Finite Group Databasebeta

← C2×#22622392 #33964537

Subgroups — C2×#22622392 #33964537

Order 18688.

1878 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×#17989295C211yesmaximal, characteristic
2C2×#17989279C211yesmaximal, characteristic
3#22622392C2116yesmaximal, direct product factor
4C2×#17988995C211yesmaximal, characteristic, complemented
5C2×#17988920C211yesmaximal, characteristic, complemented
6C2×#17988926C211yesmaximal, characteristic, complemented
7C2×#17988916C211yesmaximal, characteristic, complemented
8C2×#17988915C211yesmaximal, characteristic, complemented
9C2×#17988892C211yesmaximal, characteristic, complemented
10C2×#17988870C211yesmaximal, characteristic, complemented
11C2×#17988842C211yesmaximal, characteristic, complemented
12C2×#17988694C211yesmaximal, characteristic, complemented
13C2×#17988658C211yesmaximal, characteristic
14C2×#17988628C211yesmaximal, characteristic, complemented
15C22×#14556523C211yesmaximal, characteristic, complemented
16C2×#467×C73C211yesmaximal, characteristic, complemented
17C22×#11924011C2211yescharacteristic
18#17989295—24no—
19#17989295C2218yes—
20#17989279—24no—
21#17989279C2218yes—
22C2×#14556590C2211yescharacteristic
23C2×#14556586—21no—
24C2×#14556582—21no—
25C2×#14556582C2211yescharacteristic
26C2×#14556581—21no—
27C2×#14556575—21no—
28C2×#14556571—21no—
29C2×#14556568—21no—
30C2×#14556567C2211yescharacteristic
31C2×#14556567C2211yescharacteristic
32C2×Q8×Dic73C2211yescharacteristic
33C2×Q8×Dic73C2211yescharacteristic
34C2×C4×C22⋊D73C2211yescharacteristic
35C2×#14556551—21no—
36C2×#14556549C2211yescharacteristic
37C2×#14556547—21no—
38C22×C4⋊Dic73C2211yescharacteristic
39C22×C4⋊Dic73C2211yescharacteristic
40C2×C4⋊C4×D73C2211yescharacteristic
41#17988995C2218yescomplemented
42#17988926C2218yescomplemented
43#17988920C2218yescomplemented
44#17988916C2218yescomplemented
45#17988915C2218yescomplemented
46#17988892C2218yescomplemented
47#17988870C2218yescomplemented
48#17988842C2218yescomplemented
49#17988694C2218yescomplemented
50#17988658C2218yes—
51#17988628C2218yescomplemented
52C2×#14556524C2211yescharacteristic
53C2×#14556524C2211yescharacteristic
54C2×#14556523C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556523C2218yescomplemented
59C2×#14556522C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556515C2211yescharacteristic
65C2×#14556515C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×C22⋊Q8×C73C2211yescharacteristic
73#467×C73C2218yescomplemented
74C2×#107×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×C22⋊D73D411yescharacteristic
79C23×Dic73—21no—
80C23×Dic73—21no—
81C22×C4×D73—21no—
82C22×C4×D73C2311yescharacteristic
83C2×#11924011—24no—
84C2×#11924011C2314yes—
85C22×#10596831C2311yescharacteristic
86C22×#10596831C2311yescharacteristic
87#14556590—22no—
88#14556590C2314yes—
89#14556586—28no—
90#14556582—28no—
91#14556582—22no—
92#14556582C2314yes—
93#14556581—28no—
94#14556575—28no—
95#14556571—28no—
96#14556568—28no—
97#14556567—22no—
98#14556567—22no—
99#14556567C2314yes—
100#14556567C2314yes—
101Q8×Dic73—22no—
102Q8×Dic73—22no—
103Q8×Dic73C2314yes—
104Q8×Dic73C2314yes—
