, complemented
12C2×#16839908C211yesmaximal, characteristic, complemented
13C2×#16839915C211yesmaximal, characteristic, complemented
14C2×#16839895C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#482C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224C2211yescharacteristic, complemented
19C23×D244C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758190C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758189C2211yescharacteristic, complemented
25C22×C8×D61C2211yescharacteristic, complemented
26#16840341—24no—
27#16840341C2218yescomplemented
28#16840331—24no—
29#16840331C2218yescomplemented
30C2×#14519774—21no—
31C2×#14519765—21no—
32C2×#14519757C2211yescharacteristic, complemented
33C2×#14519756C2211yescharacteristic
34C2×#14519754—21no—
35C2×#14519752C2211yescharacteristic
36C2×#14519752C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×#14519752C2211yescharacteristic
39C2×#14519750—21no—
40C2×#14519749—21no—
41C2×#14519748—21no—
42C2×#14519748C2211yescharacteristic, complemented
43C2×#14519747—21no—
44C2×#14519747—21no—
45C2×C4⋊C4×D61C2211yescharacteristic, complemented
46#16840103C2218yescomplemented
47#16840082C2218yescomplemented
48#16840077C2218yescomplemented
49#16840014C2218yescomplemented
50#16840009C2218yescomplemented
51#16839997C2218yescomplemented
52#16839992C2218yescomplemented
53#16839915C2218yescomplemented
54#16839908C2218yescomplemented
55#16839908C2218yescomplemented
56#16839895C2218yescomplemented
57C2×#14519710C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519700C2211yescharacteristic, complemented
60C2×#14519700C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic, complemented
69C2×#121×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#482C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic
77C24×D61—21no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222D414yes—
81C2×#11758222C2314yes—
82C2×#11758224—22no—
83C2×#11758224—42no—
84C2×#11758224—42no—
85C2×#11758224C2314yescomplemented
86C22×Dic122D411yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×D244—21no—
89C22×D244—22no—
90C22×D244—21no—
91C22×D244—21no—
92C22×D244—21no—
93C22×D244—21no—
94C22×D244—42no—
95C22×D244—42no—
96C22×D244D411yescharacteristic
97C22×D244C2311yescharacteristic
98C22×D244C2311yescharacteristic
99C22×D244C2314yes—
100C22×C22⋊D61—21no—
101C22×C22⋊D61—21no—
102C22×C22⋊D61D411yescharacteristic
103C22×C22⋊D61D411yescharacteristic
104C23×Dic61—21no—
105C22×C4×D61—21no—
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C2×#11758190—42no—
109C2×#11758190—42no—
110C2×#11758190C2314yes—
111C2×#11758190C2314yes—
112C2×#11758199—42no—
113C2×#11758199—42no—
114C2×#11758199C2314yes—
115C2×#11758199C2314yes—
116C2×#11758189—42no—
117C2×#11758189C2314yescomplemented
118C22×#92418C2311yescharacteristic
119C22×#92418C2311yescharacteristic
120C2×C8×D61—42no—
121C2×C8×D61C2314yescomplemented
122#14519774—28no—
123#14519765—28no—
124#14519757—22no—
125#14519757C2314yescomplemented
126#14519756—22no—
127#14519756C2314yes—
128#14519754—28no—
129#14519752—22no—
130#14519752—22no—
131#14519752—22no—
132#14519752—22no—
133#14519752C2314yes—
134#14519752C2314yes—
135#14519752C2314yes—
136#14519752C2314yes—
137#14519750—28no—
138#14519749—28no—
139#14519748—28no—
140#14519748—22no—
141#14519748C2314yescomplemented
142#14519747—28no—
143#14519747—28no—
144C2×C4⋊Dic61—21no—
145C2×C4⋊Dic61C2311yescharacteristic
146C2×#11758196—21no—
147C2×#11758196—21no—
148C4⋊C4×D61—22no—
149C4⋊C4×D61C2314yescomplemented
150C2×C22⋊Dic61—21no—
151C2×C22⋊Dic61—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198—21no—
