Finite Group Databasebeta

← C2×#11734125 #13521648

Subgroups — C2×#11734125 #13521648

Order 1792.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6499C211yesmaximal, characteristic, complemented
2C22×#6498C211yesmaximal, characteristic, complemented
3C22×D4×Dic7C211yesmaximal, characteristic, complemented
4C22×#6441C211yesmaximal, characteristic, complemented
5C2×C7×#392C211yesmaximal, characteristic
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×#89993C211yesmaximal, characteristic, complemented
8C2×#89992C211yesmaximal, characteristic, complemented
9C2×#89720C211yesmaximal, characteristic, complemented
10C2×#89717C211yesmaximal, characteristic, complemented
11C2×#89716C211yesmaximal, characteristic, complemented
12C2×#89723C211yesmaximal, characteristic, complemented
13C2×#89722C211yesmaximal, characteristic, complemented
14#11734125C2116yesmaximal, direct product factor
15C2×#89428C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
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
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C22⋊Dic7C2211yescharacteristic
36C2×#6499—28no—
37C2×#6499C2218yescomplemented
38C2×#6498—28no—
39C2×#6498C2218yescomplemented
40C2×D4×Dic7—28no—
41C2×D4×Dic7C2218yescomplemented
42C22×C4⋊Dic7C2211yescharacteristic
43C22×C4⋊Dic7C2211yescharacteristic
44C22×C4⋊Dic7C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×C4×Dic7C2211yescharacteristic
50C22×C4×Dic7C2211yescharacteristic
51C22×C4×Dic7C2211yescharacteristic
52C2×#6441—28no—
53C2×#6441C2218yescomplemented
54C7×#392C2218yes—
55C2×C7×#95C2211yescharacteristic
56#89994C2218yescomplemented
57#89993C2218yescomplemented
58#89992C2218yescomplemented
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62C2×C7⋊#95C2211yescharacteristic
63C2×C7⋊#95C2211yescharacteristic
64#89723C2218yescomplemented
65#89722C2218yescomplemented
66#89720C2218yescomplemented
67#89717C2218yescomplemented
68#89716C2218yescomplemented
69#89428C2218yescomplemented
70#89421C2218yescomplemented
71C2×#2461—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C25×C7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—24no—
78C22×C7×D4—24no—
79C22×C7×D4—24no—
80C22×C7×D4—24no—
81C22×C7×D4—24no—
82C22×C7×D4—42no—
83C22×C7×D4—42no—
84C22×C7×D4C2314yes—
85C22×C7×D4C2314yes—
86C22×C7×D4C2314yes—
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×Dic7—24no—
92C23×Dic7—24no—
93C23×Dic7—24no—
94C23×Dic7—24no—
95C23×Dic7—42no—
96C23×Dic7—42no—
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2314yes—
102C23×Dic7C2314yes—
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C22×Dic14—24no—
108C22×Dic14—24no—
109C22×Dic14—42no—
110C22×Dic14C2314yes—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—24no—
126C2×C22⋊Dic7D418yescomplemented
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133C2×C22⋊Dic7C2314yes—
134C2×C22⋊Dic7C2314yes—
135C2×C22⋊Dic7C2314yes—
136C2×C22⋊Dic7C2314yes—
137#6499—232no—
138#6498—232no—
139D4×Dic7—232no—
140C2×C4⋊Dic7—24no—
141C2×C4⋊Dic7—24no—
142C2×C4⋊Dic7—42no—
143C2×C4⋊Dic7C2314yes—
144C2×C4⋊Dic7C2314yes—
145C2×C4⋊Dic7C2314yes—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4D418yescomplemented
150C2×Dic7⋊C4C2314yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×C4×Dic7—24no—
155C2×C4×Dic7—24no—
156C2×C4×Dic7—24no—
157C2×C4×Dic7C2314yes—
158C2×C4×Dic7C2314yes—
159C2×C4×Dic7C2314yes—
160#6441—232no—
161C7×#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#124—71no—
168C22×#123—71no—