105C4×C22⋊D73D414yes—
106C4×C22⋊D73C2314yes—
107#14556551—28no—
108#14556549—22no—
109#14556549C2314yes—
110#14556547—28no—
111C2×C4⋊Dic73—21no—
112C2×C4⋊Dic73—21no—
113C2×C4⋊Dic73—21no—
114C2×C4⋊Dic73—22no—
115C2×C4⋊Dic73—22no—
116C2×C4⋊Dic73—21no—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73C2311yescharacteristic
119C2×C4⋊Dic73C2311yescharacteristic
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2314yes—
123C2×C4⋊Dic73C2314yes—
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007D411yescharacteristic
130C4⋊C4×D73—22no—
131C4⋊C4×D73C2314yes—
132C2×C22⋊Dic73D411yescharacteristic
133C2×#11924005—21no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005D411yescharacteristic
137C2×C4×Dic73—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73C2311yescharacteristic
141#14556524C2314yes—
142#14556524C2314yes—
143#14556523C2314yes—
144#14556523C2314yes—
145#14556523C2314yes—
146#14556523C2314yes—
147#14556522C2314yes—
148#14556522C2314yes—
149#14556520C2314yes—
150#14556515C2314yes—
151#14556515C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154C22⋊#10596831C2314yes—
155#14556503C2314yes—
156#14556501C2314yes—
157C22×Q8×C73C2311yescharacteristic
158C22×Q8×C73C2311yescharacteristic
159C23×C4×C73C2311yescharacteristic
160C2×Q16×C73—24no—
161C2×Q16×C73C2314yes—
162C22×C8×C73—24no—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22⋊Q8×C73—22no—
167C22⋊Q8×C73—22no—
168C22⋊Q8×C73C2314yes—
169C22⋊Q8×C73C2314yes—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73—21no—
176#107×C73C2314yes—
177#103×C73C2314yes—
178#103×C73C2314yes—
179C23×D73C2×D411yescharacteristic
180C2×Dic146—24no—
181C2×Dic146—82no—
182C2×C22⋊D73—24no—
183C2×C22⋊D73C2×D414yes—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—24no—
189C22×Dic73—24no—
190C22×Dic73—44no—
191C22×Dic73—82no—
192C22×Dic73C2×D411yescharacteristic
193C22×Dic73C2×D411yescharacteristic
194C22×Dic73C2×D411yescharacteristic
195C2×C4×D73—22no—
196C2×C4×D73—22no—
197C2×C4×D73—24no—
198C2×C4×D73—82no—
199C2×C4×D73C2×D412yes—
200C2×C4×D73C2412yes—
201#11924011—28no—
202C2×#10596831—22no—
203C2×#10596831—22no—
204C2×#10596831C2412yes—
205C2×#10596831C2412yes—
206C4⋊Dic73—21no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209C4⋊Dic73—21no—
210C4⋊Dic73—24no—
211C4⋊Dic73—24no—
212C4⋊Dic73—24no—
213C4⋊Dic73—24no—
214C4⋊Dic73—24no—
215C4⋊Dic73C2412yes—
216C4⋊Dic73C2412yes—
217C4⋊Dic73C2412yes—
218C4⋊Dic73C2412yes—
219#11924007—24no—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007C2×D414yes—
225C22⋊Dic73C2×D414yes—
226#11924005—24no—
227#11924005—24no—
228#11924005—24no—
229#11924005C2×D414yes—
230C4×Dic73—24no—
231C4×Dic73—24no—
232C4×Dic73—24no—
233C4×Dic73C2×D412yes—
234C4×Dic73C2412yes—
235C24×C73C2×D411yescharacteristic
236C2×Q8×C73—21no—
237C2×Q8×C73—21no—
238C2×Q8×C73—22no—
239C2×Q8×C73—22no—
240C2×Q8×C73—22no—
241C2×Q8×C73—22no—
242C2×Q8×C73C2412yes—
243C2×Q8×C73C2412yes—
244C22×C4×C73—22no—
245C22×C4×C73—22no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D412yes—
252C22×C4×C73C2412yes—
253C22×C4×C73C2411yescharacteristic
254Q16×C73—28no—
255C2×C8×C73—22no—
256C2×C8×C73—28no—
257C2×C8×C73#4114yes—
