Finite Group Databasebeta

← C2×#21457794 #30556650

Subgroups — C2×#21457794 #30556650

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840465C211yesmaximal, characteristic, complemented
2C2×#16840415C211yesmaximal, characteristic, complemented
3#21457794C2116yesmaximal, direct product factor
4C2×#16840101C211yesmaximal, characteristic, complemented
5C2×#16840091C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16840011C211yesmaximal, characteristic, complemented
8C2×#16839994C211yesmaximal, characteristic, complemented
9C2×#16839964C211yesmaximal, characteristic, complemented
10C2×#16839910C211yesmaximal, characteristic, complemented
11C2×#16839910C211yesmaximal, characteristic, complemented
12C2×#16839875C211yesmaximal, characteristic, complemented
13C2×#16839835C211yesmaximal, characteristic, complemented
14C2×#16839762C211yesmaximal, characteristic, complemented
15C2×#16839757C211yesmaximal, characteristic, complemented
16C2×C61×#491C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758226C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×#11758189C2211yescharacteristic
23C22×C8×D61C2211yescharacteristic
24#16840465—24no—
25#16840465C2218yescomplemented
26#16840415—24no—
27#16840415C2218yescomplemented
28C2×#14519772—21no—
29C2×#14519762—21no—
30C2×#14519762—21no—
31C2×#14519762—21no—
32C2×#14519753C2211yescharacteristic
33C2×#14519753C2211yescharacteristic
34C2×#14519752—21no—
35C2×#14519752—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×#14519739—21no—
42C2×#14519735C2211yescharacteristic
43C2×C4⋊C4×D61—21no—
44C2×C4⋊C4×D61C2211yescharacteristic
45#16840101C2218yescomplemented
46#16840091C2218yescomplemented
47#16840059C2218yescomplemented
48#16840011C2218yescomplemented
49#16839994C2218yescomplemented
50#16839964C2218yescomplemented
51#16839910C2218yescomplemented
52#16839910C2218yescomplemented
53#16839875C2218yescomplemented
54#16839835C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59#16839762C2218yescomplemented
60#16839757C2218yescomplemented
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×#125×C61C2211yescharacteristic
71C61×#491C2218yescomplemented
72C2×#103×C61C2211yescharacteristic
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—22no—
79C2×#11758226—24no—
80C2×#11758226—24no—
81C2×#11758226—42no—
82C2×#11758226—42no—
83C2×#11758226C2314yes—
84C2×#11758226C2314yes—
85C22×D244—21no—
86C22×D244—21no—
87C22×D244—21no—
88C22×D244—21no—
89C22×D244D411yescharacteristic
90C22×D244C2311yescharacteristic
91C22×D244C2311yescharacteristic
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C22×C4×D61C2311yescharacteristic
99C2×#11758201—42no—
100C2×#11758201—42no—
101C2×#11758201C2314yes—
102C2×#11758201C2314yes—
103C2×D488—24no—
104C2×D488C2314yes—
105C2×#11758189—42no—
106C2×#11758189C2314yes—
107C22×#92418C2311yescharacteristic
108C22×#92418C2311yescharacteristic
109C2×C8×D61—42no—
110C2×C8×D61C2314yes—
111#14519772—28no—
112#14519762—28no—
113#14519762—28no—
114#14519762—28no—
115#14519753—22no—
116#14519753—22no—
117#14519753C2314yes—
118#14519753C2314yes—
119#14519752—28no—
120#14519752—28no—
121#14519752—22no—
122#14519752—22no—
123#14519752C2314yes—
124#14519752C2314yes—
125C4×D244—22no—
126C4×D244—22no—
127C4×D244D414yes—
128C4×D244C2314yes—
129C4×D244C2314yes—
130C4×D244C2314yes—
131#14519739—28no—
132#14519735—22no—
133#14519735C2314yes—
134C2×C4⋊Dic61D411yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C4⋊C4×D61—22no—
141C4⋊C4×D61—28no—
142C4⋊C4×D61C2314yes—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198D411yescharacteristic
151C2×#11758198D411yescharacteristic
152C2×C4×Dic61—21no—
153#14519710C2314yes—
