Finite Group Databasebeta

← C2×#22620229 #33954338

Subgroups — C2×#22620229 #33954338

Order 18688.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989198C211yesmaximal, characteristic
2C2×#17989063C211yesmaximal, characteristic
3#22620229C2116yesmaximal, direct product factor
4C2×#17988927C211yesmaximal, characteristic
5C2×#17988926C211yesmaximal, characteristic
6C2×#17988895C211yesmaximal, characteristic, complemented
7C2×#17988894C211yesmaximal, characteristic, complemented
8C2×#17988794C211yesmaximal, characteristic, complemented
9C2×#17988741C211yesmaximal, characteristic
10C2×#17988741C211yesmaximal, characteristic
11C2×#17988694C211yesmaximal, characteristic, complemented
12C2×#17988691C211yesmaximal, characteristic, complemented
13C2×Q16×Dic73C211yesmaximal, characteristic, complemented
14C2×#17988679C211yesmaximal, characteristic, complemented
15C2×#17988647C211yesmaximal, characteristic
16C2×#462×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20#17989198—24no—
21#17989198C2218yes—
22C2×#14556586—21no—
23C2×#14556586—21no—
24C2×#14556583C2211yescharacteristic
25C2×#14556581—21no—
26C2×#14556581—21no—
27C2×#14556567C2211yescharacteristic
28C2×#14556567C2211yescharacteristic
29#17989063—24no—
30#17989063C2218yes—
31C2×Q8×Dic73C2211yescharacteristic
32C2×Q8×Dic73C2211yescharacteristic
33C2×Q8×Dic73C2211yescharacteristic
34C2×C4×Dic146—21no—
35C2×C4×Dic146C2211yescharacteristic
36C2×#14556556—21no—
37C2×#14556556C2211yescharacteristic
38C2×#14556549—21no—
39C2×#14556549C2211yescharacteristic
40C2×#14556548—21no—
41C2×#14556548C2211yescharacteristic
42#17988927C2218yes—
43#17988926C2218yes—
44#17988895C2218yescomplemented
45#17988894C2218yescomplemented
46#17988794C2218yescomplemented
47#17988741C2218yes—
48#17988741C2218yes—
49#17988694C2218yescomplemented
50#17988691C2218yescomplemented
51Q16×Dic73C2218yescomplemented
52#17988679C2218yescomplemented
53#17988647C2218yes—
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556515C2211yescharacteristic
65C2×#14556503C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C2×C4⋊Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73#462×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C2×Q8×D73—24no—
80C2×Q8×D73—22no—
81C2×Q8×D73—24no—
82C2×Q8×D73C2314yes—
83C22×C4×D73—21no—
84C22×C4×D73C2311yescharacteristic
85C2×#11924018—24no—
86C2×#11924018—24no—
87C2×#11924018C2314yes—
88C2×#11924018C2314yes—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91#14556586—28no—
92#14556586—28no—
93#14556583—22no—
94#14556583C2314yes—
95#14556581—28no—
96#14556581—28no—
97#14556567—22no—
98#14556567—22no—
99#14556567C2314yes—
100#14556567C2314yes—
101Q8×Dic73—22no—
102Q8×Dic73—22no—
103Q8×Dic73—22no—
104Q8×Dic73C2314yes—
105Q8×Dic73C2314yes—
106Q8×Dic73C2314yes—
107C4×Dic146—28no—
108C4×Dic146—22no—
109C4×Dic146C2314yes—
110#14556556—28no—
111#14556556—22no—
112#14556556C2314yes—
113#14556549—22no—
114#14556549—28no—
115#14556549C2314yes—
116#14556548—28no—
117#14556548D414yes—
118#14556548C2314yes—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C2×#11924005—21no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005D411yescharacteristic
137C2×#11924005D411yescharacteristic
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145#14556525C2314yes—
146#14556524C2314yes—
147#14556523C2314yes—
148#14556522C2314yes—
149C4⋊#10596831C2314yes—
150#14556516C2314yes—
151#14556516C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556503C2314yes—
157#14556503C2314yes—
158#14556501C2314yes—
159C8×Dic73C2314yes—
160C22×Q8×C73C2311yescharacteristic
