Finite Group Databasebeta

← C2×#22622700 #33965766

Subgroups — C2×#22622700 #33965766

Order 18688.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989322C211yesmaximal, characteristic
2C2×#17989313C211yesmaximal, characteristic, complemented
3#22622700C2116yesmaximal, direct product factor
4C2×#17988952C211yesmaximal, characteristic
5C2×#17988948C211yesmaximal, characteristic, complemented
6C2×#17988943C211yesmaximal, characteristic, complemented
7C2×#17988894C211yesmaximal, characteristic, complemented
8C2×#17988886C211yesmaximal, characteristic, complemented
9C2×#17988876C211yesmaximal, characteristic, complemented
10C2×#17988811C211yesmaximal, characteristic, complemented
11C2×#17988811C211yesmaximal, characteristic, complemented
12C2×#17988787C211yesmaximal, characteristic
13C2×#17988715C211yesmaximal, characteristic, complemented
14C2×#17988690C211yesmaximal, characteristic, complemented
15C2×#17988672C211yesmaximal, characteristic, complemented
16C2×#441×C73C211yesmaximal, characteristic, complemented
17C22×#11924015C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19#17989322—24no—
20#17989322C2218yes—
21#17989313—24no—
22#17989313C2218yescomplemented
23C2×#14556590—21no—
24C2×#14556590C2211yescharacteristic
25C2×#14556588C2211yescharacteristic
26C2×#14556583—21no—
27C2×#14556583C2211yescharacteristic
28C2×#14556582—21no—
29C2×#14556582C2211yescharacteristic
30C2×#14556580C2211yescharacteristic
31C2×#14556580C2211yescharacteristic
32C2×#14556579—21no—
33C2×#14556576—21no—
34C2×#14556576—21no—
35C2×Q8×Dic73C2211yescharacteristic
36C2×Q8×Dic73C2211yescharacteristic
37C2×C4×Dic146—21no—
38C2×C4×Dic146C2211yescharacteristic
39C2×C4×D292—21no—
40C2×#14556553C2211yescharacteristic
41C2×#14556553C2211yescharacteristic
42#17988952C2218yes—
43#17988948C2218yescomplemented
44#17988943C2218yescomplemented
45#17988894C2218yescomplemented
46#17988886C2218yescomplemented
47#17988876C2218yescomplemented
48#17988811C2218yescomplemented
49#17988811C2218yescomplemented
50#17988787C2218yes—
51#17988715C2218yescomplemented
52#17988690C2218yescomplemented
53#17988672C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×C4⋊#10596831C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
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×Dic146D411yescharacteristic
79C22×D292—21no—
80C22×D292—21no—
81C22×D292C2311yescharacteristic
82C22×D292C2311yescharacteristic
83C22×C4×D73—21no—
84C22×C4×D73—21no—
85C2×#11924015—24no—
86C2×#11924015—24no—
87C2×#11924015C2314yes—
88C2×#11924015C2314yes—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91#14556590—28no—
92#14556590—22no—
93#14556590C2314yes—
94#14556588—22no—
95#14556588C2314yes—
96#14556583—28no—
97#14556583—22no—
98#14556583C2314yes—
99#14556582—28no—
100#14556582—22no—
101#14556582C2314yes—
102#14556580—22no—
103#14556580—22no—
104#14556580C2314yes—
105#14556580C2314yes—
106#14556579—28no—
107#14556576—28no—
