Finite Group Databasebeta

← C2×#22609918 #33085378

Subgroups — C2×#22609918 #33085378

Order 18688.

2066 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556551C211yesmaximal, characteristic
2C22×#14556505C212yesmaximal
3C2×#17988445C212yesmaximal, complemented
4#22609918C218yesmaximal, direct product factor
5C2×#17988354C211yesmaximal, characteristic, complemented
6C2×#342×C73C211yesmaximal, characteristic, complemented
7C23×C22⋊D73C2211yescharacteristic
8C24×Dic73C2211yescharacteristic
9C23×C4×D73C411yescharacteristic, complemented
10C2×#14556551—22no—
11C2×#14556551—22no—
12C2×#14556551—24no—
13C2×#14556551C414yescomplemented
14C2×#14556551C2214yes—
15C22×#11924007—22no—
16C22×#11924007C411yescharacteristic, complemented
17C22×C22⋊Dic73C2212yes—
18C22×#11924005C411yescharacteristic, complemented
19C22×C4×Dic73C411yescharacteristic, complemented
20C2×#14556505—28no—
21C2×#14556505C2218yes—
22#17988445—24no—
23#17988445C2218yescomplemented
24C2×#14556498—22no—
25#17988354C2214yescomplemented
26C22×C22⋊C4×C73C2212yes—
27C22×C22⋊C4×C73C2211yescharacteristic
28#342×C73C2214yescomplemented
29C24×D73C2×C411yescharacteristic
30C22×C22⋊D73—22no—
31C22×C22⋊D73—22no—
32C22×C22⋊D73—24no—
33C22×C22⋊D73C2×C412yes—
34C22×C22⋊D73D414yes—
35C22×C22⋊D73Q814yes—
36C22×C22⋊D73C2312yes—
37C23×Dic73—22no—
38C23×Dic73—44no—
39C23×Dic73C2×C411yescharacteristic
40C23×Dic73C2×C411yescharacteristic
41C23×Dic73C2×C411yescharacteristic
42C23×Dic73C2×C412yes—
43C23×Dic73D412yes—
44C23×Dic73D412yes—
45C23×Dic73D414yes—
46C23×Dic73C2312yes—
47C22×C4×D73—22no—
48C22×C4×D73—21no—
49C22×C4×D73—21no—
50C22×C4×D73—44no—
51C22×C4×D73C2×C414yescomplemented
52#14556551—28no—
53#14556551—28no—
54#14556551—28no—
55#14556551—28no—
56C2×#11924007—22no—
57C2×#11924007—22no—
58C2×#11924007—28no—
59C2×#11924007—48no—
60C2×#11924007C2×C414yescomplemented
61C2×C22⋊Dic73—24no—
62C2×C22⋊Dic73—22no—
63C2×C22⋊Dic73—24no—
64C2×C22⋊Dic73C2314yes—
65C2×#11924005—22no—
66C2×#11924005—22no—
67C2×#11924005C2×C414yescomplemented
68C2×C4×Dic73—22no—
69C2×C4×Dic73—21no—
70C2×C4×Dic73—21no—
71C2×C4×Dic73C2×C414yescomplemented
72#14556505—216no—
73#14556498—28no—
74C25×C73C2311yescharacteristic
75C23×C4×C73—22no—
76C23×C4×C73C2×C411yescharacteristic
77C23×C4×C73C2×C411yescharacteristic
78C2×C22⋊C4×C73—22no—
79C2×C22⋊C4×C73—22no—
80C2×C22⋊C4×C73—24no—
81C2×C22⋊C4×C73—24no—
82C2×C22⋊C4×C73—22no—
83C2×C22⋊C4×C73C2×C412yes—
84C2×C22⋊C4×C73C2314yes—
85C2×C22⋊C4×C73C2312yes—
86C23×D73—21no—
87C23×D73—21no—
88C23×D73—22no—
89C23×D73—42no—
90C23×D73—42no—
91C23×D73C4⋊C414yescomplemented
92C23×D73C22×C412yes—
93C2×C22⋊D73—24no—
94C2×C22⋊D73—24no—
95C2×C22⋊D73—28no—
96C2×C22⋊D73—28no—
97C2×C22⋊D73—28no—
