Finite Group Databasebeta

← C2×#21456677 #30550672

Subgroups — C2×#21456677 #30550672

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×#16840342C211yesmaximal, characteristic, complemented
2C2×#16840331C211yesmaximal, characteristic, complemented
3#21456677C2116yesmaximal, direct product factor
4C2×#16840082C211yesmaximal, characteristic, complemented
5C2×#16840086C211yesmaximal, characteristic, complemented
6C2×#16840077C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16840011C211yesmaximal, characteristic, complemented
9C2×#16839999C211yesmaximal, characteristic, complemented
10C2×#16839994C211yesmaximal, characteristic, complemented
11C2×#16839910C211yesmaximal, characteristic, complemented
12C2×#16839910C211yesmaximal, characteristic, complemented
13C2×#16839912C211yesmaximal, characteristic, complemented
14C2×#16839898C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#485C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic, complemented
18C22×#11758222C2211yescharacteristic
19C23×D244C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×D488C2211yescharacteristic
23C22×D488C2211yescharacteristic
24C22×#11758189C2211yescharacteristic, complemented
25C22×C8×D61C2211yescharacteristic, complemented
26#16840342—24no—
27#16840342C2218yescomplemented
28#16840331—24no—
29#16840331C2218yescomplemented
30C2×#14519774—21no—
31C2×#14519765—21no—
32C2×#14519755—21no—
33C2×#14519753C2211yescharacteristic, complemented
34C2×#14519752—21no—
35C2×#14519752C2211yescharacteristic
36C2×#14519752C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×#14519752C2211yescharacteristic
39C2×#14519752C2211yescharacteristic, complemented
40C2×#14519751C2211yescharacteristic
41C2×#14519750—21no—
42C2×#14519750—21no—
43C2×#14519747—21no—
44C2×#14519747—21no—
45C2×C4⋊C4×D61C2211yescharacteristic, complemented
46#16840086C2218yescomplemented
47#16840082C2218yescomplemented
48#16840077C2218yescomplemented
49#16840016C2218yescomplemented
50#16840011C2218yescomplemented
51#16839999C2218yescomplemented
52#16839994C2218yescomplemented
53#16839912C2218yescomplemented
54#16839910C2218yescomplemented
55#16839910C2218yescomplemented
56#16839898C2218yescomplemented
57C2×#14519710C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519699C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519697C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic, complemented
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic, complemented
69C2×C22⋊Q8×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#485C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic
77C24×D61—21no—
78C2×#11758226—22no—
79C2×#11758226—42no—
80C2×#11758226—42no—
81C2×#11758226C2314yescomplemented
82C2×#11758222—42no—
83C2×#11758222—42no—
84C2×#11758222D414yes—
85C2×#11758222C2314yes—
86C22×Dic122D411yescharacteristic
87C22×D244—21no—
88C22×D244—21no—
89C22×D244—22no—
90C22×D244—21no—
91C22×D244—21no—
92C22×D244—21no—
93C22×D244—21no—
94C22×D244—21no—
95C22×D244—42no—
96C22×D244—42no—
97C22×D244D411yescharacteristic
98C22×D244C2311yescharacteristic
99C22×D244C2311yescharacteristic
100C22×D244C2311yescharacteristic
101C22×D244C2314yes—
102C22×C22⋊D61—21no—
103C22×C22⋊D61D411yescharacteristic
104C22×C22⋊D61D411yescharacteristic
105C22×C4×D61—21no—
106C22×C4×D61—21no—
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109C2×#11758201—42no—
110C2×#11758201—42no—
111C2×#11758201C2314yes—
112C2×#11758201C2314yes—
113C2×D488—42no—
114C2×D488—42no—
115C2×D488C2314yes—
116C2×D488C2314yes—
117C2×#11758189—42no—
118C2×#11758189C2314yescomplemented
119C22×#92418C2311yescharacteristic
120C22×#92418C2311yescharacteristic
121C2×C8×D61—42no—
122C2×C8×D61C2314yescomplemented
123#14519774—28no—
124#14519765—28no—
125#14519755—28no—
126#14519753—22no—
127#14519753C2314yescomplemented
128#14519752—28no—
129#14519752—22no—
130#14519752—22no—
131#14519752—22no—
132#14519752—22no—
133#14519752—22no—
134#14519752C2314yes—
135#14519752C2314yes—
