Finite Group Databasebeta

← C2×#22620164 #33954267

Subgroups — C2×#22620164 #33954267

Order 18688.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989209C211yesmaximal, characteristic
2C2×#17989063C211yesmaximal, characteristic, complemented
3#22620164C2116yesmaximal, direct product factor
4C2×#17988927C211yesmaximal, characteristic, complemented
5C2×#17988913C211yesmaximal, characteristic
6C2×#17988880C211yesmaximal, characteristic, complemented
7C2×#17988871C211yesmaximal, characteristic, complemented
8C2×#17988812C211yesmaximal, characteristic, complemented
9C2×#17988811C211yesmaximal, characteristic, complemented
10C2×#17988741C211yesmaximal, characteristic, complemented
11C2×#17988727C211yesmaximal, characteristic
12C2×#17988689C211yesmaximal, characteristic, complemented
13C2×C4×#11924018C211yesmaximal, characteristic, complemented
14C2×C4×#11924015C211yesmaximal, characteristic, complemented
15C2×#17988649C211yesmaximal, characteristic, complemented
16C2×#441×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21#17989209—24no—
22#17989209C2218yes—
23C2×#14556590C2211yescharacteristic
24C2×#14556585—21no—
25C2×#14556580C2211yescharacteristic
26C2×#14556579—21no—
27C2×#14556576—21no—
28C2×#14556569—21no—
29C2×#14556567C2211yescharacteristic
30C2×#14556566C2211yescharacteristic
31#17989063—24no—
32#17989063C2218yescomplemented
33C2×Q8×Dic73C2211yescharacteristic
34C2×C4×Dic146—21no—
35C2×C4×Dic146C2211yescharacteristic
36C2×#14556556—21no—
37C2×#14556556C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×#14556549—21no—
40C2×#14556549C2211yescharacteristic
41C2×#14556548—21no—
42C2×#14556548C2211yescharacteristic
43#17988927C2218yescomplemented
44#17988913C2218yes—
45#17988880C2218yescomplemented
46#17988871C2218yescomplemented
47#17988812C2218yescomplemented
48#17988811C2218yescomplemented
49#17988741C2218yescomplemented
50#17988727C2218yes—
51#17988689C2218yescomplemented
52C4×#11924018C2218yescomplemented
53C4×#11924015C2218yescomplemented
54#17988649C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C4×#10596831C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×Q8×C73C2211yescharacteristic
72#441×C73C2218yescomplemented
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146C2311yescharacteristic
80C2×Q8×D73—24no—
81C2×Q8×D73—22no—
82C2×Q8×D73—24no—
83C2×Q8×D73C2314yes—
84C22×D292—21no—
85C22×D292C2311yescharacteristic
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73C2311yescharacteristic
89C2×#11924018—24no—
90C2×#11924018C2314yes—
91C2×#11924017—24no—
92C2×#11924017C2314yes—
93C2×#11924015—24no—
94C2×#11924015C2314yes—
95C22×#10596831C2311yescharacteristic
96C22×#10596831C2311yescharacteristic
97#14556590—22no—
98#14556590C2314yes—
99#14556585—28no—
100#14556580—22no—
101#14556580C2314yes—
102#14556579—28no—
103#14556576—28no—
104#14556569—28no—
105#14556567—22no—
106#14556567C2314yes—
107#14556566—22no—
108#14556566C2314yes—
109Q8×Dic73—22no—
110Q8×Dic73C2314yes—
111C4×Dic146—28no—
112C4×Dic146—22no—
113C4×Dic146C2314yes—
114#14556556—28no—
115#14556556—22no—
116#14556556C2314yes—
117C4×D292—22no—
118C4×D292C2314yes—
119#14556549—22no—
120#14556549—28no—
121#14556549C2314yes—
122#14556548—28no—
123#14556548D414yes—
124#14556548C2314yes—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007D411yescharacteristic
133C2×#11924007D411yescharacteristic
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005D411yescharacteristic
141C2×#11924005D411yescharacteristic
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556524C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556514C2314yes—
156#14556513C2314yes—
157#14556511C2314yes—
158#14556503C2314yes—
159#14556503C2314yes—