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C2×Q16×C73—24no—
164C2×Q16×C73—24no—
165C2×Q16×C73C2314yes—
166C2×Q16×C73C2314yes—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C4⋊Q8×C73—22no—
170C4⋊Q8×C73C2314yes—
171C4×Q8×C73—22no—
172C4×Q8×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73—21no—
175C2×C4⋊C4×C73—21no—
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C42×C73—21no—
178C2×C42×C73C2311yescharacteristic
179C4⋊C8×C73C2314yes—
180#103×C73C2314yes—
181#103×C73C2314yes—
182C23×D73C2×D411yescharacteristic
183C2×Dic146—28no—
184C2×Dic146—21no—
185C2×Dic146—22no—
186C2×Dic146—24no—
187C2×Dic146#4114yes—
188C2×Dic146C2412yes—
189Q8×D73—216no—
190Q8×D73—28no—
191Q8×D73—28no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73C2×D411yescharacteristic
197C22×Dic73C2×D411yescharacteristic
198C22×Dic73C2×D411yescharacteristic
199C2×C4×D73—28no—
200C2×C4×D73—24no—
201C2×C4×D73—22no—
202C2×C4×D73—22no—
203C2×C4×D73C2×D412yes—
204C2×C4×D73C2412yes—
205#11924018—28no—
206#11924018—28no—
207C2×#10596831—22no—
208C2×#10596831—22no—
209C2×#10596831C2412yes—
210C2×#10596831C2412yes—
211C4⋊Dic73—21no—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73—24no—
215C4⋊Dic73—24no—
216C4⋊Dic73—24no—
217C4⋊Dic73C2412yes—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007C2×D414yes—
227#11924007C2×D414yes—
228#11924005—24no—
229#11924005—24no—
230#11924005—24no—
231#11924005C2×D414yes—
232#11924005C2×D414yes—
233C4×Dic73—24no—
234C4×Dic73—24no—
235C4×Dic73—24no—
236C4×Dic73—24no—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73C2×D412yes—
240C4×Dic73C2412yes—
241C2×Q8×C73—21no—
242C2×Q8×C73—21no—
243C2×Q8×C73—21no—
244C2×Q8×C73—22no—
245C2×Q8×C73—22no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73—22no—
249C2×Q8×C73#4114yes—
250C2×Q8×C73C2412yes—
251C2×Q8×C73C2412yes—
252C2×Q8×C73C2412yes—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2411yescharacteristic
260Q16×C73—28no—
261Q16×C73—28no—
262C2×C8×C73—22no—
263C2×C8×C73—22no—
264C2×C8×C73C2412yes—
265C2×C8×C73C2412yes—
266C4⋊C4×C73—24no—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C2412yes—
271C42×C73—24no—
272C42×C73C2×D412yes—
273C42×C73C2412yes—
274C23×C73C22×D411yescharacteristic
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73C22×D412yes—
279Q8×C73—24no—
280Q8×C73—22no—
281Q8×C73—22no—
282Q8×C73—22no—
283Q8×C73—22no—
284Q8×C73—22no—
285Q8×C73—42no—
286Q8×C73—42no—
287Q8×C73C2×#4114yes—
288C2×C4×C73—24no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—42no—
296C2×C4×C73—42no—
297C2×C4×C73—42no—
298C2×C4×C73C22×D412yes—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4112yes—
302C2×C4×C73C2×#4112yes—
303C2×C4×C73C2511yescharacteristic
304C2×Dic73—24no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73C22×D412yes—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318C4×D73—216no—
319C4×D73—24no—
320C4×D73—22no—
321C4×D73—22no—
322Dic146—216no—
323Dic146—24no—
324Dic146—22no—
325Dic146C2×#4114yes—
326C8×C73—22no—
327C8×C73—22no—
328#10596831—22no—
329#10596831—22no—
330C22×C73#52512yes—
331C22×C73#57812yes—
332C22×C73#57812yes—
333C22×C73C23×D411yescharacteristic
334C2×D73—22no—
335C2×D73—22no—
336C2×D73—22no—
337C2×D73—44no—
338C4×C73—24no—
339C4×C73—22no—
340C4×C73—22no—
341C4×C73—42no—
342C4×C73—42no—
343C4×C73—42no—
344C4×C73#52512yes—
345C4×C73C22×#4111yescharacteristic
346C4×C73C22×#4111yescharacteristic
347Dic73—22no—
348Dic73—24no—
349Dic73—22no—
350Dic73—22no—
351Dic73—42no—
352Dic73—42no—
353Dic73—42no—
354C2×#3127—731nomaximal, Sylow
355C2×C73#312714yescomplemented
356C2×C73C2×#52511yescharacteristic
357C2×C73C2×#57811yescharacteristic