136#14519752C2314yes—
137#14519752C2314yes—
138#14519752C2314yescomplemented
139#14519751—22no—
140#14519751C2314yes—
141#14519750—28no—
142#14519750—28no—
143#14519747—28no—
144#14519747—28no—
145C2×C4⋊Dic61C2311yescharacteristic
146C2×#11758196—21no—
147C2×#11758196—21no—
148C4⋊C4×D61—22no—
149C4⋊C4×D61C2314yescomplemented
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198—21no—
157#14519710C2314yescomplemented
158#14519708C2314yescomplemented
159#14519699C2314yes—
160#14519699C2314yes—
161#14519697C2314yes—
162#14519697C2314yes—
163#14519697C2314yescomplemented
164#14519697C2314yescomplemented
165C22⋊#92418C2314yes—
166#14519689C2314yescomplemented
167#14519689C2314yescomplemented
168C22×Q8×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22⋊Q8×C61—22no—
173C22⋊Q8×C61C2314yes—
174#117×C61—22no—
175#117×C61C2314yes—
176C2×C4⋊C4×C61—21no—
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#103×C61C2314yescomplemented
186#103×C61C2314yescomplemented
187C22⋊C8×C61C2314yes—
188C24×C61C2×D411yescharacteristic
189C23×D61—21no—
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×Q8×C61—21no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61C2412yes—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D412yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—24no—
213C2×C22⋊D61—42no—
214C2×C22⋊D61—42no—
215C2×C22⋊D61—82no—
216C2×C22⋊D61C2×D414yes—
217C2×C22⋊D61C2×D414yes—
218C22×Dic61—21no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758226—44no—
222#11758226—44no—
223#11758226—48no—
224#11758222—48no—
225#11758222—44no—
226#11758222—44no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—24no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—24no—
237C2×D244—21no—
238C2×D244—24no—
239C2×D244—24no—
240C2×D244—24no—
241C2×D244—24no—
242C2×D244—24no—
243C2×D244—44no—
244C2×D244—44no—
245C2×D244—42no—
246C2×D244—44no—
247C2×D244—48no—
248C2×D244—44no—
249C2×D244—82no—
250C2×D244—82no—
251C2×D244—82no—
252C2×D244—82no—
253C2×D244—82no—
254C2×D244C2×D414yes—
255C2×D244C2412yes—
256C2×D244C2412yes—
257C2×D244C2412yes—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—44no—
265C2×C4×D61—82no—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2×D412yes—
268C2×C4×D61C2412yes—
269C2×C4×D61C2412yes—
270C2×Dic122—42no—
271C2×Dic122C2×D414yes—
272C2×C8×C61—22no—
273C2×C8×C61—22no—
274C2×C8×C61C2412yes—
275C2×C8×C61C2412yes—
276C4⋊C4×C61—24no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C2412yes—
281C4⋊C4×C61C2412yes—
282C4⋊C4×C61C2412yes—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—24no—
285C42×C61—24no—
286#11758201—44no—
287#11758201—44no—
288#11758198—24no—
289#11758198—24no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294#11758198—24no—
295C4⋊Dic61—21no—
296C4⋊Dic61C2412yes—
297#11758196—24no—
298#11758196—24no—
299C2×#92418—22no—
300C2×#92418—22no—
301C2×#92418C2412yes—
302C2×#92418C2412yes—
303D488—44no—
304D488—44no—
305#11758189—44no—
306C8×D61—44no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61C22×D412yes—
311C23×C61C22×D411yescharacteristic
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—48no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—42no—
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—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—42no—
339C2×C4×C61—22no—
340C2×C4×C61—24no—
341C2×C4×C61—22no—
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×C61—42no—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61H(5,𝔽2)12yes—
354C2×C4×C61H(5,𝔽2)12yes—
355C2×C4×C61C2511yescharacteristic
356C22⋊D61—44no—
357C22⋊D61—44no—
358C22⋊D61—84no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—42no—
363C2×Dic61C22×D412yes—
364C2×Dic61C22×D412yes—
365D244—22no—
366D244—22no—
367D244—22no—
368D244—22no—
369D244—22no—
370D244—22no—
371D244—44no—
372D244—48no—
373D244—48no—
374D244—42no—
375D244—42no—
376D244—42no—
377D244—84no—
378D244—84no—
379D244—84no—
380D244—84no—
381D244—84no—
382C4×D61—24no—
