Finite Group Databasebeta

← C2×#11734196 #13560115

Subgroups — C2×#11734196 #13560115

Order 1792.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#392C211yesmaximal, characteristic
2C2×#89994C211yesmaximal, characteristic, complemented
3C2×#89994C211yesmaximal, characteristic, complemented
4C2×#89994C211yesmaximal, characteristic, complemented
5C2×#89994C211yesmaximal, characteristic, complemented
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×#89993C211yesmaximal, characteristic, complemented
8C2×#89721C211yesmaximal, characteristic, complemented
9C2×#89724C211yesmaximal, characteristic, complemented
10C2×#89724C211yesmaximal, characteristic, complemented
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89720C211yesmaximal, characteristic, complemented
13C2×#89723C211yesmaximal, characteristic, complemented
14#11734196C2116yesmaximal, direct product factor
15C2×#89429C211yesmaximal, characteristic, complemented
16C2×#89424C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C7×#392C2218yes—
45C2×C7×#95C2211yescharacteristic
46#89994C2218yescomplemented
47#89994C2218yescomplemented
48#89994C2218yescomplemented
49#89994C2218yescomplemented
50#89994C2218yescomplemented
51#89993C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89724C2218yescomplemented
60#89724C2218yescomplemented
61#89723C2218yescomplemented
62#89721C2218yescomplemented
63#89720C2218yescomplemented
64#89720C2218yescomplemented
65#89429C2218yescomplemented
66#89424C2218yescomplemented
67C2×#2829—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C25×C7C2311yescharacteristic
71C22×C7×D4—24no—
72C22×C7×D4—42no—
73C22×C7×D4—42no—
74C22×C7×D4—42no—
75C22×C7×D4—42no—
76C22×C7×D4—42no—
77C22×C7×D4—42no—
78C22×C7×D4—42no—
79C22×C7×D4—42no—
80C22×C7×D4C2314yes—
81C22×C7×D4C2314yes—
82C22×C7×D4C2314yes—
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—42no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4C2314yes—
99C2×C7×C22⋊C4C2314yes—
100C2×C7×C22⋊C4C2314yes—
101C2×C22⋊Dic7—42no—
102C2×C22⋊Dic7—42no—
103C2×C22⋊Dic7—42no—
104C2×C22⋊Dic7—42no—
105C2×C22⋊Dic7—42no—
106C2×C22⋊Dic7—42no—
107C2×C22⋊Dic7—42no—
108C2×C22⋊Dic7—42no—
109C2×C22⋊Dic7—42no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7—42no—
112C2×C22⋊Dic7—42no—
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C4⋊Dic7—42no—
126C2×C4⋊Dic7—42no—
127C2×C4⋊Dic7C2314yes—
128C2×C4⋊Dic7C2314yes—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—42no—
131C2×Dic7⋊C4—42no—
132C2×Dic7⋊C4—42no—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×C4×Dic7—42no—
142C2×C4×Dic7C2314yes—
143C7×#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151#2829—716no—
152C2×#399—71no—
153C2×#398—71no—
154C2×#397—71no—
155C2×#397—71no—
156C2×#396—71no—
157C2×#396—71no—
158C2×#394—71no—
159C2×#394—71no—
160C2×#394—71no—
161C2×#394—71no—
162C2×#394—71no—
163C2×#392D711yescharacteristic
164C2×#390—71no—
165C2×#388—71no—
166C2×#387—71no—
167C24×C7—22no—
168C24×C7—22no—
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×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7C2412yes—
189C24×C7C2412yes—
190C24×C7C2412yes—
191C24×C7C2411yescharacteristic
192C2×C7×D4—28no—
193C2×C7×D4—44no—
194C2×C7×D4—44no—
195C2×C7×D4—44no—
196C2×C7×D4—44no—
197C2×C7×D4—44no—
198C2×C7×D4—44no—
199C2×C7×D4—44no—
200C2×C7×D4—44no—
201C2×C7×D4—416no—
202C2×C7×D4—416no—
203C2×C7×D4—416no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7#4114yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
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—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C7×C22⋊C4—28no—
253C7×C22⋊C4—44no—
254C7×C22⋊C4—44no—
255C22⋊Dic7—44no—
256C22⋊Dic7—44no—
257C22⋊Dic7—44no—
258C22⋊Dic7—44no—
259C22⋊Dic7—44no—
260C22⋊Dic7—44no—
261C22⋊Dic7—44no—
262C22⋊Dic7—44no—
263C22⋊Dic7—44no—
264C22⋊Dic7—44no—
265C22⋊Dic7—44no—
266C22⋊Dic7—44no—
267C4⋊Dic7—44no—
268C4⋊Dic7—44no—