358C2×C73C2×#57811yescharacteristic
359D73—42no—
360C2×#541—731no—
361C2×#519—731no—
362#3127—7316no—
363C2×#485—731no—
364C2×#485—731no—
365C2×#479—731no—
366C2×#479—731no—
367C2×#462—731no—
368C2×#462D7311yescharacteristic, complemented
369C2×#451—731no—
370C2×#451—731no—
371C2×#441—731no—
372C2×#441—731no—
373C2×C4×Q16—731no—
374C2×C4×Q16—731no—
375C2×#433—731no—
376C73C2×#312711yescharacteristic, complemented, Sylow
377C23×Q8—731no—
378C22×Q16—731no—
379C22×Q16—731no—
380C22×Q16C2×D7311yescharacteristic
381C22×Q16C2×D7311yescharacteristic
382#541—738no—
383#541—1464no—
384C2×C4⋊Q8C2×D7311yescharacteristic
385C2×#126—1461no—
386C2×#126—1461no—
387C2×#125—731no—
388C2×#125—1461no—
389C2×#125—1461no—
390C2×C22⋊Q8—731no—
391C2×C22⋊Q8—731no—
392#519—738no—
393#519—1464no—
394C2×C4×Q8—731no—
395C2×C4×Q8—731no—
396C2×C4×Q8—731no—
397C2×C4×Q8—731no—
398C2×C4×Q8—731no—
399C2×C4×Q8—1461no—
400C2×C4×Q8—1461no—
401C2×C4×Q8C2×D7311yescharacteristic
402C2×#117—731no—
403C2×#117—731no—
404C2×#117—1461no—
405C2×#117—1461no—
406#485—738no—
407#485—738no—
408#479—738no—
409#479—738no—
410#462—738no—
411#462C2×D7318yescomplemented
412#451—738no—
413#451—738no—
414#441—738no—
415#441—738no—
416C4×Q16—738no—
417C4×Q16—738no—
418#433—738no—
419C2×#107—731no—
420C2×#107—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×C4⋊C8—731no—
424C2×C4⋊C8C2×D7311yescharacteristic
425C2×#103—731no—
426C2×#103—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103—731no—
431C2×#103C2×D7311yescharacteristic
432C2×#103C2×D7311yescharacteristic
433C2×C22⋊C8—731no—
434C2×C22⋊C8—731no—
435C2×#97—731no—
436C2×C4×C8—731no—
437C22×Q8—734no—
438C22×Q8—731no—
439C22×Q8—1461no—
440C22×Q8—1462no—
441C22×Q8—1464no—
442C22×Q8—1464no—
443C22×Q8C22×D7311yescharacteristic
444C22×Q8C22×D7311yescharacteristic
445C22×Q8C22×D7311yescharacteristic
446C23×C4—731no—
447C23×C4—1461no—
448C2×Q16—24no—
449C2×Q16—24no—
450C2×Q16—734no—
451C2×Q16—734no—
452C2×Q16—1464no—
453C2×Q16—1464no—
454C2×Q16C22×D7314yes—
455C2×Q16C22×D7314yes—
456C22×C8—731no—
457C22×C8—731no—
458C22×C8C22×D7311yescharacteristic
459C22×C8C22×D7311yescharacteristic
460C4⋊Q8—22no—
461C4⋊Q8C22×D7314yes—
462#126—1468no—
463#126—1468no—
464#125—734no—
465#125—1468no—
466#125—1468no—
467#125—1462no—
468C22⋊Q8—734no—
469C22⋊Q8—734no—
470C22⋊Q8—1462no—
471C22⋊Q8—1462no—
472C4×Q8—22no—
473C4×Q8—734no—
474C4×Q8—734no—
475C4×Q8—734no—
476C4×Q8—734no—
477C4×Q8—734no—
478C4×Q8—1468no—
479C4×Q8—1462no—
480C4×Q8—1462no—
481C4×Q8—1462no—
482C4×Q8—1462no—
483C4×Q8—1468no—
484C4×Q8—1462no—
485C4×Q8C22×D7314yes—
486#117—734no—
487#117—734no—
488#117—734no—
489#117—1468no—
490#117—1468no—
491#117—1462no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1461no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4C22×D7311yescharacteristic
510C2×C22⋊C4—731no—
511C2×C22⋊C4—731no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C22⋊C4—1461no—
515C2×C42—21no—
516C2×C42—731no—
517C2×C42—1461no—
518C2×C42—1461no—
519C2×C42—1461no—
520C2×C42—1461no—
521C2×C42—1461no—
522C2×C42—1461no—
523C2×C42C22×D7311yescharacteristic
524#107—734no—
525#107—734no—
526#106—734no—
527#106—734no—
528C4⋊C8—734no—
529C4⋊C8C22×D7314yes—
530#103—734no—
531#103—734no—
532#103—734no—
533#103—734no—
534#103—734no—
535#103—734no—
536#103C22×D7314yes—
537#103C22×D7314yes—
538C22⋊C8—734no—
539C22⋊C8—734no—
540#97—734no—
541C4×C8—734no—
542C24—731no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—734no—
552C2×Q8—732no—
553C2×Q8—1464no—
554C2×Q8—1468no—
555C2×Q8—1468no—
556C2×Q8—14616no—
557C2×Q8—1468no—
558C2×Q8—1461no—
559C2×Q8—1462no—
