Finite Group Databasebeta

← C2×#22622709 #33965644

Subgroups — C2×#22622709 #33965644

Order 18688.

1854 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989312C211yesmaximal, characteristic, complemented
2C2×#17989293C211yesmaximal, characteristic
3#22622709C2116yesmaximal, direct product factor
4C2×#17988954C211yesmaximal, characteristic, complemented
5C2×#17988936C211yesmaximal, characteristic, complemented
6C2×#17988896C211yesmaximal, characteristic, complemented
7C2×#17988891C211yesmaximal, characteristic, complemented
8C2×#17988880C211yesmaximal, characteristic, complemented
9C2×#17988791C211yesmaximal, characteristic
10C2×#17988791C211yesmaximal, characteristic
11C2×#17988789C211yesmaximal, characteristic
12C2×#17988715C211yesmaximal, characteristic, complemented
13C2×#17988690C211yesmaximal, characteristic
14C2×#17988689C211yesmaximal, characteristic
15C2×#17988672C211yesmaximal, characteristic
16C2×#491×C73C211yesmaximal, characteristic, complemented
17C22×#11924017C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20#17989312—24no—
21#17989312C2218yescomplemented
22#17989293—24no—
23#17989293C2218yes—
24C2×#14556590C2211yescharacteristic
25C2×#14556589C2211yescharacteristic
26C2×#14556589C2211yescharacteristic
27C2×#14556582—21no—
28C2×#14556582C2211yescharacteristic
29C2×#14556581—21no—
30C2×#14556581—21no—
31C2×#14556571—21no—
32C2×#14556569—21no—
33C2×#14556569—21no—
34C2×Q8×Dic73C2211yescharacteristic
35C2×Q8×Dic73C2211yescharacteristic
36C2×C4×Dic146C2211yescharacteristic
37C2×C4×Dic146C2211yescharacteristic
38C2×#14556556—21no—
39C2×C4×D292C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×#14556553C2211yescharacteristic
42C2×C4⋊C4×D73—21no—
43#17988954C2218yescomplemented
44#17988936C2218yescomplemented
45#17988896C2218yescomplemented
46#17988891C2218yescomplemented
47#17988880C2218yescomplemented
48#17988791C2218yes—
49#17988791C2218yes—
50#17988789C2218yes—
51#17988715C2218yescomplemented
52#17988690C2218yes—
53#17988689C2218yes—
54#17988672C2218yes—
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66C2×#14556513C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×#125×C73C2211yescharacteristic
71#491×C73C2218yescomplemented
72C2×#103×C73C2211yescharacteristic
73C2×#103×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146D411yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×D292C2311yescharacteristic
81C22×C4×D73—21no—
82C22×C4×D73—21no—
83C22×C4×D73—21no—
84C2×#11924017—24no—
85C2×#11924017C2314yes—
86C2×#11924015—24no—
87C2×#11924015—24no—
88C2×#11924015C2314yes—
89C2×#11924015C2314yes—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92#14556590—22no—
93#14556590C2314yes—
94#14556589—22no—
95#14556589—22no—
96#14556589C2314yes—
97#14556589C2314yes—
98#14556582—28no—
99#14556582—22no—
100#14556582C2314yes—
101#14556581—28no—
102#14556581—28no—
103#14556571—28no—
104#14556569—28no—
105#14556569—28no—
106Q8×Dic73—22no—
