Finite Group Databasebeta

← C2×#11740998 #14230418

Subgroups — C2×#11740998 #14230418

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic
3C2×#89999C211yesmaximal, characteristic, complemented
4C2×#89999C211yesmaximal, characteristic, complemented
5C2×#89997C211yesmaximal, characteristic, complemented
6C22×#6409C211yesmaximal, characteristic, complemented
7#11740998C2116yesmaximal, direct product factor
8C2×#89855C211yesmaximal, characteristic, complemented
9C2×#89854C211yesmaximal, characteristic, complemented
10C2×#89821C211yesmaximal, characteristic, complemented
11C2×#89820C211yesmaximal, characteristic, complemented
12C2×#89816C211yesmaximal, characteristic, complemented
13C2×#89817C211yesmaximal, characteristic, complemented
14C2×#89798C211yesmaximal, characteristic, complemented
15C2×#89794C211yesmaximal, characteristic, complemented
16C2×#89783C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×C7×Q8C2211yescharacteristic
19C7×D4×Q8—24no—
20C7×D4×Q8C2218yescomplemented
21C2×C7×C4⋊Q8—21no—
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8—21no—
24C2×C7×C22⋊Q8—21no—
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×C22⋊Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4—21no—
29C2×C4×C7×D4C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C22×#1143C2211yescharacteristic
32C22×#1143C2211yescharacteristic
33C2×#6502—21no—
34C2×#6493C2211yescharacteristic
35C2×#6493C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×#1136C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40#90256—24no—
41#90256C2218yes—
42C2×#6461—21no—
43C2×#6446—21no—
44C2×(C22⋊D7)⋊C4—21no—
45C2×C4×D28C2211yescharacteristic
46C2×#6433C2211yescharacteristic
47#89999C2218yescomplemented
48#89999C2218yescomplemented
49#89997C2218yescomplemented
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56C2×#6409C2211yescharacteristic
57C2×#6409C2211yescharacteristic
58C2×#6409C2211yescharacteristic
59C2×#6409C2218yescomplemented
60C2×C22⋊(C7⋊C8)C2211yescharacteristic
61C2×C22⋊(C7⋊C8)C2211yescharacteristic
62#89855C2218yescomplemented
63#89854C2218yescomplemented
64#89821C2218yescomplemented
65#89820C2218yescomplemented
66#89817C2218yescomplemented
67#89816C2218yescomplemented
68#89798C2218yescomplemented
69#89794C2218yescomplemented
70#89783C2218yescomplemented
71C2×#6383C2211yescharacteristic
72C2×#6382C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3320—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—21no—
80C22×C7×Q8—22no—
81C22×C7×Q8—22no—
82C22×C7×Q8—24no—
83C22×C7×Q8—24no—
84C22×C7×Q8—42no—
85C22×C7×Q8—42no—
86C22×C7×Q8C2311yescharacteristic
87C22×C7×Q8C2311yescharacteristic
88C22×C7×Q8C2314yes—
89C22×C7×Q8C2314yes—
90C22×C7×Q8C2311yescharacteristic
91C22×C7×D4D411yescharacteristic
92C23×C4×C7—21no—
93C23×C4×C7—21no—
94C23×C4×C7C2311yescharacteristic
95C23×C4×C7C2311yescharacteristic
96C22×C22⋊D7—21no—
97C22×C22⋊D7—21no—
98C23×Dic7—21no—
99C22×D28C2311yescharacteristic
100C22×C4×D7—21no—
101C7×C4⋊Q8—28no—
102C7×C4⋊Q8—22no—
103C7×C4⋊Q8C2314yes—
104C7×C22⋊Q8—22no—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8—28no—
107C7×C22⋊Q8—28no—
108C7×C22⋊Q8C2314yes—
109C7×C22⋊Q8C2314yes—
110C4×C7×Q8—22no—
111C4×C7×Q8C2314yes—
112C4×C7×D4—28no—
