Finite Group Databasebeta

← C2×#21457906 #30556545

Subgroups — C2×#21457906 #30556545

Order 15616.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic, complemented
2C2×#16840403C211yesmaximal, characteristic
3#21457906C2116yesmaximal, direct product factor
4C2×#16840123C211yesmaximal, characteristic, complemented
5C2×#16840095C211yesmaximal, characteristic, complemented
6C2×#16840077C211yesmaximal, characteristic, complemented
7C2×#16840041C211yesmaximal, characteristic, complemented
8C2×#16840011C211yesmaximal, characteristic, complemented
9C2×#16839986C211yesmaximal, characteristic, complemented
10C2×#16839923C211yesmaximal, characteristic, complemented
11C2×#16839912C211yesmaximal, characteristic, complemented
12C2×#16839865C211yesmaximal, characteristic, complemented
13C2×#16839833C211yesmaximal, characteristic, complemented
14C2×#16839762C211yesmaximal, characteristic, complemented
15C22×#14519699C211yesmaximal, characteristic, complemented
16C2×C61×#467C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758189C2211yescharacteristic, complemented
22#16840470—24no—
23#16840470C2218yescomplemented
24#16840403—24no—
25#16840403C2218yes—
26C2×#14519776C2211yescharacteristic, complemented
27C2×#14519767—21no—
28C2×#14519766C2211yescharacteristic
29C2×#14519762—21no—
30C2×#14519757—21no—
31C2×#14519754—21no—
32C2×#14519753C2211yescharacteristic, complemented
33C2×#14519752—21no—
34C2×#14519752C2211yescharacteristic
35C2×#14519747—21no—
36C2×Q8×Dic61C2211yescharacteristic, complemented
37C2×#14519739C2211yescharacteristic
38C2×C4×C22⋊D61C2211yescharacteristic
39C2×#14519737—21no—
40C22×C4⋊Dic61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic, complemented
42C2×C22⋊C4×D61—21no—
43#16840123C2218yescomplemented
44#16840095C2218yescomplemented
45#16840077C2218yescomplemented
46#16840041C2218yescomplemented
47#16840011C2218yescomplemented
48#16839986C2218yescomplemented
49#16839923C2218yescomplemented
50#16839912C2218yescomplemented
51#16839865C2218yescomplemented
52#16839833C2218yescomplemented
53C2×#14519710C2211yescharacteristic, complemented
54C2×#14519710C2211yescharacteristic, complemented
55C2×#14519706C2211yescharacteristic, complemented
56#16839762C2218yescomplemented
57C2×#14519701C2211yescharacteristic, complemented
58C2×#14519701C2211yescharacteristic, complemented
59C2×#14519699C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2218yescomplemented
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519687C2211yescharacteristic, complemented
69C22×Q16×C61C2211yescharacteristic, complemented
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#467C2218yescomplemented
74C2×#107×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×#103×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758226—22no—
79C2×#11758226—24no—
80C2×#11758226—42no—
81C2×#11758226C2314yes—
82C22×Dic122—21no—
83C22×D244—24no—
84C22×D244—21no—
85C22×D244—21no—
86C22×D244—22no—
87C22×D244—21no—
88C22×D244—42no—
89C22×D244C2311yescharacteristic
90C22×D244C2314yes—
91C22×D244C2311yescharacteristic
92C22×C22⋊D61D411yescharacteristic
93C23×Dic61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C2×#11758201—24no—
99C2×#11758201—42no—
100C2×#11758201C2314yes—
101C2×#11758201C2314yes—
102C2×#11758189—42no—
103C2×#11758189C2314yescomplemented
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106#14519776—22no—
107#14519776C2314yescomplemented
108#14519767—28no—
109#14519766—22no—
110#14519766C2314yes—
111#14519762—28no—
112#14519757—28no—
113#14519754—28no—
114#14519753—22no—
115#14519753C2314yescomplemented
116#14519752—22no—
117#14519752—28no—