157#14519710C2314yescomplemented
158#14519708C2314yescomplemented
159#14519700C2314yescomplemented
160#14519700C2314yescomplemented
161#14519699C2314yes—
162#14519699C2314yes—
163#14519697C2314yes—
164#14519697C2314yes—
165C22⋊#92418C2314yes—
166#14519689C2314yescomplemented
167#14519689C2314yescomplemented
168C22×D4×C61—21no—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173#121×C61—22no—
174#121×C61C2314yes—
175#117×C61—22no—
176#117×C61C2314yes—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C42×C61—21no—
183#107×C61C2314yescomplemented
184#106×C61C2314yescomplemented
185#102×C61C2314yescomplemented
186#102×C61C2314yescomplemented
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—24no—
193C23×D61—44no—
194C23×D61—82no—
195C23×D61—82no—
196C23×D61C2×D411yescharacteristic
197C23×D61C2×D411yescharacteristic
198C2×D4×C61—24no—
199C2×D4×C61—21no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—82no—
203C2×D4×C61C2412yes—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—24no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—42no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—44no—
218C2×C22⋊D61—82no—
219C2×C22⋊D61C2×D414yes—
220C2×C22⋊D61C2×D414yes—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—24no—
224C22×Dic61—44no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227#11758224—44no—
228#11758224—44no—
229#11758224—48no—
230#11758222—48no—
231#11758222—44no—
232#11758222—44no—
233C2×D244—22no—
234C2×D244—22no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—24no—
240C2×D244—24no—
241C2×D244—24no—
242C2×D244—24no—
243C2×D244—24no—
244C2×D244—44no—
245C2×D244—44no—
246C2×D244—42no—
247C2×D244—44no—
248C2×D244—48no—
249C2×D244—82no—
250C2×D244—82no—
251C2×D244—82no—
252C2×D244—82no—
253C2×D244C2×D414yes—
254C2×D244C2412yes—
255C2×D244C2412yes—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—24no—
261C2×C4×D61—82no—
262C2×C4×D61C2×D412yes—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—21no—
269C2×Dic122—42no—
270C2×Dic122C2×D414yes—
271C2×Dic122C2412yes—
272C2×C8×C61—22no—
273C2×C8×C61—22no—
274C2×C8×C61C2412yes—
275C2×C8×C61C2412yes—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2412yes—
280C4⋊C4×C61C2412yes—
281C4⋊C4×C61C2412yes—
282C22⋊C4×C61—24no—
283C22⋊C4×C61—24no—
284C42×C61—24no—
285C22⋊Dic61—24no—
286C22⋊Dic61—24no—
287#11758199—44no—
288#11758199—44no—
289#11758198—24no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294C4⋊Dic61—21no—
295C4⋊Dic61—24no—
296C4⋊Dic61C2412yes—
297#11758196—24no—
298#11758196—24no—
299C2×#92418—22no—
300C2×#92418—22no—
301C2×#92418C2412yes—
302C2×#92418C2412yes—
303#11758190—44no—
304#11758190—44no—
305#11758189—44no—
306C8×D61—44no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61C22×D412yes—
315C23×C61C22×D411yescharacteristic
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—48no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—84no—
332C22×D61—84no—
333C22×D61—816no—
334C22×D61C22×D412yes—
335C22×D61C22×D412yes—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—42no—
339D4×C61—84no—
340C2×C4×C61—22no—
341C2×C4×C61—24no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61C22×D412yes—
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61H(5,𝔽2)12yes—
353C2×C4×C61H(5,𝔽2)12yes—
354C2×C4×C61C2511yescharacteristic
355C22⋊D61—44no—
356C22⋊D61—44no—
357C22⋊D61—48no—
358C22⋊D61—84no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—48no—
364C2×Dic61—42no—
365C2×Dic61—42no—
366C2×Dic61C22×D412yes—
367C2×Dic61C22×D412yes—
368D244—22no—
369D244—22no—
370D244—22no—
371D244—22no—
372D244—44no—
373D244—48no—