108#14556576—28no—
109Q8×Dic73—22no—
110Q8×Dic73—22no—
111Q8×Dic73C2314yes—
112Q8×Dic73C2314yes—
113C4×Dic146—28no—
114C4×Dic146D414yes—
115C4×Dic146C2314yes—
116C4×D292—28no—
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×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C2×#11924005—21no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73C2311yescharacteristic
142C2×C4×Dic73C2311yescharacteristic
143#14556524C2314yes—
144#14556522C2314yes—
145C4⋊#10596831C2314yes—
146#14556520C2314yes—
147#14556520C2314yes—
148#14556515C2314yes—
149#14556515C2314yes—
150#14556513C2314yes—
151#14556513C2314yes—
152#14556513C2314yes—
153#14556513C2314yes—
154#14556511C2314yes—
155#14556511C2314yes—
156#14556501C2314yes—
157C8×Dic73C2314yes—
158C22×Q8×C73C2311yescharacteristic
159C22×Q8×C73C2311yescharacteristic
160C2×Q16×C73—24no—
161C2×Q16×C73C2314yes—
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164C4×Q8×C73—22no—
165C4×Q8×C73—22no—
166C4×Q8×C73C2314yes—
167C4×Q8×C73C2314yes—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C42×C73—21no—
173C2×C42×C73—21no—
174C2×C42×C73C2311yescharacteristic
175#106×C73C2314yes—
176#103×C73C2314yes—
177#103×C73C2314yes—
178#97×C73C2314yes—
179C23×D73—21no—
180C23×D73—21no—
181C2×Dic146—24no—
182C2×Dic146—42no—
183C2×Dic146—44no—
184C2×Dic146C2×D414yes—
185C2×D292—22no—
186C2×D292—22no—
187C2×D292—22no—
188C2×D292—22no—
189C2×D292—21no—
190C2×D292—21no—
191C2×D292—24no—
192C2×D292—24no—
193C2×D292—44no—
194C2×D292—82no—
195C2×D292C2412yes—
196C2×D292C2412yes—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C2×C4×D73—24no—
204C2×C4×D73—24no—
205C2×C4×D73—82no—
206C2×C4×D73—82no—
207#11924015—28no—
208#11924015—28no—
209C2×#10596831—22no—
210C2×#10596831—22no—
211C2×#10596831C2412yes—
212C2×#10596831C2412yes—
213C4⋊Dic73—21no—
214C4⋊Dic73—21no—
215C4⋊Dic73—24no—
216C4⋊Dic73—24no—
217C4⋊Dic73—24no—
218C4⋊Dic73C2×D414yes—
219C4⋊Dic73C2412yes—
220C4⋊Dic73C2412yes—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007C2×D414yes—
226#11924007C2×D414yes—
227#11924005—24no—
228#11924005—24no—
229#11924005—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—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#4114yes—
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
254Q16×C73—28no—
255C2×C8×C73—22no—
256C2×C8×C73—22no—
257C2×C8×C73C2412yes—
258C2×C8×C73C2412yes—
259C4⋊C4×C73—24no—
260C4⋊C4×C73—24no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73C2412yes—
264C4⋊C4×C73C2412yes—
265C42×C73—24no—
266C42×C73—24no—
267C42×C73C2×D412yes—
268C42×C73C2412yes—
269C23×C73C22×D411yescharacteristic
270C22×D73—22no—
271C22×D73—22no—
272C22×D73—42no—
273C22×D73—42no—
274C22×D73—42no—
275C22×D73—42no—
276C22×D73—42no—
277C22×D73—42no—
278Q8×C73—24no—
279Q8×C73—22no—
280Q8×C73—22no—
281Q8×C73—22no—
282Q8×C73—42no—
283Q8×C73C2×#4114yes—
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×C73C22×D412yes—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C2×#4112yes—