169C22×C22⋊Q8—71no—
170C22×C4×D4—71no—
171#2461—716no—
172C2×#396—71no—
173C2×#395—71no—
174C2×#394—71no—
175C2×#392D711yescharacteristic
176C2×#390—71no—
177C2×#388—71no—
178C2×#388—71no—
179C2×#388—71no—
180C2×#386—71no—
181C2×#385—71no—
182C2×C4×C4⋊C4—71no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7—22no—
196C24×C7—22no—
197C24×C7—22no—
198C24×C7—22no—
199C24×C7—22no—
200C24×C7—22no—
201C24×C7—22no—
202C24×C7C2×D414yes—
203C24×C7#4114yes—
204C24×C7C2412yes—
205C24×C7C2412yes—
206C24×C7C2412yes—
207C24×C7C2411yescharacteristic
208C2×C7×D4—232no—
209C2×C7×D4—28no—
210C2×C7×D4—28no—
211C2×C7×D4—28no—
212C2×C7×D4—28no—
213C2×C7×D4—28no—
214C2×C7×D4—28no—
215C2×C7×D4—28no—
216C2×C7×D4—44no—
217C2×C7×D4—44no—
218C2×C7×D4—416no—
219C2×C7×D4—416no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7C2×D414yes—
230C22×C4×C7#4114yes—
231C22×C4×C7#4114yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
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×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—28no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—28no—
258C22×Dic7—28no—
259C22×Dic7—28no—
260C22×Dic7—44no—
261C22×Dic7—44no—
262C22×Dic7—416no—
263C22×Dic7—416no—
264C22×Dic7C2×D414yes—
265C22×Dic7C2×D414yes—
266C22×Dic7C2×D414yes—
267C22×Dic7C2×D414yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C22×Dic7C2412yes—
275C22×Dic7C2412yes—
276C2×Dic14—28no—
277C2×Dic14—28no—
278C2×Dic14—44no—
279C2×Dic14—416no—
280C7×C22⋊C4—28no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—28no—
283C22⋊Dic7—28no—
284C22⋊Dic7—28no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—28no—
289C22⋊Dic7—28no—
290C22⋊Dic7—28no—
291C22⋊Dic7—28no—
292C22⋊Dic7C2×D4116yescomplemented
293C4⋊Dic7—28no—
294C4⋊Dic7—28no—
295C4⋊Dic7—44no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4C2×D4116yescomplemented
300C4×Dic7—28no—
301C4×Dic7—28no—
302C4×Dic7—28no—
303C23×Q8—71no—
304C23×D4C2×D711yescharacteristic
305C23×D4C2×D711yescharacteristic
306C23×D4C2×D711yescharacteristic
307C24×C4—71no—
308C24×C4—71no—
309C2×#124—78no—
310C2×#124—148no—
311C2×#123—78no—
312C2×#123—148no—
313C2×C22⋊Q8—78no—
314C2×C22⋊Q8—148no—
315C2×C4×D4—78no—
316C2×C4×D4—148no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C42—71no—
338C22×C42—71no—
339C22×C42—71no—
340#396—78no—
341#395—78no—
342#394—78no—
343#392C2×D718yes—
344#390—78no—
345#388—78no—
346#388—78no—
347#388—78no—
348#386—78no—
349#385—78no—
350C4×C4⋊C4—78no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95C2×D711yescharacteristic
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—28no—
361C23×C7—28no—
362C23×C7—28no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—44no—
383C23×C7—44no—
384C23×C7—44no—
385C23×C7—44no—
386C23×C7—44no—
387C23×C7—44no—
388C23×C7—44no—
389C23×C7—44no—
390C23×C7—44no—
391C23×C7—44no—
392C23×C7—44no—
393C23×C7—44no—
394C23×C7—44no—
395C23×C7—44no—
396C23×C7—44no—
397C23×C7C22×D414yes—
398C23×C7C22×D412yes—
399C23×C7C22×D412yes—
400C23×C7C2×#4114yes—
401C23×C7C2×#4112yes—
402C23×C7C2×#4112yes—
403C23×C7C2×#4112yes—
404C23×C7H(5,𝔽2)12yes—
405C23×C72−1+412yes—
406C23×C7C2511yescharacteristic
407C7×D4—232no—
408C7×D4—416no—
409C7×D4—416no—
410C2×C4×C7—28no—
411C2×C4×C7—28no—
412C2×C4×C7—28no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—44no—
423C2×C4×C7C22×D414yes—
424C2×C4×C7C2×#4114yes—
425C2×C4×C7C2×#4114yes—
426C2×Dic7—28no—
427C2×Dic7—28no—
428C2×Dic7—28no—
429C2×Dic7—28no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—416no—