374D244—42no—
375D244—42no—
376D244—84no—
377D244—84no—
378D244—84no—
379D244—84no—
380C4×D61—24no—
381C4×D61—24no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—84no—
387Dic122—22no—
388Dic122—22no—
389Dic122—44no—
390Dic122—42no—
391C8×C61—22no—
392C8×C61—22no—
393#92418—22no—
394#92418—22no—
395C2×#3198—611nomaximal, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—44no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—84no—
404C22×C61#53412yes—
405C22×C61#57612yes—
406C22×C61#57712yes—
407C22×C61C23×D411yescharacteristic
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—44no—
415C2×D61—44no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—816no—
423C2×D61—84no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61—42no—
429C4×C61#53412yes—
430C4×C61C2×H(5,𝔽2)11yescharacteristic
431C4×C61C2×H(5,𝔽2)11yescharacteristic
432Dic61—22no—
433Dic61—22no—
434Dic61—42no—
435Dic61—42no—
436C2×#537—611no—
437C2×#535—611no—
438#3198—6116no—
439C2×#481—611no—
440C2×#485—611no—
441C2×#482D6111yescharacteristic, complemented
442C2×#480—611no—
443C2×#469—611no—
444C2×#468—611no—
445C2×#466—611no—
446C2×#465—611no—
447C2×#449—611no—
448C2×#449—611no—
449C2×#450—611no—
450C2×#447—611no—
451C2×#408—611no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61#319814yescomplemented
455C2×C61C2×#53411yescharacteristic
456C2×C61C2×#57611yescharacteristic
457C2×C61C2×#57711yescharacteristic
458D61—42no—
459D61—42no—
460D61—82no—
461D61—82no—
462C22×#41—611no—
463C22×#41—611no—
464C23×D4—611no—
465C22×SD16—611no—
466C22×SD16—611no—
467C22×D8—611no—
468C22×D8—611no—
469C22×M16—611no—
470C23×C8—611no—
471#537—618no—
472#537—1224no—
473#535—618no—
474#535—1224no—
475C2×#127—1221no—
476C2×#124—1221no—
477C2×C22⋊Q8—611no—
478C2×C22⋊Q8—611no—
479C2×C22⋊Q8—1221no—
480C2×#121—611no—
481C2×#121—611no—
482C2×#121—611no—
483C2×#121—611no—
484C2×#121—611no—
485C2×#121—1221no—
486C2×#121—1221no—
487C2×#121—1221no—
488C2×#121C2×D6111yescharacteristic
489C2×#120—1221no—
490C2×#120—1221no—
491C2×#117C2×D6111yescharacteristic
492C22×C4⋊C4—611no—
493#485—618no—
494#482C2×D6118yescomplemented
495#481—618no—
496#480—618no—
497#469—618no—
498#468—618no—
499#466—618no—
500#465—618no—
501#450—618no—
502#449—618no—
503#449—618no—
504#447—618no—
505C2×#107—611no—
506C2×#107C2×D6111yescharacteristic, complemented
507C2×#106—611no—
508C2×#106C2×D6111yescharacteristic, complemented
509C2×#103—611no—
510C2×#103—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102C2×D6111yescharacteristic, complemented
516C2×#102C2×D6111yescharacteristic, complemented
517#408—618no—
518C2×C22⋊C8—611no—
519C2×C22⋊C8—611no—
520C2×C22⋊C8—611no—
521C2×C22⋊C8C2×D6111yescharacteristic
522C61C2×#319811yescharacteristic, complemented, Sylow
523C25—1221no—
524C2×#41—614no—
525C2×#41—614no—
526C2×#41—614no—
527C2×#41—1222no—
528C2×#41—2442no—
529C2×#41—2442no—
530C2×#41—2442no—
531C2×#41—2442no—
532C22×Q8—611no—
533C22×Q8—611no—
534C22×D4—21no—
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—611no—
538C22×D4—611no—
539C22×D4—611no—
540C22×D4—614no—
541C22×D4—1221no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1221no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4—1222no—
549C22×D4—2442no—
550C22×D4—2442no—
551C22×D4C22×D6111yescharacteristic
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C2×SD16—614no—
558C2×SD16—614no—
559C2×SD16—2442no—
560C2×SD16—2442no—
561C2×D8—614no—
562C2×D8—614no—
563C2×D8—2442no—
564C2×D8—2442no—
565C2×M16—614no—
566C2×M16—2442no—
567C22×C8—611no—
568C22×C8—611no—
569C22×C8—614no—
570C22×C8—2442no—
571C22×C8C22×D6111yescharacteristic