118#14519752C2314yes—
119#14519747—28no—
120Q8×Dic61—22no—
121Q8×Dic61C2314yescomplemented
122#14519739—22no—
123#14519739C2314yes—
124C4×C22⋊D61D414yes—
125C4×C22⋊D61C2314yes—
126#14519737—28no—
127C2×C4⋊Dic61—22no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2314yes—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C4⋊C4×D61—22no—
138C4⋊C4×D61C2314yescomplemented
139C2×C22⋊Dic61D411yescharacteristic
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C22⋊C4×D61—28no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yescomplemented
150#14519710C2314yescomplemented
151#14519706C2314yescomplemented
152#14519701C2314yescomplemented
153#14519701C2314yescomplemented
154#14519699C2314yes—
155#14519699C2314yes—
156#14519699C2314yes—
157#14519699C2314yes—
158#14519697C2314yes—
159#14519697C2314yes—
160C22⋊#92418C2314yes—
161#14519689C2314yescomplemented
162#14519687C2314yescomplemented
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C2×Q16×C61—42no—
167C2×Q16×C61C2314yescomplemented
168C22×C8×C61—42no—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2314yes—
172C22⋊Q8×C61—22no—
173C22⋊Q8×C61—22no—
174C22⋊Q8×C61C2314yes—
175C22⋊Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182#107×C61C2314yescomplemented
183#103×C61C2314yescomplemented
184#103×C61C2314yescomplemented
185C24×C61C2×D411yescharacteristic
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—24no—
189C23×D61—44no—
190C23×D61—44no—
191C23×D61—82no—
192C23×D61C2×D411yescharacteristic
193C2×Q8×C61—21no—
194C2×Q8×C61—21no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61C2412yes—
200C2×Q8×C61C2412yes—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2412yes—
210C22×C4×C61C2411yescharacteristic
211C2×C22⋊D61—24no—
212C2×C22⋊D61C2×D414yes—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—82no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220#11758226—28no—
221#11758226—44no—
222#11758226—48no—
223C2×D244—21no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—22no—
227C2×D244—28no—
228C2×D244—24no—
229C2×D244—24no—
230C2×D244—21no—
231C2×D244—24no—
232C2×D244—44no—
233C2×D244—48no—
234C2×D244—44no—
235C2×D244—44no—
236C2×D244—82no—
237C2×D244#4114yes—
238C2×D244C2412yes—
239C2×D244C2412yes—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—24no—
245C2×C4×D61—44no—
246C2×C4×D61—82no—
247C2×C4×D61—82no—
248C2×C4×D61C2×D412yes—
249C2×C4×D61C2412yes—
250C2×Dic122—24no—
251C2×Dic122—82no—
252Q16×C61—44no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61—44no—
256C2×C8×C61C2412yes—
257C2×C8×C61C2412yes—
258C4⋊C4×C61—24no—
259C4⋊C4×C61—24no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61C2412yes—
263C4⋊C4×C61C2412yes—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—24no—
266C22⋊Dic61C2×D414yes—
267#11758201—28no—
268#11758201—44no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198C2×D414yes—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—24no—
278C4⋊Dic61—24no—
279C4⋊Dic61C2412yes—
280C4⋊Dic61C2412yes—
281#11758196—24no—
282#11758196—24no—
283#11758196—24no—
284#11758196C2×D414yes—
285C4×Dic61—24no—
286C4×Dic61C2×D412yes—
287C4×Dic61C2412yes—
288C2×#92418—22no—
289C2×#92418—22no—
290C2×#92418C2412yes—
291C2×#92418C2412yes—
292#11758189—44no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61#13714yes—
296C23×C61C22×D412yes—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—24no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—48no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—48no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—84no—
312C22×D61—816no—
313C22×D61C22×D412yes—
314Q8×C61—22no—
315Q8×C61—22no—