107Q8×Dic73—22no—
108Q8×Dic73C2314yes—
109Q8×Dic73C2314yes—
110C4×Dic146—22no—
111C4×Dic146D414yes—
112C4×Dic146C2314yes—
113C4×Dic146C2314yes—
114#14556556—28no—
115C4×D292—22no—
116C4×D292C2314yes—
117#14556553—22no—
118#14556553—22no—
119#14556553C2314yes—
120#14556553C2314yes—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73D411yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007D411yescharacteristic
135C2×#11924007D411yescharacteristic
136C4⋊C4×D73—28no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73C2311yescharacteristic
144C2×C4×Dic73C2311yescharacteristic
145#14556525C2314yes—
146#14556524C2314yes—
147#14556522C2314yes—
148C4⋊#10596831C2314yes—
149#14556520C2314yes—
150#14556520C2314yes—
151#14556516C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154#14556514C2314yes—
155#14556514C2314yes—
156#14556513C2314yes—
157#14556501C2314yes—
158C8×Dic73C2314yes—
159C22×Q8×C73C2311yescharacteristic
160C22×Q8×C73C2311yescharacteristic
161C22×C8×C73C2311yescharacteristic
162C22×C8×C73C2311yescharacteristic
163C4⋊Q8×C73—22no—
164C4⋊Q8×C73C2314yes—
165#125×C73—22no—
166#125×C73C2314yes—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C42×C73C2311yescharacteristic
174#103×C73C2314yes—
175#103×C73C2314yes—
176#103×C73C2314yes—
177#103×C73C2314yes—
178#97×C73C2314yes—
179C23×D73—21no—
180C2×Dic146—24no—
181C2×Dic146—22no—
182C2×Dic146—22no—
183C2×Dic146—21no—
184C2×Dic146—24no—
185C2×Dic146—82no—
186C2×Dic146C2×D414yes—
187C2×Dic146C2412yes—
188C2×D292—21no—
189C2×D292—22no—
190C2×D292#4114yes—
191C2×D292C2412yes—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73C2×D411yescharacteristic
196C22×Dic73C2×D411yescharacteristic
197C22×Dic73C2×D411yescharacteristic
198C22×Dic73C2×D411yescharacteristic
199C2×C4×D73—24no—
200C2×C4×D73—24no—
201C2×C4×D73—24no—
202C2×C4×D73—44no—
203C2×C4×D73—82no—
204C2×C4×D73—82no—
205#11924017—28no—
206#11924015—28no—
207#11924015—28no—
208C2×#10596831—22no—
209C2×#10596831—22no—
210C2×#10596831C2412yes—
211C2×#10596831C2412yes—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73—24no—
215C4⋊Dic73—24no—
216C4⋊Dic73—24no—
217C4⋊Dic73C2×D414yes—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227#11924007C2×D414yes—
228#11924007C2×D414yes—
229#11924005—24no—
230#11924005—24no—
231#11924005—24no—
232C4×Dic73—24no—
233C4×Dic73—24no—
234C4×Dic73—24no—
235C4×Dic73C2×D412yes—
236C4×Dic73C2×D412yes—
237C4×Dic73C2412yes—
238C4×Dic73C2412yes—
239C2×Q8×C73—21no—
240C2×Q8×C73—21no—
241C2×Q8×C73—22no—
242C2×Q8×C73—22no—
243C2×Q8×C73—22no—
244C2×Q8×C73—22no—
245C2×Q8×C73C2412yes—
246C2×Q8×C73C2412yes—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2411yescharacteristic
254C2×C8×C73—22no—
255C2×C8×C73—22no—
256C2×C8×C73C2412yes—
257C2×C8×C73C2412yes—
258C4⋊C4×C73—24no—
259C4⋊C4×C73—24no—
260C4⋊C4×C73—24no—
261C4⋊C4×C73—24no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73C2412yes—
265C4⋊C4×C73C2412yes—