572C22×C8C22×D6111yescharacteristic
573#127—1228no—
574#124—1228no—
575C22⋊Q8—614no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8—1222no—
580#121—22no—
581#121—614no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1228no—
587#121—1222no—
588#121—1222no—
589#121—1222no—
590#121—1222no—
591#121—1222no—
592#121—1228no—
593#121—1228no—
594#121C22×D6114yes—
595#120—1228no—
596#120—1228no—
597#117—22no—
598#117C22×D6114yes—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—614no—
601C2×C4⋊C4—1222no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4C22×D6111yescharacteristic
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C42—21no—
618#107—614no—
619#107C22×D6114yescomplemented
620#106—614no—
621#106C22×D6114yescomplemented
622#103—614no—
623#103—614no—
624#102—614no—
625#102—614no—
626#102—614no—
627#102—614no—
628#102C22×D6114yescomplemented
629#102C22×D6114yescomplemented
630C22⋊C8—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633C22⋊C8C22×D6114yes—
634C24—21no—
635C24—611no—
636C24—611no—
637C24—1224no—
638C24—1221no—
639C24—1221no—
640C24—4882no—
641C24—4882no—
642C24—2444no—
643C24D4×D6111yescharacteristic
644#41—2448no—
645#41—2444no—
646#41—2444no—
647#41—2444no—
648#41—2444no—
649#41—2448no—
650C2×Q8—614no—
651C2×Q8—612no—
652C2×Q8—1221no—
653C2×Q8—1222no—
654C2×Q8—1222no—
655C2×Q8—2442no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—614no—
662C2×D4—614no—
663C2×D4—614no—
664C2×D4—612no—
665C2×D4—612no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1224no—
671C2×D4—1224no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1224no—
675C2×D4—1222no—
676C2×D4—1222no—
677C2×D4—1222no—
678C2×D4—1222no—
679C2×D4—4882no—
680C2×D4—4882no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—4882no—
684C2×D4—2444no—
685C2×D4—2444no—
686C2×D4—2442no—
687C2×D4—2444no—
688C2×D4—2448no—
689C2×D4—2442no—
690C2×D4—2442no—
691C2×D4—2444no—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—1224no—
705C22×C4—1224no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—4882no—
713C22×C4—2444no—
714C22×C4D4×D6112yes—
715C22×C4D4×D6111yescharacteristic
716C22×C4C23×D6112yes—
717C22×C4C23×D6111yescharacteristic
718SD16—2444no—
719SD16—2444no—
720D8—2444no—
721D8—2444no—
722M16—2444no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—612no—
726C2×C8—612no—
727C2×C8—1222no—
728C2×C8—1222no—
729C2×C8—2444no—
730C2×C8C23×D6112yes—
731C2×C8C23×D6112yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—612no—
736C4⋊C4—1224no—
737C4⋊C4—1224no—
738C4⋊C4—1221no—
739C4⋊C4—1224no—
740C4⋊C4C23×D6112yes—
741C4⋊C4C23×D6112yes—
742C4⋊C4C23×D6112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—1224no—
746C22⋊C4—1224no—
747C22⋊C4—1224no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C42—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—612no—
761C23—612no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1222no—
766C23—1222no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—4884no—
771C23—4884no—
772C23—48816no—
773C23—2448no—
774C23—2442no—
775C23—2442no—
776C23—2442no—
777C23—2442no—
778C23—2442no—
779C23—2442no—
780C23C2×D4×D6112yes—
781C23C2×D4×D6111yescharacteristic
782Q8—1222no—
783Q8—1222no—
784Q8—2444no—
785Q8—2442no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—1222no—
791D4—1222no—
792D4—1222no—
793D4—1222no—
794D4—4884no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—2444no—
800D4—2448no—
801D4—2444no—
802D4—2444no—
803D4—2448no—
804D4—2442no—
805D4—2442no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—612no—
817C2×C4—612no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1224no—