154#14519709C2314yes—
155#14519708C2314yes—
156C4⋊#92418C2314yes—
157#14519701C2314yes—
158#14519701C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161#14519697C2314yes—
162#14519697C2314yes—
163#14519689C2314yes—
164#14519689C2314yes—
165C22×Q8×C61C2311yescharacteristic
166C22×Q8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4⋊Q8×C61—22no—
170C4⋊Q8×C61C2314yes—
171#125×C61—22no—
172#125×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C42×C61C2311yescharacteristic
180#103×C61C2314yes—
181#103×C61C2314yes—
182#103×C61C2314yes—
183#103×C61C2314yes—
184#97×C61C2314yes—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61C2×D411yescharacteristic
188C23×D61C2×D411yescharacteristic
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61C2412yes—
196C2×Q8×C61C2412yes—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208#11758226—28no—
209#11758226—28no—
210#11758226—44no—
211#11758226—44no—
212#11758226—48no—
213#11758226—48no—
214C2×D244—21no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—24no—
219C2×D244—24no—
220C2×D244—24no—
221C2×D244—21no—
222C2×D244—24no—
223C2×D244—42no—
224C2×D244—44no—
225C2×D244—44no—
226C2×D244—44no—
227C2×D244—82no—
228C2×D244C2×D414yes—
229C2×D244#4114yes—
230C2×D244C2412yes—
231C2×D244C2412yes—
232C2×C4×D61—22no—
233C2×C4×D61—22no—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—24no—
241C2×C4×D61—44no—
242C2×C4×D61—44no—
243C2×C4×D61—44no—
244C2×C4×D61—82no—
245C2×C4×D61—82no—
246C2×C4×D61C2×D412yes—
247C2×C4×D61C2×D412yes—
248C2×C4×D61C2412yes—
249C2×C4×D61C2412yes—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61C2412yes—
253C2×C8×C61C2412yes—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—24no—
257C4⋊C4×C61—24no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61C2412yes—
261C4⋊C4×C61C2412yes—
262C42×C61C2×D412yes—
263C42×C61C2412yes—
264#11758201—44no—
265#11758201—44no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198C2×D414yes—
274#11758198C2×D414yes—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61C2×D414yes—
278C4⋊Dic61C2412yes—
279C4⋊Dic61C2412yes—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283C4×Dic61—24no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288D488—28no—
289#11758189—44no—
290C8×D61—44no—
291C23×C61C22×D411yescharacteristic
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—24no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61C22×D412yes—
307C22×D61C22×D412yes—
308Q8×C61—22no—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—42no—
313Q8×C61—42no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4112yes—
328C2×C4×C61H(5,𝔽2)12yes—
329C2×C4×C61C2511yescharacteristic
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338D244—24no—
339D244—22no—
340D244—22no—
341D244—22no—
342D244—44no—
343D244—48no—
344D244—48no—
345D244—48no—
346D244—42no—
347D244—84no—
348D244C2×#4114yes—
349C4×D61—24no—
350C4×D61—24no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—48no—
356C4×D61—48no—
357C4×D61—48no—
358C4×D61—84no—
359C4×D61—84no—
360C8×C61—22no—
361C8×C61—22no—
362#92418—22no—
363#92418—22no—
364C2×#3307—611nomaximal, Sylow
365C22×C61#54612yes—
366C22×C61#57512yes—
367C22×C61#57712yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—24no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—44no—
377C2×D61—44no—
378C2×D61—48no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—84no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61#54612yes—
392C4×C61C22×#4111yescharacteristic
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394Dic61—22no—
395Dic61—22no—
396Dic61—42no—
397Dic61—42no—
398C2×#553—611no—
399C2×#547—611no—
400#3307—6116no—