383C4×D61—24no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—22no—
387C4×D61—22no—
388C4×D61—48no—
389C4×D61—84no—
390Dic122—44no—
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#53412yes—
401C22×C61#57612yes—
402C22×C61#57712yes—
403C22×C61C23×D411yescharacteristic
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—44no—
411C2×D61—44no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—816no—
422C2×D61—84no—
423C2×D61—84no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61—42no—
429C4×C61—42no—
430C4×C61#53412yes—
431C4×C61C2×H(5,𝔽2)11yescharacteristic
432C4×C61C2×H(5,𝔽2)11yescharacteristic
433Dic61—22no—
434Dic61—22no—
435Dic61—42no—
436C2×#537—611no—
437C2×#535—611no—
438#3198—6116no—
439C2×#481—611no—
440C2×#485D6111yescharacteristic, complemented
441C2×#482—611no—
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#319814yescomplemented
454C2×C61C2×#53411yescharacteristic
455C2×C61C2×#57611yescharacteristic
456C2×C61C2×#57711yescharacteristic
457D61—42no—
458D61—42no—
459D61—82no—
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—1221no—
479C2×C22⋊Q8C2×D6111yescharacteristic
480C2×#121—611no—
481C2×#121—611no—
482C2×#121—611no—
483C2×#121—611no—
484C2×#121—611no—
485C2×#121—611no—
486C2×#121—1221no—
487C2×#121—1221no—
488C2×#121—1221no—
489C2×#120—1221no—
490C2×#120—1221no—
491C2×#117C2×D6111yescharacteristic
492C22×C4⋊C4—611no—
493#485C2×D6118yescomplemented
494#482—618no—
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×#103C2×D6111yescharacteristic, complemented
510C2×#103C2×D6111yescharacteristic, complemented
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102—611no—
516C2×#102—611no—
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×Q8C22×D6111yescharacteristic
534C22×D4—611no—
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—1221no—
549C22×D4—1222no—
550C22×D4—2442no—
551C22×D4—2442no—
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—22no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8C22×D6114yes—
580#121—614no—
581#121—614no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1228no—
587#121—1228no—
588#121—1222no—
589#121—1222no—
590#121—1222no—
591#121—1222no—
592#121—1222no—
593#121—1228no—
594#121—1222no—
595#120—1228no—
596#120—1228no—
597#117—22no—
598#117C22×D6114yes—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—614no—
602C2×C4⋊C4—1222no—
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#103C22×D6114yescomplemented
623#103C22×D6114yescomplemented
624#102—614no—
625#102—614no—
626#102—614no—
627#102—614no—
628#102—614no—
629#102—614no—
630C22⋊C8—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633C22⋊C8C22×D6114yes—
634C24—611no—
635C24—611no—
636C24—1224no—
637C24—1221no—
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—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—614no—
654C2×Q8—2442no—
655C2×Q8C23×D6112yes—
656C2×D4—614no—
657C2×D4—614no—
658C2×D4—614no—
659C2×D4—612no—
660C2×D4—612no—
661C2×D4—612no—
662C2×D4—1224no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1224no—
673C2×D4—1222no—
674C2×D4—1222no—
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—4882no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2442no—
688C2×D4—2444no—
689C2×D4—2448no—
690C2×D4—2444no—
691C2×D4—2442no—
692C2×D4—2442no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—1224no—
706C22×C4—1224no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1222no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—612no—
737C4⋊C4—1224no—
738C4⋊C4—1224no—
739C4⋊C4—1221no—
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—612no—
757C23—612no—
758C23—1222no—
759C23—1222no—
760C23—1222no—
761C23—1222no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1222no—
766C23—1222no—
767C23—4884no—
768C23—4884no—
769C23—48816no—
770C23—2448no—
771C23—2442no—
772C23—2442no—
773C23—2442no—
774C23—2442no—
775C23—2442no—
776C23—2442no—
777C23—2442no—
778C23—2442no—
779C23—2442no—