821C2×C4—1224no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—4884no—
829C2×C4—2448no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4C2×D4×D6112yes—
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4#1451982312yes—
835C2×C4#1451982312yes—
836C2×C4C24×D6111yescharacteristic
837C8—22no—
838C8—22no—
839C8—1222no—
840C8—1222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—1222no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—48816no—
856C22—4884no—
857C22—4884no—
858C22—2442no—
859C22—2442no—
860C22—2442no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2444no—
865C22—2444no—
866C22#1684032312yes—
867C22#1684056612yes—
868C22#1684056912yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1222no—
875C4—1222no—
876C4—2442no—
877C4—2442no—
878C4#1684032312yes—
879C4C2×#1451982311yescharacteristic
880C4C2×#1451982311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4882no—
884C2—4882no—
885C2—2442no—
886C2—2442no—
887C2#2145666914yesdirect product factor
888C2C2×#1684032311yescharacteristic
889C2C2×#1684056611yescharacteristic
890C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#482C2
socleC23×C61C22×D4
hypercenterC2×#482D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16840341C2semidirect
2. C2×#16840331C2semidirect
3. #21456669C2direct (N × H)
4. C2×#16840082C2semidirect
5. C2×#16840103C2semidirect
6. C2×#16840077C2semidirect
7. C2×#16840014C2semidirect
8. C2×#16840009C2semidirect
9. C2×#16839997C2semidirect
10. C2×#16839992C2semidirect
11. C2×#16839908C2semidirect
12. C2×#16839908C2semidirect
13. C2×#16839915C2semidirect
14. C2×#16839895C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#482C2semidirect
18. C22×#11758224C22semidirect
24. C22×#11758189C22semidirect
25. C22×C8×D61C22semidirect
27. #16840341C22semidirect
29. #16840331C22semidirect
32. C2×#14519757C22semidirect
42. C2×#14519748C22semidirect
45. C2×C4⋊C4×D61C22semidirect
46. #16840103C22semidirect
47. #16840082C22semidirect
48. #16840077C22semidirect
49. #16840014C22semidirect
50. #16840009C22semidirect
51. #16839997C22semidirect
52. #16839992C22semidirect
53. #16839915C22semidirect
54. #16839908C22semidirect
55. #16839908C22semidirect
56. #16839895C22semidirect
57. C2×#14519710C22semidirect
58. C2×#14519708C22semidirect
59. C2×#14519700C22semidirect
60. C2×#14519700C22semidirect
65. #16839727C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
71. C61×#482C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×#102×C61C22semidirect
75. C2×#102×C61C22semidirect
85. C2×#11758224C23semidirect
117. C2×#11758189C23semidirect
121. C2×C8×D61C23semidirect
125. #14519757C23semidirect
141. #14519748C23semidirect
149. C4⋊C4×D61C23semidirect
157. #14519710C23semidirect
158. #14519708C23semidirect
159. #14519700C23semidirect
160. #14519700C23semidirect
166. #14519689C23semidirect
167. #14519689C23semidirect
183. #107×C61C23semidirect
184. #106×C61C23semidirect
185. #102×C61C23semidirect
186. #102×C61C23semidirect
441. C2×#482D61semidirect
454. C2×C61#3198semidirect
494. #482C2×D61semidirect
506. C2×#107C2×D61semidirect
508. C2×#106C2×D61semidirect
515. C2×#102C2×D61semidirect
516. C2×#102C2×D61semidirect
522. C61C2×#3198semidirect
619. #107C22×D61semidirect
621. #106C22×D61semidirect
628. #102C22×D61semidirect
629. #102C22×D61semidirect
887. C2#21456669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403412
C2×#168403312
#214566692
C2×#168400822
C2×#168401032
C2×#168400772
C2×#168400142
C2×#168400092
C2×#168399972
C2×#168399922
C2×#168399082
C2×#168399152
C2×#168398952
C2×#168397272
C2×C61×#4822
C2×#319861