401C2×#491D6111yescharacteristic, complemented
402C2×#485—611no—
403C2×#483—611no—
404C2×#478—611no—
405C2×#468—611no—
406C2×#465—611no—
407C2×#461—611no—
408C2×#449—611no—
409C2×#449—611no—
410C2×#442—611no—
411C2×#435—611no—
412C2×#417—611no—
413C2×#416—611no—
414C2×C61#330714yescomplemented
415C2×C61C2×#54611yescharacteristic
416C2×C61C2×#57511yescharacteristic
417C2×C61C2×#57711yescharacteristic
418D61—42no—
419D61—42no—
420D61—44no—
421D61—82no—
422C22×#41—611no—
423C22×#41—611no—
424C22×SD16—611no—
425C22×SD16—611no—
426C22×D8—611no—
427C22×M16—611no—
428C23×C8—611no—
429#553—618no—
430#553—1224no—
431#547—618no—
432#547—1224no—
433C2×C4⋊Q8C2×D6111yescharacteristic
434C2×#126—1221no—
435C2×#125C2×D6111yescharacteristic
436C2×#123—1221no—
437C2×#123—1221no—
438C2×#123—1221no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8—611no—
441C2×#121—611no—
442C2×#121—611no—
443C2×#121—1221no—
444C2×#121—1221no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×#117—611no—
450C22×C4⋊C4—611no—
451C22×C4⋊C4—1221no—
452#491C2×D6118yescomplemented
453#485—618no—
454#483—618no—
455#478—618no—
456#468—618no—
457#465—618no—
458#461—618no—
459#449—618no—
460#449—618no—
461#442—618no—
462#435—618no—
463C2×#107—611no—
464C2×#106—611no—
465C2×#106—611no—
466C2×C4⋊C8—611no—
467#417—618no—
468#416—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103C2×D6111yescharacteristic
472C2×#103C2×D6111yescharacteristic
473C2×#103C2×D6111yescharacteristic
474C2×#103C2×D6111yescharacteristic
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×#97C2×D6111yescharacteristic
482C61C2×#330711yescharacteristic, complemented, Sylow
483C2×#41—614no—
484C2×#41—614no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1224no—
488C2×#41—1224no—
489C2×#41—2442no—
490C2×#41—2442no—
491C22×Q8C22×D6111yescharacteristic
492C22×Q8C22×D6111yescharacteristic
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4—1221no—
507C2×SD16—614no—
508C2×SD16—614no—
509C2×SD16—2442no—
510C2×SD16—2442no—
511C2×D8—614no—
512C2×D8—1224no—
513C2×M16—614no—
514C2×M16—2442no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—614no—
518C22×C8—2442no—
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6111yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8C22×D6114yes—
523#126—1228no—
524#125—22no—
525#125C22×D6114yes—
526#123—1228no—
527#123—1228no—
528#123—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—614no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533#121—614no—
534#121—614no—
535#121—1222no—
536#121—1222no—
537#121—1228no—
538#121—1228no—
539C4×D4—614no—
540C4×D4—614no—
541C4×D4—614no—
542C4×D4—614no—
543C4×D4—1228no—
544C4×D4—1222no—
545C4×D4—1222no—
546#117—614no—
547#117—1222no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—614no—
556C2×C4⋊C4—1228no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—611no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575#106—614no—
576#106—614no—
577C4⋊C8—614no—
578#103—614no—
579#103—614no—
580#103C22×D6114yes—
581#103C22×D6114yes—
582#103C22×D6114yes—
583#103C22×D6114yes—
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588C22⋊C8—614no—
589C22⋊C8—614no—
590#97C22×D6114yes—
591C24—611no—
592C24—611no—
593C24—1221no—
594C24—1221no—
595#41—1228no—
596#41—1228no—
597#41—2444no—
598#41—2444no—
599#41—2448no—
600#41—2448no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8C23×D6112yes—
608C2×Q8C23×D6112yes—
609C2×D4—614no—
610C2×D4—614no—
611C2×D4—612no—
612C2×D4—612no—
613C2×D4—1224no—
614C2×D4—1224no—
615C2×D4—1224no—
616C2×D4—1224no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4—1222no—
622C2×D4—4882no—
623C2×D4—2442no—
624C2×D4—2444no—
625C2×D4—2444no—