258C2×C8×C73C2412yes—
259C2×C8×C73C2412yes—
260C4⋊C4×C73—24no—
261C4⋊C4×C73—24no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73C2412yes—
265C4⋊C4×C73C2412yes—
266C22⋊C4×C73—24no—
267C22⋊C4×C73—24no—
268C23×C73—22no—
269C23×C73—22no—
270C23×C73#13714yes—
271C23×C73C22×D412yes—
272C23×C73C22×D411yescharacteristic
273C22×D73—22no—
274C22×D73—22no—
275C22×D73—22no—
276C22×D73C22×D412yes—
277Q8×C73—22no—
278Q8×C73—22no—
279Q8×C73—22no—
280Q8×C73—22no—
281Q8×C73—42no—
282Q8×C73—42no—
283C2×C4×C73—22no—
284C2×C4×C73—24no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—42no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C2×#4112yes—
298C2×C4×C732−1+412yes—
299C2×C4×C73C2511yescharacteristic
300C22⋊D73—28no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—48no—
309C2×Dic73—42no—
310C2×Dic73—42no—
311C2×Dic73—42no—
312C2×Dic73—42no—
313C2×Dic73—84no—
314C2×Dic73C22×D412yes—
315C2×Dic73C22×D412yes—
316C2×Dic73C22×D412yes—
317C4×D73—24no—
318C4×D73—22no—
319C4×D73—22no—
320C4×D73—84no—
321Dic146—84no—
322C8×C73—22no—
323C8×C73C2×#4114yes—
324#10596831—22no—
325#10596831—22no—
326C22×C73—28no—
327C22×C73—22no—
328C22×C73—22no—
329C22×C73#54712yes—
330C22×C73C2×#13714yes—
331C22×C73C2×#13712yes—
332C22×C73#57712yes—
333C22×C73C23×D411yescharacteristic
334C2×D73—22no—
335C2×D73—22no—
336C2×D73—22no—
337C2×D73—44no—
338C4×C73—22no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73—42no—
343C4×C73#54712yes—
344C4×C73C22×#4111yescharacteristic
345C4×C73C2×2−1+411yescharacteristic
346Dic73—22no—
347Dic73—22no—
348Dic73—22no—
349Dic73—42no—
350Dic73—42no—
351Dic73—42no—
352Dic73—42no—
353C2×#3344—731nomaximal, Sylow
354C2×C73—24no—
355C2×C73#334414yescomplemented
356C2×C73C2×#54711yescharacteristic
357C2×C73C22×#13711yescharacteristic
358C2×C73C2×#57711yescharacteristic
359D73—42no—
360C2×#554—731no—
361C2×#552—731no—
362#3344—7316no—
363C2×#501—731no—
364C2×#484—731no—
365C2×#485—731no—
366C2×#483—731no—
367C2×#483—731no—
368C2×#479—731no—
369C2×#475—731no—
370C2×#470—731no—
371C2×#467D7311yescharacteristic, complemented
372C2×#441—731no—
373C2×#435—731no—
374C2×#428—731no—
375C22×#106—731no—
376C73C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16C2×D7311yescharacteristic
378C22×M16—731no—
379C23×C8C2×D7311yescharacteristic
380#554—738no—
381#554—1464no—
382#552—738no—
383#552—1464no—
384C2×C4⋊Q8—731no—
385C2×#126—1461no—
386C2×#125—731no—
387C2×#125—1461no—
388C2×#125—1461no—
389C2×#123—1461no—
390C2×C22⋊Q8—731no—
391C2×C22⋊Q8—731no—
392C2×C22⋊Q8—1461no—
393C2×C22⋊Q8—1461no—
394C2×C22⋊Q8C2×D7311yescharacteristic
395C2×C22⋊Q8C2×D7311yescharacteristic
396C2×C4×Q8—731no—
397C2×C4×Q8—731no—
398C2×C4×D4—731no—
399C2×C4×D4—1461no—
400C2×#117—731no—
401C2×#117—1461no—
402C22×C4⋊C4—731no—
403C22×C4⋊C4—731no—
404C22×C4⋊C4—731no—
405#501—738no—
406#485—738no—
407#484—738no—
408#483—738no—
409#483—738no—
410#479—738no—
411#475—738no—
412#470—738no—
413#467C2×D7318yescomplemented
414#441—738no—
415#435—738no—
416#428—738no—
417C2×#107—731no—
418C2×#107—731no—
419C2×#107C2×D7311yescharacteristic
420C2×#106—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×#106—731no—