451C2×Dic7—416no—
452C2×Dic7—44no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455C2×Dic7—44no—
456C2×Dic7C22×D414yes—
457C2×Dic7C22×D414yes—
458C2×Dic7C22×D414yes—
459C2×Dic7C22×D414yes—
460Dic14—416no—
461C25C22×D711yescharacteristic
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C22×Q8—74no—
465C22×Q8—144no—
466C22×Q8—144no—
467C22×Q8—282no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—42no—
476C22×D4—42no—
477C22×D4C22×D714yes—
478C22×D4C22×D714yes—
479C22×D4C22×D714yes—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—74no—
489C23×C4—74no—
490C23×C4—144no—
491C23×C4—144no—
492C23×C4—144no—
493C23×C4—144no—
494C23×C4—282no—
495C23×C4—282no—
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500#124—1432no—
501#123—1432no—
502C22⋊Q8—1432no—
503C4×D4—1432no—
504C2×C4⋊C4—78no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—74no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—144no—
513C2×C4⋊C4—144no—
514C2×C4⋊C4—144no—
515C2×C4⋊C4—144no—
516C2×C4⋊C4—144no—
517C2×C4⋊C4—282no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—78no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—144no—
533C2×C22⋊C4—144no—
534C2×C22⋊C4—144no—
535C2×C22⋊C4—144no—
536C2×C22⋊C4—144no—
537C2×C22⋊C4—144no—
538C2×C22⋊C4—144no—
539C2×C22⋊C4—144no—
540C2×C22⋊C4—144no—
541C2×C22⋊C4C22×D714yes—
542C2×C22⋊C4C22×D714yes—
543C2×C22⋊C4C22×D714yes—
544C2×C42—74no—
545C2×C42—74no—
546C2×C42—74no—
547C2×C42—144no—
548C2×C42—144no—
549C2×C42—144no—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95C22×D714yes—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—24no—
559C22×C7—24no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—416no—
571C22×C7—416no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—88no—
580C22×C7#52514yes—
581C22×C7#53214yes—
582C22×C7#54214yes—
583C22×C7D4214yes—
584C22×C7#54714yes—
585C22×C7#54814yes—
586C22×C7#55114yes—
587C22×C7C23×D411yescharacteristic
588C22×C7C23×D411yescharacteristic
589C22×C7C22×#4111yescharacteristic
590C22×C7C22×#4111yescharacteristic
591C22×C7C22×#4111yescharacteristic
592C22×C7C2×H(5,𝔽2)11yescharacteristic
593C22×C7C2×2−1+411yescharacteristic
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—24no—
597C4×C7—42no—
598Dic7—24no—
599Dic7—24no—
600Dic7—24no—
601Dic7—24no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24D4×D714yes—
626C24#115914yes—
627C24C23×D712yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×Q8—148no—
632C2×Q8—148no—
633C2×Q8—284no—
634C2×Q8—2816no—
635C2×D4—232no—
636C2×D4—28no—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—28no—
640C2×D4—28no—
641C2×D4—28no—
642C2×D4—28no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—416no—
646C2×D4—416no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—74no—
657C22×C4—74no—
658C22×C4—74no—
659C22×C4—74no—
660C22×C4—72no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—148no—
669C22×C4—148no—
670C22×C4—148no—
671C22×C4—142no—
672C22×C4—142no—
673C22×C4—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—148no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—284no—
693C22×C4—284no—
694C22×C4—2816no—
695C22×C4—2816no—
696C22×C4D4×D714yes—
697C22×C4#115914yes—
698C22×C4#115914yes—
699C22×C4C23×D712yes—
700C22×C4C23×D712yes—
701C22×C4C23×D712yes—
702C22×C4C23×D712yes—
703C4⋊C4—716no—
704C4⋊C4—148no—
705C4⋊C4—148no—
706C4⋊C4—148no—
707C4⋊C4—148no—
708C4⋊C4—148no—
709C4⋊C4—284no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