626C2×D4—2444no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—1224no—
638C22×C4—1224no—
639C22×C4—1224no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1224no—
647C22×C4—1224no—
648C22×C4—4882no—
649C22×C4—4882no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656SD16—2444no—
657SD16—2444no—
658D8—1228no—
659M16—2444no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8—2444no—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—614no—
676C4⋊C4—612no—
677C4⋊C4—612no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4C23×D6112yes—
684C4⋊C4C23×D6112yes—
685C22⋊C4—614no—
686C22⋊C4—614no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C42—1224no—
695C42D4×D6112yes—
696C42C23×D6112yes—
697C23—612no—
698C23—612no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1224no—
707C23—1222no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23—2442no—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—42no—
719Q8—42no—
720D4—614no—
721D4—1222no—
722D4—1222no—
723D4—1222no—
724D4—1224no—
725D4—4884no—
726D4—2444no—
727D4—2448no—
728D4—2448no—
729D4—2448no—
730D4—2442no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1224no—
750C2×C4—1224no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—4884no—
754C2×C4—4884no—
755C2×C4—2448no—
756C2×C4—2448no—
757C2×C4—2448no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4C2×D4×D6112yes—
761C2×C4C2×D4×D6112yes—
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4#41×D6112yes—
764C2×C4#1451982312yes—
765C2×C4C24×D6111yescharacteristic
766C8—22no—
767C8—22no—
768C8—1222no—
769C8—1222no—
770C22—1222no—
771C22—1222no—
772C22—1224no—
773C22—1222no—
774C22—1222no—
775C22—1222no—
776C22—1222no—
777C22—4884no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2444no—
784C22—2444no—
785C22—2448no—
786C22#1684040512yes—
787C22#1684056112yes—
788C22#1684057112yes—
789C22C22×D4×D6111yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—1222no—
797C4—1222no—
798C4—2442no—
799C4—2442no—
800C4#1684040512yes—
801C4C2×#41×D6111yescharacteristic
802C4C2×#1451982311yescharacteristic
803C2—4882no—
804C2—2442no—
805C2—2442no—
806C2—2444no—
807C2#2145779414yesdirect product factor
808C2C2×#1684040511yescharacteristic
809C2C2×#1684056111yescharacteristic
810C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#491C2
socleC23×C61C22×D4
hypercenterC2×#491D61
hypocenterC61C2×#3307
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#16840465C2semidirect
2. C2×#16840415C2semidirect
3. #21457794C2direct (N × H)
4. C2×#16840101C2semidirect
5. C2×#16840091C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16840011C2semidirect
8. C2×#16839994C2semidirect
9. C2×#16839964C2semidirect
10. C2×#16839910C2semidirect
11. C2×#16839910C2semidirect
12. C2×#16839875C2semidirect
13. C2×#16839835C2semidirect
14. C2×#16839762C2semidirect
15. C2×#16839757C2semidirect
16. C2×C61×#491C2semidirect
25. #16840465C22semidirect
27. #16840415C22semidirect
45. #16840101C22semidirect
46. #16840091C22semidirect
47. #16840059C22semidirect
48. #16840011C22semidirect
49. #16839994C22semidirect
50. #16839964C22semidirect
51. #16839910C22semidirect
52. #16839910C22semidirect
53. #16839875C22semidirect
54. #16839835C22semidirect
59. #16839762C22semidirect
60. #16839757C22semidirect
71. C61×#491C22semidirect
401. C2×#491D61semidirect
414. C2×C61#3307semidirect
452. #491C2×D61semidirect
482. C61C2×#3307semidirect
807. C2#21457794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404652
C2×#168404152
#214577942
C2×#168401012
C2×#168400912
C2×#168400592
C2×#168400112
C2×#168399942
C2×#168399642
C2×#168399102
C2×#168398752
C2×#168398352
C2×#168397622
C2×#168397572
C2×C61×#4912
C2×#330761