160C4×#10596831C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C2×Q16×C73—24no—
164C2×Q16×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C4×Q8×C73—22no—
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C4×Q8×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C42×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#106×C73C2314yes—
179#103×C73C2314yes—
180#103×C73C2314yes—
181#97×C73C2314yes—
182C23×D73—21no—
183C23×D73C2×D411yescharacteristic
184C2×Dic146—28no—
185C2×Dic146—21no—
186C2×Dic146—22no—
187C2×Dic146—24no—
188C2×Dic146—24no—
189C2×Dic146—82no—
190C2×Dic146#4114yes—
191C2×Dic146C2412yes—
192Q8×D73—216no—
193Q8×D73—28no—
194Q8×D73—28no—
195C2×D292—22no—
196C2×D292—22no—
197C2×D292—21no—
198C2×D292—24no—
199C2×D292—82no—
200C2×D292C2412yes—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—28no—
208C2×C4×D73—24no—
209C2×C4×D73—22no—
210C2×C4×D73—22no—
211C2×C4×D73—24no—
212C2×C4×D73—82no—
213C2×C4×D73C2×D412yes—
214C2×C4×D73C2412yes—
215#11924018—28no—
216#11924017—28no—
217#11924015—28no—
218C2×#10596831—22no—
219C2×#10596831—22no—
220C2×#10596831C2412yes—
221C2×#10596831C2412yes—
222C4⋊Dic73—21no—
223C4⋊Dic73—21no—
224C4⋊Dic73—24no—
225C4⋊Dic73C2412yes—
226C4⋊Dic73C2412yes—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007C2×D414yes—
232#11924007C2×D414yes—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005C2×D414yes—
240#11924005C2×D414yes—
241C4×Dic73—24no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C4×Dic73C2×D412yes—
246C4×Dic73C2412yes—
247C2×Q8×C73—21no—
248C2×Q8×C73—21no—
249C2×Q8×C73—22no—
250C2×Q8×C73—22no—
251C2×Q8×C73—22no—
252C2×Q8×C73#4114yes—
253C2×Q8×C73C2412yes—
254C2×Q8×C73C2412yes—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2411yescharacteristic
262Q16×C73—28no—
263C2×C8×C73—22no—
264C2×C8×C73—22no—
265C2×C8×C73C2412yes—
266C2×C8×C73C2412yes—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73C2412yes—
272C4⋊C4×C73C2412yes—
273C42×C73—24no—
274C42×C73—24no—
275C42×C73C2×D412yes—
276C42×C73C2412yes—
277C23×C73C22×D411yescharacteristic
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—42no—
283C22×D73—42no—
284C22×D73—42no—
285C22×D73C22×D412yes—
286Q8×C73—24no—
287Q8×C73—22no—
288Q8×C73—22no—
289Q8×C73—22no—
290Q8×C73—42no—
291Q8×C73C2×#4114yes—
292C2×C4×C73—24no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—42no—
300C2×C4×C73—42no—
301C2×C4×C73—42no—
302C2×C4×C73C22×D412yes—
303C2×C4×C73C22×D412yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C2×#4112yes—
306C2×C4×C73C2×#4112yes—
307C2×C4×C73C2511yescharacteristic
308C2×Dic73—24no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319C2×Dic73C22×D412yes—
320D292—22no—
321D292—22no—
322D292—42no—
323D292—84no—
324C4×D73—216no—
325C4×D73—24no—
326C4×D73—22no—
327C4×D73—22no—
328C4×D73—84no—
329Dic146—216no—
330Dic146—24no—
331Dic146—22no—
332Dic146—84no—
333Dic146C2×#4114yes—
334C8×C73—22no—
335C8×C73—22no—
336#10596831—22no—
337#10596831—22no—
338C22×C73#52512yes—
339C22×C73#57712yes—
340C22×C73#57812yes—
341C22×C73C23×D411yescharacteristic
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—22no—
345C2×D73—44no—
346C2×D73—42no—
347C2×D73—42no—
348C2×D73—42no—
349C2×D73—84no—
350C4×C73—24no—
351C4×C73—22no—
352C4×C73—22no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73#52512yes—
357C4×C73C22×#4111yescharacteristic
358C4×C73C22×#4111yescharacteristic
359Dic73—22no—
360Dic73—24no—
361Dic73—22no—
362Dic73—22no—
363Dic73—42no—
364Dic73—42no—
365C2×#3121—731nomaximal, Sylow
366C2×C73#312114yescomplemented
367C2×C73C2×#52511yescharacteristic
368C2×C73C2×#57711yescharacteristic
369C2×C73C2×#57811yescharacteristic
370D73—42no—
371D73—82no—
372C2×#542—731no—
373C2×#519—731no—
374#3121—7316no—