113C4×C7×D4D414yes—
114C4×C7×D4C2314yes—
115C2×C7×C4⋊C4—21no—
116C2×C7×C4⋊C4—21no—
117C2×C7×C4⋊C4—21no—
118C2×C7×C4⋊C4—21no—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4D411yescharacteristic
121C2×C7×C4⋊C4C2311yescharacteristic
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4D411yescharacteristic
125C2×C7×C22⋊C4D411yescharacteristic
126C2×C42×C7—21no—
127C2×C42×C7C2311yescharacteristic
128C2×C22⋊Dic7—21no—
129C2×#1143—24no—
130C2×#1143—42no—
131C2×#1143—42no—
132C2×#1143C2314yes—
133C2×#1143C2314yes—
134C2×#1143C2314yes—
135#6502—28no—
136#6493—22no—
137#6493—22no—
138#6493C2314yes—
139#6493C2314yes—
140C2×(C2×D7)⋊C4—21no—
141C2×(C2×D7)⋊C4—21no—
142C2×(C2×D7)⋊C4—21no—
143#6489—22no—
144#6489C2314yes—
145C2×C4⋊Dic7—21no—
146C2×C4⋊Dic7—22no—
147C2×C4⋊Dic7C2311yescharacteristic
148C2×C4⋊Dic7C2311yescharacteristic
149C2×C4⋊Dic7C2311yescharacteristic
150C2×C4⋊Dic7C2314yes—
151C2×Dic7⋊C4—21no—
152C2×Dic7⋊C4—21no—
153C2×C4×Dic7—21no—
154C2×#1136—42no—
155C2×#1136C2314yes—
156C22×C7⋊C8—42no—
157C22×C7⋊C8C2311yescharacteristic
158C22×C7⋊C8C2311yescharacteristic
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2314yes—
162#6461—28no—
163#6446—28no—
164(C22⋊D7)⋊C4—28no—
165C4×D28—22no—
166C4×D28C2314yes—
167#6433—22no—
168#6433C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6409C2314yes—
176#6409C2314yes—
177#6409C2314yes—
178C22⋊(C7⋊C8)C2314yes—
179C22⋊(C7⋊C8)C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183#6381C2314yes—
184C4⋊(C7⋊C8)C2314yes—
185#6377C2314yes—
186C2×#553—71no—
187C2×D4×Q8D711yescharacteristic, complemented
188#3320—716no—
189C2×#491—71no—
190C2×#484—71no—
191C2×#485—71no—
192C2×#479—71no—
193C2×#468—71no—
194C2×#465—71no—
195C2×#461—71no—
196C2×#448—71no—
197C2×#448—71no—
198C2×#440—71no—
199C2×#435—71no—
200C2×#419—71no—
201C22×#103—71no—
202C24×C7C2×D411yescharacteristic
203C24×C7C2×D411yescharacteristic
204C23×D7—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—24no—
207C2×C7×Q8—24no—
208C2×C7×Q8—21no—
209C2×C7×Q8—21no—
210C2×C7×Q8—22no—
211C2×C7×Q8—28no—
212C2×C7×Q8—28no—
213C2×C7×Q8—22no—
214C2×C7×Q8—22no—
215C2×C7×Q8—22no—
216C2×C7×Q8—22no—
217C2×C7×Q8—44no—
218C2×C7×Q8—44no—
219C2×C7×Q8—44no—
220C2×C7×Q8—44no—
221C2×C7×Q8—48no—
222C2×C7×Q8—48no—
223C2×C7×Q8#4114yes—
224C2×C7×Q8C2412yes—
225C2×C7×Q8C2412yes—
226C2×C7×Q8C2412yes—
227C2×C7×D4—24no—
228C2×C7×D4C2×D414yes—
229C22×C4×C7—21no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—24no—
238C22×C4×C7—24no—
239C22×C4×C7—44no—
240C22×C4×C7—44no—
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D412yes—
246C22×C4×C7C2×D412yes—
247C22×C4×C7C2412yes—
248C22×C4×C7C2412yes—
249C22×C4×C7C2411yescharacteristic
250C2×C22⋊D7—24no—
251C2×C22⋊D7—24no—
252C2×C22⋊D7—44no—
253C2×C22⋊D7—82no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—24no—
258C22×Dic7—82no—
259C2×D28—22no—
260C2×D28—22no—
261C2×D28—21no—
262C2×D28C2412yes—
263C2×C4×D7—24no—
264C2×C4×D7—82no—
265C7×C4⋊C4—24no—
266C7×C4⋊C4—24no—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4C2×D414yes—
272C7×C4⋊C4C2412yes—
273C7×C22⋊C4—24no—
274C7×C22⋊C4—24no—
275C7×C22⋊C4C2×D414yes—
276C7×C22⋊C4C2×D414yes—
277C42×C7—24no—
278C42×C7C2×D412yes—
279C42×C7C2412yes—
280C22⋊Dic7—24no—