266C42×C73C2×D412yes—
267C42×C73C2412yes—
268C23×C73C22×D411yescharacteristic
269C22×D73—24no—
270C22×D73—22no—
271C22×D73—42no—
272C22×D73—42no—
273Q8×C73—22no—
274Q8×C73—22no—
275Q8×C73—22no—
276Q8×C73—22no—
277Q8×C73—42no—
278Q8×C73—42no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—42no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73—42no—
289C2×C4×C73C22×D412yes—
290C2×C4×C73C22×D412yes—
291C2×C4×C73C22×D411yescharacteristic
292C2×C4×C73C2×#4112yes—
293C2×C4×C732−1+412yes—
294C2×C4×C73C2511yescharacteristic
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—42no—
302C2×Dic73—42no—
303C2×Dic73—42no—
304C2×Dic73#13714yes—
305C2×Dic73C22×D412yes—
306C2×Dic73C22×D412yes—
307C2×Dic73C22×D412yes—
308C2×Dic73C22×D412yes—
309D292—24no—
310D292—22no—
311D292C2×#4114yes—
312C4×D73—48no—
313C4×D73—84no—
314C4×D73—84no—
315Dic146—28no—
316Dic146—22no—
317Dic146—22no—
318Dic146—42no—
319Dic146—84no—
320C8×C73—22no—
321C8×C73—22no—
322#10596831—22no—
323#10596831—22no—
324C22×C73#54812yes—
325C22×C73C2×#13712yes—
326C22×C73#57712yes—
327C22×C73C23×D411yescharacteristic
328C2×D73—24no—
329C2×D73—48no—
330C2×D73—42no—
331C2×D73—42no—
332C4×C73—22no—
333C4×C73—22no—
334C4×C73—42no—
335C4×C73—42no—
336C4×C73—42no—
337C4×C73—42no—
338C4×C73#54812yes—
339C4×C73C22×#4111yescharacteristic
340C4×C73C2×2−1+411yescharacteristic
341Dic73—22no—
342Dic73—22no—
343Dic73—22no—
344Dic73—42no—
345Dic73—42no—
346Dic73—42no—
347Dic73C2×#13714yes—
348C2×#3372—731nomaximal, Sylow
349C2×C73#337214yescomplemented
350C2×C73C2×#54811yescharacteristic
351C2×C73C22×#13711yescharacteristic
352C2×C73C2×#57711yescharacteristic
353D73—44no—
354C2×#557—731no—
355C2×#554—731no—
356#3372—7316no—
357C2×#491—731no—
358C2×#491D7311yescharacteristic, complemented
359C2×#487—731no—
360C2×#479—731no—
361C2×#479—731no—
362C2×#477—731no—
363C2×#461—731no—
364C2×#461—731no—
365C2×#461—731no—
366C2×#446—731no—
367C2×#440—731no—
368C2×#440—731no—
369C2×C4×SD16—731no—
370C73C2×#337211yescharacteristic, complemented, Sylow
371C22×SD16—731no—
372C22×SD16—731no—
373C22×SD16—731no—
374#557—738no—
375#557—1464no—
376#554—738no—
377#554—1464no—
378C2×C4⋊Q8—731no—
379C2×C4⋊Q8—731no—
380C2×C4⋊Q8—731no—
381C2×C4⋊Q8C2×D7311yescharacteristic
382C2×#125—731no—
383C2×#125—1461no—
384C2×#125—1461no—
385C2×#125—1461no—
386C2×#125C2×D7311yescharacteristic
387C2×C22⋊Q8—1461no—
388C2×C22⋊Q8—1461no—
389C2×C22⋊Q8—1461no—
390C2×C4×Q8—731no—
391C2×C4×Q8—731no—
392C2×C4×Q8—731no—
393C2×C4×Q8—731no—
394C2×C4×Q8—1461no—
395C2×C4×D4—731no—
396C2×C4×D4—731no—
397C2×C4×D4—731no—
398C22×C4⋊C4—1461no—
399#491—738no—
400#491C2×D7318yescomplemented
401#487—738no—
402#479—738no—
403#479—738no—
404#477—738no—
405#461—738no—
406#461—738no—
407#461—738no—
408#446—738no—
409#440—738no—
410#440—738no—
411C4×SD16—738no—
412C2×#107—731no—
413C2×#107—731no—
414C2×#106—731no—
415C2×C4⋊C8—731no—
416C2×C4⋊C8—731no—
417C2×C4⋊C8—731no—
418C2×#103—731no—