375C2×#485—731no—
376C2×#482—731no—
377C2×#477—731no—
378C2×#475—731no—
379C2×#464—731no—
380C2×#464—731no—
381C2×#451—731no—
382C2×#448—731no—
383C2×#441D7311yescharacteristic, complemented
384C2×#440—731no—
385C2×C4×Q16—731no—
386C2×C4×SD16—731no—
387C2×#433—731no—
388C73C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8—731no—
390C22×Q16—731no—
391C22×Q16C2×D7311yescharacteristic
392C22×SD16—731no—
393C22×SD16—731no—
394#542—738no—
395#542—1464no—
396C2×C4⋊Q8—731no—
397C2×#126—1461no—
398C2×#124—731no—
399C2×#124—1461no—
400C2×#123—1461no—
401C2×C22⋊Q8—731no—
402C2×C22⋊Q8—1461no—
403C2×#121—731no—
404#519—738no—
405#519—1464no—
406C2×C4×Q8—731no—
407C2×C4×Q8—731no—
408C2×C4×Q8—731no—
409C2×C4×Q8—1461no—
410C2×C4×Q8—1461no—
411C2×C4×Q8C2×D7311yescharacteristic
412C2×C4×Q8C2×D7311yescharacteristic
413C2×C4×D4—731no—
414C2×#117—731no—
415C2×#117—731no—
416C2×#117—1461no—
417C2×#117—1461no—
418#485—738no—
419#482—738no—
420#477—738no—
421#475—738no—
422#464—738no—
423#464—738no—
424#451—738no—
425#448—738no—
426#441C2×D7318yescomplemented
427#440—738no—
428C4×Q16—738no—
429C4×SD16—738no—
430#433—738no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#106—731no—
434C2×#106C2×D7311yescharacteristic
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#103C2×D7311yescharacteristic
442C2×#103C2×D7311yescharacteristic
443C2×#102—731no—
444C2×#102—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×#97C2×D7311yescharacteristic
448C2×C4×C8—731no—
449C22×Q8—734no—
450C22×Q8—731no—
451C22×Q8—1461no—
452C22×Q8—1461no—
453C22×Q8—1462no—
454C22×Q8—1464no—
455C22×Q8—1464no—
456C22×Q8C22×D7311yescharacteristic
457C22×Q8C22×D7311yescharacteristic
458C22×D4—731no—
459C22×D4—1461no—
460C23×C4—731no—
461C23×C4—1461no—
462C23×C4—1461no—
463C2×Q16—24no—
464C2×Q16—734no—
465C2×Q16—1464no—
466C2×Q16C22×D7314yes—
467C2×SD16—734no—
468C2×SD16—734no—
469C2×SD16—1464no—
470C2×SD16—1464no—
471C22×C8—731no—
472C22×C8—731no—
473C22×C8C22×D7311yescharacteristic
474C22×C8C22×D7311yescharacteristic
475C4⋊Q8—734no—
476C4⋊Q8—1462no—
477#126—1468no—
478#124—734no—
479#124—1468no—
480#124—1462no—
481#123—1468no—
482C22⋊Q8—734no—
483C22⋊Q8—1468no—
484C22⋊Q8—1462no—
485#121—734no—
486#121—1462no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—734no—
490C4×Q8—734no—
491C4×Q8—734no—
492C4×Q8—1468no—
493C4×Q8—1462no—
494C4×Q8—1462no—
495C4×Q8—1468no—
496C4×Q8—1462no—
497C4×Q8C22×D7314yes—
498C4×Q8C22×D7314yes—
499C4×D4—734no—
500C4×D4—1462no—
501#117—734no—
502#117—734no—
503#117—734no—
504#117—1468no—
505#117—1468no—
506#117—1462no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C4⋊C4C22×D7311yescharacteristic
520C2×C22⋊C4—731no—
521C2×C22⋊C4—731no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—731no—
531C2×C42—1461no—
532C2×C42—1461no—
533C2×C42—1461no—
534C2×C42—1461no—
535C2×C42C22×D7311yescharacteristic
536#107—734no—
537#107—734no—
538#106—734no—
539#106C22×D7314yes—
540C4⋊C8—734no—
541C4⋊C8—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#103—734no—
546#103C22×D7314yes—
547#103C22×D7314yes—
548#102—734no—
549#102—734no—
550C22⋊C8—734no—
551C22⋊C8—734no—
552#97C22×D7314yes—
553C4×C8—734no—
554C24—731no—
555C24—1461no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—5842no—
562C2×Q8—734no—
563C2×Q8—732no—
564C2×Q8—1464no—
565C2×Q8—1464no—
566C2×Q8—1468no—
567C2×Q8—1468no—
568C2×Q8—14616no—
569C2×Q8—1468no—
570C2×Q8—1461no—
571C2×Q8—1462no—
572C2×Q8#1192402814yes—
573C2×Q8C23×D7312yes—
574C2×Q8C23×D7312yes—
575C2×D4—5842no—
576C2×D4—732no—
577C2×D4—1464no—
578C2×D4—1461no—
579C2×D4—1462no—
580C2×D4—1462no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—5842no—
586C22×C4—731no—
587C22×C4—731no—
588C22×C4—731no—
589C22×C4—732no—