424C2×#106—738no—
425C2×#106—731no—
426C2×#106—731no—
427C2×C4⋊C8—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103—731no—
431C2×#103—731no—
432C2×#103C2×D7311yescharacteristic
433C2×#103C2×D7311yescharacteristic
434C2×C22⋊C8—731no—
435C2×C22⋊C8—731no—
436C2×#97—731no—
437C22×Q8—1461no—
438C22×Q8C22×D7311yescharacteristic
439C22×Q8C22×D7311yescharacteristic
440C22×D4—731no—
441C23×C4—731no—
442C23×C4—1461no—
443C23×C4—1461no—
444C23×C4—1461no—
445C23×C4C22×D7311yescharacteristic
446C2×Q16—24no—
447C2×Q16C22×D7314yes—
448C2×M16—734no—
449C2×M16—1464no—
450C22×C8—24no—
451C22×C8—731no—
452C22×C8—731no—
453C22×C8C22×D7311yescharacteristic
454C22×C8C22×D7314yes—
455C22×C8C22×D7311yescharacteristic
456C4⋊Q8—734no—
457C4⋊Q8—1462no—
458#126—1468no—
459#125—734no—
460#125—1462no—
461#125—1468no—
462#125—1468no—
463#123—1468no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—734no—
467C22⋊Q8—734no—
468C22⋊Q8—1468no—
469C22⋊Q8—1468no—
470C22⋊Q8—1462no—
471C22⋊Q8—1462no—
472C22⋊Q8C22×D7314yes—
473C22⋊Q8C22×D7314yes—
474C4×Q8—734no—
475C4×Q8—734no—
476C4×Q8—1462no—
477C4×Q8—1462no—
478C4×D4—734no—
479C4×D4—734no—
480C4×D4—1468no—
481#117—734no—
482#117—1468no—
483#117—1462no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—731no—
487C2×C4⋊C4—731no—
488C2×C4⋊C4—731no—
489C2×C4⋊C4—731no—
490C2×C4⋊C4—731no—
491C2×C4⋊C4—734no—
492C2×C4⋊C4—734no—
493C2×C4⋊C4—734no—
494C2×C4⋊C4—1462no—
495C2×C4⋊C4—1461no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1461no—
498C2×C4⋊C4—1461no—
499C2×C4⋊C4—1461no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1462no—
506C2×C4⋊C4—1462no—
507C2×C4⋊C4C22×D7311yescharacteristic
508C2×C4⋊C4C22×D7311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—731no—
512C2×C22⋊C4—731no—
513C2×C22⋊C4—1461no—
514C2×C22⋊C4—1461no—
515C2×C22⋊C4—1461no—
516C2×C42—731no—
517C2×C42—1461no—
518C2×C42—1461no—
519C2×C42—1461no—
520#107—734no—
521#107—734no—
522#107C22×D7314yes—
523#106—734no—
524#106—734no—
525#106—734no—
526#106—734no—
527#106—734no—
528#106—734no—
529C4⋊C8—734no—
530#103—734no—
531#103—734no—
532#103—734no—
533#103—734no—
534#103C22×D7314yes—
535#103C22×D7314yes—
536C22⋊C8—734no—
537C22⋊C8—734no—
538#97—734no—
539C24—731no—
540C24D4×D7311yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—5842no—
548C2×Q8—1464no—
549C2×Q8C23×D7312yes—
550C2×Q8C23×D7312yes—
551C2×D4—734no—
552C2×D4—1464no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—2924no—
560C22×C4—5842no—
561C22×C4—5842no—
562C22×C4—731no—
563C22×C4—731no—
564C22×C4—731no—
565C22×C4—732no—
566C22×C4—732no—
567C22×C4—1464no—
568C22×C4—1464no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1464no—
574C22×C4—1462no—
575C22×C4—1462no—
576C22×C4D4×D7312yes—
577C22×C4D4×D7311yescharacteristic
578C22×C4C23×D7312yes—
579C22×C4C23×D7311yescharacteristic
580Q16—28no—
581M16—1468no—
582C2×C8—22no—
583C2×C8—28no—
584C2×C8—732no—
585C2×C8—732no—
586C2×C8—1462no—
587C2×C8—1462no—
588C2×C8#1192402714yes—
589C2×C8C23×D7312yes—
590C2×C8C23×D7312yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—734no—
596C4⋊C4—732no—
597C4⋊C4—732no—
598C4⋊C4—732no—
599C4⋊C4—732no—