298C2×C4×C732−1+412yes—
299C2×C4×C73C2511yescharacteristic
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—42no—
307C2×Dic73—42no—
308C2×Dic73C22×D412yes—
309C2×Dic73C22×D412yes—
310C2×Dic73C22×D412yes—
311C2×Dic73C22×D412yes—
312D292—22no—
313D292—22no—
314D292—22no—
315D292—22no—
316D292—48no—
317D292—42no—
318D292—42no—
319D292—84no—
320C4×D73—84no—
321C4×D73—84no—
322Dic146—44no—
323Dic146—48no—
324C8×C73—22no—
325C8×C73—22no—
326#10596831—22no—
327#10596831—22no—
328C22×C73#54812yes—
329C22×C73#57512yes—
330C22×C73#57712yes—
331C22×C73C23×D411yescharacteristic
332C2×D73—42no—
333C2×D73—42no—
334C2×D73—42no—
335C2×D73—42no—
336C2×D73—42no—
337C2×D73—42no—
338C2×D73—84no—
339C2×D73—84no—
340C4×C73—24no—
341C4×C73—22no—
342C4×C73—22no—
343C4×C73—42no—
344C4×C73—42no—
345C4×C73—42no—
346C4×C73#54812yes—
347C4×C73C22×#4111yescharacteristic
348C4×C73C2×2−1+411yescharacteristic
349Dic73—22no—
350Dic73—22no—
351Dic73—22no—
352Dic73—22no—
353Dic73—42no—
354Dic73—42no—
355C2×#3371—731nomaximal, Sylow
356C2×C73#337114yescomplemented
357C2×C73C2×#54811yescharacteristic
358C2×C73C2×#57511yescharacteristic
359C2×C73C2×#57711yescharacteristic
360D73—82no—
361D73—82no—
362C2×#559—731no—
363C2×#557—731no—
364#3371—7316no—
365C2×#490—731no—
366C2×#489—731no—
367C2×#488—731no—
368C2×#479—731no—
369C2×#478—731no—
370C2×#476—731no—
371C2×#464—731no—
372C2×#464—731no—
373C2×#460—731no—
374C2×#446—731no—
375C2×#441D7311yescharacteristic, complemented
376C2×#440—731no—
377C2×C4×SD16—731no—
378C73C2×#337111yescharacteristic, complemented, Sylow
379C22×Q16C2×D7311yescharacteristic
380C22×SD16—731no—
381C22×SD16—731no—
382#559—738no—
383#559—1464no—
384#557—738no—
385#557—1464no—
386C2×C4⋊Q8—731no—
387C2×C4⋊Q8—1461no—
388C2×#127—731no—
389C2×#125—731no—
390C2×#125—731no—
391C2×#125—1461no—
392C2×#125—1461no—
393C2×#124—731no—
394C2×#124—731no—
395C2×#124—1461no—
396C2×#123—1461no—
397C2×#123—1461no—
398C2×C4×Q8—731no—
399C2×C4×Q8—731no—
400C2×C4×Q8—731no—
401C2×C4×Q8—1461no—
402C2×C4×Q8C2×D7311yescharacteristic
403C2×C4×Q8C2×D7311yescharacteristic
404C2×C4×D4—731no—
405C2×C4×D4—731no—
406C2×C4×D4—1461no—
407#490—738no—
408#489—738no—
409#488—738no—
410#479—738no—
411#478—738no—
412#476—738no—
413#464—738no—
414#464—738no—
415#460—738no—
416#446—738no—
417#441C2×D7318yescomplemented
418#440—738no—
419C4×SD16—738no—
420C2×#107—731no—
421C2×#106—731no—
422C2×#106C2×D7311yescharacteristic
423C2×C4⋊C8—731no—
424C2×C4⋊C8—731no—
425C2×C4⋊C8—731no—
426C2×#103—731no—
427C2×#103—731no—
428C2×#103C2×D7311yescharacteristic
429C2×#103C2×D7311yescharacteristic
430C2×#102—731no—
431C2×#102—731no—
432C2×#102—731no—
433C2×#102—731no—
434C2×#102—731no—
435C2×#102—731no—
436C2×#97—731no—
437C2×#97C2×D7311yescharacteristic
438C2×C4×C8—731no—
439C22×Q8—731no—
440C22×Q8—1461no—
441C22×Q8C22×D7311yescharacteristic
442C22×Q8C22×D7311yescharacteristic