269Dic7⋊C4—28no—
270Dic7⋊C4—44no—
271Dic7⋊C4—44no—
272Dic7⋊C4—44no—
273Dic7⋊C4—44no—
274Dic7⋊C4—44no—
275C4×Dic7—44no—
276C23×D4C2×D711yescharacteristic
277C23×D4C2×D711yescharacteristic
278C23×D4C2×D711yescharacteristic
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
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×C22⋊C4—71no—
288C22×C22⋊C4—71no—
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⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C22⋊C4C2×D711yescharacteristic
302C22×C42—71no—
303#399—78no—
304#398—78no—
305#397—78no—
306#397—78no—
307#396—78no—
308#396—78no—
309#394—78no—
310#394—78no—
311#394—78no—
312#394—78no—
313#394—78no—
314#392C2×D718yes—
315#390—78no—
316#388—78no—
317#387—78no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95C2×D711yescharacteristic
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
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—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7—44no—
355C23×C7—44no—
356C23×C7—44no—
357C23×C7—44no—
358C23×C7—44no—
359C23×C7—44no—
360C23×C7—44no—
361C23×C7—44no—
362C23×C7—44no—
363C23×C7—44no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7C2×#4112yes—
369C23×C7H(5,𝔽2)12yes—
370C23×C7H(5,𝔽2)12yes—
371C23×C7H(5,𝔽2)12yes—
372C23×C7H(5,𝔽2)12yes—
373C23×C7H(5,𝔽2)12yes—
374C23×C72−1+412yes—
375C23×C7C2511yescharacteristic
376C7×D4—416no—
377C7×D4—416no—
378C7×D4—416no—
379C2×C4×C7—28no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—44no—
392C2×C4×C7—44no—
393C2×C4×C7—44no—
394C2×C4×C7C2×#4114yes—
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—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—44no—
420C2×Dic7—44no—
421C2×Dic7—44no—
422C2×Dic7—44no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7—44no—
426C2×Dic7—44no—
427C25C22×D711yescharacteristic
428C25C22×D711yescharacteristic
429C25C22×D711yescharacteristic
430C22×D4—24no—
431C22×D4—42no—
432C22×D4—42no—
433C22×D4—42no—
434C22×D4—42no—
435C22×D4—42no—
436C22×D4—42no—
437C22×D4—42no—
438C22×D4—42no—
439C22×D4C22×D714yes—
440C22×D4C22×D714yes—
441C22×D4C22×D714yes—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C2×C4⋊C4—74no—
455C2×C4⋊C4—74no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—282no—
464C2×C4⋊C4—282no—
465C2×C4⋊C4—282no—
466C2×C4⋊C4—282no—
467C2×C4⋊C4—282no—
468C2×C4⋊C4—282no—
469C2×C4⋊C4—282no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—74no—
477C2×C22⋊C4—74no—
478C2×C22⋊C4—74no—
479C2×C22⋊C4—74no—
480C2×C22⋊C4—74no—
481C2×C22⋊C4—74no—
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4—74no—
485C2×C22⋊C4—282no—
486C2×C22⋊C4—282no—
487C2×C22⋊C4—282no—
488C2×C22⋊C4—282no—
489C2×C22⋊C4—282no—
490C2×C22⋊C4—282no—
491C2×C22⋊C4—282no—
492C2×C22⋊C4—282no—
493C2×C22⋊C4—282no—
494C2×C22⋊C4—282no—
495C2×C22⋊C4—282no—
496C2×C22⋊C4—282no—
497C2×C22⋊C4C22×D714yes—
498C2×C22⋊C4C22×D714yes—
499C2×C22⋊C4C22×D714yes—
500C2×C42—74no—
501C2×C42—282no—
502#95—74no—
503#95—74no—
504#95—74no—
505#95—74no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95C22×D714yes—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—42no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7—42no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—88no—
532C22×C7—88no—
533C22×C7—88no—
534C22×C7#53814yes—
535C22×C7#54014yes—
536C22×C7#54214yes—
537C22×C7#56014yes—
538C22×C7#56014yes—
539C22×C7#56214yes—
540C22×C7#56214yes—
541C22×C7C22×#4111yescharacteristic
542C22×C7C2×H(5,𝔽2)11yescharacteristic
543C22×C7C2×H(5,𝔽2)11yescharacteristic
544C22×C7C2×H(5,𝔽2)11yescharacteristic
545C22×C7C2×H(5,𝔽2)11yescharacteristic
546C22×C7C2×H(5,𝔽2)11yescharacteristic
547C22×C7C2×2−1+411yescharacteristic
548C4×C7—24no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7—42no—
552Dic7—42no—
553Dic7—42no—
554Dic7—42no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24C23×D712yes—
582C24C23×D712yes—
583C24C23×D712yes—
584C24C23×D711yescharacteristic