98C2×C22⋊D73—28no—
99C2×C22⋊D73—24no—
100C2×C22⋊D73—24no—
101C2×C22⋊D73C4⋊C418yescomplemented
102C2×C22⋊D73C2×D414yes—
103C2×C22⋊D73C2×Q814yes—
104C22×Dic73—21no—
105C22×Dic73—21no—
106C22×Dic73—22no—
107C22×Dic73—28no—
108C22×Dic73—24no—
109C22×Dic73—24no—
110C22×Dic73—44no—
111C22×Dic73—48no—
112C22×Dic73—44no—
113C22×Dic73—42no—
114C22×Dic73—44no—
115C22×Dic73—44no—
116C22×Dic73—44no—
117C22×Dic73—44no—
118C22×Dic73C22⋊C412yes—
119C22×Dic73C22⋊C411yescharacteristic
120C22×Dic73C22⋊C412yes—
121C22×Dic73C22⋊C414yes—
122C22×Dic73C22⋊C412yes—
123C22×Dic73C22⋊C414yes—
124C22×Dic73C22⋊C411yescharacteristic
125C22×Dic73C4⋊C414yescomplemented
126C22×Dic73C22×C412yes—
127C22×Dic73C22×C412yes—
128C22×Dic73C22×C412yes—
129C22×Dic73C2×D414yes—
130C22×Dic73C2×D414yes—
131C2×C4×D73—24no—
132C2×C4×D73—24no—
133C2×C4×D73—44no—
134C2×C4×D73—48no—
135C2×C4×D73—44no—
136C2×C4×D73—48no—
137#11924007—28no—
138#11924007—416no—
139C22⋊Dic73—24no—
140C22⋊Dic73—24no—
141C22⋊Dic73—44no—
142#11924005—28no—
143C4×Dic73—24no—
144C4×Dic73—24no—
145C24×C73—42no—
146C24×C73—42no—
147C24×C73C22×C411yescharacteristic
148C24×C73C22×C411yescharacteristic
149C24×C73C2×D412yes—
150C24×C73C2×D412yes—
151C24×C73C2×D412yes—
152C24×C73C2×Q812yes—
153C24×C73#4114yes—
154C24×C73C2411yescharacteristic
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—24no—
160C22×C4×C73—42no—
161C22×C4×C73—42no—
162C22×C4×C73—44no—
163C22×C4×C73—44no—
164C22×C4×C73—44no—
165C22×C4×C73C22×C412yes—
166C22×C4×C73C22×C412yes—
167C22⋊C4×C73—24no—
168C22⋊C4×C73—24no—
169C22⋊C4×C73—24no—
170C22⋊C4×C73—24no—
171C22⋊C4×C73—44no—
172C23×C73—22no—
173C23×C73—24no—
174C23×C73—22no—
175C23×C73—24no—
176C23×C73—41no—
177C23×C73—41no—
178C23×C73—44no—
179C23×C73—42no—
180C23×C73—42no—
181C23×C73—44no—
182C23×C73—48no—
183C23×C73—41no—
184C23×C73—41no—
185C23×C73C2×C22⋊C412yes—
186C23×C73C2×C22⋊C411yescharacteristic
187C23×C73C2×C22⋊C411yescharacteristic
188C23×C73C2×C4⋊C412yes—
189C23×C73C2×C4⋊C412yes—
190C23×C73#11712yes—
191C23×C73#11712yes—
192C23×C73#12114yes—
193C23×C73#12114yes—
194C23×C73C22⋊Q814yes—
195C23×C73C22⋊Q814yes—
196C23×C73C23×C411yescharacteristic
197C23×C73C22×D412yes—
198C23×C73C22×D411yescharacteristic
199C23×C73C22×Q811yescharacteristic
200C23×C73C2×#4112yes—
201C22×D73—22no—
202C22×D73—22no—
203C22×D73—24no—
204C22×D73—24no—
205C22×D73—42no—
206C22×D73—48no—
207C22×D73—42no—
208C22×D73—42no—
209C22×D73—42no—
210C22×D73—42no—
211C22×D73—48no—
212C22×D73—42no—
213C22×D73C2×C4⋊C414yescomplemented
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—42no—
217C2×C4×C73—42no—
218C2×C4×C73—42no—
219C2×C4×C73—42no—
220C2×C4×C73—42no—
221C2×C4×C73—42no—
222C2×C4×C73—44no—
223C2×C4×C73—44no—