316Q8×C61—22no—
317Q8×C61—22no—
318Q8×C61—42no—
319Q8×C61—42no—
320C2×C4×C61—22no—
321C2×C4×C61—24no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4112yes—
335C2×C4×C61H(5,𝔽2)12yes—
336C2×C4×C61C2511yescharacteristic
337C22⋊D61—28no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—84no—
346C2×Dic61C22×D412yes—
347C2×Dic61C22×D412yes—
348C2×Dic61C22×D412yes—
349D244—24no—
350D244—22no—
351D244—22no—
352D244—22no—
353D244—48no—
354D244—48no—
355D244—42no—
356D244—84no—
357D244C2×#4114yes—
358C4×D61—24no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—48no—
362C4×D61—84no—
363C4×D61—84no—
364Dic122—84no—
365C8×C61—22no—
366C8×C61—22no—
367#92418—22no—
368#92418—22no—
369C2×#3314—611nomaximal, Sylow
370C22×C61—22no—
371C22×C61—28no—
372C22×C61—22no—
373C22×C61#54612yes—
374C22×C61C2×#13714yes—
375C22×C61C2×#13712yes—
376C22×C61#57612yes—
377C22×C61C23×D411yescharacteristic
378C2×D61—22no—
379C2×D61—24no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—44no—
383C2×D61—48no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—816no—
390C2×D61—84no—
391C4×C61—22no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61#54612yes—
397C4×C61C22×#4111yescharacteristic
398C4×C61C2×H(5,𝔽2)11yescharacteristic
399Dic61—22no—
400Dic61—22no—
401Dic61—22no—
402Dic61—42no—
403Dic61—42no—
404C2×#554—611no—
405C2×#546—611no—
406#3314—6116no—
407C2×#489—611no—
408C2×#484—611no—
409C2×#480—611no—
410C2×#474—611no—
411C2×#468—611no—
412C2×#467D6111yescharacteristic, complemented
413C2×#464—611no—
414C2×#452—611no—
415C2×#450—611no—
416C2×#440—611no—
417C2×#435—611no—
418C2×#417—611no—
419C22×#102—611no—
420C2×C61—24no—
421C2×C61#331414yescomplemented
422C2×C61C2×#54611yescharacteristic
423C2×C61C22×#13711yescharacteristic
424C2×C61C2×#57611yescharacteristic
425D61—42no—
426D61—44no—
427D61—82no—
428C22×#41—611no—
429C23×D4—611no—
430C22×Q16C2×D6111yescharacteristic, complemented
431C22×SD16—611no—
432C22×SD16—611no—
433C22×M16—611no—
434C23×C8C2×D6111yescharacteristic
435#554—618no—
436#554—1224no—
437#546—618no—
438#546—1224no—
439C2×C4⋊Q8—611no—
440C2×#125—1221no—
441C2×#124—611no—
442C2×#123—1221no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—1221no—
445C2×C22⋊Q8—1221no—
446C2×C22⋊Q8C2×D6111yescharacteristic
447C2×C22⋊Q8C2×D6111yescharacteristic
448C2×#121—611no—
449C2×#121—1221no—
450C2×#120—1221no—
451C2×C4×Q8—611no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×C4×D4—1221no—
455C22×C4⋊C4—611no—
456C22×C4⋊C4—611no—
457C22×C22⋊C4—1221no—
458#489—618no—
459#484—618no—
460#480—618no—
461#474—618no—
462#468—618no—
463#467C2×D6118yescomplemented
464#464—618no—
465#452—618no—
466#450—618no—
467#440—618no—
468#435—618no—
469C2×#107—611no—
470C2×#107—611no—
471C2×#107C2×D6111yescharacteristic, complemented
472C2×C4⋊C8—611no—
473#417—618no—
474C2×#103—611no—
475C2×#103—611no—
476C2×#103C2×D6111yescharacteristic, complemented
477C2×#103C2×D6111yescharacteristic, complemented
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—618no—
483C2×#102—611no—
484C2×#102—611no—
485C2×C22⋊C8—611no—
486C2×C22⋊C8—611no—
487C2×#97—611no—
488C61C2×#331411yescharacteristic, complemented, Sylow
489C25—1221no—
490C2×#41—614no—
491C2×#41—1222no—
492C2×#41—1224no—
493C2×#41—2442no—
494C22×Q8—1221no—
495C22×Q8C22×D6111yescharacteristic
496C22×Q8C22×D6111yescharacteristic
497C22×D4—611no—
498C22×D4—611no—
499C22×D4—611no—
500C22×D4—614no—
501C22×D4—1224no—
502C22×D4—1221no—
503C22×D4—1221no—
504C22×D4—1221no—
505C22×D4—1222no—
506C22×D4—2442no—
507C23×C4—611no—
508C23×C4—1221no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4—1221no—