585C2×D4—28no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—44no—
594C2×D4—416no—
595C2×D4—416no—
596C2×D4—416no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—72no—
609C22×C4—72no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—72no—
613C22×C4—72no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—142no—
628C22×C4—142no—
629C22×C4—142no—
630C22×C4—142no—
631C22×C4—142no—
632C22×C4—142no—
633C22×C4—142no—
634C22×C4—142no—
635C22×C4—142no—
636C22×C4—142no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4#115914yes—
641C22×C4C23×D712yes—
642C22×C4C23×D712yes—
643C22×C4C23×D712yes—
644C22×C4C23×D712yes—
645C4⋊C4—148no—
646C4⋊C4—284no—
647C4⋊C4—284no—
648C4⋊C4—284no—
649C4⋊C4—284no—
650C4⋊C4—284no—
651C4⋊C4—284no—
652C4⋊C4—284no—
653C22⋊C4—28no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—284no—
657C22⋊C4—284no—
658C22⋊C4—284no—
659C22⋊C4—284no—
660C22⋊C4—284no—
661C22⋊C4—284no—
662C22⋊C4—284no—
663C22⋊C4—284no—
664C22⋊C4—284no—
665C22⋊C4—284no—
666C22⋊C4—284no—
667C22⋊C4—284no—
668C42—284no—
669C2×C7—82no—
670C2×C7—82no—
671C2×C7—82no—
672C2×C7#282918yescomplemented
673C2×C7C2×#53811yescharacteristic
674C2×C7C2×#54011yescharacteristic
675C2×C7C2×#54211yescharacteristic
676C2×C7C2×#56011yescharacteristic
677C2×C7C2×#56011yescharacteristic
678C2×C7C2×#56211yescharacteristic
679C2×C7C2×#56211yescharacteristic
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23C2×#115912yes—
723C23#654812yes—
724C23#654812yes—
725C23#654812yes—
726C23#654812yes—
727C23#654812yes—
728C23#655412yes—
729C23C24×D711yescharacteristic
730D4—416no—
731D4—416no—
732D4—416no—
733C2×C4—28no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—284no—
773C2×C4—284no—
774C2×C4—284no—
775C2×C4—284no—
776C2×C4—284no—
777C2×C4—284no—
778C2×C4—284no—
779C2×C4—284no—
780C2×C4C2×#115914yes—
781C7C2×#282911yescharacteristic, complemented, Sylow
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—88no—
804C22—88no—
805C22—88no—
806C22#9028414yes—
807C22#9028614yes—
808C22#9028614yes—
809C22#9029414yes—
810C22#9031214yes—
811C22#9031214yes—
812C22#9041014yes—
813C22C22×#115911yescharacteristic
814C22C2×#654811yescharacteristic
815C22C2×#654811yescharacteristic
816C22C2×#654811yescharacteristic
817C22C2×#654811yescharacteristic
818C22C2×#654811yescharacteristic
819C22C2×#655411yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—282no—
825C4—282no—
826C4—282no—
827C4—282no—
828C4—282no—
829C4—282no—
830C4—282no—
831C4—282no—
832C2—82no—
833C2—82no—
834C2—82no—
835C2#1173419618yesdirect product factor
836C2C2×#9028411yescharacteristic
837C2C2×#9028611yescharacteristic
838C2C2×#9028611yescharacteristic
839C2C2×#9029411yescharacteristic
840C2C2×#9031211yescharacteristic
841C2C2×#9031211yescharacteristic
842C2C2×#9041011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC2×C7×#392C2
socleC24×C7C24
hypercenterC2×#392D7
hypocenterC7C2×#2829
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
2. C2×#89994C2semidirect
3. C2×#89994C2semidirect
4. C2×#89994C2semidirect
5. C2×#89994C2semidirect
6. C2×#89994C2semidirect
7. C2×#89993C2semidirect
8. C2×#89721C2semidirect
9. C2×#89724C2semidirect
10. C2×#89724C2semidirect
11. C2×#89720C2semidirect
12. C2×#89720C2semidirect
13. C2×#89723C2semidirect
14. #11734196C2direct (N × H)
15. C2×#89429C2semidirect
16. C2×#89424C2semidirect
46. #89994C22semidirect
47. #89994C22semidirect
48. #89994C22semidirect
49. #89994C22semidirect
50. #89994C22semidirect
51. #89993C22semidirect
59. #89724C22semidirect
60. #89724C22semidirect
61. #89723C22semidirect
62. #89721C22semidirect
63. #89720C22semidirect
64. #89720C22semidirect
65. #89429C22semidirect
66. #89424C22semidirect
672. C2×C7#2829semidirect
781. C7C2×#2829semidirect
835. C2#11734196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3922
C2×#899942
C2×#899932
C2×#897212
C2×#897242
C2×#897202
C2×#897232
#117341962
C2×#894292
C2×#894242
C2×#28297