224C2×C4×C73—44no—
225C2×C4×C73—88no—
226C22⋊D73—28no—
227C22⋊D73—28no—
228C22⋊D73—216no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—24no—
232C2×Dic73—24no—
233C2×Dic73—22no—
234C2×Dic73—24no—
235C2×Dic73—28no—
236C2×Dic73—24no—
237C2×Dic73—24no—
238C2×Dic73—28no—
239C2×Dic73—44no—
240C2×Dic73—42no—
241C2×Dic73—42no—
242C2×Dic73—44no—
243C2×Dic73—44no—
244C2×Dic73—44no—
245C2×Dic73—44no—
246C2×Dic73—88no—
247C2×Dic73#9914yescomplemented
248C2×Dic73C2×C22⋊C412yes—
249C2×Dic73C2×C22⋊C414yes—
250C2×Dic73C2×C22⋊C412yes—
251C2×Dic73C2×C4⋊C414yescomplemented
252C4×D73—48no—
253C4×D73—48no—
254C22×C73—28no—
255C22×C73—24no—
256C22×C73—24no—
257C22×C73—28no—
258C22×C73—22no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—22no—
262C22×C73—22no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—22no—
266C22×C73—42no—
267C22×C73—42no—
268C22×C73—44no—
269C22×C73—44no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—42no—
273C22×C73#38012yes—
274C22×C73#38014yes—
275C22×C73#38012yes—
276C22×C73C2×#9912yes—
277C22×C73#41012yes—
278C22×C73C22×C22⋊C411yescharacteristic
279C22×C73C22×C4⋊C411yescharacteristic
280C22×C73C2×#11711yescharacteristic
281C22×C73C2×#12112yes—
282C22×C73C2×C22⋊Q812yes—
283C2×D73—24no—
284C2×D73—44no—
285C2×D73—48no—
286C2×D73—48no—
287C2×D73—42no—
288C2×D73—42no—
289C2×D73—44no—
290C4×C73—42no—
291C4×C73—42no—
292C4×C73—84no—
293Dic73—22no—
294Dic73—24no—
295Dic73—24no—
296Dic73—84no—
297Dic73C2×#9914yescomplemented
298C2×#1799—731nomaximal, Sylow
299C2×C73—22no—
300C2×C73—21no—
301C2×C73—21no—
302C2×C73—22no—
303C2×C73—22no—
304C2×C73—24no—
305C2×C73#179914yescomplemented
306C2×C73C2×#38011yescharacteristic
307C2×C73C22×#9911yescharacteristic
308C2×C73C2×#41011yescharacteristic
309D73—44no—
310C22×C4×D4—731no—
311C22×#99—732no—
312C2×#380—732no—
313#1799—738no—
314C2×#342—731no—
315C2×#342D7311yescharacteristic, complemented
316C73C2×#179911yescharacteristic, complemented, Sylow
317C23×D4—731no—
318C24×C4—731no—
319C24×C4—731no—
320C2×C4×D4—734no—
321C2×C4×D4—734no—
322C2×C4×D4—1462no—
323C2×C4×D4—1464no—
324C2×C4×D4—1462no—
325C22×C4⋊C4—731no—
326C22×C4⋊C4—1462no—
327C22×C22⋊C4—731no—
328C22×C22⋊C4—732no—
329C22×C22⋊C4C2×D7312yes—
330C22×C22⋊C4C2×D7311yescharacteristic
331C22×C42—731no—
332C2×#99—738no—
333C2×#99—1468no—
334#380—738no—
335#380—1464no—
336C2×#95—1462no—
337#342—734no—
338#342C2×D7314yescomplemented
339C25—731no—
340C25C22×D7311yescharacteristic
341C22×D4—732no—
342C22×D4—734no—
343C22×D4—734no—
344C22×D4—732no—
345C22×D4—1462no—
346C22×D4—1462no—
347C22×D4—1464no—
348C23×C4—22no—
349C23×C4—2924no—
350C23×C4—2924no—
351C23×C4—731no—
352C23×C4—732no—
353C23×C4—732no—
354C23×C4—734no—
355C23×C4—732no—