512C23×C4C22×D6111yescharacteristic
513C2×Q16—42no—
514C2×Q16C22×D6114yescomplemented
515C2×SD16—614no—
516C2×SD16—614no—
517C2×SD16—1224no—
518C2×SD16—2442no—
519C2×M16—614no—
520C2×M16—2442no—
521C22×C8—42no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8C22×D6111yescharacteristic
525C22×C8C22×D6111yescharacteristic
526C22×C8C22×D6114yes—
527C4⋊Q8—614no—
528C4⋊Q8—1222no—
529#125—1228no—
530#124—614no—
531#124—1222no—
532#123—1228no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—614no—
536C22⋊Q8—1228no—
537C22⋊Q8—1228no—
538C22⋊Q8—1222no—
539C22⋊Q8C22×D6114yes—
540C22⋊Q8C22×D6114yes—
541#121—614no—
542#121—1228no—
543#121—1222no—
544#120—1228no—
545C4×Q8—614no—
546C4×Q8—1222no—
547C4×D4—614no—
548C4×D4—614no—
549C4×D4—614no—
550C4×D4—1222no—
551C4×D4—1228no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—614no—
558C2×C4⋊C4—614no—
559C2×C4⋊C4—1222no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1222no—
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—1228no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C42—611no—
579C2×C42—1221no—
580#107—614no—
581#107—614no—
582#107C22×D6114yescomplemented
583C4⋊C8—614no—
584#103—614no—
585#103—614no—
586#103C22×D6114yescomplemented
587#103C22×D6114yescomplemented
588#102—614no—
589#102—614no—
590#102—614no—
591#102—614no—
592#102—614no—
593#102—614no—
594C22⋊C8—614no—
595C22⋊C8—614no—
596#97—614no—
597C24—611no—
598C24—1221no—
599C24—1224no—
600C24—1221no—
601C24—4882no—
602C24—2444no—
603C24—2444no—
604C24D4×D6111yescharacteristic
605#41—1228no—
606#41—2444no—
607#41—2448no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—1224no—
615C2×Q8—4882no—
616C2×Q8C23×D6112yes—
617C2×Q8C23×D6112yes—
618C2×D4—614no—
619C2×D4—614no—
620C2×D4—612no—
621C2×D4—612no—
622C2×D4—1228no—
623C2×D4—1224no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1221no—
627C2×D4—1224no—
628C2×D4—1221no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—4882no—
633C2×D4—2444no—
634C2×D4—2448no—
635C2×D4—2444no—
636C2×D4—2444no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—1224no—
649C22×C4—1224no—
650C22×C4—1224no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1224no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—4882no—
657C22×C4—4882no—
658C22×C4—4882no—
659C22×C4—2444no—
660C22×C4D4×D6112yes—
661C22×C4D4×D6111yescharacteristic
662C22×C4C23×D6112yes—
663C22×C4C23×D6111yescharacteristic
664Q16—44no—
665SD16—1228no—
666SD16—2444no—
667M16—2444no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—44no—
671C2×C8—612no—
672C2×C8—612no—
673C2×C8—1222no—
674C2×C8—1222no—
675C2×C8C23×D6112yes—
676C2×C8C23×D6112yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—614no—
682C4⋊C4—612no—
683C4⋊C4—612no—
684C4⋊C4—1224no—
685C4⋊C4—1224no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—1221no—
689C4⋊C4—1224no—
690C4⋊C4—1221no—
691C4⋊C4C23×D6112yes—
692C4⋊C4C23×D6112yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—614no—
696C22⋊C4—614no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C42—612no—
703C42—612no—
704C42—1224no—
705C23—22no—
706C23—22no—
707C23—612no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—1222no—
712C23—1224no—
713C23—1222no—
714C23—48816no—
715C23—4884no—
716C23—2448no—
717C23—2448no—
718C23—2442no—
719C23—2442no—
720C23—2442no—
721C23—2442no—
722C23—2442no—
723C23#1451980914yes—
724C23C2×D4×D6112yes—
725C23C2×D4×D6111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—4884no—
733D4—614no—
734D4—1228no—
735D4—1222no—
736D4—1222no—
737D4—1222no—
738D4—1224no—
739D4—4884no—
740D4—2448no—
741D4—2448no—