281#1143—28no—
282#1143—44no—
283#1143—44no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4—24no—
287C4⋊Dic7—21no—
288C4⋊Dic7—21no—
289C4⋊Dic7—21no—
290C4⋊Dic7—24no—
291C4⋊Dic7C2412yes—
292C4⋊Dic7C2412yes—
293C4⋊Dic7C2412yes—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296C4×Dic7—24no—
297#1136—44no—
298C2×C7⋊C8—22no—
299C2×C7⋊C8—22no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8—22no—
302C2×C7⋊C8—44no—
303C2×C7⋊C8C2412yes—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306C2×C7⋊C8C2412yes—
307C23×Q8C2×D711yescharacteristic
308C23×Q8C2×D711yescharacteristic
309C22×SD16—71no—
310C22×SD16—71no—
311C22×SD16—71no—
312C22×M16—71no—
313C23×C8—71no—
314#553—78no—
315#553—144no—
316D4×Q8—24no—
317D4×Q8C2×D718yescomplemented
318C2×C4⋊Q8—21no—
319C2×C4⋊Q8C2×D711yescharacteristic
320C2×#126—141no—
321C2×#125—71no—
322C2×#123—141no—
323C2×C22⋊Q8—21no—
324C2×C22⋊Q8—21no—
325C2×C22⋊Q8C2×D711yescharacteristic
326C2×C22⋊Q8C2×D711yescharacteristic
327C2×#121—71no—
328C2×#121—71no—
329C2×#121—141no—
330C2×C4×Q8C2×D711yescharacteristic
331C2×C4×D4—21no—
332C2×C4×D4—71no—
333C2×C4×D4—141no—
334C2×C4×D4C2×D711yescharacteristic
335C2×#117—71no—
336C22×C4⋊C4—71no—
337#491—78no—
338#485—78no—
339#484—78no—
340#479—78no—
341#468—78no—
342#465—78no—
343#461—78no—
344#448—78no—
345#448—78no—
346#440—78no—
347#435—78no—
348C2×#107—71no—
349C2×#107—71no—
350C2×#106—71no—
351C2×C4⋊C8—71no—
352#419—78no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#103—71no—
362C2×#103—78no—
363C2×#102—71no—
364C2×C22⋊C8—71no—
365C2×C22⋊C8—71no—
366C2×#97—71no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7#13714yes—
373C23×C7C22×D412yes—
374C23×C7C22×D412yes—
375C23×C7C22×D411yescharacteristic
376C22×D7—22no—
377C22×D7—42no—
378C22×D7—42no—
379C22×D7—42no—
380C7×Q8—24no—
381C7×Q8—22no—
382C7×Q8—22no—
383C7×Q8—22no—
384C7×Q8—22no—
385C7×Q8—22no—
386C7×Q8—48no—
387C7×Q8—48no—
388C7×Q8—42no—
389C7×Q8—42no—
390C7×Q8C2×#4114yes—
391C7×D4—28no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—24no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—24no—
399C2×C4×C7—24no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—48no—
408C2×C4×C7—48no—
409C2×C4×C7—42no—
410C2×C4×C7—42no—
411C2×C4×C7—42no—
412C2×C4×C7C22×D412yes—
413C2×C4×C7C22×D412yes—
414C2×C4×C7C22×D412yes—
415C2×C4×C7C22×D412yes—
416C2×C4×C7C22×D411yescharacteristic
417C2×C4×C7C2×#4112yes—
418C2×C4×C7H(5,𝔽2)12yes—
419C2×C4×C7C2511yescharacteristic
420C22⋊D7—48no—
421C22⋊D7—84no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—42no—
426C2×Dic7—42no—
427C2×Dic7—42no—
428C2×Dic7—84no—
429D28—22no—
430D28—22no—
431D28—42no—
432C4×D7—84no—
433C7⋊C8—22no—
434C7⋊C8—22no—
435C7⋊C8—22no—
436C7⋊C8—22no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—22no—
440C22×Q8—22no—
441C22×Q8—24no—
442C22×Q8—24no—
443C22×Q8—42no—
444C22×Q8—42no—
445C22×Q8C22×D711yescharacteristic
446C22×Q8C22×D711yescharacteristic
447C22×Q8C22×D714yes—
448C22×Q8C22×D714yes—
449C22×Q8C22×D711yescharacteristic
450C22×D4—71no—
451C22×D4—141no—
452C22×D4—141no—
453C22×D4C22⋊D711yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—141no—
457C23×C4—141no—
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C2×SD16—74no—