356C23×C4—734no—
357C23×C4—731no—
358C23×C4—731no—
359C23×C4—732no—
360C23×C4—1462no—
361C23×C4—1461no—
362C23×C4—1461no—
363C23×C4—1462no—
364C23×C4C4×D7311yescharacteristic
365C23×C4C4×D7311yescharacteristic
366C4×D4—1468no—
367C4×D4—1468no—
368C4×D4—1468no—
369C4×D4—1468no—
370C2×C4⋊C4—2928no—
371C2×C4⋊C4—734no—
372C2×C4⋊C4—1468no—
373C2×C4⋊C4—1462no—
374C2×C4⋊C4—1462no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—734no—
381C2×C22⋊C4—734no—
382C2×C22⋊C4—1462no—
383C2×C22⋊C4—1464no—
384C2×C22⋊C4—1464no—
385C2×C22⋊C4—1462no—
386C2×C22⋊C4—1462no—
387C2×C22⋊C4C4×D7312yes—
388C2×C22⋊C4C22×D7314yes—
389C2×C22⋊C4C22×D7312yes—
390C2×C42—734no—
391C2×C42—1462no—
392C2×C42—1461no—
393C2×C42—1461no—
394#99—14616no—
395#95—1468no—
396C24—42no—
397C24—42no—
398C24—2922no—
399C24—2922no—
400C24—734no—
401C24—732no—
402C24—1461no—
403C24—1461no—
404C24—1462no—
405C24C2×C4×D7311yescharacteristic
406C24C2×C4×D7311yescharacteristic
407C24D4×D7312yes—
408C24D4×D7312yes—
409C24D4×D7312yes—
410C24Q8×D7312yes—
411C24#1192402814yes—
412C24C23×D7311yescharacteristic
413C2×D4—738no—
414C2×D4—734no—
415C2×D4—734no—
416C2×D4—1464no—
417C2×D4—1464no—
418C2×D4—1468no—
419C2×D4—1468no—
420C2×D4—1468no—
421C2×D4—1468no—
422C2×D4—1464no—
423C2×D4—1464no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—2924no—
435C22×C4—2928no—
436C22×C4—2924no—
437C22×C4—2928no—
438C22×C4—2924no—
439C22×C4—2922no—
440C22×C4—2924no—
441C22×C4—2928no—
442C22×C4—2924no—
443C22×C4—2924no—
444C22×C4—2924no—
445C22×C4—2924no—
446C22×C4—732no—
447C22×C4—734no—
448C22×C4—732no—
449C22×C4—734no—
450C22×C4—731no—
451C22×C4—732no—
452C22×C4—734no—
453C22×C4—731no—
454C22×C4—732no—
455C22×C4—734no—
456C22×C4—732no—
457C22×C4—732no—
458C22×C4—734no—
459C22×C4—1464no—
460C22×C4—1464no—
461C22×C4—1464no—
462C22×C4—1468no—
463C22×C4—1464no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4—1462no—
467C22×C4C2×C4×D7312yes—
468C22×C4C2×C4×D7312yes—
469C4⋊C4—29216no—
470C4⋊C4—1468no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—44no—
476C22⋊C4—2924no—
477C22⋊C4—1468no—
478C22⋊C4—1464no—
479C22⋊C4—1464no—
480C42—1464no—
481C42—1464no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—42no—
491C23—44no—
492C23—44no—
493C23—48no—
494C23—41no—
495C23—2922no—
496C23—2922no—
497C23—2928no—
498C23—2922no—
499C23—2922no—
500C23—2928no—
501C23—2922no—
502C23—2922no—
503C23—734no—
504C23—1464no—
505C23—1464no—
506C23—1462no—
507C23—1462no—
508C23C22⋊C4×D7312yes—
509C23C22⋊C4×D7311yescharacteristic
510C23C22⋊C4×D7311yescharacteristic
511C23C4⋊C4×D7312yes—
512C23C4⋊C4×D7312yes—
513C23#1455654812yes—
514C23#1455654812yes—
515C23#1455656414yes—
516C23#1455656414yes—
517C23#1455656914yes—
518C23#1455656914yes—