742D4—2442no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1224no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—4884no—
767C2×C4—4884no—
768C2×C4—4884no—
769C2×C4—2448no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4C2×D4×D6112yes—
773C2×C4C2×D4×D6111yescharacteristic
774C2×C4#41×D6112yes—
775C2×C4#1451982212yes—
776C2×C4C24×D6111yescharacteristic
777C8—22no—
778C8—22no—
779C8—1222no—
780C8—1222no—
781C22—22no—
782C22—22no—
783C22—28no—
784C22—1222no—
785C22—1224no—
786C22—1222no—
787C22—1222no—
788C22—48816no—
789C22—4884no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22—2444no—
796C22—2448no—
797C22#1684040112yes—
798C22C2×#1451980914yes—
799C22C2×#1451980912yes—
800C22#1684056412yes—
801C22C22×D4×D6111yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1222no—
808C4—1222no—
809C4—1222no—
810C4—2442no—
811C4—2442no—
812C4#1684040112yes—
813C4C2×#41×D6111yescharacteristic
814C4C2×#1451982211yescharacteristic
815C2—24no—
816C2—4882no—
817C2—2442no—
818C2—2444no—
819C2#2145790614yesdirect product factor
820C2C2×#1684040111yescharacteristic
821C2C22×#1451980911yescharacteristic
822C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#467C2
socleC23×C61C22×D4
prime radicalC2×#16840403C2
hypercenterC2×#467D61
hypocenterC61C2×#3314
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#16840470C2semidirect
3. #21457906C2direct (N × H)
4. C2×#16840123C2semidirect
5. C2×#16840095C2semidirect
6. C2×#16840077C2semidirect
7. C2×#16840041C2semidirect
8. C2×#16840011C2semidirect
9. C2×#16839986C2semidirect
10. C2×#16839923C2semidirect
11. C2×#16839912C2semidirect
12. C2×#16839865C2semidirect
13. C2×#16839833C2semidirect
14. C2×#16839762C2semidirect
15. C22×#14519699C2semidirect
16. C2×C61×#467C2semidirect
21. C22×#11758189C22semidirect
23. #16840470C22semidirect
26. C2×#14519776C22semidirect
32. C2×#14519753C22semidirect
36. C2×Q8×Dic61C22semidirect
41. C2×C4⋊C4×D61C22semidirect
43. #16840123C22semidirect
44. #16840095C22semidirect
45. #16840077C22semidirect
46. #16840041C22semidirect
47. #16840011C22semidirect
48. #16839986C22semidirect
49. #16839923C22semidirect
50. #16839912C22semidirect
51. #16839865C22semidirect
52. #16839833C22semidirect
53. C2×#14519710C22semidirect
54. C2×#14519710C22semidirect
55. C2×#14519706C22semidirect
56. #16839762C22semidirect
57. C2×#14519701C22semidirect
58. C2×#14519701C22semidirect
63. C2×#14519699C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519687C22semidirect
69. C22×Q16×C61C22semidirect
73. C61×#467C22semidirect
74. C2×#107×C61C22semidirect
75. C2×#103×C61C22semidirect
76. C2×#103×C61C22semidirect
103. C2×#11758189C23semidirect
107. #14519776C23semidirect
115. #14519753C23semidirect
121. Q8×Dic61C23semidirect
138. C4⋊C4×D61C23semidirect
149. #14519710C23semidirect
150. #14519710C23semidirect
151. #14519706C23semidirect
152. #14519701C23semidirect
153. #14519701C23semidirect
161. #14519689C23semidirect
162. #14519687C23semidirect
167. C2×Q16×C61C23semidirect
182. #107×C61C23semidirect
183. #103×C61C23semidirect
184. #103×C61C23semidirect
412. C2×#467D61semidirect
421. C2×C61#3314semidirect
430. C22×Q16C2×D61semidirect
463. #467C2×D61semidirect
471. C2×#107C2×D61semidirect
476. C2×#103C2×D61semidirect
477. C2×#103C2×D61semidirect
488. C61C2×#3314semidirect
514. C2×Q16C22×D61semidirect
582. #107C22×D61semidirect
586. #103C22×D61semidirect
587. #103C22×D61semidirect
819. C2#21457906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168404032
#214579062
C2×#168401232
C2×#168400952
C2×#168400772
C2×#168400412
C2×#168400112
C2×#168399862
C2×#168399232
C2×#168399122
C2×#168398652
C2×#168398332
C2×#168397622
C22×#145196992
C2×C61×#4672
C2×#331461