Finite Group Databasebeta

← C2×#11734428 #13520204

Subgroups — C2×#11734428 #13520204

Order 1792.

2958 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic7C211yesmaximal, characteristic
2C22×#6441C211yesmaximal, characteristic, complemented
3C2×C7×#394C211yesmaximal, characteristic
4C2×#89994C211yesmaximal, characteristic
5C2×#89756C211yesmaximal, characteristic, complemented
6C2×#89753C211yesmaximal, characteristic, complemented
7C2×#89725C211yesmaximal, characteristic, complemented
8C2×#89724C211yesmaximal, characteristic, complemented
9C2×#89724C211yesmaximal, characteristic, complemented
10C2×#89719C211yesmaximal, characteristic, complemented
11C2×#89722C211yesmaximal, characteristic, complemented
12C2×#89718C211yesmaximal, characteristic, complemented
13C2×#89715C211yesmaximal, characteristic, complemented
14#11734428C2116yesmaximal, direct product factor
15C2×#89428C211yesmaximal, characteristic, complemented
16C2×#89424C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C2×D4×Dic7—28no—
33C2×D4×Dic7C2218yes—
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6441—28no—
43C2×#6441C2218yescomplemented
44C7×#394C2218yes—
45C2×C7×#95C2211yescharacteristic
46#89994C2218yes—
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89756C2218yescomplemented
59#89753C2218yescomplemented
60#89725C2218yescomplemented
61#89724C2218yescomplemented
62#89724C2218yescomplemented
63#89722C2218yescomplemented
64#89719C2218yescomplemented
65#89718C2218yescomplemented
66#89715C2218yescomplemented
67#89428C2218yescomplemented
68#89424C2218yescomplemented
69C2×#2638—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C22×C7×D4—24no—
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4C2314yes—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×Dic7—24no—
82C23×Dic7—42no—
83C23×Dic7—42no—
84C23×Dic7—42no—
85C23×Dic7—42no—
86C23×Dic7D418yes—
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2314yes—
96C23×Dic7C2314yes—
97C22×Dic14—24no—
98C22×Dic14—42no—
99C22×Dic14—42no—
100C22×Dic14C2314yes—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4C2314yes—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—42no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C7×C22⋊C4C2314yes—
110C2×C7×C22⋊C4C2314yes—
111C2×C22⋊Dic7—24no—
112C2×C22⋊Dic7—24no—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—42no—
116C2×C22⋊Dic7—42no—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123D4×Dic7—232no—
124C2×C4⋊Dic7—24no—
125C2×C4⋊Dic7—24no—
126C2×C4⋊Dic7—42no—
127C2×C4⋊Dic7C2314yes—
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×C4×Dic7—24no—
139C2×C4×Dic7C2314yes—
140#6441—232no—
141C7×#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×C22⋊Q8—71no—
154C22×C4×D4—71no—
155#2638—716no—
156C2×#398—71no—
157C2×#397—71no—
158C2×#397—71no—
159C2×#397—71no—
160C2×#395—71no—
161C2×#394—71no—
162C2×#394D711yescharacteristic
163C2×#393—71no—
164C2×#387—71no—
165C2×#387—71no—
166C2×#385—71no—
167C2×#385—71no—
168C2×#381—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7C2×D414yes—
182C24×C7#4114yes—
183C24×C7C2412yes—
184C24×C7C2412yes—
185C24×C7C2411yescharacteristic
186C2×C7×D4—232no—
187C2×C7×D4—28no—
188C2×C7×D4—28no—
189C2×C7×D4—28no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7#4114yes—
205C22×C4×C7C2412yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2412yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—28no—
233C22×Dic7—416no—
234C22×Dic7—44no—
235C22×Dic7—44no—
236C22×Dic7—44no—
237C22×Dic7—44no—
238C22×Dic7—416no—
239C22×Dic7C2×D414yes—
240C22×Dic7C2×D414yes—
241C22×Dic7C2×D4116yes—
242C22×Dic7C2412yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C2×Dic14—28no—
251C2×Dic14—44no—
252C2×Dic14—44no—
253C2×Dic14—416no—
254C7×C4⋊C4—28no—
255C7×C22⋊C4—28no—
256C7×C22⋊C4—28no—
257C7×C22⋊C4—44no—
258C7×C22⋊C4—44no—
259C22⋊Dic7—28no—
260C22⋊Dic7—28no—
261C22⋊Dic7—28no—
262C22⋊Dic7—28no—
263C22⋊Dic7—44no—