780C23C2×D4×D6112yes—
781C23C2×D4×D6111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—2444no—
786D4—1222no—
787D4—1222no—
788D4—1222no—
789D4—1222no—
790D4—1222no—
791D4—1222no—
792D4—4884no—
793D4—4884no—
794D4—4884no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—2444no—
799D4—2448no—
800D4—2448no—
801D4—2444no—
802D4—2444no—
803D4—2442no—
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—22no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—612no—
819C2×C4—612no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1224no—
823C2×C4—1224no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—4884no—
830C2×C4—2448no—
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—1222no—
846C22—1222no—
847C22—1222no—
848C22—1222no—
849C22—1222no—
850C22—1222no—
851C22—48816no—
852C22—4884no—
853C22—4884no—
854C22—4884no—
855C22—2442no—
856C22—2442no—
857C22—2442no—
858C22—2442no—
859C22—2442no—
860C22—2442no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2444no—
865C22—2444no—
866C22#1684032312yes—
867C22#1684056412yes—
868C22#1684057112yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—1222no—
876C4—1222no—
877C4—2442no—
878C4#1684032312yes—
879C4C2×#1451982311yescharacteristic
880C4C2×#1451982311yescharacteristic
881C2—42no—
882C2—4882no—
883C2—4882no—
884C2—4882no—
885C2—2442no—
886C2—2442no—
887C2#2145667714yesdirect product factor
888C2C2×#1684032311yescharacteristic
889C2C2×#1684056411yescharacteristic
890C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#485C2
socleC23×C61C22×D4
hypercenterC2×#485D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16840342C2semidirect
2. C2×#16840331C2semidirect
3. #21456677C2direct (N × H)
4. C2×#16840082C2semidirect
5. C2×#16840086C2semidirect
6. C2×#16840077C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16840011C2semidirect
9. C2×#16839999C2semidirect
10. C2×#16839994C2semidirect
11. C2×#16839910C2semidirect
12. C2×#16839910C2semidirect
13. C2×#16839912C2semidirect
14. C2×#16839898C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#485C2semidirect
17. C22×#11758226C22semidirect
24. C22×#11758189C22semidirect
25. C22×C8×D61C22semidirect
27. #16840342C22semidirect
29. #16840331C22semidirect
33. C2×#14519753C22semidirect
39. C2×#14519752C22semidirect
45. C2×C4⋊C4×D61C22semidirect
46. #16840086C22semidirect
47. #16840082C22semidirect
48. #16840077C22semidirect
49. #16840016C22semidirect
50. #16840011C22semidirect
51. #16839999C22semidirect
52. #16839994C22semidirect
53. #16839912C22semidirect
54. #16839910C22semidirect
55. #16839910C22semidirect
56. #16839898C22semidirect
57. C2×#14519710C22semidirect
58. C2×#14519708C22semidirect
63. C2×#14519697C22semidirect
64. C2×#14519697C22semidirect
65. #16839727C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
71. C61×#485C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×#103×C61C22semidirect
75. C2×#103×C61C22semidirect
81. C2×#11758226C23semidirect
118. C2×#11758189C23semidirect
122. C2×C8×D61C23semidirect
127. #14519753C23semidirect
138. #14519752C23semidirect
149. C4⋊C4×D61C23semidirect
157. #14519710C23semidirect
158. #14519708C23semidirect
163. #14519697C23semidirect
164. #14519697C23semidirect
166. #14519689C23semidirect
167. #14519689C23semidirect
183. #107×C61C23semidirect
184. #106×C61C23semidirect
185. #103×C61C23semidirect
186. #103×C61C23semidirect
440. C2×#485D61semidirect
453. C2×C61#3198semidirect
493. #485C2×D61semidirect
506. C2×#107C2×D61semidirect
508. C2×#106C2×D61semidirect
509. C2×#103C2×D61semidirect
510. C2×#103C2×D61semidirect
522. C61C2×#3198semidirect
619. #107C22×D61semidirect
621. #106C22×D61semidirect
622. #103C22×D61semidirect
623. #103C22×D61semidirect
887. C2#21456677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403422
C2×#168403312
#214566772
C2×#168400822
C2×#168400862
C2×#168400772
C2×#168400162
C2×#168400112
C2×#168399992
C2×#168399942
C2×#168399102
C2×#168399122
C2×#168398982
C2×#168397272
C2×C61×#4852
C2×#319861