419C2×#103—731no—
420C2×#103—731no—
421C2×#103—731no—
422C2×#103—731no—
423C2×#103C2×D7311yescharacteristic
424C2×#103C2×D7311yescharacteristic
425C2×#103C2×D7311yescharacteristic
426C2×#103C2×D7311yescharacteristic
427C2×#102—731no—
428C2×#97—731no—
429C2×#97C2×D7311yescharacteristic
430C2×C4×C8—731no—
431C22×Q8—731no—
432C22×Q8—731no—
433C22×Q8—1461no—
434C22×Q8C22×D7311yescharacteristic
435C22×Q8C22×D7311yescharacteristic
436C22×D4—731no—
437C23×C4—1461no—
438C23×C4—1461no—
439C23×C4—1461no—
440C2×SD16—734no—
441C2×SD16—734no—
442C2×SD16—734no—
443C2×SD16—1464no—
444C2×SD16—1464no—
445C2×SD16—1464no—
446C22×C8—731no—
447C22×C8—731no—
448C22×C8C22×D7311yescharacteristic
449C22×C8C22×D7311yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8—734no—
452C4⋊Q8—734no—
453C4⋊Q8—734no—
454C4⋊Q8—1462no—
455C4⋊Q8—1462no—
456C4⋊Q8—1462no—
457C4⋊Q8C22×D7314yes—
458#125—22no—
459#125—734no—
460#125—1462no—
461#125—1468no—
462#125—1468no—
463#125—1468no—
464#125C22×D7314yes—
465C22⋊Q8—1468no—
466C22⋊Q8—1468no—
467C22⋊Q8—1468no—
468C4×Q8—734no—
469C4×Q8—734no—
470C4×Q8—734no—
471C4×Q8—734no—
472C4×Q8—734no—
473C4×Q8—1462no—
474C4×Q8—1462no—
475C4×Q8—1468no—
476C4×Q8—1462no—
477C4×D4—734no—
478C4×D4—734no—
479C4×D4—734no—
480C4×D4—1462no—
481C4×D4—1462no—
482C4×D4—1462no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—731no—
488C2×C4⋊C4—731no—
489C2×C4⋊C4—731no—
490C2×C4⋊C4—731no—
491C2×C4⋊C4—731no—
492C2×C4⋊C4—1468no—
493C2×C4⋊C4—1461no—
494C2×C4⋊C4—1461no—
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⋊C4C22×D7311yescharacteristic
504C2×C4⋊C4C22×D7311yescharacteristic
505C2×C22⋊C4—1461no—
506C2×C22⋊C4—1461no—
507C2×C22⋊C4—1461no—
508C2×C42—731no—
509C2×C42—731no—
510C2×C42—1461no—
511C2×C42—1461no—
512C2×C42—1461no—
513C2×C42C22×D7311yescharacteristic
514#107—734no—
515#107—734no—
516#106—734no—
517C4⋊C8—734no—
518C4⋊C8—734no—
519C4⋊C8—734no—
520#103—734no—
521#103—734no—
522#103—734no—
523#103—734no—
524#103—734no—
525#103C22×D7314yes—
526#103C22×D7314yes—
527#103C22×D7314yes—
528#103C22×D7314yes—
529#102—734no—
530#97—734no—
531#97C22×D7314yes—
532C4×C8—734no—
533C24—1461no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—5842no—
541C2×Q8—734no—
542C2×Q8—732no—
543C2×Q8—1464no—
544C2×Q8—1464no—
545C2×Q8—1462no—
546C2×Q8—1462no—
547C2×Q8—1461no—
548C2×Q8C23×D7312yes—
549C2×Q8C23×D7312yes—
550C2×D4—734no—
551C2×D4—732no—
552C2×D4—1461no—
553C2×D4—1462no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—2924no—
559C22×C4—5842no—
560C22×C4—5842no—
561C22×C4—731no—
562C22×C4—731no—
563C22×C4—731no—
564C22×C4—731no—
565C22×C4—1464no—
566C22×C4—1464no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1464no—
571C22×C4D4×D7311yescharacteristic
572C22×C4D4×D7311yescharacteristic
573C22×C4C23×D7311yescharacteristic
574SD16—1468no—
575SD16—1468no—
576SD16—1468no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—732no—
580C2×C8—732no—
581C2×C8—1462no—
582C2×C8—1462no—