461C2×SD16—74no—
462C2×SD16—74no—
463C2×SD16—144no—
464C2×SD16—282no—
465C2×SD16—282no—
466C2×M16—74no—
467C2×M16—282no—
468C22×C8—71no—
469C22×C8—71no—
470C22×C8—71no—
471C22×C8—71no—
472C22×C8—74no—
473C22×C8—282no—
474C4⋊Q8—28no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D714yes—
477#126—148no—
478#125—74no—
479#125—142no—
480#123—148no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—28no—
484C22⋊Q8—28no—
485C22⋊Q8C22×D714yes—
486C22⋊Q8C22×D714yes—
487#121—74no—
488#121—74no—
489#121—148no—
490#121—142no—
491#121—142no—
492C4×Q8—22no—
493C4×Q8C22×D714yes—
494C4×D4—28no—
495C4×D4—74no—
496C4×D4—148no—
497C4×D4—142no—
498C4×D4C22⋊D714yes—
499C4×D4C22×D714yes—
500#117—74no—
501#117—142no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—71no—
508C2×C4⋊C4—71no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4C22⋊D711yescharacteristic
516C2×C4⋊C4C22×D711yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—141no—
520C2×C22⋊C4—141no—
521C2×C22⋊C4—141no—
522C2×C22⋊C4—141no—
523C2×C22⋊C4C22⋊D711yescharacteristic
524C2×C22⋊C4C22⋊D711yescharacteristic
525C2×C42—21no—
526C2×C42—141no—
527C2×C42C22×D711yescharacteristic
528#107—74no—
529#107—74no—
530#106—74no—
531C4⋊C8—74no—
532#103—74no—
533#103—74no—
534#103—74no—
535#103—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#103—74no—
540#103—74no—
541#102—74no—
542C22⋊C8—74no—
543C22⋊C8—74no—
544#97—74no—
545C22×C7—22no—
546C22×C7—28no—
547C22×C7—22no—
548C22×C7—22no—
549C22×C7—22no—
550C22×C7—22no—
551C22×C7—44no—
552C22×C7#54612yes—
553C22×C7C2×#13714yes—
554C22×C7C2×#13712yes—
555C22×C7#57712yes—
556C22×C7C23×D411yescharacteristic
557C2×D7—42no—
558C2×D7—42no—
559C2×D7—42no—
560C2×D7—84no—
561C4×C7—22no—
562C4×C7—22no—
563C4×C7—24no—
564C4×C7—22no—
565C4×C7—22no—
566C4×C7—42no—
567C4×C7—42no—
568C4×C7—42no—
569C4×C7#54612yes—
570C4×C7C22×#4111yescharacteristic
571C4×C7C2×H(5,𝔽2)11yescharacteristic
572Dic7—42no—
573Dic7—42no—
574Dic7—42no—
575C24—141no—
576C24C2×C22⋊D711yescharacteristic
577C24C2×C22⋊D711yescharacteristic
578C2×Q8—22no—
579C2×Q8—21no—
580C2×Q8—24no—
581C2×Q8—24no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—28no—
585C2×Q8—28no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—44no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—48no—
596C2×Q8#115914yes—
597C2×Q8C23×D712yes—
598C2×Q8C23×D712yes—
599C2×Q8C23×D712yes—
600C2×D4—24no—
601C2×D4—72no—
602C2×D4—144no—
603C2×D4—144no—
604C2×D4—142no—
605C2×D4—142no—
606C2×D4—141no—
607C2×D4—284no—
608C2×D4—562no—
609C2×D4C2×C22⋊D714yes—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—141no—
625C22×C4—144no—
626C22×C4—144no—
627C22×C4—562no—
628C22×C4—562no—
629C22×C4C2×C22⋊D712yes—
630C22×C4C2×C22⋊D712yes—
631C22×C4C2×C22⋊D711yescharacteristic
632C22×C4C2×C22⋊D711yescharacteristic
633C22×C4C2×C22⋊D711yescharacteristic
634C22×C4C2×C22⋊D711yescharacteristic
635C22×C4C23×D712yes—
636C22×C4C23×D712yes—
637C22×C4C23×D711yescharacteristic
638SD16—148no—
639SD16—284no—
640SD16—284no—
641M16—284no—
642C2×C8—72no—
643C2×C8—72no—
644C2×C8—72no—
645C2×C8—72no—
646C2×C8—142no—
647C2×C8—142no—
648C2×C8—142no—
649C2×C8—142no—
650C2×C8—284no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—21no—
657C4⋊C4—72no—
658C4⋊C4—72no—