560C2×Q8#1192402714yes—
561C2×Q8C23×D7312yes—
562C2×Q8C23×D7312yes—
563C2×Q8C23×D7312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—731no—
569C22×C4—731no—
570C22×C4—731no—
571C22×C4—732no—
572C22×C4—732no—
573C22×C4—1464no—
574C22×C4—1468no—
575C22×C4—1461no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4D4×D7311yescharacteristic
582C22×C4D4×D7311yescharacteristic
583C22×C4C23×D7311yescharacteristic
584Q16—28no—
585Q16—28no—
586Q16—1468no—
587Q16—1468no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—732no—
591C2×C8—732no—
592C2×C8—1462no—
593C2×C8—1462no—
594C2×C8C23×D7312yes—
595C2×C8C23×D7312yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—734no—
601C4⋊C4—734no—
602C4⋊C4—732no—
603C4⋊C4—732no—
604C4⋊C4—732no—
605C4⋊C4—1464no—
606C4⋊C4—1464no—
607C4⋊C4—1464no—
608C4⋊C4—1464no—
609C4⋊C4—1464no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1461no—
615C4⋊C4—1461no—
616C4⋊C4—1461no—
617C4⋊C4C23×D7312yes—
618C22⋊C4—734no—
619C22⋊C4—734no—
620C22⋊C4—1464no—
621C22⋊C4—1464no—
622C22⋊C4—1464no—
623C42—24no—
624C42—732no—
625C42—732no—
626C42—1464no—
627C42—1464no—
628C42—1464no—
629C42—1464no—
630C42—1464no—
631C42—1464no—
632C42D4×D7312yes—
633C42C23×D7312yes—
634C23—732no—
635C23—1462no—
636C23—1462no—
637C23—1462no—
638C23C2×D4×D7311yescharacteristic
639Q8—22no—
640Q8—24no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—42no—
647Q8—734no—
648Q8—14616no—
649Q8—1462no—
650Q8—1464no—
651Q8C2×#1192402714yes—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—2922no—
663C2×C4—2922no—
664C2×C4—2922no—
665C2×C4—732no—
666C2×C4—732no—
667C2×C4—732no—
668C2×C4—14616no—
669C2×C4—1462no—
670C2×C4—1462no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4—1464no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1464no—
680C2×C4C2×D4×D7312yes—
681C2×C4C2×D4×D7312yes—
682C2×C4C2×D4×D7311yescharacteristic
683C2×C4#41×D7312yes—
684C2×C4C2×#1192402712yes—
685C2×C4C24×D7311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1462no—
689C8—1462no—
690C22—2924no—
691C22—1462no—
692C22—1462no—
693C22—1462no—
694C22#1798909712yes—
695C22#1798940012yes—
696C22#1798940312yes—
697C22C22×D4×D7311yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—2922no—
705C4—2922no—
706C4—2922no—
707C4—1462no—
708C4—1462no—
709C4—1462no—
710C4—1464no—
711C4#1798909712yes—
712C4C2×#41×D7311yescharacteristic
713C4C22×#1192402711yescharacteristic
714C2—2922no—
715C2#2262022914yesdirect product factor
716C2C2×#1798909711yescharacteristic
717C2C2×#1798940011yescharacteristic
718C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#462×C73C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
hypercenterC2×#462D73
hypocenterC73C2×#3127
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #22620229C2direct (N × H)
6. C2×#17988895C2semidirect
7. C2×#17988894C2semidirect
8. C2×#17988794C2semidirect
11. C2×#17988694C2semidirect
12. C2×#17988691C2semidirect
13. C2×Q16×Dic73C2semidirect
14. C2×#17988679C2semidirect
16. C2×#462×C73C2semidirect
44. #17988895C22semidirect
45. #17988894C22semidirect
46. #17988794C22semidirect
49. #17988694C22semidirect
50. #17988691C22semidirect
51. Q16×Dic73C22semidirect
52. #17988679C22semidirect
73. #462×C73C22semidirect
355. C2×C73#3127semidirect
368. C2×#462D73semidirect
376. C73C2×#3127semidirect
411. #462C2×D73semidirect
715. C2#22620229direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891982
C2×#179890632
#226202292
C2×#179889272
C2×#179889262
C2×#179888952
C2×#179888942
C2×#179887942
C2×#179887412
C2×#179886942
C2×#179886912
C2×Q16×Dic732
C2×#179886792
C2×#179886472
C2×#462×C732
C2×#312773