264C22⋊Dic7—44no—
265C4⋊Dic7—28no—
266C4⋊Dic7—28no—
267C4⋊Dic7—44no—
268Dic7⋊C4—28no—
269Dic7⋊C4—28no—
270Dic7⋊C4—28no—
271Dic7⋊C4—44no—
272C4×Dic7—28no—
273C23×Q8—71no—
274C23×D4C2×D711yescharacteristic
275C24×C4—71no—
276C24×C4—71no—
277C2×C22⋊Q8—78no—
278C2×C22⋊Q8—148no—
279C2×C4×D4—78no—
280C2×C4×D4—148no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4C2×D711yescharacteristic
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4C2×D711yescharacteristic
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C42—71no—
300#398—78no—
301#397—78no—
302#397—78no—
303#397—78no—
304#395—78no—
305#394—78no—
306#394C2×D718yes—
307#393—78no—
308#387—78no—
309#387—78no—
310#385—78no—
311#385—78no—
312#381—78no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95C2×D711yescharacteristic
325C23×C7—28no—
326C23×C7—28no—
327C23×C7—28no—
328C23×C7—28no—
329C23×C7—28no—
330C23×C7—28no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—44no—
344C23×C7—44no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7C22×D414yes—
352C23×C7C22×D412yes—
353C23×C7C2×#4114yes—
354C23×C7C2×#4112yes—
355C23×C7C2×#4112yes—
356C23×C7H(5,𝔽2)12yes—
357C23×C7H(5,𝔽2)12yes—
358C23×C72−1+412yes—
359C23×C72−1+412yes—
360C23×C7C2511yescharacteristic
361C7×D4—232no—
362C2×C4×C7—28no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—44no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7C2×#4114yes—
382C2×Dic7—28no—
383C2×Dic7—28no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—416no—
407C2×Dic7—416no—
408C2×Dic7—44no—
409C2×Dic7—44no—
410C2×Dic7—44no—
411C2×Dic7—44no—
412C2×Dic7—44no—
413C2×Dic7—44no—
414C2×Dic7C22×D414yes—
415C2×Dic7C22×D414yes—
416Dic14—416no—
417C25C22×D711yescharacteristic
418C25C22×D711yescharacteristic
419C22×Q8—74no—
420C22×Q8—144no—
421C22×Q8—282no—
422C22×Q8—282no—
423C22×D4—24no—
424C22×D4—24no—
425C22×D4—24no—
426C22×D4C22×D714yes—
427C23×C4—71no—
428C23×C4—71no—
429C23×C4—78no—
430C23×C4—74no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—71no—
437C23×C4—74no—
438C23×C4—144no—
439C23×C4—282no—
440C23×C4—282no—
441C23×C4—282no—
442C23×C4—282no—
443C23×C4C22×D711yescharacteristic
444C23×C4C22×D711yescharacteristic
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C23×C4C22×D711yescharacteristic
448C22⋊Q8—1432no—
449C4×D4—1432no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—74no—
452C2×C4⋊C4—74no—
453C2×C4⋊C4—74no—
454C2×C4⋊C4—74no—
455C2×C4⋊C4—74no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—144no—
459C2×C4⋊C4—144no—
460C2×C4⋊C4—144no—
461C2×C4⋊C4—144no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—282no—
464C2×C4⋊C4—282no—
465C2×C4⋊C4C22×D714yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—74no—
471C2×C22⋊C4—74no—
472C2×C22⋊C4—74no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—144no—
480C2×C22⋊C4—282no—
481C2×C22⋊C4—282no—
482C2×C22⋊C4C22×D714yes—
483C2×C22⋊C4C22×D714yes—
484C2×C22⋊C4C22×D714yes—
485C2×C22⋊C4C22×D714yes—
486C2×C42—74no—
487C2×C42—144no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
495#95—74no—
496#95—74no—
497#95—74no—
498#95—74no—
499#95C22×D714yes—
500C22×C7—24no—
501C22×C7—24no—
502C22×C7—24no—
503C22×C7—24no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—416no—
507C22×C7—416no—
508C22×C7—42no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—42no—
516C22×C7#52514yes—
517C22×C7#53414yes—
518C22×C7#53614yes—
519C22×C7#53914yes—
520C22×C7#53914yes—
521C22×C7#54214yes—
522C22×C7#54214yes—
523C22×C7C23×D411yescharacteristic
524C22×C7C22×#4111yescharacteristic
525C22×C7C22×#4111yescharacteristic
526C22×C7C2×H(5,𝔽2)11yescharacteristic
527C22×C7C2×H(5,𝔽2)11yescharacteristic
528C22×C7C2×2−1+411yescharacteristic
529C22×C7C2×2−1+411yescharacteristic
530C4×C7—24no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535Dic7—24no—
536Dic7—24no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24D4×D714yes—
556C24#115914yes—
557C24C23×D712yes—