590C22×C4—732no—
591C22×C4—1464no—
592C22×C4—1468no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1464no—
596C22×C4—1461no—
597C22×C4—1462no—
598C22×C4—1462no—
599C22×C4D4×D7311yescharacteristic
600C22×C4D4×D7311yescharacteristic
601C22×C4C23×D7311yescharacteristic
602Q16—28no—
603Q16—1468no—
604SD16—1468no—
605SD16—1468no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—732no—
609C2×C8—732no—
610C2×C8—1462no—
611C2×C8—1462no—
612C2×C8C23×D7312yes—
613C2×C8C23×D7312yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—734no—
619C4⋊C4—734no—
620C4⋊C4—732no—
621C4⋊C4—732no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1461no—
628C4⋊C4—1461no—
629C4⋊C4C23×D7312yes—
630C4⋊C4C23×D7312yes—
631C22⋊C4—734no—
632C22⋊C4—734no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—24no—
640C42—24no—
641C42—732no—
642C42—732no—
643C42—1464no—
644C42—1464no—
645C42—1464no—
646C42—1464no—
647C42D4×D7312yes—
648C42C23×D7312yes—
649C23—2922no—
650C23—2922no—
651C23—2922no—
652C23—732no—
653C23—1462no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23C2×D4×D7311yescharacteristic
658Q8—22no—
659Q8—24no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—5844no—
664Q8—734no—
665Q8—14616no—
666Q8—1462no—
667Q8—1464no—
668Q8C2×#1192402814yes—
669D4—2922no—
670D4—5844no—
671D4—1462no—
672D4—1462no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—2922no—
684C2×C4—2922no—
685C2×C4—5844no—
686C2×C4—732no—
687C2×C4—732no—
688C2×C4—732no—
689C2×C4—14616no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1464no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1464no—
700C2×C4C2×D4×D7312yes—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4#41×D7312yes—
704C2×C4C2×#1192402812yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1462no—
709C8—1462no—
710C22—2924no—
711C22—2922no—
712C22—2922no—
713C22—2922no—
714C22—5844no—
715C22—1462no—
716C22—1462no—
717C22—1462no—
718C22#1798909612yes—
719C22#1798939612yes—
720C22#1798940312yes—
721C22C22×D4×D7311yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—2922no—
729C4—2922no—
730C4—1462no—
731C4—1462no—
732C4—1462no—
733C4—1464no—
734C4#1798909612yes—
735C4C2×#41×D7311yescharacteristic
736C4C22×#1192402811yescharacteristic
737C2—2922no—
738C2—5842no—
739C2#2262016414yesdirect product factor
740C2C2×#1798909611yescharacteristic
741C2C2×#1798939611yescharacteristic
742C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#441×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556566C22
hypercenterC2×#441D73
hypocenterC73C2×#3121
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
2. C2×#17989063C2semidirect
3. #22620164C2direct (N × H)
4. C2×#17988927C2semidirect
6. C2×#17988880C2semidirect
7. C2×#17988871C2semidirect
8. C2×#17988812C2semidirect
9. C2×#17988811C2semidirect
10. C2×#17988741C2semidirect
12. C2×#17988689C2semidirect
13. C2×C4×#11924018C2semidirect
14. C2×C4×#11924015C2semidirect
15. C2×#17988649C2semidirect
16. C2×#441×C73C2semidirect
32. #17989063C22semidirect
43. #17988927C22semidirect
45. #17988880C22semidirect
46. #17988871C22semidirect
47. #17988812C22semidirect
48. #17988811C22semidirect
49. #17988741C22semidirect
51. #17988689C22semidirect
52. C4×#11924018C22semidirect
53. C4×#11924015C22semidirect
54. #17988649C22semidirect
72. #441×C73C22semidirect
366. C2×C73#3121semidirect
383. C2×#441D73semidirect
388. C73C2×#3121semidirect
426. #441C2×D73semidirect
739. C2#22620164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892092
C2×#179890632
#226201642
C2×#179889272
C2×#179889132
C2×#179888802
C2×#179888712
C2×#179888122
C2×#179888112
C2×#179887412
C2×#179887272
C2×#179886892
C2×C4×#119240182
C2×C4×#119240152
C2×#179886492
C2×#441×C732
C2×#312173