443C22×D4—731no—
444C22×D4—731no—
445C22×D4—1461no—
446C22×D4—1461no—
447C23×C4—1461no—
448C23×C4—1461no—
449C2×Q16—24no—
450C2×Q16C22×D7314yes—
451C2×SD16—734no—
452C2×SD16—734no—
453C2×SD16—1464no—
454C2×SD16—1464no—
455C22×C8—731no—
456C22×C8—731no—
457C22×C8C22×D7311yescharacteristic
458C22×C8C22×D7311yescharacteristic
459C4⋊Q8—734no—
460C4⋊Q8—1462no—
461C4⋊Q8—1468no—
462#127—734no—
463#127—1462no—
464#125—734no—
465#125—734no—
466#125—1468no—
467#125—1462no—
468#125—1468no—
469#125—1462no—
470#124—734no—
471#124—734no—
472#124—1468no—
473#124—1462no—
474#124—1462no—
475#123—1468no—
476#123—1468no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—734no—
480C4×Q8—734no—
481C4×Q8—734no—
482C4×Q8—734no—
483C4×Q8—1468no—
484C4×Q8—1462no—
485C4×Q8—1462no—
486C4×Q8C22×D7314yes—
487C4×Q8C22×D7314yes—
488C4×D4—734no—
489C4×D4—734no—
490C4×D4—1468no—
491C4×D4—1462no—
492C4×D4—1462no—
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⋊C4C22×D7311yescharacteristic
508C2×C4⋊C4C22×D7311yescharacteristic
509C2×C22⋊C4—1461no—
510C2×C22⋊C4—1461no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C22⋊C4—1461no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—731no—
518C2×C42—731no—
519C2×C42—1461no—
520C2×C42—1461no—
521C2×C42C22×D7311yescharacteristic
522#107—734no—
523#106—734no—
524#106C22×D7314yes—
525C4⋊C8—734no—
526C4⋊C8—734no—
527C4⋊C8—734no—
528#103—734no—
529#103—734no—
530#103C22×D7314yes—
531#103C22×D7314yes—
532#102—734no—
533#102—734no—
534#102—734no—
535#102—734no—
536#102—734no—
537#102—734no—
538#97—734no—
539#97C22×D7314yes—
540C4×C8—734no—
541C24—1461no—
542C24—1461no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—2922no—
549C2×Q8—2924no—
550C2×Q8—734no—
551C2×Q8—1464no—
552C2×Q8#1192402814yes—
553C2×Q8C23×D7312yes—
554C2×Q8C23×D7312yes—
555C2×D4—2924no—
556C2×D4—5842no—
557C2×D4—732no—
558C2×D4—732no—
559C2×D4—1464no—
560C2×D4—1461no—
561C2×D4—1461no—
562C2×D4—1464no—
563C2×D4—1462no—
564C2×D4—1462no—
565C2×D4—1462no—
566C2×D4—1462no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—5842no—
572C22×C4—5842no—
573C22×C4—731no—
574C22×C4—731no—
575C22×C4—731no—
576C22×C4—731no—
577C22×C4—1464no—
578C22×C4—1464no—
579C22×C4—1461no—
580C22×C4—1461no—
581C22×C4D4×D7311yescharacteristic
582C22×C4D4×D7311yescharacteristic
583C22×C4C23×D7311yescharacteristic
584Q16—28no—
585SD16—1468no—
586SD16—1468no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—732no—
590C2×C8—732no—
591C2×C8—1462no—
592C2×C8—1462no—
593C2×C8C23×D7312yes—
594C2×C8C23×D7312yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—734no—
600C4⋊C4—734no—
601C4⋊C4—734no—
602C4⋊C4—732no—
603C4⋊C4—732no—
604C4⋊C4—1464no—
605C4⋊C4—1464no—
606C4⋊C4—1464no—
607C4⋊C4—1464no—
608C4⋊C4—1464no—
609C4⋊C4—1464no—
610C4⋊C4—1464no—
611C4⋊C4—1461no—
612C4⋊C4—1461no—
613C4⋊C4C23×D7312yes—
614C4⋊C4C23×D7312yes—
615C22⋊C4—1464no—
616C22⋊C4—1464no—
617C22⋊C4—1464no—
618C22⋊C4—1464no—
619C22⋊C4—1464no—