659C4⋊C4—72no—
660C4⋊C4—144no—
661C4⋊C4—144no—
662C4⋊C4—141no—
663C4⋊C4—141no—
664C4⋊C4—144no—
665C4⋊C4—141no—
666C4⋊C4C2×C22⋊D714yes—
667C4⋊C4C23×D712yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—144no—
671C22⋊C4—144no—
672C22⋊C4—144no—
673C22⋊C4—144no—
674C22⋊C4C2×C22⋊D714yes—
675C22⋊C4C2×C22⋊D714yes—
676C42—24no—
677C42—144no—
678C42C2×C22⋊D712yes—
679C42C23×D712yes—
680C2×C7—24no—
681C2×C7—42no—
682C2×C7#332014yescomplemented
683C2×C7C2×#54611yescharacteristic
684C2×C7C22×#13711yescharacteristic
685C2×C7C2×#57711yescharacteristic
686D7—82no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—142no—
693C23—282no—
694C23—282no—
695C23—282no—
696C23#650514yes—
697C23C22×C22⋊D712yes—
698C23C22×C22⋊D712yes—
699C23C22×C22⋊D711yescharacteristic
700Q8—24no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—48no—
707Q8—48no—
708Q8—42no—
709Q8—42no—
710Q8C2×#115914yes—
711D4—28no—
712D4—142no—
713D4—142no—
714D4—288no—
715D4—282no—
716D4—564no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—282no—
741C2×C4—282no—
742C2×C4—282no—
743C2×C4—564no—
744C2×C4—564no—
745C2×C4C2×#115912yes—
746C2×C4#654812yes—
747C2×C4C22×C22⋊D712yes—
748C2×C4C22×C22⋊D712yes—
749C2×C4C22×C22⋊D712yes—
750C2×C4C22×C22⋊D712yes—
751C2×C4C22×C22⋊D711yescharacteristic
752C2×C4C24×D711yescharacteristic
753C8—142no—
754C8—142no—
755C8—142no—
756C8—142no—
757C7C2×#332011yescharacteristic, complemented, Sylow
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—282no—
766C22—282no—
767C22—282no—
768C22—564no—
769C22#9049712yes—
770C22C2×#650514yes—
771C22C2×#650512yes—
772C22#9052812yes—
773C22C23×C22⋊D711yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—282no—
783C4—282no—
784C4—282no—
785C4#9049712yes—
786C4C22×#115911yescharacteristic
787C4C2×#654811yescharacteristic
788C2—24no—
789C2—42no—
790C2—562no—
791C2#1174099814yesdirect product factor
792C2C2×#9049711yescharacteristic
793C2C22×#650511yescharacteristic
794C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×D4×Q8C2
socleC23×C7C22×D4
prime radicalC2×#90256C2
hypercenterC2×D4×Q8D7
hypocenterC7C2×#3320
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C7×D4×Q8C2semidirect
3. C2×#89999C2semidirect
4. C2×#89999C2semidirect
5. C2×#89997C2semidirect
6. C22×#6409C2semidirect
7. #11740998C2direct (N × H)
8. C2×#89855C2semidirect
9. C2×#89854C2semidirect
10. C2×#89821C2semidirect
11. C2×#89820C2semidirect
12. C2×#89816C2semidirect
13. C2×#89817C2semidirect
14. C2×#89798C2semidirect
15. C2×#89794C2semidirect
16. C2×#89783C2semidirect
20. C7×D4×Q8C22semidirect
47. #89999C22semidirect
48. #89999C22semidirect
49. #89997C22semidirect
59. C2×#6409C22semidirect
62. #89855C22semidirect
63. #89854C22semidirect
64. #89821C22semidirect
65. #89820C22semidirect
66. #89817C22semidirect
67. #89816C22semidirect
68. #89798C22semidirect
69. #89794C22semidirect
70. #89783C22semidirect
187. C2×D4×Q8D7semidirect
317. D4×Q8C2×D7semidirect
682. C2×C7#3320semidirect
757. C7C2×#3320semidirect
791. C2#11740998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×D4×Q82
C2×#902562
C2×#899992
C2×#899972
C22×#64092
#117409982
C2×#898552
C2×#898542
C2×#898212
C2×#898202
C2×#898162
C2×#898172
C2×#897982
C2×#897942
C2×#897832
C2×#33207