713C22⋊C4—716no—
714C22⋊C4—148no—
715C22⋊C4—148no—
716C22⋊C4—148no—
717C22⋊C4—148no—
718C22⋊C4—148no—
719C22⋊C4—148no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C42—148no—
724C42—148no—
725C42—148no—
726C2×C7—44no—
727C2×C7—44no—
728C2×C7—82no—
729C2×C7#246118yescomplemented
730C2×C7C2×#52511yescharacteristic
731C2×C7C2×#53211yescharacteristic
732C2×C7C2×#54211yescharacteristic
733C2×C7C2×D4211yescharacteristic
734C2×C7C2×#54711yescharacteristic
735C2×C7C2×#54811yescharacteristic
736C2×C7C2×#55111yescharacteristic
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23C2×D4×D714yes—
778C23C2×D4×D712yes—
779C23C2×D4×D712yes—
780C23C2×#115914yes—
781C23C2×#115912yes—
782C23C2×#115912yes—
783C23C2×#115912yes—
784C23#654812yes—
785C23#655412yes—
786C23C24×D711yescharacteristic
787Q8—2816no—
788D4—232no—
789D4—416no—
790D4—416no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—44no—
804C2×C4—74no—
805C2×C4—74no—
806C2×C4—74no—
807C2×C4—74no—
808C2×C4—148no—
809C2×C4—148no—
810C2×C4—148no—
811C2×C4—148no—
812C2×C4—142no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—2816no—
833C2×C4—2816no—
834C2×C4—284no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4C2×D4×D714yes—
839C2×C4C2×#115914yes—
840C2×C4C2×#115914yes—
841C7C2×#246111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—88no—
866C22#9027714yes—
867C22#9027814yes—
868C22#9028114yes—
869C22#9028914yes—
870C22#9029414yes—
871C22#9030214yes—
872C22#9040714yes—
873C22C22×D4×D711yescharacteristic
874C22C22×D4×D711yescharacteristic
875C22C22×#115911yescharacteristic
876C22C22×#115911yescharacteristic
877C22C22×#115911yescharacteristic
878C22C2×#654811yescharacteristic
879C22C2×#655411yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—144no—
885C4—144no—
886C4—144no—
887C4—144no—
888C4—282no—
889C4—282no—
890C4—282no—
891C4—282no—
892C2—44no—
893C2—44no—
894C2—82no—
895C2#1173412518yesdirect product factor
896C2C2×#9027711yescharacteristic
897C2C2×#9027811yescharacteristic
898C2C2×#9028111yescharacteristic
899C2C2×#9029411yescharacteristic
900C2C2×#9030211yescharacteristic
901C2C2×#9028911yescharacteristic
902C2C2×#9040711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC2×C7×#392C2
socleC24×C7C24
hypercenterC2×#392D7
hypocenterC7C2×#2461
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#6499C2semidirect
2. C22×#6498C2semidirect
3. C22×D4×Dic7C2semidirect
4. C22×#6441C2semidirect
6. C2×#89994C2semidirect
7. C2×#89993C2semidirect
8. C2×#89992C2semidirect
9. C2×#89720C2semidirect
10. C2×#89717C2semidirect
11. C2×#89716C2semidirect
12. C2×#89723C2semidirect
13. C2×#89722C2semidirect
14. #11734125C2direct (N × H)
15. C2×#89428C2semidirect
16. C2×#89421C2semidirect
37. C2×#6499C22semidirect
39. C2×#6498C22semidirect
41. C2×D4×Dic7C22semidirect
53. C2×#6441C22semidirect
56. #89994C22semidirect
57. #89993C22semidirect
58. #89992C22semidirect
64. #89723C22semidirect
65. #89722C22semidirect
66. #89720C22semidirect
67. #89717C22semidirect
68. #89716C22semidirect
69. #89428C22semidirect
70. #89421C22semidirect
126. C2×C22⋊Dic7D4semidirect
149. C2×Dic7⋊C4D4semidirect
292. C22⋊Dic7C2×D4semidirect
299. Dic7⋊C4C2×D4semidirect
729. C2×C7#2461semidirect
841. C7C2×#2461semidirect
895. C2#11734125direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64992
C22×#64982
C22×D4×Dic72
C22×#64412
C2×C7×#3922
C2×#899942
C2×#899932
C2×#899922
C2×#897202
C2×#897172
C2×#897162
C2×#897232
C2×#897222
#117341252
C2×#894282
C2×#894212
C2×#24617