620C22⋊C4—1464no—
621C42—24no—
622C42—24no—
623C42—732no—
624C42—732no—
625C42—732no—
626C42—732no—
627C42—1464no—
628C42—1464no—
629C42D4×D7312yes—
630C42C23×D7312yes—
631C23—2922no—
632C23—2922no—
633C23—2922no—
634C23—2922no—
635C23—2922no—
636C23—2922no—
637C23—1462no—
638C23—1462no—
639C23C2×D4×D7311yescharacteristic
640Q8—22no—
641Q8—24no—
642Q8—22no—
643Q8—22no—
644Q8—42no—
645Q8—2924no—
646Q8—2928no—
647Q8C2×#1192402814yes—
648D4—2928no—
649D4—2922no—
650D4—2922no—
651D4—5844no—
652D4—1462no—
653D4—1462no—
654D4—1462no—
655D4—1462no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—2922no—
667C2×C4—2922no—
668C2×C4—5844no—
669C2×C4—5844no—
670C2×C4—732no—
671C2×C4—732no—
672C2×C4—732no—
673C2×C4—732no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4C2×D4×D7312yes—
681C2×C4C2×D4×D7312yes—
682C2×C4C2×D4×D7311yescharacteristic
683C2×C4C2×#1192402812yes—
684C2×C4#1455663812yes—
685C2×C4C24×D7311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1462no—
689C8—1462no—
690C22—2922no—
691C22—2922no—
692C22—2922no—
693C22—2922no—
694C22—2922no—
695C22—2922no—
696C22—5844no—
697C22—5844no—
698C22#1798924612yes—
699C22#1798938612yes—
700C22#1798939612yes—
701C22C22×D4×D7311yescharacteristic
702C4—24no—
703C4—22no—
704C4—22no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—2922no—
709C4—2922no—
710C4—1462no—
711C4—1462no—
712C4—1462no—
713C4—1462no—
714C4#1798924612yes—
715C4C22×#1192402811yescharacteristic
716C4C2×#1455663811yescharacteristic
717C2—5842no—
718C2—5842no—
719C2#2262270014yesdirect product factor
720C2C2×#1798924611yescharacteristic
721C2C2×#1798938611yescharacteristic
722C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#441×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556588C22
hypercenterC2×#441D73
hypocenterC73C2×#3371
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×#17989313C2semidirect
3. #22622700C2direct (N × H)
5. C2×#17988948C2semidirect
6. C2×#17988943C2semidirect
7. C2×#17988894C2semidirect
8. C2×#17988886C2semidirect
9. C2×#17988876C2semidirect
10. C2×#17988811C2semidirect
11. C2×#17988811C2semidirect
13. C2×#17988715C2semidirect
14. C2×#17988690C2semidirect
15. C2×#17988672C2semidirect
16. C2×#441×C73C2semidirect
22. #17989313C22semidirect
43. #17988948C22semidirect
44. #17988943C22semidirect
45. #17988894C22semidirect
46. #17988886C22semidirect
47. #17988876C22semidirect
48. #17988811C22semidirect
49. #17988811C22semidirect
51. #17988715C22semidirect
52. #17988690C22semidirect
53. #17988672C22semidirect
72. #441×C73C22semidirect
356. C2×C73#3371semidirect
375. C2×#441D73semidirect
378. C73C2×#3371semidirect
417. #441C2×D73semidirect
719. C2#22622700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893222
C2×#179893132
#226227002
C2×#179889522
C2×#179889482
C2×#179889432
C2×#179888942
C2×#179888862
C2×#179888762
C2×#179888112
C2×#179887872
C2×#179887152
C2×#179886902
C2×#179886722
C2×#441×C732
C2×#337173