558C24C23×D712yes—
559C24C23×D711yescharacteristic
560C2×Q8—148no—
561C2×Q8—284no—
562C2×Q8—284no—
563C2×Q8—2816no—
564C2×D4—232no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—28no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—74no—
583C22×C4—74no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—716no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—148no—
594C22×C4—142no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—2816no—
617C22×C4—284no—
618C22×C4—284no—
619C22×C4—284no—
620C22×C4—284no—
621C22×C4—2816no—
622C22×C4#115914yes—
623C22×C4C23×D712yes—
624C22×C4C23×D712yes—
625C22×C4C23×D712yes—
626C22×C4C23×D712yes—
627C22×C4C23×D712yes—
628C4⋊C4—28no—
629C4⋊C4—148no—
630C4⋊C4—148no—
631C4⋊C4—148no—
632C4⋊C4—148no—
633C4⋊C4—148no—
634C4⋊C4—284no—
635C4⋊C4—284no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—148no—
641C22⋊C4—148no—
642C22⋊C4—148no—
643C22⋊C4—148no—
644C22⋊C4—284no—
645C22⋊C4—284no—
646C42—148no—
647C2×C7—44no—
648C2×C7—44no—
649C2×C7#263818yescomplemented
650C2×C7C2×#52511yescharacteristic
651C2×C7C2×#53411yescharacteristic
652C2×C7C2×#53611yescharacteristic
653C2×C7C2×#53911yescharacteristic
654C2×C7C2×#53911yescharacteristic
655C2×C7C2×#54211yescharacteristic
656C2×C7C2×#54211yescharacteristic
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—28no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23C2×D4×D714yes—
684C23C2×D4×D712yes—
685C23C2×#115914yes—
686C23C2×#115912yes—
687C23C2×#115912yes—
688C23#654812yes—
689C23#655312yes—
690C23#655412yes—
691C23#655412yes—
692C23C24×D711yescharacteristic
693Q8—2816no—
694D4—232no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—74no—
715C2×C4—74no—
716C2×C4—148no—
717C2×C4—148no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—2816no—
741C2×C4—2816no—
742C2×C4—284no—
743C2×C4—284no—
744C2×C4—284no—
745C2×C4—284no—
746C2×C4—284no—
747C2×C4—284no—
748C2×C4C2×#115914yes—
749C7C2×#263811yescharacteristic, complemented, Sylow
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—416no—
763C22—416no—
764C22—42no—
765C22—42no—
766C22#9027714yes—
767C22#9029314yes—
768C22#9029414yes—
769C22#9029614yes—
770C22#9033914yes—
771C22#9035614yes—
772C22#9037314yes—
773C22C22×D4×D711yescharacteristic
774C22C22×#115911yescharacteristic
775C22C22×#115911yescharacteristic
776C22C2×#654811yescharacteristic
777C22C2×#655311yescharacteristic
778C22C2×#655411yescharacteristic
779C22C2×#655411yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—144no—
786C4—144no—
787C4—282no—
788C4—282no—
789C4—282no—
790C4—282no—
791C4—282no—
792C4—282no—
793C2—44no—
794C2—44no—
795C2#1173442818yesdirect product factor
796C2C2×#9027711yescharacteristic
797C2C2×#9029311yescharacteristic
798C2C2×#9029411yescharacteristic
799C2C2×#9029611yescharacteristic
800C2C2×#9033911yescharacteristic
801C2C2×#9035611yescharacteristic
802C2C2×#9037311yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#394D7
hypocenterC7C2×#2638
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#6441C2semidirect
5. C2×#89756C2semidirect
6. C2×#89753C2semidirect
7. C2×#89725C2semidirect
8. C2×#89724C2semidirect
9. C2×#89724C2semidirect
10. C2×#89719C2semidirect
11. C2×#89722C2semidirect
12. C2×#89718C2semidirect
13. C2×#89715C2semidirect
14. #11734428C2direct (N × H)
15. C2×#89428C2semidirect
16. C2×#89424C2semidirect
43. C2×#6441C22semidirect
58. #89756C22semidirect
59. #89753C22semidirect
60. #89725C22semidirect
61. #89724C22semidirect
62. #89724C22semidirect
63. #89722C22semidirect
64. #89719C22semidirect
65. #89718C22semidirect
66. #89715C22semidirect
67. #89428C22semidirect
68. #89424C22semidirect
649. C2×C7#2638semidirect
749. C7C2×#2638semidirect
795. C2#11734428direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic72
C22×#64412
C2×C7×#3942
C2×#899942
C2×#897562
C2×#897532
C2×#897252
C2×#897242
C2×#897192
C2×#897222
C2×#897182
C2×#897152
#117344282
C2×#894282
C2×#894242
C2×#26387