519C23C22×C4×D7311yescharacteristic
520C23C2×D4×D7312yes—
521C23C2×D4×D7311yescharacteristic
522C23C2×Q8×D7311yescharacteristic
523C23C2×#1192402812yes—
524D4—14616no—
525D4—1468no—
526D4—1468no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—88no—
539C2×C4—2928no—
540C2×C4—2928no—
541C2×C4—2924no—
542C2×C4—2924no—
543C2×C4—2924no—
544C2×C4—2924no—
545C2×C4—2924no—
546C2×C4—2922no—
547C2×C4—2922no—
548C2×C4—5848no—
549C2×C4—732no—
550C2×C4—734no—
551C2×C4—732no—
552C2×C4—734no—
553C2×C4—734no—
554C2×C4—1468no—
555C2×C4—1464no—
556C2×C4—1464no—
557C2×C4—1468no—
558C2×C4—1464no—
559C2×C4—1464no—
560C2×C4—1462no—
561C2×C4—1462no—
562C2×C4—1462no—
563C2×C4—1464no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—28no—
573C22—24no—
574C22—24no—
575C22—28no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22—2924no—
584C22—2928no—
585C22—2924no—
586C22—2922no—
587C22—2922no—
588C22—2928no—
589C22—1464no—
590C22#1798844612yes—
591C22#1798844614yes—
592C22#1798844612yes—
593C22#99×D7312yes—
594C22#1798855912yes—
595C22C2×C22⋊C4×D7311yescharacteristic
596C22C2×C4⋊C4×D7311yescharacteristic
597C22C2×#1455654811yescharacteristic
598C22C2×#1455656412yes—
599C22C2×#1455656912yes—
600C4—42no—
601C4—42no—
602C4—84no—
603C4—5844no—
604C4—734no—
605C4—1462no—
606C4—1464no—
607C4—1464no—
608C2—22no—
609C2—22no—
610C2—21no—
611C2—21no—
612C2—24no—
613C2—22no—
614C2—2924no—
615C2#2260991814yesdirect product factor
616C2C2×#1798844611yescharacteristic
617C2C2×#99×D7311yescharacteristic
618C2C2×#1798855911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC2×#342×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC23×C22⋊D73C22
cosocleC24×C73C24
hypercenterC2×#342D73
hypocenterC73C2×#1799
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×#17988445C2semidirect
4. #22609918C2direct (N × H)
5. C2×#17988354C2semidirect
6. C2×#342×C73C2semidirect
9. C23×C4×D73C4semidirect
13. C2×#14556551C4semidirect
16. C22×#11924007C4semidirect
18. C22×#11924005C4semidirect
19. C22×C4×Dic73C4semidirect
23. #17988445C22semidirect
25. #17988354C22semidirect
28. #342×C73C22semidirect
51. C22×C4×D73C2×C4semidirect
60. C2×#11924007C2×C4semidirect
67. C2×#11924005C2×C4semidirect
71. C2×C4×Dic73C2×C4semidirect
91. C23×D73C4⋊C4semidirect
101. C2×C22⋊D73C4⋊C4semidirect
125. C22×Dic73C4⋊C4semidirect
213. C22×D73C2×C4⋊C4semidirect
247. C2×Dic73#99semidirect
251. C2×Dic73C2×C4⋊C4semidirect
297. Dic73C2×#99semidirect
305. C2×C73#1799semidirect
315. C2×#342D73semidirect
316. C73C2×#1799semidirect
338. #342C2×D73semidirect
615. C2#22609918direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565512
C22×#145565052
C2×#179884452
#226099182
C2×#179883542
C2×#342×C732
C2×#179973