600C4⋊C4—1464no—
601C4⋊C4—1464no—
602C4⋊C4—1464no—
603C4⋊C4—1464no—
604C4⋊C4—1464no—
605C4⋊C4—1464no—
606C4⋊C4—1464no—
607C4⋊C4—1464no—
608C4⋊C4—1461no—
609C4⋊C4—1461no—
610C4⋊C4—1464no—
611C4⋊C4—1461no—
612C4⋊C4—1461no—
613C4⋊C4—1464no—
614C4⋊C4C23×D7312yes—
615C4⋊C4C23×D7312yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—734no—
619C22⋊C4—734no—
620C22⋊C4—1464no—
621C22⋊C4—1464no—
622C22⋊C4—1464no—
623C42—732no—
624C42—732no—
625C42—1464no—
626C42—1464no—
627C42—1464no—
628C23—22no—
629C23—22no—
630C23—732no—
631C23—1462no—
632C23—1462no—
633C23—1462no—
634C23#1455662314yes—
635C23C2×D4×D7312yes—
636C23C2×D4×D7311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—5844no—
644D4—1468no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—2928no—
658C2×C4—2922no—
659C2×C4—2922no—
660C2×C4—2922no—
661C2×C4—2922no—
662C2×C4—5844no—
663C2×C4—5844no—
664C2×C4—732no—
665C2×C4—732no—
666C2×C4—732no—
667C2×C4—1462no—
668C2×C4—1462no—
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×C4C2×D4×D7312yes—
678C2×C4C2×D4×D7311yescharacteristic
679C2×C4C2×#1192402712yes—
680C2×C4#1455663812yes—
681C2×C4C24×D7311yescharacteristic
682C8—22no—
683C8—1462no—
684C8—1462no—
685C8C2×#1192402714yes—
686C22—22no—
687C22—22no—
688C22—28no—
689C22—2924no—
690C22—1462no—
691C22—1462no—
692C22—1462no—
693C22#1798923712yes—
694C22C2×#1455662314yes—
695C22C2×#1455662312yes—
696C22#1798939412yes—
697C22C22×D4×D7311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—2922no—
704C4—2922no—
705C4—2922no—
706C4—2922no—
707C4—1462no—
708C4—1462no—
709C4—1462no—
710C4#1798923712yes—
711C4C22×#1192402711yescharacteristic
712C4C2×#1455663811yescharacteristic
713C2—24no—
714C2—2922no—
715C2#2262239214yesdirect product factor
716C2C2×#1798923711yescharacteristic
717C2C22×#1455662311yescharacteristic
718C2C2×#1798939411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#467×C73C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
hypercenterC2×#467D73
hypocenterC73C2×#3344
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #22622392C2direct (N × H)
4. C2×#17988995C2semidirect
5. C2×#17988920C2semidirect
6. C2×#17988926C2semidirect
7. C2×#17988916C2semidirect
8. C2×#17988915C2semidirect
9. C2×#17988892C2semidirect
10. C2×#17988870C2semidirect
11. C2×#17988842C2semidirect
12. C2×#17988694C2semidirect
14. C2×#17988628C2semidirect
15. C22×#14556523C2semidirect
16. C2×#467×C73C2semidirect
41. #17988995C22semidirect
42. #17988926C22semidirect
43. #17988920C22semidirect
44. #17988916C22semidirect
45. #17988915C22semidirect
46. #17988892C22semidirect
47. #17988870C22semidirect
48. #17988842C22semidirect
49. #17988694C22semidirect
51. #17988628C22semidirect
58. C2×#14556523C22semidirect
73. #467×C73C22semidirect
355. C2×C73#3344semidirect
371. C2×#467D73semidirect
376. C73C2×#3344semidirect
413. #467C2×D73semidirect
715. C2#22622392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892952
C2×#179892792
#226223922
C2×#179889952
C2×#179889202
C2×#179889262
C2×#179889162
C2×#179889152
C2×#179888922
C2×#179888702
C2×#179888422
C2×#179886942
C2×#179886582
C2×#179886282
C22×#145565232
C2×#467×C732
C2×#334473