583C2×C8C23×D7312yes—
584C2×C8C23×D7312yes—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—734no—
592C4⋊C4—734no—
593C4⋊C4—734no—
594C4⋊C4—732no—
595C4⋊C4—732no—
596C4⋊C4—1464no—
597C4⋊C4—1464no—
598C4⋊C4—1464no—
599C4⋊C4—1464no—
600C4⋊C4—1464no—
601C4⋊C4—1464no—
602C4⋊C4—1464no—
603C4⋊C4—1464no—
604C4⋊C4—1464no—
605C4⋊C4—1464no—
606C4⋊C4—1461no—
607C4⋊C4—1461no—
608C4⋊C4C23×D7312yes—
609C4⋊C4C23×D7312yes—
610C22⋊C4—1464no—
611C22⋊C4—1464no—
612C22⋊C4—1464no—
613C42—732no—
614C42—732no—
615C42—732no—
616C42—732no—
617C42—1464no—
618C42—1464no—
619C42—1464no—
620C42D4×D7312yes—
621C42C23×D7312yes—
622C23—2922no—
623C23—2922no—
624C23—1462no—
625C23—1464no—
626C23C2×D4×D7311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—42no—
633Q8—2922no—
634Q8—5844no—
635Q8—1468no—
636Q8—1462no—
637Q8—1462no—
638D4—734no—
639D4—1462no—
640D4—1464no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—2928no—
652C2×C4—2922no—
653C2×C4—2922no—
654C2×C4—2922no—
655C2×C4—5844no—
656C2×C4—5844no—
657C2×C4—734no—
658C2×C4—732no—
659C2×C4—732no—
660C2×C4—732no—
661C2×C4—732no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4C2×D4×D7312yes—
669C2×C4C2×D4×D7312yes—
670C2×C4C2×D4×D7311yescharacteristic
671C2×C4#41×D7312yes—
672C2×C4#1455663812yes—
673C2×C4C24×D7311yescharacteristic
674C8—22no—
675C8—22no—
676C8—1462no—
677C8—1462no—
678C22—2922no—
679C22—2922no—
680C22—2928no—
681C22—1464no—
682C22#1798924512yes—
683C22#137×D7312yes—
684C22#1798939612yes—
685C22C22×D4×D7311yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—2922no—
693C4—2922no—
694C4—2922no—
695C4—734no—
696C4—1462no—
697C4—1462no—
698C4—1462no—
699C4#1798924512yes—
700C4C2×#41×D7311yescharacteristic
701C4C2×#1455663811yescharacteristic
702C2—2924no—
703C2#2262270914yesdirect product factor
704C2C2×#1798924511yescharacteristic
705C2C2×#137×D7311yescharacteristic
706C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#491×C73C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenterC2×#491D73
hypocenterC73C2×#3372
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#17989312C2semidirect
3. #22622709C2direct (N × H)
4. C2×#17988954C2semidirect
5. C2×#17988936C2semidirect
6. C2×#17988896C2semidirect
7. C2×#17988891C2semidirect
8. C2×#17988880C2semidirect
12. C2×#17988715C2semidirect
16. C2×#491×C73C2semidirect
21. #17989312C22semidirect
43. #17988954C22semidirect
44. #17988936C22semidirect
45. #17988896C22semidirect
46. #17988891C22semidirect
47. #17988880C22semidirect
51. #17988715C22semidirect
71. #491×C73C22semidirect
349. C2×C73#3372semidirect
358. C2×#491D73semidirect
370. C73C2×#3372semidirect
400. #491C2×D73semidirect
703. C2#22622709direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893122
C2×#179892932
#226227092
C2×#179889542
C2×#179889362
C2×#179888962
C2×#179888912
C2×#179888802
C2×#179887912
C2×#179887892
C2×#179887152
C2×#179886902
C2×#179886892
C2×#179886722
C2×#491×C732
C2×#337273